ForumThe Sun: The SunThe Liquid Metallic Hydrogen Sola …

Please or Register to create posts and topics.

The Liquid Metallic Hydrogen Solar Model

#1 · January 4, 2020, 7:37 am

Quote from smAsh on January 4, 2020, 7:37 am
Forty Lines of Evidence for Condensed Matter — The Sun on Trial:
Liquid Metallic Hydrogen as a Solar Building Block
Pierre-Marie Robitaille
LINK:
http://www.ptep-online.com/2013/PP-35-16.PDF
Abstract
Our Sun has confronted humanity with overwhelming evidence that it is comprised of condensed matter. Dismissing this reality, the standard solar models continue to be anchored on the gaseous plasma. In large measure, the endurance of these theories can be attributed to 1) the mathematical elegance of the equations for the gaseous state, 2) the apparent success of the mass-luminosity relationship, and 3) the long-lasting influence of leading proponents of these models. Unfortunately, no direct physical finding supports the notion that the solar body is gaseous. Without exception, all observations are most easily explained by recognizing that the Sun is primarily comprised of condensed matter. However, when a physical characteristic points to condensed matter, a postori arguments are invoked to account for the behavior using the gaseous state. In isolation, many of these treatments appear plausible. As a result, the gaseous models continue to be accepted. There seems to be an overarching belief in solar science that the problems with the gaseous models are few and inconsequential. In reality, they are numerous and, while often subtle, they are sometimes daunting. The gaseous equations of state have introduced far more dilemmas than they have solved. Many of the conclusions derived from these approaches are likely to have led solar physics down unproductive avenues, as deductions have been accepted which bear little or no relationship to the actual nature of the Sun. It could be argued that, for more than 100 years, the gaseous models have prevented mankind from making real progress relative to understanding the Sun and the universe. Hence, the Sun is now placed on trial. Forty lines of evidence will be presented that the solar body is comprised of, and surrounded by, condensed matter. These ‘proofs’ can be divided into seven broad categories: 1) Planckian, 2) spectroscopic, 3) structural, 4) dynamic, 5) helioseismic, 6) elemental, and 7) earthly. Collectively, these lines of evidence provide a systematic challenge to the gaseous models of the Sun and expose the many hurdles faced by modern approaches. Observational astronomy and laboratory physics have remained unable to properly justify claims that the solar body must be gaseous. At the same time, clear signs of condensed matter interspersed with gaseous plasma in the chromosphere and corona have been regrettably dismissed. As such, it is hoped that this exposition will serve as an invitation to consider condensed matter, especially metallic hydrogen, when pondering the phase of the Sun.

Forty Lines of Evidence for Condensed Matter — The Sun on Trial:
Liquid Metallic Hydrogen as a Solar Building Block
Pierre-Marie Robitaille

LINK:

http://www.ptep-online.com/2013/PP-35-16.PDF

Abstract

Our Sun has confronted humanity with overwhelming evidence that it is comprised of condensed matter. Dismissing this reality, the standard solar models continue to be anchored on the gaseous plasma. In large measure, the endurance of these theories can be attributed to 1) the mathematical elegance of the equations for the gaseous state, 2) the apparent success of the mass-luminosity relationship, and 3) the long-lasting influence of leading proponents of these models. Unfortunately, no direct physical finding supports the notion that the solar body is gaseous. Without exception, all observations are most easily explained by recognizing that the Sun is primarily comprised of condensed matter. However, when a physical characteristic points to condensed matter, a postori arguments are invoked to account for the behavior using the gaseous state. In isolation, many of these treatments appear plausible. As a result, the gaseous models continue to be accepted. There seems to be an overarching belief in solar science that the problems with the gaseous models are few and inconsequential. In reality, they are numerous and, while often subtle, they are sometimes daunting. The gaseous equations of state have introduced far more dilemmas than they have solved. Many of the conclusions derived from these approaches are likely to have led solar physics down unproductive avenues, as deductions have been accepted which bear little or no relationship to the actual nature of the Sun. It could be argued that, for more than 100 years, the gaseous models have prevented mankind from making real progress relative to understanding the Sun and the universe. Hence, the Sun is now placed on trial. Forty lines of evidence will be presented that the solar body is comprised of, and surrounded by, condensed matter. These ‘proofs’ can be divided into seven broad categories: 1) Planckian, 2) spectroscopic, 3) structural, 4) dynamic, 5) helioseismic, 6) elemental, and 7) earthly. Collectively, these lines of evidence provide a systematic challenge to the gaseous models of the Sun and expose the many hurdles faced by modern approaches. Observational astronomy and laboratory physics have remained unable to properly justify claims that the solar body must be gaseous. At the same time, clear signs of condensed matter interspersed with gaseous plasma in the chromosphere and corona have been regrettably dismissed. As such, it is hoped that this exposition will serve as an invitation to consider condensed matter, especially metallic hydrogen, when pondering the phase of the Sun.

SkyThing has reacted to this post.

Regards, Dan, a. k. a. smAshomAsh

#2 · January 4, 2020, 7:38 am

Pierre-Marie Robitaille's research while affiliated with The Ohio State University and other places:

https://www.researchgate.net/scientific-contributions/2061937221_Pierre-Marie_Robitaille

Regards, Dan, a. k. a. smAshomAsh

#3 · January 4, 2020, 7:50 am

To Understand From Where the Idea of a Gaseous Sun Came, Watch-

History of the Gaseous Sun with Dr. Robitaille:

https://youtu.be/GxEokSd-o5o

Regards, Dan, a. k. a. smAshomAsh

#4 · January 4, 2020, 7:51 am

A Thermodynamic History of the Solar Constitution — II:
The Theory of a Gaseous Sun and Jeans’ Failed Liquid Alternative
Pierre-Marie Robitaille

http://ptep-online.com/2011/PP-26-06.PDF

In this work, the development of solar theory is followed from the concept that the Sun
was an ethereal nuclear body with a partially condensed photosphere to the creation of
a fully gaseous object. An overview will be presented of the liquid Sun. A powerful
lineage has brought us the gaseous Sun and two of its main authors were the direct scientific descendants of Gustav Robert Kirchhoff: Franz Arthur Friedrich Schuster and
Arthur Stanley Eddington. It will be discovered that the seminal ideas of Father Secchi
and Herve Faye were not abandoned by astronomy until the beginning of 20th century. ´
The central role of carbon in early solar physics will also be highlighted by revisiting George Johnstone Stoney. The evolution of the gaseous models will be outlined,
along with the contributions of Johann Karl Friedrich Zollner, James Clerk Maxwell, ¨
Jonathan Homer Lane, August Ritter, William Thomson, William Huggins, William
Edward Wilson, George Francis FitzGerald, Jacob Robert Emden, Frank Washington
Very, Karl Schwarzschild, and Edward Arthur Milne. Finally, with the aid of Edward
Arthur Milne, the work of James Hopwood Jeans, the last modern advocate of a liquid
Sun, will be rediscovered. Jeans was a staunch advocate of the condensed phase, but
deprived of a proper building block, he would eventually abandon his non-gaseous stars.
For his part, Subrahmanyan Chandrasekhar would spend nine years of his life studying
homogeneous liquid masses. These were precisely the kind of objects which Jeans had
considered for his liquid stars.

SkyThing has reacted to this post.

Regards, Dan, a. k. a. smAshomAsh

#5 · January 4, 2020, 7:52 am

A Thermodynamic History of the Solar Constitution — I:
The Journey to a Gaseous Sun
Pierre-Marie Robitaille

http://ptep-online.com/2011/PP-26-01.PDF

History has the power to expose the origin and evolution of scientific ideas. How did
humanity come to visualize the Sun as a gaseous plasma? Why is its interior thought to
contain blackbody radiation? Who were the first people to postulate that the density of
the solar body varied greatly with depth? When did mankind first conceive that the solar
surface was merely an illusion? What were the foundations of such thoughts? In this
regard, a detailed review of the Sun’s thermodynamic history provides both a necessary
exposition of the circumstance which accompanied the acceptance of the gaseous models and a sound basis for discussing modern solar theories. It also becomes an invitation
to reconsider the phase of the photosphere. As such, in this work, the contributions of
Pierre Simon Laplace, Alexander Wilson, William Herschel, Hermann von Helmholtz,
Herbert Spencer, Richard Christopher Carrington, John Frederick William Herschel,
Father Pietro Angelo Secchi, Herve August Etienne Albans Faye, Edward Frankland, ´
Joseph Norman Lockyer, Warren de la Rue, Balfour Stewart, Benjamin Loewy, and
Gustav Robert Kirchhoff, relative to the evolution of modern stellar models, will be
discussed. Six great pillars created a gaseous Sun: 1) Laplace’s Nebular Hypothesis,
2) Helmholtz’ contraction theory of energy production, 3) Andrew’s elucidation of critical temperatures, 4) Kirchhoff’s formulation of his law of thermal emission, 5) Plucker ¨
and Hittorf’s discovery of pressure broadening in gases, and 6) the evolution of the stellar equations of state. As these are reviewed, this work will venture to highlight not
only the genesis of these revolutionary ideas, but also the forces which drove great men
to advance a gaseous Sun.

SkyThing has reacted to this post.

Regards, Dan, a. k. a. smAshomAsh

#6 · January 4, 2020, 8:14 am

Quote from smAsh on January 4, 2020, 8:14 am
A LOT MORE PAPERS BY ROBITAILLE:
http://vixra.org/author/pierre-marie_robitaille
Pierre-Marie Robitaille
[63] viXra:1903.0563 submitted on 2019-03-31 19:38:45, (488 unique-IP downloads)
Eddington’s Mass-Luminosity Relationship: A Violation of the Laws of Thermodynamics
Authors: Stephen J. Crothers, Pierre-Marie Robitaille
Category: Astrophysics
[62] viXra:1811.0157 submitted on 2018-11-11 05:13:57, (472 unique-IP downloads)
The Unruh Effect: Insight from the Laws of Thermodynamics (Aps Meeting)
Authors: Stephen J. Crothers, Pierre-Marie Robitaille
Category: Relativity and Cosmology
[61] viXra:1810.0019 submitted on 2018-10-02 14:36:12, (403 unique-IP downloads)
Dynamics of the Solar Wind: Parker's Treatment and the Laws of Thermodynamics
Authors: Pierre-Marie Robitaille, Stephen J. Crothers
Category: Astrophysics
[60] viXra:1806.0079 submitted on 2018-06-08 04:43:09, (153 unique-IP downloads)
Thermodynamics and the Virial Theorem, Gravitational Collapse and the Virial Theorem: Insight from the Laws of Thermodynamics
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[59] viXra:1806.0078 submitted on 2018-06-08 04:52:51, (146 unique-IP downloads)
Kirchhoff ’s Law of Thermal Emission: Blackbody and Cavity Radiation Reconsidered
Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy
[58] viXra:1803.0639 submitted on 2018-03-24 19:12:22, (94 unique-IP downloads)
Chromospheric Emission Lines: Rules of Formation
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[57] viXra:1803.0264 submitted on 2018-03-17 16:45:33, (588 unique-IP downloads)
Hawking Radiation: A Violation of the Zeroth Law of Thermodynamics
Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy
[56] viXra:1708.0053 submitted on 2017-08-06 04:31:47, (731 unique-IP downloads)
Kirchhoff’s Law of Thermal Emission: What Happens When a Law of Physics Fails an Experimental Test?
Authors: Pierre-Marie Robitaille, Joseph Luc Robitaille
Category: Thermodynamics and Energy
[55] viXra:1602.0005 submitted on 2016-02-01 08:30:24, (104 unique-IP downloads)
Further Insight Relative to Cavity Radiation III: Gedanken Experiments, Irreversibility, and Kirchhoff's Law
Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy
[54] viXra:1602.0004 submitted on 2016-02-01 08:44:56, (149 unique-IP downloads)
A Re-examination of Kirchhoff's Law of Thermal Radiation in Relation to Recent Criticisms: Reply
Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy
[53] viXra:1510.0134 submitted on 2015-10-15 21:37:17, (110 unique-IP downloads)
Polarized Light from the Sun: Unification of the Corona and Analysis of the Second Solar Spectrum – Further Implications of a Liquid Metallic Hydrogen Solar Model
Authors: Pierre-Marie Robitaille, Dmitri Rabounski
Category: Astrophysics
[52] viXra:1502.0007 replaced on 2015-07-02 15:31:53, (2318 unique-IP downloads)
“The Theory of Heat Radiation” Revisited: A Commentary on the Validity of Kirchhoff’s Law of Thermal Emission and Max Planck’s Claim of Universality
Authors: Pierre-Marie Robitaille, Stephen J. Crothers
Category: Thermodynamics and Energy
[51] viXra:1405.0103 submitted on 2014-05-07 10:17:59, (304 unique-IP downloads)
Blackbody Radiation in Optically Thick Gases?
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[50] viXra:1405.0005 replaced on 2014-12-31 12:03:07, (230 unique-IP downloads)
On the Equation which Governs Cavity Radiation II
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[49] viXra:1403.0936 submitted on 2014-03-25 21:57:34, (121 unique-IP downloads)
Further Insight Relative to Cavity Radiation II: Gedanken Experiments and Kirchhoff’s Law
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[48] viXra:1403.0935 replaced on 2014-12-26 16:34:37, (564 unique-IP downloads)
On the Equation which Governs Cavity Radiation
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[47] viXra:1401.0098 replaced on 2014-01-18 05:25:23, (289 unique-IP downloads)
Further Insight Relative to Cavity Radiation: A Thought Experiment Refuting Kirchhoff's Law
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[46] viXra:1401.0097 replaced on 2014-01-18 05:20:23, (178 unique-IP downloads)
The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere VIII. `Futile' Processes in the Chromosphere
Authors: Joseph Luc Robitaille, Pierre-Marie Robitaille
Category: Astrophysics
[45] viXra:1310.0160 submitted on 2013-10-16 09:14:52, (106 unique-IP downloads)
Commentary Relative to the Seismic Structure of the Sun: Internal Rotation, Oblateness, and Solar Shape
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[44] viXra:1310.0159 submitted on 2013-10-16 09:18:05, (133 unique-IP downloads)
Commentary on the Radius of the Sun: Optical Illusion or Manifestation of a Real Surface?
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[43] viXra:1310.0158 submitted on 2013-10-16 09:21:27, (100 unique-IP downloads)
Commentary on the Liquid Metallic Hydrogen Model of the Sun: Insight Relative to Coronal Holes, Sunspots, and Solar Activity
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[42] viXra:1310.0157 submitted on 2013-10-16 09:24:11, (75 unique-IP downloads)
Commentary on the Liquid Metallic Hydrogen Model of the Sun II. Insight Relative to Coronal Rain and Splashdown Events
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[41] viXra:1310.0156 submitted on 2013-10-16 09:29:14, (77 unique-IP downloads)
Commentary on the Liquid Metallic Hydrogen Model of the Sun III. Insight into Solar Lithium Abundances
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[40] viXra:1310.0155 submitted on 2013-10-16 09:34:12, (59 unique-IP downloads)
Commentary Relative to the Emission Spectrum of the Solar Atmosphere: Further Evidence for a Distinct Solar Surface
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[39] viXra:1310.0154 submitted on 2013-10-16 09:38:10, (102 unique-IP downloads)
The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere I. Continuous Emission and Condensed Matter Within the Chromosphere
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[38] viXra:1310.0153 submitted on 2013-10-16 09:41:57, (96 unique-IP downloads)
The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere II. Continuous Emission and Condensed Matter Within the Corona
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[37] viXra:1310.0152 submitted on 2013-10-16 09:45:20, (72 unique-IP downloads)
The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere III. Importance of Continuous Emission Spectra from Flares, Coronal Mass Ejections, Prominences, and Other Coronal Structures
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[36] viXra:1310.0151 submitted on 2013-10-16 09:49:50, (68 unique-IP downloads)
The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere IV. On the Nature of the Chromosphere
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[35] viXra:1310.0150 submitted on 2013-10-16 09:53:32, (114 unique-IP downloads)
The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere V. On the Nature of the Corona
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[34] viXra:1310.0149 submitted on 2013-10-16 10:01:10, (144 unique-IP downloads)
The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere VI. Helium in the Chromosphere
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[33] viXra:1310.0148 submitted on 2013-10-16 10:07:17, (95 unique-IP downloads)
The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere VII. Further Insights into the Chromosphere and Corona
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[32] viXra:1310.0145 submitted on 2013-10-16 07:30:11, (148 unique-IP downloads)
A Thermodynamic History of the Solar Constitution - I: The Journey to a Gaseous Sun
Authors: Pierre-Marie Robitaille
Category: History and Philosophy of Physics
[31] viXra:1310.0144 submitted on 2013-10-16 07:36:54, (141 unique-IP downloads)
A Thermodynamic History of the Solar Constitution - II: The Theory of a Gaseous Sun and Jeans’ Failed Liquid Alternative
Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy
[30] viXra:1310.0143 submitted on 2013-10-16 07:41:29, (254 unique-IP downloads)
Liquid Metallic Hydrogen: A Building Block for the Liquid Sun
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[29] viXra:1310.0142 submitted on 2013-10-16 07:47:47, (63 unique-IP downloads)
On the Presence of a Distinct Solar Surface: A Reply to Hervé Faye
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[28] viXra:1310.0141 submitted on 2013-10-16 07:56:28, (84 unique-IP downloads)
On Solar Granulations, Limb Darkening, and Sunspots: Brief Insights in Remembrance of Father Angelo Secchi
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[27] viXra:1310.0140 submitted on 2013-10-16 08:02:59, (137 unique-IP downloads)
On the Temperature of the Photosphere: Energy Partition in the Sun
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[26] viXra:1310.0139 submitted on 2013-10-16 08:07:36, (124 unique-IP downloads)
Stellar Opacity: The Achilles’ Heel of the Gaseous Sun
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[25] viXra:1310.0138 submitted on 2013-10-16 08:13:49, (92 unique-IP downloads)
Lessons from the Sun
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[24] viXra:1310.0137 submitted on 2013-10-16 08:21:58, (72 unique-IP downloads)
Magnetic Fields and Directional Spectral Emissivity in Sunspots and Faculae: Complimentary Evidence of Metallic Behavior on the Surface of the Sun
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[23] viXra:1310.0136 submitted on 2013-10-16 08:27:45, (86 unique-IP downloads)
Liquid Metallic Hydrogen II. A Critical Assessment of Current and Primordial Helium Levels in the Sun
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[22] viXra:1310.0135 submitted on 2013-10-16 08:33:08, (89 unique-IP downloads)
Liquid Metallic Hydrogen III. Intercalation and Lattice Exclusion Versus Gravitational Settling and Their Consequences Relative to Internal Structure, Surface Activity, and Solar Winds in the Sun
Authors: Joseph Christophe Robitaille, Pierre-Marie Robitaille
Category: Astrophysics
[21] viXra:1310.0134 submitted on 2013-10-16 09:10:53, (69 unique-IP downloads)
Commentary Relative to the Distribution of Gamma-Ray Flares on the Sun: Further Evidence for a Distinct Solar Surface
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[20] viXra:1310.0129 submitted on 2013-10-15 14:06:08, (212 unique-IP downloads)
Water, Hydrogen Bonding, and the Microwave Background
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[19] viXra:1310.0128 submitted on 2013-10-15 14:10:44, (184 unique-IP downloads)
Global Warming and the Microwave Background
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[18] viXra:1310.0127 submitted on 2013-10-15 14:18:02, (154 unique-IP downloads)
Kirchhoff’s Law of Thermal Emission: 150 Years
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[17] viXra:1310.0126 submitted on 2013-10-15 14:22:46, (452 unique-IP downloads)
Blackbody Radiation and the Loss of Universality: Implications for Planck’s Formulation and Boltzmann’s Constant
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[16] viXra:1310.0125 submitted on 2013-10-15 14:32:59, (294 unique-IP downloads)
COBE: A Radiological Analysis
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[15] viXra:1310.0124 submitted on 2013-10-15 14:39:09, (109 unique-IP downloads)
Calibration of Microwave Reference Blackbodies and Targets for Use in Satellite Observations: An Analysis of Errors in Theoretical Outlooks and Testing Procedures
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[14] viXra:1310.0123 submitted on 2013-10-15 14:43:13, (217 unique-IP downloads)
The Planck Satellite LFI and the Microwave Background: Importance of the 4 K Reference Targets
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[13] viXra:1310.0121 submitted on 2013-10-15 06:20:59, (546 unique-IP downloads)
WMAP: A Radiological Analysis
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[12] viXra:1310.0120 submitted on 2013-10-15 06:34:21, (150 unique-IP downloads)
On the Origins of the CMB: Insight from the COBE, WMAP, and Relikt-1 Satellites
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[11] viXra:1310.0119 submitted on 2013-10-15 06:40:54, (110 unique-IP downloads)
A High Temperature Liquid Plasma Model of the Sun
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[10] viXra:1310.0118 submitted on 2013-10-15 06:46:02, (162 unique-IP downloads)
On the Earth Microwave Background: Absorption and Scattering by the Atmosphere
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[9] viXra:1310.0117 submitted on 2013-10-15 06:56:51, (364 unique-IP downloads)
The Little Heat Engine: Heat Transfer in Solids, Liquids and Gases
Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy
[8] viXra:1310.0116 submitted on 2013-10-15 07:03:09, (94 unique-IP downloads)
On the Nature of the Microwave Background at the Lagrange 2 Point. Part I
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[7] viXra:1310.0115 submitted on 2013-10-15 07:09:04, (196 unique-IP downloads)
Max Karl Ernst Ludwig Planck (1858-1947)
Authors: Pierre-Marie Robitaille
Category: History and Philosophy of Physics
[6] viXra:1310.0114 submitted on 2013-10-15 07:17:17, (120 unique-IP downloads)
The Earth Microwave Background (EMB), Atmospheric Scattering and the Generation of Isotropy
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[5] viXra:1310.0113 submitted on 2013-10-15 07:27:52, (103 unique-IP downloads)
A Critical Analysis of Universality and Kirchhoff's Law: A Return to Stewart's Law of Thermal Emission
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[4] viXra:1310.0112 submitted on 2013-10-15 07:34:11, (245 unique-IP downloads)
Blackbody Radiation and the Carbon Particle
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[3] viXra:1310.0110 submitted on 2013-10-15 05:45:49, (386 unique-IP downloads)
Forty Lines of Evidence for Condensed Matter - The Sun on Trial: Liquid Metallic Hydrogen as a Solar Building Block
Authors: Pierre-Marie Robitaille
Category: Astrophysics
[2] viXra:1310.0109 submitted on 2013-10-15 05:59:59, (229 unique-IP downloads)
An Analysis of Universality in Blackbody Radiation
Authors: Pierre-Marie Robitaille
Category: Condensed Matter
[1] viXra:1310.0108 submitted on 2013-10-15 06:08:53, (158 unique-IP downloads)
The Solar Photosphere: Evidence for Condensed Matter
Authors: Pierre-Marie Robitaille
Category: Astrophysics

A LOT MORE PAPERS BY ROBITAILLE:

http://vixra.org/author/pierre-marie_robitaille

Pierre-Marie Robitaille

[63] viXra:1903.0563 submitted on 2019-03-31 19:38:45, (488 unique-IP downloads)

Eddington’s Mass-Luminosity Relationship: A Violation of the Laws of Thermodynamics

Authors: Stephen J. Crothers, Pierre-Marie Robitaille
Category: Astrophysics

[62] viXra:1811.0157 submitted on 2018-11-11 05:13:57, (472 unique-IP downloads)

The Unruh Effect: Insight from the Laws of Thermodynamics (Aps Meeting)

Authors: Stephen J. Crothers, Pierre-Marie Robitaille
Category: Relativity and Cosmology

[61] viXra:1810.0019 submitted on 2018-10-02 14:36:12, (403 unique-IP downloads)

Dynamics of the Solar Wind: Parker's Treatment and the Laws of Thermodynamics

Authors: Pierre-Marie Robitaille, Stephen J. Crothers
Category: Astrophysics

[60] viXra:1806.0079 submitted on 2018-06-08 04:43:09, (153 unique-IP downloads)

Thermodynamics and the Virial Theorem, Gravitational Collapse and the Virial Theorem: Insight from the Laws of Thermodynamics

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[59] viXra:1806.0078 submitted on 2018-06-08 04:52:51, (146 unique-IP downloads)

Kirchhoff ’s Law of Thermal Emission: Blackbody and Cavity Radiation Reconsidered

Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy

[58] viXra:1803.0639 submitted on 2018-03-24 19:12:22, (94 unique-IP downloads)

Chromospheric Emission Lines: Rules of Formation

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[57] viXra:1803.0264 submitted on 2018-03-17 16:45:33, (588 unique-IP downloads)

Hawking Radiation: A Violation of the Zeroth Law of Thermodynamics

Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy

[56] viXra:1708.0053 submitted on 2017-08-06 04:31:47, (731 unique-IP downloads)

Kirchhoff’s Law of Thermal Emission: What Happens When a Law of Physics Fails an Experimental Test?

Authors: Pierre-Marie Robitaille, Joseph Luc Robitaille
Category: Thermodynamics and Energy

[55] viXra:1602.0005 submitted on 2016-02-01 08:30:24, (104 unique-IP downloads)

Further Insight Relative to Cavity Radiation III: Gedanken Experiments, Irreversibility, and Kirchhoff's Law

Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy

[54] viXra:1602.0004 submitted on 2016-02-01 08:44:56, (149 unique-IP downloads)

A Re-examination of Kirchhoff's Law of Thermal Radiation in Relation to Recent Criticisms: Reply

Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy

[53] viXra:1510.0134 submitted on 2015-10-15 21:37:17, (110 unique-IP downloads)

Polarized Light from the Sun: Unification of the Corona and Analysis of the Second Solar Spectrum – Further Implications of a Liquid Metallic Hydrogen Solar Model

Authors: Pierre-Marie Robitaille, Dmitri Rabounski
Category: Astrophysics

[52] viXra:1502.0007 replaced on 2015-07-02 15:31:53, (2318 unique-IP downloads)

“The Theory of Heat Radiation” Revisited: A Commentary on the Validity of Kirchhoff’s Law of Thermal Emission and Max Planck’s Claim of Universality

Authors: Pierre-Marie Robitaille, Stephen J. Crothers
Category: Thermodynamics and Energy

[51] viXra:1405.0103 submitted on 2014-05-07 10:17:59, (304 unique-IP downloads)

Blackbody Radiation in Optically Thick Gases?

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[50] viXra:1405.0005 replaced on 2014-12-31 12:03:07, (230 unique-IP downloads)

On the Equation which Governs Cavity Radiation II

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[49] viXra:1403.0936 submitted on 2014-03-25 21:57:34, (121 unique-IP downloads)

Further Insight Relative to Cavity Radiation II: Gedanken Experiments and Kirchhoff’s Law

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[48] viXra:1403.0935 replaced on 2014-12-26 16:34:37, (564 unique-IP downloads)

On the Equation which Governs Cavity Radiation

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[47] viXra:1401.0098 replaced on 2014-01-18 05:25:23, (289 unique-IP downloads)

Further Insight Relative to Cavity Radiation: A Thought Experiment Refuting Kirchhoff's Law

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[46] viXra:1401.0097 replaced on 2014-01-18 05:20:23, (178 unique-IP downloads)

The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere VIII. `Futile' Processes in the Chromosphere

Authors: Joseph Luc Robitaille, Pierre-Marie Robitaille
Category: Astrophysics

[45] viXra:1310.0160 submitted on 2013-10-16 09:14:52, (106 unique-IP downloads)

Commentary Relative to the Seismic Structure of the Sun: Internal Rotation, Oblateness, and Solar Shape

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[44] viXra:1310.0159 submitted on 2013-10-16 09:18:05, (133 unique-IP downloads)

Commentary on the Radius of the Sun: Optical Illusion or Manifestation of a Real Surface?

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[43] viXra:1310.0158 submitted on 2013-10-16 09:21:27, (100 unique-IP downloads)

Commentary on the Liquid Metallic Hydrogen Model of the Sun: Insight Relative to Coronal Holes, Sunspots, and Solar Activity

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[42] viXra:1310.0157 submitted on 2013-10-16 09:24:11, (75 unique-IP downloads)

Commentary on the Liquid Metallic Hydrogen Model of the Sun II. Insight Relative to Coronal Rain and Splashdown Events

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[41] viXra:1310.0156 submitted on 2013-10-16 09:29:14, (77 unique-IP downloads)

Commentary on the Liquid Metallic Hydrogen Model of the Sun III. Insight into Solar Lithium Abundances

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[40] viXra:1310.0155 submitted on 2013-10-16 09:34:12, (59 unique-IP downloads)

Commentary Relative to the Emission Spectrum of the Solar Atmosphere: Further Evidence for a Distinct Solar Surface

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[39] viXra:1310.0154 submitted on 2013-10-16 09:38:10, (102 unique-IP downloads)

The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere I. Continuous Emission and Condensed Matter Within the Chromosphere

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[38] viXra:1310.0153 submitted on 2013-10-16 09:41:57, (96 unique-IP downloads)

The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere II. Continuous Emission and Condensed Matter Within the Corona

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[37] viXra:1310.0152 submitted on 2013-10-16 09:45:20, (72 unique-IP downloads)

The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere III. Importance of Continuous Emission Spectra from Flares, Coronal Mass Ejections, Prominences, and Other Coronal Structures

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[36] viXra:1310.0151 submitted on 2013-10-16 09:49:50, (68 unique-IP downloads)

The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere IV. On the Nature of the Chromosphere

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[35] viXra:1310.0150 submitted on 2013-10-16 09:53:32, (114 unique-IP downloads)

The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere V. On the Nature of the Corona

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[34] viXra:1310.0149 submitted on 2013-10-16 10:01:10, (144 unique-IP downloads)

The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere VI. Helium in the Chromosphere

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[33] viXra:1310.0148 submitted on 2013-10-16 10:07:17, (95 unique-IP downloads)

The Liquid Metallic Hydrogen Model of the Sun and the Solar Atmosphere VII. Further Insights into the Chromosphere and Corona

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[32] viXra:1310.0145 submitted on 2013-10-16 07:30:11, (148 unique-IP downloads)

A Thermodynamic History of the Solar Constitution - I: The Journey to a Gaseous Sun

Authors: Pierre-Marie Robitaille
Category: History and Philosophy of Physics

[31] viXra:1310.0144 submitted on 2013-10-16 07:36:54, (141 unique-IP downloads)

A Thermodynamic History of the Solar Constitution - II: The Theory of a Gaseous Sun and Jeans’ Failed Liquid Alternative

Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy

[30] viXra:1310.0143 submitted on 2013-10-16 07:41:29, (254 unique-IP downloads)

Liquid Metallic Hydrogen: A Building Block for the Liquid Sun

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[29] viXra:1310.0142 submitted on 2013-10-16 07:47:47, (63 unique-IP downloads)

On the Presence of a Distinct Solar Surface: A Reply to Hervé Faye

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[28] viXra:1310.0141 submitted on 2013-10-16 07:56:28, (84 unique-IP downloads)

On Solar Granulations, Limb Darkening, and Sunspots: Brief Insights in Remembrance of Father Angelo Secchi

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[27] viXra:1310.0140 submitted on 2013-10-16 08:02:59, (137 unique-IP downloads)

On the Temperature of the Photosphere: Energy Partition in the Sun

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[26] viXra:1310.0139 submitted on 2013-10-16 08:07:36, (124 unique-IP downloads)

Stellar Opacity: The Achilles’ Heel of the Gaseous Sun

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[25] viXra:1310.0138 submitted on 2013-10-16 08:13:49, (92 unique-IP downloads)

Lessons from the Sun

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[24] viXra:1310.0137 submitted on 2013-10-16 08:21:58, (72 unique-IP downloads)

Magnetic Fields and Directional Spectral Emissivity in Sunspots and Faculae: Complimentary Evidence of Metallic Behavior on the Surface of the Sun

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[23] viXra:1310.0136 submitted on 2013-10-16 08:27:45, (86 unique-IP downloads)

Liquid Metallic Hydrogen II. A Critical Assessment of Current and Primordial Helium Levels in the Sun

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[22] viXra:1310.0135 submitted on 2013-10-16 08:33:08, (89 unique-IP downloads)

Liquid Metallic Hydrogen III. Intercalation and Lattice Exclusion Versus Gravitational Settling and Their Consequences Relative to Internal Structure, Surface Activity, and Solar Winds in the Sun

Authors: Joseph Christophe Robitaille, Pierre-Marie Robitaille
Category: Astrophysics

[21] viXra:1310.0134 submitted on 2013-10-16 09:10:53, (69 unique-IP downloads)

Commentary Relative to the Distribution of Gamma-Ray Flares on the Sun: Further Evidence for a Distinct Solar Surface

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[20] viXra:1310.0129 submitted on 2013-10-15 14:06:08, (212 unique-IP downloads)

Water, Hydrogen Bonding, and the Microwave Background

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[19] viXra:1310.0128 submitted on 2013-10-15 14:10:44, (184 unique-IP downloads)

Global Warming and the Microwave Background

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[18] viXra:1310.0127 submitted on 2013-10-15 14:18:02, (154 unique-IP downloads)

Kirchhoff’s Law of Thermal Emission: 150 Years

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[17] viXra:1310.0126 submitted on 2013-10-15 14:22:46, (452 unique-IP downloads)

Blackbody Radiation and the Loss of Universality: Implications for Planck’s Formulation and Boltzmann’s Constant

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[16] viXra:1310.0125 submitted on 2013-10-15 14:32:59, (294 unique-IP downloads)

COBE: A Radiological Analysis

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[15] viXra:1310.0124 submitted on 2013-10-15 14:39:09, (109 unique-IP downloads)

Calibration of Microwave Reference Blackbodies and Targets for Use in Satellite Observations: An Analysis of Errors in Theoretical Outlooks and Testing Procedures

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[14] viXra:1310.0123 submitted on 2013-10-15 14:43:13, (217 unique-IP downloads)

The Planck Satellite LFI and the Microwave Background: Importance of the 4 K Reference Targets

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[13] viXra:1310.0121 submitted on 2013-10-15 06:20:59, (546 unique-IP downloads)

WMAP: A Radiological Analysis

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[12] viXra:1310.0120 submitted on 2013-10-15 06:34:21, (150 unique-IP downloads)

On the Origins of the CMB: Insight from the COBE, WMAP, and Relikt-1 Satellites

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[11] viXra:1310.0119 submitted on 2013-10-15 06:40:54, (110 unique-IP downloads)

A High Temperature Liquid Plasma Model of the Sun

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[10] viXra:1310.0118 submitted on 2013-10-15 06:46:02, (162 unique-IP downloads)

On the Earth Microwave Background: Absorption and Scattering by the Atmosphere

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[9] viXra:1310.0117 submitted on 2013-10-15 06:56:51, (364 unique-IP downloads)

The Little Heat Engine: Heat Transfer in Solids, Liquids and Gases

Authors: Pierre-Marie Robitaille
Category: Thermodynamics and Energy

[8] viXra:1310.0116 submitted on 2013-10-15 07:03:09, (94 unique-IP downloads)

On the Nature of the Microwave Background at the Lagrange 2 Point. Part I

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[7] viXra:1310.0115 submitted on 2013-10-15 07:09:04, (196 unique-IP downloads)

Max Karl Ernst Ludwig Planck (1858-1947)

Authors: Pierre-Marie Robitaille
Category: History and Philosophy of Physics

[6] viXra:1310.0114 submitted on 2013-10-15 07:17:17, (120 unique-IP downloads)

The Earth Microwave Background (EMB), Atmospheric Scattering and the Generation of Isotropy

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[5] viXra:1310.0113 submitted on 2013-10-15 07:27:52, (103 unique-IP downloads)

A Critical Analysis of Universality and Kirchhoff's Law: A Return to Stewart's Law of Thermal Emission

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[4] viXra:1310.0112 submitted on 2013-10-15 07:34:11, (245 unique-IP downloads)

Blackbody Radiation and the Carbon Particle

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[3] viXra:1310.0110 submitted on 2013-10-15 05:45:49, (386 unique-IP downloads)

Forty Lines of Evidence for Condensed Matter - The Sun on Trial: Liquid Metallic Hydrogen as a Solar Building Block

Authors: Pierre-Marie Robitaille
Category: Astrophysics

[2] viXra:1310.0109 submitted on 2013-10-15 05:59:59, (229 unique-IP downloads)

An Analysis of Universality in Blackbody Radiation

Authors: Pierre-Marie Robitaille
Category: Condensed Matter

[1] viXra:1310.0108 submitted on 2013-10-15 06:08:53, (158 unique-IP downloads)

The Solar Photosphere: Evidence for Condensed Matter

Authors: Pierre-Marie Robitaille
Category: Astrophysics

Bestowic has reacted to this post.

Regards, Dan, a. k. a. smAshomAsh

#7 · February 1, 2020, 12:20 pm

Quote from smAsh on February 1, 2020, 12:20 pm
April, 2013 PROGRESS IN PHYSICS Volume 2
Liquid Metallic Hydrogen II. A Critical Assessment of Current and Primordial
Helium Levels in the Sun
Pierre-Marie Robitaille
Department of Radiology, The Ohio State University, 395 W. 12th Ave, Columbus, Ohio 43210, USA. E-mail: robitaille.1@osu.edu
Before a solar model becomes viable in astrophysics, one must consider how the elemental constitution of the Sun was ascertained, especially relative to its principle components: hydrogen and helium. Liquid metallic hydrogen has been proposed as a solar
structural material for models based on condensed matter (e.g. Robitaille P.-M. Liquid Metallic Hydrogen: A Building Block for the Liquid Sun. Progr. Phys., 2011,
v. 3, 60–74). There can be little doubt that hydrogen plays a dominant role in the universe and in the stars; the massive abundance of hydrogen in the Sun was established
long ago. Today, it can be demonstrated that the near isointense nature of the Sun’s
Balmer lines provides strong confirmatory evidence for a distinct solar surface. The
situation relative to helium remains less conclusive. Still, helium occupies a prominent
role in astronomy, both as an element associated with cosmology and as a byproduct
of nuclear energy generation, though its abundances within the Sun cannot be reliably
estimated using theoretical approaches. With respect to the determination of helium levels, the element remains spectroscopically silent at the level of the photosphere. While
helium can be monitored with ease in the chromosphere and the prominences of the
corona using spectroscopic methods, these measures are highly variable and responsive
to elevated solar activity and nuclear fragmentation. Direct assays of the solar winds
are currently viewed as incapable of providing definitive information regarding solar
helium abundances. As a result, insight relative to helium remains strictly based on theoretical estimates which couple helioseismological approaches to metrics derived from
solar models. Despite their “state of the art” nature, helium estimates based on solar
models and helioseismology are suspect on several fronts, including their reliance on
solar opacities. The best knowledge can only come from the solar winds which, though
highly variable, provide a wealth of data. Evaluations of primordial helium levels based
on 1) the spectroscopic study of H-II regions and 2) microwave anisotropy data, remain highly questionable. Current helium levels, both within the stars (Robitaille J. C.
and Robitaille P.-M. Liquid Metallic Hydrogen III. Intercalation and Lattice Exclusion
versus Gravitational Settling, and Their Consequences Relative to Internal Structure,
Surface Activity, and Solar Winds in the Sun. Progr. Phys., 2013, v. 2, in press) and
the universe at large, appear to be overstated. A careful consideration of available observational data suggests that helium abundances are considerably lower than currently
believed.
At the age of five Cecilia [Payne] saw a meteor, and
thereupon decided to become an Astronomer. She
remarked that she must begin quickly, in case there
should be no research left when she grew up.
Betty Grierson Leaf, 1923 [1, p. 72–73]
1 Introduction
Knowledge that helium [2,3] was first observed in the Sun by
Pierre Jules C´esar Janssen [4] and Joseph Norman Lockyer
[5], before being discovered on Earth by William Ramsay [6],
might prompt the belief that the element was abundant on the
solar surface. In fact, helium has never been identified in the
absorption spectra of the quiet Sun. Janssen and Lockyer’s
fortunate discovery was restricted to helium lines appearing
within the prominences of the corona and within the disturbed
chromosphere [4,5]. While the element was easily detectable
in these regions [7], helium has remained relatively spectroscopically silent on the Sun. Conversely, the stars and the
Sun display signs of extreme hydrogen abundance, as first observed by Cecilia Payne [8], Albrecht Uns¨old [9], and Henry
Norris Russell [10]. Few would take issue with the conclusion that the visible universe is primarily comprised of hydrogen. Helium abundances present a more arduous question.
Despite all the difficulties, several lines of reasoning sustain the tremendous attention that solar helium levels have
received in astronomy. First, helium is the end product of
the nuclear reactions currently believed to fuel many of the
stars, either in the pp process or the CNO cycle [11–15]. Second, solar helium levels are inherently linked to the gaseous
models of the Sun [16–18] and the application of theoretical
findings to the interpretation of helioseismic results [19–23].
Finally, helium is thought to be a key primordial element in
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 35
Volume 2 PROGRESS IN PHYSICS April, 2013
Big Bang cosmology [3, 24–30]. As a result, the evaluation
of helium levels in the Sun brings a unified vision of astrophysics, wherein accepted solar values lend credence to our
current concept of the formation of the universe. Still, questions remain relative to the accuracy of modern helium determinations.
A flurry of initial studies had suggested that helium abundances in the stars approached 27% by mass (see [3] for a
review). The findings provided support for those who proposed primordial formation of helium prior to the existence of
the objects which populate the main sequence [3, 24]. However, these ideas were challenged when it was discovered that
certain B-type stars, which should have been rich in helium
lines, were almost devoid of such features [3]. As a result,
in certain stars, helium was said to be gravitationally settling
towards the interior [3,31]. The desire to link helium levels in
the Sun with those anticipated from the primordial synthesis
continues to dominate modern solar theory [18]. Nonetheless, it can be demonstrated that the methods used to estimate
primordial helium levels in the universe [24] are either highly
suspect or implausible. Given these complexities, it is appropriate to compose a critical review of how helium abundances
have been historically obtained and how they are currently determined, both in the Sun and in the universe at large.
2 Assessing elemental abundances in stellar spectra
2.1 The Saha Equations
Reasoning, like Lindemann [32] and Eggert [33] before him,
that the fragmentation of an atom into an ion and an electron
was analogous to the dissociation of a molecule, Megh Nad
Saha [34, 35] formulated the ionization equations [36, 37] in
the early 1920s. In so doing, he called upon the Nernst equation [38] and suggested that the free electron could be viewed
as an ideal gas. He also relied on thermal equilibrium and
the ionization potentials of the elements. Since Saha’s equation was inherently related to parameters associated with the
ideal gas (i.e. [39, p. 29–36] and [40, p. 107–117]) he demonstrated that the level of ionization could be increased either
with elevated temperature or decreased pressure. Saha hypothesized that the pressure of the reversing layer approached
0.1–1 atm [36, p. 481] and was the first to utilize this assumption to account for the appearance of spectral lines across
stellar classes as simple functions of temperature [36, 37].
He was concerned with the marginal appearance of spectral
lines [36,37], that point at which these features first appeared
on a photographic plate. Cecilia Payne [1, 41] would soon
estimate the abundance of the elements in the universe using
the same criterion [8].
In his initial work, Saha would comment on the impossibility of solar temperatures increasing as one moves from
the photosphere to the upper chromosphere: “Lockyer’s theory. . . [that elements become more ionized as higher elevations are reached within the chromosphere] . . . would lead us
to the hypothesis that the outer chromosphere is at a substantially higher temperature than the photosphere, and the
lower chromosphere; and that the temperature of the sun increases as we pass radially outwards. This hypothesis is,
however, quite untenable and is in flagrant contradiction to
all accepted theories of physics” [36, p. 473]. Saha had not
suspected that 20th century solar theorists would maintain
such a position. Lockyer’s analysis was correct: ionization
increased with elevation in the chromosphere. This was an
important lesson relative to thermal equilibrium. In any case,
Saha did observe that hydrogen was not fully ionized in the
chromosphere, since the lines from Hα and Hβ were evident at
this level. He also recognized that hydrogen should be essentially ionized in O class stars and that the lines coincident with
the Balmer series in these stars had originated from ionized
helium. At the same time, he outlined that the same spectral lines for classes later than B2A were completely due to
hydrogen [37, p. 151].
Subrahmanyan Chandrasekhar’s (Nobel Prize, 1983 [42])
thesis advisor, Sir Ralph H. Fowler [43], had provided significant insight and criticisms into Saha’s second manuscript [37,
p. 153] and the resulting text was masterful. In 1927, Megh
Nad Saha was elected a Fellow of the Royal Society [34].
In the meantime, Fowler [43] and Edward Arthur Milne
[44] would collaborate and construct a wonderful extension
[45,46] of Saha’s seminal papers [36,37]. They improved the
treatment of ionization to consider not only principle lines
arising from atoms in their lowest energy states, but also the
subordinate lines produced by excited atoms and ions [45,46].
For his part, Saha had concentrated on the excitation and ionization of the neutral atom [36, 37]. Fowler and Milne understood that the marginal appearance of a spectral line could
be used in determining relative concentrations and provided
some indication of the minimum number of atoms necessary
for appearance [45, 46]. They emphasized the idea that: “the
intensity of a given absorption line in a stellar spectrum is
proportional to the concentration of atoms in the stellar atmosphere capable of absorbing the line” [45, p. 404]. Their
first paper also highlighted the value of the maximum of a
spectral line in assessing the temperature and pressure of the
reversing layer and outlined that this problem was not affected
by the relative abundance of the element studied [45]. Using
stellar data from the lines of Ca, Mg, Sr, and Ba they determined that the electron pressure of the reversing layer was
on the order of 10−4
atm [45]. Fowler and Milne understood
that electron pressure, Pe, of the reversing layer was not determined by a single ionization process, but by the ionization
of many elements: “In thus regarding Pe as fundamental we
are in effect assuming that, due to the presence of more easily ionised atoms, there are so many electrons present that
the partial electron pressure is practically independent of the
degree of ionization of the element under discussion” [45,
p. 409]. They expressed concern that their results led to the
assumption that absorbing species had very large absorption
36 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
coefficients [45]. Milne had already determined that the absorption coefficients should be very large [47] and would later
devote another theoretical paper to their determination [48].
In their work together, Fowler and Milne explicitly assumed
that the reversing layer could be treated as existing under
conditions of thermal equilibrium, as Saha’s treatment required [36]. The validity of such assumptions is not simple to
ascertain.
At Cambridge, Milne met Cecilia Payne [1, p. 121], a student at Newnham College [1, p. 112] and learned of her impending access to the vast collection of photographic plates
used to generate the Henry Draper Catalogue at the Harvard
Observatory [1, p. 144–153]. Prior to the advent of the modern MKK classification [49], the Henry Draper Catalogue was
the largest stellar library collection, with over 200,000 classified stars [1, p. 144–153]. Milne suggested that “if he had. . .
[Payne’s] . . . opportunity, he would go after the observations
that would test and verify the Saha theory” [1, p. 155]. Cecila
Payne soon left Cambridge and sailed to America.
2.2 Cecilia Payne: What is the universe made of?
“I remember when, as a student at Cambridge, I decided I wanted to be an astronomer and asked the
advice of Colonel Stratton, he replied, “You can’t
expect to be anything but an amateur”. I should have
been discouraged, but I wasn’t, so I asked Eddington the same question. He (as was his way) thought
it over a very long time and finally said: “I can see
no insuperable obstacle” [50, xv].
Nineteenth century scientists had little on which to base their
understanding of the composition of the universe. Their clues
could only come from the Earth itself and from the meteorites
which occasionally tumbled onto its surface. Consequently, it
was not unreasonable to expect that the universe’s composition matched the terrestrial setting. However, stellar spectra,
already stored on photographic plates throughout Europe and
especially in the vast Henry Draper Collection, were hiding
a drastically altered viewpoint. With the arrival of yet another woman at the Harvard Observatory [51–60], the stars
could not much longer conceal their story. Surrounded by
Pickering’s Harem [51–60], Cecilia Payne [1, 41] completed
her classic report on the abundance of the elements [8] and
became the first to underscore the importance of hydrogen as
the constitutive atom of universe. Her thesis had been carefully prepared and presented supportive laboratory evidence,
not only of ionization potentials, but of the validity of Saha’s
treatment [8, p. 105–115].
Stellar spectra signaled hydrogen [61] was so abundant
that several scientists, including Henry Norris Russell, could
not fully accept the conclusion. Payne had written an early
manuscript detailing the tremendous presence of hydrogen [1,
p. 19]. Her thesis advisor, Harlow Shapley, forwarded the
work to Russell who commented: “It is clearly impossible
that hydrogen should be a million times more abundant than
the metals” [1, p. 19]. That early manuscript was never published and has since been lost [1, p. 20]. Tempered by Russell and Shapley, Cecilia Payne finally produced her famous
PhD dissertation: Stellar Atmospheres: A Contribution to the
Observational Study of High Temperature in the Reversing
Layers of Stars [8]. She would comment on hydrogen in this
manner: “Although hydrogen and helium are manifestly very
abundant in stellar atmospheres, the actual values derived
from the estimates of marginal appearance are regarded as
spurious” [8, p. 186]. A little later she would add: “The outstanding discrepancies between the astrophysical and terrestrial abundances are displayed for hydrogen and helium. The
enormous abundance derived for these elements in the stellar atmospheres is almost certainly not real” [8, p. 188] and
“The lines of both atoms appear to be far more persistent,
at high and low temperatures, than those of any other element” [8, p. 189].
For her part, Payne privately maintained that hydrogen
was tremendously abundant in the stars: “When I returned to
visit Cambridge after I finished this first essay in astrophysics,
I went to see Eddington. In a burst of youthful enthusiasm, I
told him that I believed that there was far more hydrogen in
the stars than any other atom. ‘You don’t mean in the stars,
you mean on the stars’, was his comment. In this case, indeed,
I was in the right, and in later years he was to recognize it
too” [1, p. 165].
Payne’s work also highlighted the importance of helium
in the O and B class stars [8]. For the first time, hydrogen
and helium became the focus of scrutiny for their role as potential building blocks of the stars and the cosmos [8]. She
emphasized that: “there is no reason to assume a sensible departure from uniform composition for members of the normal
sequence” [8, p. 179] and “The uniformity of composition of
stellar atmospheres is an established fact” [8, p. 189]. She
also held, as Eddington and Zeipel had advanced, that given
their gaseous nature: “an effect of rotation of a star will be
to keep the constituents well mixed, so that the outer portions
of the sun or of a star are probably fairly representative of
the interior” [8, p. 185]. Still, Payne was cautious relative to
extending her results as reflecting the internal composition of
the stars: “The observations on abundances refer merely to
the stellar atmosphere, and it is not possible to arrive in this
way at conclusions as to internal composition. But marked
differences of internal composition from star to star might be
expected to affect the atmosphere to a noticeable extent, and
it is therefore somewhat unlikely that such differences do occur” [8, p. 189].
Payne would conclude her thesis with a wonderful exposition of the Henry Draper Classification system [8, p. 190–
198]. Otto Struve would come to regard the study as “the most
brilliant Ph.D. thesis ever written in astronomy” [41]. Edwin
Hubble would comment relative to Payne: “She’s the best
man at Harvard” [1, p. 184]. As Milne suggested, the first
dissertation of the Harvard College Observatory was founded
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 37
Volume 2 PROGRESS IN PHYSICS April, 2013
upon the application of the ionization equations [36,37,45,46]
to the detailed analysis of spectral lines across stellar classes.
It did not specifically address elemental abundances in the
Sun. Nonetheless, Payne’s 1925 dissertation heralded the application of quantitative spectral analysis in astronomy [8].
2.3 Albrecht Unsold, hydrogen abundance, and evi- ¨
dence for a solar surface
Albrecht Uns¨old extended Payne’s studies with a focus on
the solar spectra [9]. Following in her footsteps [8], in 1928
[9], he applied the ionization formula [36, 37] to the chromosphere and estimated the levels of sodium, aluminum, calcium, strontium, and barium. In addition, Uns¨old determined
that the electron gas pressure in the chromosphere stood at
∼ 10−6
atm [9]. He also concluded that hydrogen must be
about one million times more abundant than any other element in the Sun [9, 62]. William McCrea was soon to echo
Uns¨old, finding that hydrogen was a million times more abundant than Ca+ within the chromosphere [62, 63].
Importantly, Uns¨old also documented that the absorbance
of the hydrogen β, γ, and δ lines did not decrease across
the Balmer series (Hα =1; Hβ = 0.73; Hγ = 0.91; Hδ = 1.0) as
expected from quantum mechanical considerations (Hα =1;
Hβ = 0.19; Hγ =0.07; Hδ =0.03) [9]. This was an important
finding relative to the nature of the Sun. Recently, the behavior of hydrogen emission lines has been analyzed with
non-LTE methods [64]. It has been concluded that the “n =3
and higher levels are in detailed balance deep in the photosphere, but they develop a non-LTE underpopulation further
out. However, the levels with higher n-values stay in detailed
balance relative to each other at these atmospheric depths,
and they also collisionally couple tightly to the continuum”
[64]. Yet, in the gaseous models of the Sun, the continuum is
not composed of condensed matter [65]. It represents an area
of profoundly increased solar opacity [65]. Nevertheless, the
behavior of the Balmer series in the solar atmosphere strongly
supports the idea that the Sun is comprised of condensed matter. Only a physical entity of sufficient density, such as a
surface, can permit tight collisional coupling to the continuum, as it is impossible to couple to the opacity changes
which characterize the continuum in gaseous models [65].
These findings comprise the sixteenth and seventeenth lines
of evidence that the Sun is comprised of condensed matter.
The others are outlined by the author in recent publications
(e.g. [66]).
2.4 Henry Norris Russell: Inability to estimate Helium
from spectral lines
Soon Henry Norris Russell [67] surpassed Uns¨old in his analysis of solar spectral lines and provided a detailed compositional analysis of the Sun. Relative to the occupied energy
levels within atoms on the Sun, Russell affirmed that: “It must
further be born in mind that even at solar temperatures the
great majority of the atoms of any given kind, whether ionized
or neutral, will be in the state of lowest energy” [10, p. 21]. At
the same time, Russell realized that this rule was not observed
by hydrogen, leading him to the conclusion that the element
was extremely abundant in the Sun: “One non-metal, however, presents a real and glaring exception to the general rule.
The hydrogen lines of the Balmer series, and, as Babcock
has recently shown, of the Paschen series as well, are very
strong in the Sun, though the energy required to put an atom
into condition to absorb these series is, respectively, 10.16
and 12.04 volts - higher than for any other solar absorption
lines. The obvious explanation — that hydrogen is far more
abundant than the other elements — appears to be the only
one” [10, p. 22]. In fact, even the hydrogen Brackett lines
can be visualized in the infrared spectrum of the Sun [68].
Russell also highlighted Uns¨old’s observation [9] that the hydrogen β, γ, and δ lines did not decrease as expected. That
the hydrogen lines were extremely broad in the Sun had already been well established. Russell echoed some of his contemporaries and suggested that this might result from a Stark
effect [10, p. 50].
Finally, Russell accepted Payne’s findings relative to hydrogen and reported her numbers for the elements without
comment in his table XVI [10, p. 65]. He stated that: “The
most important previous determination of the abundance of
the elements by astrophysical means is that by Miss Payne. . . ”
[10, p. 64]. Russell found the correlation between their works
to display “a very gratifying agreement” [10, p. 65]
Like Payne, Russell had relied on the work of Fowler and
Milne [45, 46] to set the composition of the Sun. He implemented their suggestion that electron pressures, Pe, could be
gathered by considering the spectra and the ionization potential for elements like Ca, Sc, Ti, Sr and Yt. From these, he deduced a Pe of 3.1 ×10−6
atm, in close agreement with Milne
(2.5 ×10−5
atm), and Payne and Hogg (2.54 ×10−6
atm) in
class G0 stars [10, p. 54–55]. Along with John Quincy Stewart, Russell had previously considered various means of determining the pressures at the Sun’s surface and had determined
that the pressure of the reversion layer could not be more than
10−4
atm [69]. But Russell reported a factor of at least 10 in
discordance in calculating electron pressures based on either
the ionization formula or the numbers of metallic atoms and
ions [10, p. 70–71]. He would resolve the difficulty at the end
of his treatise when setting the final elemental composition
for the Sun [10, p. 72].
At the same time, while Payne had understood the importance of local thermal equilibrium (LTE) for the proper application of Saha’s equation [8, p. 92–101], she did not attempt
to make an explicit correction for the lack of equilibrium.
Conversely, Russell placed a correction factor in his work for
departure from LTE: “We have finally to take into consideration the fact that the atmosphere may not be in thermodynamic equilibrium. The comparison of solar and stellar spectra affords evidence that this is the case” [10, p. 52]. Relative
38 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
to his final abundances he commented: “The main source of
uncertainty which affects them is the magnitude of the correction for departure from thermodynamic equilibrium” [10,
p. 58] and “If the correction for departure from thermodynamic equilibrium should be wholly disregarded, the calculated abundance of hydrogen — already very great — would
be increased thirty fold” [10, p. 62]. In the 1920s, of course,
there was hesitancy concerning the tremendous levels of hydrogen observed in the solar atmosphere.
For Russell, oxygen appeared as abundant as all other
metals combined. He also argued against, although did not
fully dismiss, gravitational settling in the Sun for the heaviest
metals: “It does not appear necessary, therefore, to assume
that downward diffusion depletes the sun’s atmosphere of the
heavier elements, though the possibility of such an influence
remains” [10, p. 59]. Importantly, he noted: “The statement
that enhanced lines are found in the sun for those elements
which have lines of low excitation potential in the accessible
region has therefore few exceptions” [10, p. 35]. At the same
time, he advanced that for those elements “which fail to show
enhancement lines in the sun, the excitation potentials for the
accessible lines are high in every case for which they have
been determined” [10, p. 35]. Furthermore Russell hypothesized that: “It appears, therefore, that the principle factor
which is unfavourable to the appearance of a spectral line in
the sun is a high excitation potential” [10, p. 35]. This was
precisely the case relative to helium.
With respect to the second element, Russell wrote: “There
is but one element known to exist in the sun for which no estimate of abundance has now been made - and this is He. The
intensity of its lines in the chromosphere shows that it must be
present in considerable amount, but no quantitative estimate
seems possible” [10, p. 62]. Here was an explicit admission
that solar helium abundances could not be ascertained using
spectral data.
Helium was abundantly visible in early type stars, as Cecilia Payne had already discovered [8] and Paul Rudnick [70]
and Anne Underhill continued to confirm [71–73]. Estimates
of the number of hydrogen to helium atoms in O and B type
stars varied from values as low as 3.2 to more than 27 [73,
p. 156]. A factor of nearly 10 in relative abundances from
spectral lines in such stars was hardly reassuring. Nonetheless, Underhill still surmised that the number of helium atoms
was at the 4–5% level [73]. Yet for the Sun, data about helium
abundance remained wanting.
2.5 Local Thermal Equilibrium
Milne was perhaps the greatest authority relative to local thermal equilibrium (LTE) in astronomy [74–77] and many of
the most salient aspects of his arguments have been reviewed
[78]. Milne advocated that LTE existed in the center of a
star and that his treatment permitted “us to see in a general way why the state of local thermodynamic equilibrium
in the interior of a star breaks down as we approach the surface” [77, p. 81–83]. In 1928, Milne would express concern
relative to the appropriateness of the inferred thermal equilibrium in the reversing layer, as required by the Saha equations [36, 37], although he believed that studies based on the
validity of the ionization equations should be pursued: “The
recent work of Adams and Russell brings forward evidence
that the reversing layers of stars are not in thermodynamic
equilibrium. This suggests a degree of caution in applying the
fundamental method and formulae of Saha to stellar spectra.
Nevertheless, departure from thermodynamic equilibrium can
only be found by pushing to as great a refinement as possible
the theory which assumes thermodynamic equilibrium” [48].
Gerasimovic had already advanced corrections for small deviations from thermal equilibrium [79] and Russell applied
corrections directly in his work [10]. By 1925, the Saha equations had been generally confirmed under experimental conditions (e.g. [8, p. 111–112] and [80]), but only in the broadest sense. Over time, the ionization equations continued to be
widely studied and the problems considered were extended
to include two-temperature plasmas (e.g. [81]), high pressures (e.g. [82]), varying opacities (e.g. [83]), and non-LTE
(e.g. [84–88]). The Saha equations eventually became a useful staple in the treatment of plasma physics [89, p. 164] and
stellar atmospheres [90–92].
As Auer highlighted relative to solar models [88], under
non-LTE, a set of rate equations enters into the problem of
determining the abundance of any given electronic state. Furthermore, the radiation field is introduced directly into the
equations [88] utilized to calculate both opacities and populations. The problem therefore becomes dependent on “simultaneous knowledge of the radiation field at all frequencies
and all depths” [88, p. 576].
While ionization appeared tractable given modern computing, the solution became linked to the knowledge of stellar opacities, an area of theory whose weaknesses have already been outlined [78]. Nonetheless, non-LTE approaches
have been successful in addressing the spectra of early type
stars [93–95]. Today, such methods also account for electronic, atomic, and ionic collision processes [64]. Non-LTE
approaches have provided considerable insight into the Balmer and Paschen series associated with the hydrogen spectrum of the Sun [64].
Finally, it appears that the treatment adopted by Cecilia
Payne might not have been too far afield [8]. For many of
the cooler stars, simple LTE seems sufficient to address ionization problems [94]. Non-LTE methods become most important for the O and A class stars [93–95]. In any case,
helium cannot be assessed on the Sun using the ionization
equations due to the lack of appropriate spectral lines. As a
result, while the LTE and non-LTE settings may be fundamental to the proper treatment of spectral lines, the methods
have little bearing on the proper evaluation of helium levels
in the Sun.
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 39
Volume 2 PROGRESS IN PHYSICS April, 2013
3 Helium from solar theory
3.1 Henry Norris Russell
Since Russell was not able to extract helium abundances directly from spectral lines, he did so, without further scientific
justification, by assuming that the Sun had an mean molecular weight of ∼2 [10, p. 72–73]. Such a value had also been
suggested by Saha [36, p. 476], who had in turn adopted it
from Eddington [96, p. 596]. As for Eddington, he had previously examined the radiation equilibrium of the stars using
a mean molecular weight of 54 [97]. In 1916, this value had
been selected based on the belief that the stars were principally composed of elements such as oxygen, silicon, and iron
prior to full ionization [1, viii]. Eddington lowered the mean
molecular weight to a value of 2 in 1917 [96, p. 596], based
on the idea that the elements would be fully ionized in the
stars. In the fully ionized state, hydrogen has a mean molecular weight of 0.5, helium of ∼1.3, and iron of ∼ 2 (see [40,
p. 102–104] for a full discussion of mean molecular weights
in astrophysics). It was this value which Russell was to adopt
in his calculations.
Using a mean molecular weight corresponding to a metal
rich star, Russell concluded that helium was 13% as abundant as hydrogen by weight [10, p. 73]. He then computed
that the Sun had equal percentages of oxygen and other metals (∼24% each) and that hydrogen comprised just under half
of the constitution (∼ 45%) by weight (see table XX in [10,
p. 73]. If Russell had selected a mean atomic weight of ∼0.5,
there would be dramatic changes in the calculated helium
levels.
3.2 Early abundance calculations
In arbitrarily selecting mean molecular weights [96, 97], Eddington determined the mean central stellar temperatures and
pressures along with the acceleration due to gravity at the surface (e.g. [97, p. 22]). In turn, these parameters altered the
calculated absorption coefficient, and hence opacity, of stellar interiors [97, p. 22]. Consequently, the setting of mean
atomic weight had a profound implication on nearly every
aspect of stellar modeling, but opacity would always remain
paramount. In 1922, Eddington had derived a relationship
between opacity and temperature [98] which would become
known as Kramer’s law [99].
Soon, Str¨omgren introduced an interesting twist to Eddington’s approach [100, 101]. Rather than assuming a mean
atomic weight, Str¨omgren began his calculations by computing opacity values, and from there, estimating the fractional
composition of hydrogen within several stars [100], relying
in part on Russell’s elemental composition [10]. He concluded that the fractional abundance of hydrogen was ∼ 0.3
and maintained that the presence of helium would have little
effect on these calculations since “hydrogen and helium do
not contribute to the opacity directly” [100, p. 139]. Str¨omgren would write: “we have neglected the influence of helium.
The helium proportion is rather uncertain and the error introduced by neglecting helium altogether small [100, p. 142].
Modern stellar theory would come to rely greatly on the opacity contributions of the negative hydrogen ion (H−
) [102].
Str¨omgren’s assumptions were premature. Still, he championed the idea of initially computing opacity, and from these
values obtaining both solar parameters and elemental abundances [100, 101].
Following the publication of a key modeling paper by
Cowling [103], Martin Schwarzschild was to take the next
theoretical step [104]. First, he made use of the massluminosity relation while expressing mean molecular weight
and opacity as a function of elemental composition (X = hydrogen, Y = helium) [104]. Then, reasoning that the energy
output in the Sun from the CNO cycle [13] was directly related to elemental composition, he derived a fractional elemental composition for hydrogen, helium, and the metals
equal to 0.47, 0.41, and 0.12, respectively [104]. The results
were once again critically dependent on estimated opacities,
which Schwartzchild, like Str¨omgren before him [100, 101],
assumed to display Eddington’s [98] −3.5 power dependence
on temperature (see Eq. 9 in [104]). In fact, Schwarzschild
utilized an even greater dependence on temperature for energy production, allowing a 17th power in the exponential
(see Eq. 11 in [104]). Yugo Iinuma then advanced a broader
approach to the stellar composition problem [105]. He was
concerned with ranges of reasonable starting points, both for
hydrogen concentration and average molecular weight. His
treatment remained dependent on opacity computations,
though less rigid in its conclusions [105]. Schwarzschild et
al. [106] then introduced the effects of inhomogeneity in the
solar interior and convective envelopes along with solar age
into the abundance problem. They reached the conclusion
that the temperatures at the core of the Sun were such that
the carbon cycle should start to contribute to the problem.
Hydrogen abundances were assumed in order to arrive both
at a convection parameter and at helium values [106]. The
critical link to opacity remained [106]. Weymann, who like
Schwarzschild, was also at the Institute for Advanced Study,
built on his findings [107]. Taking account of the carbon cycle, Weymann found that the core of the Sun was not convective [107]. Powers of 4 and 20 for temperature were assumed in the energy generation laws associated with the pp
and CNO cycles [107]. The hydrogen fractional composition
of the Sun was assumed and ranged from 0.60 to 0.80 (see
Table 3 in [107]). This resulted in helium and metallic fractional compositions of 0.19–0.32 and 0.01–0.08, respectively
(see Table 3 in [107]).
In 1961, Osterbrock and Rogerson would elegantly summarize the situation relative to estimating helium abundances
in the Sun: “Though helium is observed in the upper chromosphere and in prominences, the physical conditions in these
regions are too complicated and imperfectly understood for
the abundance ratio to be determined from measurements of
40 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
these emission lines. Hence the only reliable way to find the
helium abundance in the Sun is by analysis of its internal
structure” [108]. Yet, given the progress to date, the determination of elemental compositions within the Sun had been
a complex adventure involving either assumed values of average molecular weights, hydrogen abundances, energy generation reactions, and opacity. The latter would eventually
present the greatest difficulties [78]. Osterbrock and Rogerson would utilize Weymann’s calculation, along with making
an assumption by setting the Z/X ratio at 6.4 ×10−2
[108],
to estimate interior solar fractional abundances at X = 0.67,
Y = 0.29, and Z = 0.04. They were guided in this estimation
by the belief that: “the solar, planetary nebula, and interstellar abundances are all essentially the same” [108, p. 132].
For the planetary nebula NGC 7027 they set the fractional
abundances at X = 0.64, Y = 0.32, and Z = 0.04 [108]. Solar
elemental composition became decidedly linked to estimates
from remote objects. The stage was set for conclusively linking solar elemental composition to stellar evolution and primordial nucleosynthesis.
3.3 Modern abundance calculation
Eventually, the solar neutrino problem entered theoretical
modeling [16, 109]. In his simulations, John Bahcall would
utilize fractional abundances of relatively narrow range (X =
0.715 − 0.80, Y = 0.19 − 0.258 and Z = 0.01 − 0.027), setting the central densities and temperatures near 150 g/cm3
and 15 million Kelvin, respectively [16]. The results, as before, were reliant on the use of solar opacity estimates [78].
By the beginning of the 1970s, fractional abundances for helium and the metals were settling on values near 0.28 and
0.02 [25]. Solar models became increasingly complex, relying on stellar opacity tables [110–118], energy generation
equations, neutrino flux, and solar age to arrive at internally
consistent results [17, 18]. Complexity was also introduced
by considering helium and heavy element diffusion throughout the solar body [17, 18, 119, 120]. It became important to
establish not only modern helium content, but also the initial
helium abundance in the Sun [17,21,121]. Gough had already
suggested that helioseismology could be used to help establish fractional abundances: “Thus one might anticipate inferring the hydrogen-helium abundance ratio by comparing the
measured values with a sequence of model solar envelopes”
[19, p. 21]. Helioseismological results became strongly incorporated into solar modeling [20–23] and “helioseismic techniques . . . [became] . . . the most accurate way to determine
the solar helium abundance” [20, p. 235]. The techniques remained linked to the equations of state which contained six
unknowns including: elemental composition, density, temperature, and pressure [20, p. 224]. Moreover, the problems
required an explicit knowledge of opacity [20, p. 224] from
its associated tables [110–118].
Relative to solar models, the central problem remains
linked to the determination of internal solar opacity. The
questions are complex and have been addressed in detail already by the author [78]. In the end, opacity tables [110–118]
have no place in the treatment of stellar problems, precisely
because they are incapable of reproducing the thermal emission spectrum required [78]. They simply mask ignorance
of a fundamental problem in astronomy: the mechanism for
the production of a thermal spectrum. Their inability to account for the production of a single photon by graphite on
Earth [78], establishes that stellar opacity derived from isolated atoms and ions can play no role in the proper understanding of thermal emissivity in the stars. As a result, helium levels can never be established using theoretical modeling based on the gaseous equations of state and their inherent
association with stellar opacity tables [78].
4 Primordial helium abundances
The quest to understand helium levels in the stars has been
further complicated by the inferred association of this element with primordial nucleosynthesis in Big Bang cosmology [24–30]. Early on, Alpher, Bethe, and Gamow postulated
that the elements had been synthesized in a primordial fireball [122]. This nucleosynthesis was proposed to include the
entire periodic table and even unstable elements, with short
lifetimes, of greater atomic number [122]. Soon, the idea that
the composition of the stars was largely related to primordial
conditions was born, especially relative to hydrogen and helium [24, 123]. No other scheme appeared likely to explain
the tremendous He levels in stellar atmospheres, which approached 27% by weight [3,24]: “It is the purpose of this article to suggest that mild ‘cooking’ [such as found in stars]
is not enough and that most, if not all, of the material of
our everyday world, of the Sun, of the stars in our Galaxy
and probably of the whole local group of galaxies, if not the
whole Universe, has been ’cooked’ to a temperature in excess
of 1010K” [123, p. 1108]. By then, the astrophysical community had already accepted that the heavy elements, which constituted trivial amounts of matter compared to hydrogen and
helium, had largely been synthesized in the stars [14]. Only
1H, 2H, 3He, 4He, and 7Li became candidates for synthesis
through a primordial process [124, 125].
The postulate that “helium abundance is universal and
was generated in a Big Bang” [125] eventually came to wide
acceptance. The entire theory was hinged on elevated helium
abundances: “We can now say that if the Universe originated
in a singular way the He/H ratio cannot be less than about
0.14. This value is of the same order of magnitude as the
observed ratios although it is somewhat larger than most of
them. However, if it can be established empirically that the
ratio is appreciably less than this in any astronomical object
in which diffussive seperation is out of the question, we can
assert that the Universe did not have a singular origin” [123,
p. 1109]. Elevated helium levels, along with the discovery
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 41
Volume 2 PROGRESS IN PHYSICS April, 2013
of the microwave background [126] and the red-shifts of distant galaxies [127, 128] became one of the three great pillars
of Big Bang cosmology [24, 129, 130]. This explained why
gravitational settling had become critical in discounting low
helium abundances of certain B type stars [3, 30, 31]. If empirical helium levels fell into question and a mechanism existed to accept the tremendously decreased helium levels in
these special B type stars [3, 31] by preventing gravitational
settling [131], Big Bang cosmology could not survive. Stellar and solar helium abundances cannot be allowed to drop in
modern cosmology.
Today, the quest to link helium abundances and primordial nucleosynthesis has continued [26–30] using two lines
of reasoning: 1) the analysis of anisotropy in the microwave
background [132, 133] and 2) the observation of helium and
hydrogen lines from low-metallicity extragalactic HII regions
[26, 134–137].
Unfortunately, the use of anisotropy data [132,133] to analyze primordial helium abundances are highly suspect. First,
insurmountable problems exist with the WMAP data sets, as
already highlighted by the author [138]. WMAP suffers from
significant galactic foreground contamination which cannot
be properly removed [138]. In addition, the WMAP team
cannot distinguish between signal arising from a hypothetically primordial origin from those produced throughout the
universe as a result of normal stellar activity [138]. While
evident ’point sources’ are taken into account, it remains impossible to determine, on a pixel by pixel basis, whether the
signal has a primordial origin, or originates from an unidentified non-cosmological object [138]. Furthermore, WMAP
raw data has proven to be unstable from year to year in a
manner inconsistent with the hypothesized cosmological origins of these signals [138]. The data suffers from poor signal
to noise and the ILC coefficients used for generating the final
anisotropy maps do not remain constant between data releases
[138]. Most troubling, the data sets cannot be combined using a unique combination of spectral channels [138]. As a
result, since no unique anisotropy data set can be extracted
[138], the data has no scientific value in analyzing helium
abundances. Similar problems will occur when data from the
Planck satellite finally becomes available [139]. As a result,
all helium abundances derived from microwave anisotropy
data sets must be viewed with a high degree of suspicion.
On the surface, the extraction of primordial helium abundances from H II regions appears more feasible [26, 134–
137]. H II regions are rich in both hydrogen and helium but
have low heavy element abundances (∼1/40 solar) [140]. Unlike H I regions (∼60K), H II regions exist at temperatures
between 7,500 and 13,000 K [141]. In H II regions “the 4He
abundance is derived from the recombination lines of singly
and doubly ionized 4He; neutral 4He is unobserved” [140,
p. 50]. Unfortunately, experiments which utilized H II regions to assess primordial helium cannot easily ascertain that
the sample has a uniform elemental composition. Furthermore, the use of H II regions for this purpose discounts the
idea that helium has been synthesized locally. Such a suggestion should not be easily dismissed, as the temperatures
of observation [141] are well above those in equilibrium with
the hypothesized residual temperature of the Big Bang (∼3K)
[130]. Only low metallicity supports the idea that these helium concentrations are primordial. Nothing should prevent
stellar systems from creating regions of low metallicity outside of a cosmological context. In this regard, the elevated
temperatures of H II regions suggest that a process well beyond primordial considerations is now influencing elemental
abundances in these regions. As such, it is imprudent to derive primordial helium abundances from H II regions.
We do not know, and will probably never be able to ascertain, primordial helium abundances. In order to observe helium in astronomy, elevated temperatures are required. These
immediately imply that the processes observed are no longer
in thermal equilibrium with those of interest in cosmology
[130].
5 Solar winds: The key to understanding helium
Helium abundances can also be monitored in the solar wind
[143–152]. Presumably, the results are so dynamic that they
cannot be utilized to establish helium levels in the Sun itself.
However, solar winds [143–152] have presented astronomy
with a wealth of scientific information, which could be used
to profoundly alter our understanding of the Sun [131].
Already in 1971, it was recognized that solar wind helium
abundance measurements gave values which were lower than
those ascertained from theoretical experiments [143, p. 369].
The study of solar winds became linked to models of the
corona. Although the relative abundance and velocities of hydrogen to helium were advanced as profoundly dependent on
location [143], it remained evident that solar winds harbored a
great deal of reliable information. Early on, it was known that
helium to hydrogen density ratios in the solar wind could experience dramatic fluctuations [144], especially in slow winds
[147], though values appeared more stable at high solar wind
speeds [145]. Extremely low ratios of 0.01, rising to 0.08,
with an average of 0.037, were reported [144]. Clearly, such
values were in direct conflict with the elevated helium levels expected in the Sun from primordial arguments [123]. As
such, solar wind measurements became viewed as unreliable
relative to estimating helium abundances in the Sun [148].
Nonetheless, something truly fascinating was present in
solar wind data. The Sun appeared to be expelling helium
(J. C. Robitaille, personal communication [131]) with increased activity. The helium to hydrogen ratio was observed
to increase in association with the onset of geomagnetic
storms [144] and was highly responsive to the solar cycle
[146, 149, 151]. The helium abundance could rise from average values of less than 2% at the solar minimum to around
4.5% at maximum [149]. After the early 1970s, the vari42 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
ation in solar wind helium abundance became increasingly
pronounced. By 1982, helium abundances in the solar wind
came to vary from values as low as 0.001 to as elevated as
0.35 [147]. A single value as high as 0.40 was reported [147].
At least half of all elevated helium abundance events were
related to a transient interplanetary shock wave disturbance
[147], though a significant portion were not associated with
such events. Each of these extremes highlighted something
phenomenal relative to solar winds. To explain the variability, theoretical models turned to the large scale structure of
plasma. It was assumed that elevated helium abundance originated in regions of high magnetic field activity in the corona
[131]. It was found that helium abundance “enhancements often have unusually high ionization temperatures, indicative of
an origin in active solar processes. . . Collectively, these observations suggest that. . . [helium abundance] . . . enhancements in the solar wind signal the arrival of plasma ejected
from low in the corona during a disturbance such as a large
solar flare or an eruptive prominence” [147]. While solar
winds had a close link to the “composition of the source material” it could then “be modified by the processes which operate in the transition zone and in the inner corona” [148].
Primordial helium abundances within the Sun could be saved
by discounting that solar wind helium abundances had any
meaning whatsoever relative to the composition of the Sun
itself. The idea that solar activity reflected the expulsion of
helium from the Sun (J. C. Robitaille, personal communication [131]) was never advanced. While the scientific community maintained that helium abundances were not reliable,
they claimed that it was possible to ascertain the fractional
isotopic composition of the elements in the solar wind and relate them directly to the solar convective zone: “The variability of the elemental abundances in the solar wind on all time
scales and the FIP. . . [first ionization potential] . . . effect,
and its variability, will make it difficult to derive accurate
solar abundances from solar wind measurements, with the
exception of isotopic determinations” [150]. Of course, isotope analysis could never constitute a challenge to the existence of large amounts of primordial helium in the Sun [123].
Solar wind helium abundances had to be simply correlated
to the coronal magnetic field, although the correlation coefficient was not powerful (σ∼0.3) [152]. Nonetheless, helium
abundance depressions could not be explained under such a
scenario [152]. At the same time, it is currently believed that
“solar wind abundances are not a genuine, unbiased sample of solar abundances, but they are fractionated. One such
fractionation depends on the first ionization potential (FIP):
When comparing solar wind to solar abundances, elements
with low FIP (<10 eV) are enriched by a significant factor, the
FIP bias, over those with a high FIP . . . Another fractionation
process affects mainly helium, causing its abundance in the
SW to be only about half of the solar abundance. . . It is most
likely due to insufficient Coulomb drag between protons and
alpha particles in the accelerating solar wind” [154, p. 16].
Herein was an explicit admission that the cause of extremely
low helium levels in the solar wind could not be adequately
understood. Conversely, fractionation models continued to
insist that elevated helium abundances were linked to the fractionation of large atoms by collisions with protons [152,153].
Nothing could be gathered about solar helium abundances
from solar winds precisely because theoretical constructs forbade such conclusions.
6 Conclusions
Modern day reports of elemental abundances in the Sun [154–
156] maintain that the Sun has a relatively large proportion of
helium with Y values typically near 0.248 and primordial values of 0.275. These values come from theoretical modeling,
as helium remains spectroscopically silent in the photosphere
and solar winds are viewed as unreliable [155, p. 166]. Therefore, claims that helium has “very high abundance” [155,
p. 166] in the Sun are not supported by observational fact.
In the end, mankind understands much less about this central element than a cursory review of the literature might suggest. Careful consideration of solar modeling establishes that
all theoretical estimates of helium levels in the Sun cannot
be relied upon, given their dependence of solar opacity tables [78]. This also applies to theoretical results which attempt to extract helium levels from helioseismology [156].
For this reason, it is simply not possible to establish elevated
helium levels in the Sun from theory. As helium levels cannot be established spectroscopically, we are left with the solar
winds for guidance.
Currently, solar winds are viewed as too complex to yield
information relative to solar abundances. In large measure,
this is because scientists are trying to understand this data in
the context of an object whose helium abundance has been
largely set in primordial times [24, 123, 155]. The idea that
the Sun and the stars are actively working to control their helium levels has never been previously considered [131]. Nevertheless, the association of solar activity and elevated helium
levels [146, 149, 151] strongly suggests that the active Sun is
expelling helium and excluding it from its hydrogen based lattice (J. C. Robitaille, personal communication [131]). Herein
can be found the cause of extremely low helium abundance
often obtained in the slow solar wind: the Sun works to keep
its helium levels low and solar activity represent a direct manisfestation of this fact. In the quiet Sun the slow solar winds
can report fractional abundances of less than 2% and these
should be viewed as steady state helium removal from the
convective zone of the Sun. Such an idea strongly supports
the contention that the Sun and the stars are primarily comprised of hydrogen in the liquid metallic state [131, 157].
In advancing that the universe is largely composed of hydrogen and that helium is being excluded from the stars
(J. C. Robitaille, personal communication [131]), perhapsit is
appropriate to turn once again to Cecilia Payne, as the first asP.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 43
Volume 2 PROGRESS IN PHYSICS April, 2013
tronomer to highlight the tremendous abundance of hydrogen
in the universe [8]. As a child, she had been eager to become
an astronomer “in case there should be no research left when
she grew up” [1, p. 72–73]. Yet, her position changed dramatically with age: “Looking back on my years of research,
I don’t like to dwell only on my mistakes; I am inclined to
count my blessings, and two seem to me to be very especially
valuable. The first blessing is that the process of discovery
is gradual — if we were confronted with all the facts at once
we should be so bewildered that we should not know how to
interpret them. The second blessing is that we are not immortal. I say this because, after all, the human mind is not pliable
enough to adapt to the continual changes in scientific ideas
and techniques. I suspect there are still many astronomers
who are working on problems, and with equipment, that are
many years out of date. Now that I am old, I see that it is dangerous to be in too much of a hurry, to be too anxious to see
the final result oneself. Our research does not belong to us, to
our institution, or to our country. It belongs to mankind. And
so I say to you, the young generation of astronomers: more
power to you. May you continue to expand the picture of the
universe, and may you never lose the thrill it gave you when it
first broke on you in all its glory” [Cecilia Payne-Gaposchkin,
April 10, 1968 [50, p. xv]].
Dedication
This work is dedicated to my oldest son, Jacob.
Submitted on: December 25, 2012 / Accepted on: December 31, 2012
First published in online on: January 6, 2012
References
1. Haramundanis K. Cecilia Payne-Gaposchkin: An autobiography and
other recollections (2nd Edition). Cambridge University Press, Cambridge, U.K., 1996.
2. Kragh H. The solar element: A reconsideration of helium’s early history. Ann. Science, 2009, v. 66(2), 157–182.
3. Taylor R.J. The helium problem. Quart. J. Roy. Astron. Soc., 1967, v. 8,
313–333.
4. Janssen J. Indications de quelques-uns des r´esultats obt´enus `a Guntoor,
pendant l’´eclipse du mois d’aoˆut dernier. Comptes Rendus, 1868, v. 67,
838–39.
5. Lockyer J.N. Notice of an observation of the spectrum of a solar prominence. Proc. Roy. Soc. London, 1868, v. 17, 91–92.
6. Ramsey W. On a gas showing the spectrum of helium, the reputed cause
of D3, one of the lines in the coronal spectrum. Preliminary note. Proc.
Roy. Soc. London, 1895, v. 58, 347–352.
7. Hirayama T. The abundance of helium in the prominences and in the
chromosphere. Solar Physics, 1971, v. 19, 384–400.
8. Payne C.H. The relative abundances of the elements. Stellar Atmospheres. Harvard Observatory Monograph no. 1 (Harlow Shapley, Editor), Harvard University Press, Cambridge, MA, 1925 (reprinted in part
in Lang K.R. and Gingerich O. A source book in astronomy and astrophysics, 1900–1975, Harvard University Press, Cambridge, MA, 1979,
p.245–248).
9. Uns¨old A. Uber die Struktur der Fraunhofersehen Linien und die quan- ¨
titative Spektralanalyse der Sonnenatmosph¨are. Zeitschrift f¨ur Physik,
1928, v.46(11–12), 765–781.
10. Russell H.N. On the composition of the Sun’s atmosphere. Astrophys. J., 1929, v.70, 11–82.
11. Bethe H.A. and Critchfield C.L. The formation of deuterons by proton
combination. Phys. Rev., 1938, v. 54, 248–254.
12. Bethe H.A. Energy production in stars. Phys. Rev., 1939, v. 55(1), 103.
13. Bethe H.A. Energy production in stars. Phys. Rev., 1939, v. 55(1), 434–
456.
14. Burbidge E.M., Burbidge G.R., Fowler W.A. and Hoyle F. Synthesis of
the elements in the stars. Rev. Modern Phys., 1957, v. 29(4), 547–650.
15. Wallerstein G., Icko I., Parker P., Boesgaard A.M., Hale G.M., Champagne A.E., Barnes C.A., K¨appeler F., Smith V.V., Hoffman R.D.,
Timmes F.X., Sneden C., Boyd R.N., Meyer B.S. and Lambert D.L.
Synthesis of the elements in stars: forty years of progress. Rev. Modern
Phys., 1997, v. 69(4), 995–1084.
16. Bahcall J.N., Bahcall N.A. and Shaviv G. Present status of the theoretical predictions for the 37Cl solar-neutrino experiment. Phys. Rev. Lett.,
1968, v. 20(21), 1209–1212.
17. Bahcall J.N. and Pinsonneault M.H. Standard solar models, with and
without helium diffusion, and the solar neutrino problem. Rev. Mod.
Phys., 1992, v. 64(4), 885–926.
18. Bachall J.N., Pinsonneault M.H. and Wasserburg G.J. Solar models
with helium and heavy-element diffusion. Rev. Mod. Phys., 1995, 67(4),
781–808.
19. Gough D.O. Towards a solar model. Mem. Soc. Astron. Ital., 1984, v. 1–
2, 13–35.
20. Basu S. and Antia H.M. Helioseismology and solar abundances. Phys.
Rep., 2008, v. 457, 217–283.
21. Serenelli A.M. and Basu S. Determining the initial helium abundance
of the Sun. Astrophys. J., 2010, v. 719(1), 865–872.
22. Delahaye F. and Pinsonneault M.H. The solar heavy-element abundances. I. Constraints from stellar interiors. Astrophys. J., 2006, v. 649,
529–540.
23. van Saders J.L. and Pinsonneault M.H. The sensitivity of convection
zone depth to stellar abundances: An absolute stellar abundance scale
from asteroseismology. Astrophys. J., 2012, v. 746, 16 (16 pages).
24. Peebles P.J.E. Primordial helium abundance and the primordial fireball.
II. Astrophys. J., 1966, v. 146, 542–552.
25. Danzinger I.J. The cosmic abundance of helium. Ann. Rev. Astron. Astrophys., 1970, v. 8, 161–178.
26. Izotov Y.I. and Thuan T.X. The primordial abundance of 4He revisited.
Astrophys. J., 1998, v. 500, 188–216.
27. Olive K.A., Steigman G. and Walker T.P. Primordial nucleosynthesis:
Theory and observations. Phys. Rep., 2000, v. 333–334, 389–407.
28. Pagel B.E.J. Helium and Big Bang Nucleosynthesis. Phys. Rep., 2000,
v. 333–334, 433–447.
29. Steigman G. Primordial nucleosynthesis: Successes and challenges.
Int. J. Mod. Phys. E, 2006, v. 15, 1–36.
30. Peimbert M. The primordial helium abundance. Curr. Sci., 2008, v. 95,
1165–1176; arXiv: astro-ph/0811.2980.
31. Greenstein G.S., Truran J.W. and Cameron A.G.W. Helium deficiency
in old halo B type stars. Nature, 1967, v. 213, 871.
32. Lindemann F.A. LXX. Note on the theory of magnetic storms. Phil.
Mag., 1919, v. 38(228), 669–684.
33. Eggert. J. Uber den Dissoziationszustand der Fixsterngase. ¨ Physikalische Zeitschrift, 1919, v. 20, 570–574.
34. Kothari D.S. Meghnad Saha. 1893–1956. Biogr. Mems. Fell. R. Soc.,
1960, v. 5, 216–236.
35. Chatterjee S. Meghnad Saha — The scientist and the institution builder.
Ind. J. Hist. Sci., 1994, v. 29(1), 99–110; http://www.new.dli.ernet.
in/rawdataupload/upload/insa/INSA 1/20005b68 99.pdf
44 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
36. Saha M.H. LIII. Ionization in the solar chromosphere. Phil. Mag.
Series 6, 1920, v. 40, 472–488.
37. Saha M.H. On the physical theory of stellar spectra. Proc. Roy. Soc.
London A, 1921, v. 99, 135–153.
38. Nernst W. Die theoretische un experimentellen Grundlagen des neuen
W¨armesatzes. Verlag von Wilhelm Knapp, Halle, 1918, p.154.
39. Clayton D.D. Principles of stellar evolution and nucleosynthesis.
Mcgraw-Hill, New York, N.Y., 1968.
40. Kippenhahn R. and Weigert A. Stellar structure and evolution.
Springer-Verlag, Berlin, 1990.
41. Gingerich O. Obituary — Payne-Gaposchkin Cecilia. Quart. J. Roy.
Astron. Soc., 1982, v. 23, 450–451.
42. McCrea W. Obituary: Subramanyan Chandrasekhar. The Observatory,
1996, v. 116, 121–124.
43. Chandrasekhar S. Ralph Howard Fowler. Astrophys. J., 1945, v.101(1),
1–5.
44. Taylor R.J. E.A. Milne(1896-1950) and the structure of stellar atmospheres and stellar interiors. Quart. J. Roy. Astron. Soc., 1996, v. 37,
355–363.
45. Fowler R.H. and Milne E.A. The intensities of absorption lines in stellar
spectra, and the temperature and pressures in the reversing layers of
stars. Mon. Not. Roy. Astron. Soc., 1923, v. 83, 403–424.
46. Fowler R.H. and Milne E.A. The maxima of absorption lines in stellar
spectra (Second Paper). Mon. Not. Roy. Astron. Soc., 1923, v. 83, 403–
424.
47. Milne E.A. XVIII. Statistical equilibrium in relation to the photoelectric effect, and its application the determination of the absorption
coefficients. Phil. Mag. Ser. 6, 1924, v. 47, 209–241.
48. Milne E.A. Ionization in stellar atmospheres. Part 1. Generalised Saha
formulae, maximum intensities, and the determination of the coefficient
of opacity. Mon. Not. Roy. Astron. Soc., 1928, v. 89, 17–49.
49. Morgan W.W., Keenan P.C. and Kellman E. An atlas of stellar spectra.
University of Chicago Press, Chicago, Il, 1943.
50. Gingerich O. Theory and observation of normal stellar atmospheres:
Proceedings of the third Harvard-Smithsonian conference on stellar atmospheres. The M.I.T. Press, Cambridge, M.A., 1969.
51. Mitchell H.B. Henrietta Leavitt and the Cepheid variables. The Physics
Teacher, 1976, v. 14(3), 162-–167.
52. Bok P.F. Annie Jump Cannon 1863–1941. Publ. Astron. Soc. Pac.,
1941, v. 53, 168–170.
53. Merrill P. Annie Jump Cannon. Mon. Not. Roy. Astron. Soc., 1942,
v. 102(2), 74–76.
54. Gaposchkin C.P. Annie Jump Cannon. Science, 1941, v. 93(2419), 443–
444.
55. Hoffleit D. Antonia C. Maury. Sky & Telescope, 1952, v. 11(5), 106.
56. Cannon A.J. Williamina Paton Fleming. Science, 1911, v. 33(861),
987–988.
57. Cannon A.J. Williamina Paton Fleming. Astrophys. J., 1911, v. 34, 314–
317.
58. Spradley J.L. The Industrious Mrs. Fleming. Astronomy, 1990, v. 18(7),
48–51.
59. Spradley J.L. Two centennials of star catalogs compiled by women.
Astron. Quart., 1990, v. 7(3), 177–184.
60. Lankford J. and Slavings R.L. Gender and Science: Women in American Astronomy, 1859–1940. Phys. Today, 1990, v. 43(3), 58–65.
61. Merton T.R. and Barratt S. Bakerian Lecture: On the spectrum of hydrogen. Phil. Trans. Roy. Soc. London, 1922, v. 222, 369–400.
62. Lang K.R. and Gingerich O. A source book in astronomy and astrophysics, 1900–1975. Harvard University Press, Cambridge, MA, 1979,
Chap. 39, p.244.
63. McCrea W.H. The hydrogen chromosphere. Mon. Not. Roy. Astron.
Soc., 1929, v. 89, 483–497.
64. Przybilla N. and Butler K. The solar hydrogen spectrum in non-local
thermodynamic equilibrium. Astrophys. J., 2004, v. 610, L61–L24.
65. Robitaille P.-M. On the Presence of a Distinct Solar Surface: A Reply
to Herv´e Faye. Prog. Phys., 2011, v. 3, 75–78.
66. Robitaille P.-M. Magnetic Fields and Directional Spectral Emissivity in
Sunspots and Faculae: Complimentary Evidence of Metallic Behavior
on the Surface of the Sun. Prog. Phys., 2013, v. 1, 19–24.
67. Moore C.E. Henry Norris Russell. The Observatory, 1957, v. 77, 67–
68.
68. de Jager C., Migeotte M., and Neven L. The profile of the Brackett
alpha line in the solar spectrum. Ann. Astrophys., 1956, v. 19, 9–18.
69. Russell H.N. and Stewart J.Q. Pressures at the Sun’s surface. Astrophys.
J., 1924, v. 59, 197–209.
70. Rudnick P. A quantitative investigation of spectral line intensities in Oand B-type stars. Astrophys. J., 1936, v. 83, 439–475.
71. Underhill A.B. and Petrie W. The stark effect of helium in some B type
stars. J. Roy. Astron. Soc. Canada, 1944, v. 38, 385–394.
72. Underhill A.B. The relative abundance of hydrogen to helium in stars.
J. Roy. Astron. Soc. Canada, 1953, v. 47, 153–159.
73. Underhill A.B. On the strength of the helium line in O-type stars. Les
Processus Nucl´eaires dans les Astres. Communications pr´esent´ees au
cinqui`eme Colloque International d’Astrophysique tenu `a Li`ege les 10-
12 Septembre, 1953, 374–386.
74. Milne E.A. Selective radiation-pressure and the structure of a stellar
atmosphere. Mon. Not. Roy. Astron. Soc., 1927, v. 87, 697–708.
75. Milne E.A. The effect of collisions on monochromatic radiative equilibrium. Mon. Not. Roy. Astron. Soc., 1928, v. 88, 493–502.
76. Milne E.A. Bakerian Lecture: The structure and opacity of a stellar
atmosphere. Phil. Trans. Roy. Soc. London, 1929, v. 228, 421–461.
77. Milne E.A. Thermodynamics of the stars. Handbuch der Astrophysik,
1930, v.3, Part 1, 65–255 (also in Menzel D.H. Selected Papers on the
Transfer of Radiation: 6 papers by Arthur Schuster, K. Schwarzschild,
A.S. Eddington, S. Rosseland, E.A. Milne. Dover Publications, Inc.,
New York, 1966, 77–269).
78. Robitaille P.M. Stellar opacity: The Achilles’ heel of the gaseous Sun.
Progr. Phys., 2011, v. 3, 93–99.
79. Gerasimovic B.P. On the correction to Saha’s formula for small deviations from thermodynamic equilibrium. Proc. Nat. Acad. Sci. USA,
1927, v. 13(4), 180–185.
80. Noyes A.A. and Wilson H.A. The thermal ionization of gaseous elements at high temperatures: a confirmation of Saha theory. Astrophys. J., 1923, v. 57, 20–32.
81. van der Mullen J.A.M., Benoy D.A., Fey F.H.A.G. and van der Sijde
B. Saha equation for two-temperature plasmas: Theories, experimental
evidence, and interpretation. Phys. Rev. B, 1994, v. 50(5), 3925–3934.
82. Sweeney M.A. Thermodynamic inconsistency of the modified Saha
equation at high pressures. Astrophys. J., 1978, v. 220, 335–338.
83. Pottasch S.R. and Thomas R.N. Departures from the Saha equation
under varying conditions of Lyman continuous opacity. Astrophys. J.,
1959, v. 130, 941–953.
84. Krawec R. Steady-state composition of low-density nonequilibrium hydrogen plasma. NASA Technical Note D-3457, Washington, D.C., October 1966.
85. Kurochka L.N. Saha’s equation under deviation from thermodynamic
equilibrium. Bull. Astron. Inst. Czechoslovakia, 1973, v. 24(4), 210–
212.
86. Avrett E.H. Solution of non-LTE transfer problems. J. Quant. Spectrosc. Radiat. Trans., 1971, v. 11(6), 511–529.
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 45
Volume 2 PROGRESS IN PHYSICS April, 2013
87. Canal G.P., Luna H., Galv˜ao R.M.O. and Castell R. An approach to a
non-LTE Saha equation based on Druyvesteyn energy distribution function: A comparison between electron temperature obtained from OES
and the Langmuir probe analysis. J. Phys. D: Appl. Phys., 2009, v. 42,
135202 (6 pages).
88. Auer L.H. The stellar atmosphere problem. J. Quant. Spectrosc. Radiat.
Transfer, 1971, v. 11, 573–587.
89. Fridman A.A. and Kennedy L.A. Plasma physics and engineering. Taylor & Francis, New York, N.Y., 2004.
90. Mihalas D. Stellar atmospheres (2nd Edition). W.H. Freeman and Company, San Francisco, CA, 1978
91. Hubeny I. Theory and modeling of stellar atmospheres. AIP Conf.
Proc., 2010, v. 1268, 73–115.
92. Werner K. and Dreizler S. The classical stellar atmosphere problem. J.
Comp. Appl. Math., 1999, v. 109(1–2), 65-93.
93. Lecar M. Departures from local thermodynamic equilibrium in an A0
stellar atmosphere. NASA Technical Note, D 2110, 1964.
94. Przybilla N., Nieva M.-F. and Butler K. Testing common classical LTE
and NLTE model atmosphere and line-formation codes for quantitative spectroscopy of early-type stars. J. Phys. Conf. Ser., 2011, v. 328,
012015 (12 pages).
95. Nieva M.F. and Przybilla N. Hydrogen and helium line formation in
OB dwarfs and giants: A hybrid non-LTE approach. Astron. Astrophys.,
2007, v. 467, 295–309.
96. Eddington A.S. Further notes on the radiative equilibrium of the stars.
Mon. Not. Roy. Astron. Soc., 1917, v. 77, 596–612.
97. Eddington A.S. On the radiative equilibrium of the stars. Mon. Not.
Roy. Astron. Soc., 1916, v. 77, 16–35.
98. Eddington A.S. On the absorption of radiation inside a star. Mon. Not.
Roy. Astron. Soc., 1922, v. 83, 32–46.
99. Kramers H.A. XCIII. On the theory of x-ray absorption and of the continuous x-ray spectrum. Phil. Mag., 1923, 46(275), 836–871.
100. Str¨omgren B. The opacity of stellar matter and the hydrogen content of
the stars. Zeitschrift f¨ur Astrophysik, 1932, v. 4, 118–152.
101. Str¨omgren B. On the interpretation of the Hertzaprung-RussellDiagram. Zeitschrift f¨ur Astrophysik, 1933, v. 7, 222–248.
102. Wildt R. Electron affnity in astrophysics. Astrophys. J., 1939, v. 89,
295–301.
103. Cowling T.G. The stability of gaseous stars. Mon. Not. Roy. Astron.
Soc., 1935, v. 96, 42–60.
104. Schwarzschild M. On the helium content of the Sun. Astrophys. J.,
1946, v. 104, 203–207.
105. Iinuma Y. On the determination of chemical composition of stars. Publ.
Astron. Soc. Japan, 1949, v. 1(1–2), 18–23.
106. Schwarzschild M., Howard R. and H¨arm R. Inhomogeneous stellar
models. V. A solar model with convective envelope and inhomogeneous
interior. Astrophys. J., 1957, v. 125, 233–241.
107. Weymann R. Inhomogeneous stellar models. VI. An improved solar
model with the carbon cycle included. Astrophys. J., 1957, v. 126, 208–
212.
108. Osterbrock D.E. and Rogerson J.B. The helium and heavy-element
content of gaseous nebulae and the Sun. Publ. Astron. Soc. Pac., 1961,
v. 73, 129–134.
109. Bahcall J.N., Fowler W.A., Iben I. and Sears R.L. Solar neutrino flux.
Astrophys. J., 1963, v. 137, 344–346.
110. Carson T.R. Stellar opacity. Ann. Rev. Astron. Astrophys., 1976, v. 14,
95–117.
111. Rozsnyai B.F. Solar opacities. J. Quant. Spec. Rad. Trans., 2001, v. 71,
655–663.
112. The Opacity Project Team. The Opacity Project. Institute of Physics
Publishing, Bristol, UK, 1995, v.1.
113. The Opacity Project Team. The Opacity Project. Institute of Physics
Publishing, Bristol, UK, 1996, v.2.
114. Rogers F.J. and Iglesias C.A. Stellar opacity. Lawrence Livermore National Laboratory, Preprint UCLRL-JC-137066.
115. Iglesias C.A. and Rogers F.J. Opacities for the solar radiative interior.
Astrophys. J., 1991, v. 371, 408–417.
116. Iglesias C.A. and Rogers F.J. Radiative opacities for carbon- and
oxygen-rich mixtures. Astrophys. J., 1993, v. 412, 752–760.
117. Rogers F.J. and Iglesias C.A. Rosseland mean opacities for variable
compositions. Astrophys. J., 1992, v. 401, 361–366.
118. Iglesias C.A. and Rogers F.J. Updated OPAL opacities. Astrophys. J.,
1996, v. 464, 943–953.
119. Aller L.H. and Chapman S. Diffusion in the Sun. Astrophys. J., 1960,
v. 132, 461–472.
120. Noerdlinger P.D. Diffusion of helium in the Sun. Astron. Astrophys.,
1977, v. 57, 407–415.
121. Aldo M. Serenelli A.M. and Basu S. Determining the initial helium
abundance of the Sun. Astrophys. J., 2010, v. 719(1), 865–872.
122. Alpher R.A., Bethe H., and Gamow G. The origin of chemical elements. Phys. Rev., 1948, v. 73(7), 803–804.
123. Hoyle F. and Taylor R.J. The Mystery of the Cosmic Helium Abundance. Nature, 1964, v. 203(4950), 1108–1110.
124. Wagoner R.V., Fowler W.A. and Hoyle F. On the synthesis of elements
at very high temperatures. Astrophys. J., 1967, v. 148, 3–49.
125. Burbidge G. Cosmic helium. Comm. Astrophys. Space Phys., 1969,
v. 1, 101–106.
126. Penzias A. A. and Wilson R.W. A measurement of excess antenna temperature at 4080 Mc/s. Astrophys. J., 1965, v. 1, 419–421.
127. Hubble E. A relation between distance and radial velocity among extragalactic nebulae. PNAS, 1929, v. 15(3), 168–173.
128. Rabounski D. On the Exact Solution Explaining the Accelerate Expanding Universe According to General Relativity. Progr. Phys., 2012,
v. 2, L1–L6.
129. Lemaˆıtre G. Un Univers homog`ene de masse constante et de rayon
croissant rendant compte de la vitesse radiale des n´ebuleuses extragalactiques. Annales de la Societ´e Scientifique de Bruxelles, ser.A,
1927, v. 47, 49–59.
130. Dicke R.H., Peebles P.J.E., Roll P.G., and Wilkinson D.T. Cosmic
black-body radiation. Astrophys. J., 1965, v. 1, 414–419.
131. Robitaille J.C. and Robitaille P.M. Liquid metallic hydrogen III. Intercalation and lattice exclusion versus gravitational settling, and their
consequences relative to internal structure, surface activity, and solar
winds in the Sun. Progr. Phys., 2013, v. 2, in press.
132. Komatsu E., Smith K.M, Dunkley J., Bennett C.L., Gold B., Hinshaw
G., Jarosik N., Larson D., Nolta M.R., Page L., Spergel D.N., Halpern
M., Hill R.S., Kogut A., Limon M., Meyer S.S., Odegard N., Tucker
G.S., Weiland J.L., Wollack W. and Wright E.L. Seven-year wilkinson microwave anisotropy probe (WMAP*) observations: Cosmological interpretation. Astrophys. J. Suppl. Ser., 2011, v. 192, 18 (47 pp).
133. Hinshaw G., Larson D., Komatsu E., Spergel D.N., Bennett C.L.,
Dunkley J., Nolta M.R., Halpern M., Hill R.S., Odegard N., Page L.,
Smith K.M., Weiland J.L., Gold B., Jarosik N., Kogut A., Limon M.,
Meyer S.S., Tucker G.S., Wollack E. and Wright E.L. Nine-year wilkinson microwave anisotropy probe (WMAP) observations: Cosmological
parameter results. arXiv: astro-ph.CO/1212.5226.
134. Pagel B.E.J, Simonson E.A., Terlevich R.J. and Edmunds M.J. The
primordial helium abundance from observations of extragalactic H II
regions. Mon. Not. Roy. Astron. Soc., 1992, v. 255, 325–345.
135. Peimbert M., Peimbert A. and Ruiz M.T. The chemical composition of
the Small Magellanic Cloud H II region NGC 346 and the primordial
helium abundance. Astrophys. J., 2000, v. 541, 688–700.
46 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
136. Luridiana V., Peimbert A., Peimbert M. and Cervi˜no M. The effect of
collisional enhancement of Balmer lines on the determination of the
primordial helium abundance. Astrophys. J., 2003, v. 592, 846–865.
137. Izotov Y.I. and Thuan T.X. Systematic effects and a new determination
of the primordial abundance of 4He and dY/dZ from observations of
blue compact galaxies. Astrophys. J., 2004, v. 602, 200–230.
138. Robitaille P.M. WMAP: A radiological analysis. Progr. Phys., 2006,
v. 1, 3–18.
139. Planck Satellite website: http://www.rssd.esa.int/index.php?project=
planck
140. Olive K.A. and Steigman G. On the abundance of primordial helium.
Astrophys. J. Suppl. Ser., 1995, v. 97, 49–58.
141. Spitzer L. and Savedoff M.P. The temperature of interstellar matter III.
Astrophys. J., 1950, v. 111, 593–608.
142. Dicke R.H., Peebles P.J.E., Roll P.G., and Wilkinson D.T. Cosmic
black-body radiation. Astrophys. J., 1965, v. 1, 414–419.
143. Formisano V. and Moreno G. Helium and heavy ions in the solar winds.
Revista del Nuovo Cimento, 1971, v. 1(3), 365–422.
144. Robbins D.E., Hundhausen A.J. and Bame S.J. Helium in the solar
wind. J. Geophys. Res., 1970, v. 75(7), 1178–1187.
145. Ogilvie K.W. and Hirshberg J. The solar cycle variation of the solar
wind helium abundance. J. Geophys. Res., 1974, v. 79(31), 4595–4602.
146. Bame S.J., Asbridge J.R., Feldman W.C. and Gosling J.T. Evidence for
a structure-free state at high solar wind speeds. J. Geophys. Res., 1977,
v. 82(10), 1487–1492.
147. Borrini G., Gosling J.T., Bame S.J., and Feldman W.C. Helium
abundance enhancements in the solar wind. J. Geophys. Res., 1982,
v. 87(A9), 7370–7378.
148. Bochsler P. Structure of the solar wind and compositional variations.
Space Sci. Rev., 1998, v. 85, 291–302.
149. Aellig M.R., Lazarus A.J. and Steinberg J.T. The solar wind helium
abundance: Variations with wind speed and solar cycle. Geophys. Res.
Let., 2001, v. 28(14), 2767–2770.
150. Wurz P. Solar Wind Composition. In: The Dynamic Sun: Challenges
for Theory and Observations, ESA SP-600, 2005, v. 5.2, 1–9.
151. Kasper J.C., Stevens M.L., Lazarus A.J. and Ogilvie K.W. Solar wind
and helium abundance as a function of speed and heliographic latitude:
Variation through a solar cycle. Astrophys. J., 2007, v. 660, 901–910.
152. Wang Y.M. Relating the solar wind helium abundance to the coronal
magnetic field. Astrophys. J., 2008, v. 683, 499–509.
153. Geiss J. and Bochsler P. Long time variations in solar wind properties: possible causes versus observations. In: The Sun in Time (Sonett
C.P., Giampapa M.S., Matthews M.S., eds.), The University of Arizona
Press, Tucson, AZ, 1991, p.98-117.
154. von Steiger R., Vial J.C., Bochsler P., Chaussidon M., Cohen C.M.S.,
Fleck B., Heber V.S., Holweger H., Issautier K., Lazarus A.J., Ogilvie
K.W., Paquette J.A., Reisenfeld D.B, Teriaca L., Wilhelm K., Yusainee
S., Laming J.M., and Wiens R.C. Measuring solar abundances. AIP
Conf. Proc., 2001, v. 598, 13–22.
155. Grevesse N. and Sauval A.J. Standard solar composition. Space Science Reviews, 1998, v. 85, 161–174.
156. Asplund M., Grevesse N., Sauval A.J. and Scott P. The chemical composition of the Sun. Ann. Rev. Astron. Astrophys., 2009, v. 47, 481–522.
157. Robitaille P.M. Liquid Metallic Hydrogen: A Building Block for the
Liquid Sun. Progr. Phys., 2011, v. 3, 60–74.
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 47
from: https://www.researchgate.net/publication/257931269_Liquid_Metallic_Hydrogen_II_A_Critical_Assessment_of_Current_and_Primordial_Helium_Levels_in_the_Sun/fulltext/57ab150d08ae3765c3b70637/Liquid-Metallic-Hydrogen-II-A-Critical-Assessment-of-Current-and-Primordial-Helium-Levels-in-the-Sun.pdf

April, 2013 PROGRESS IN PHYSICS Volume 2
Liquid Metallic Hydrogen II. A Critical Assessment of Current and Primordial
Helium Levels in the Sun
Pierre-Marie Robitaille
Department of Radiology, The Ohio State University, 395 W. 12th Ave, Columbus, Ohio 43210, USA. E-mail: robitaille.1@osu.edu
Before a solar model becomes viable in astrophysics, one must consider how the elemental constitution of the Sun was ascertained, especially relative to its principle components: hydrogen and helium. Liquid metallic hydrogen has been proposed as a solar
structural material for models based on condensed matter (e.g. Robitaille P.-M. Liquid Metallic Hydrogen: A Building Block for the Liquid Sun. Progr. Phys., 2011,
v. 3, 60–74). There can be little doubt that hydrogen plays a dominant role in the universe and in the stars; the massive abundance of hydrogen in the Sun was established
long ago. Today, it can be demonstrated that the near isointense nature of the Sun’s
Balmer lines provides strong confirmatory evidence for a distinct solar surface. The
situation relative to helium remains less conclusive. Still, helium occupies a prominent
role in astronomy, both as an element associated with cosmology and as a byproduct
of nuclear energy generation, though its abundances within the Sun cannot be reliably
estimated using theoretical approaches. With respect to the determination of helium levels, the element remains spectroscopically silent at the level of the photosphere. While
helium can be monitored with ease in the chromosphere and the prominences of the
corona using spectroscopic methods, these measures are highly variable and responsive
to elevated solar activity and nuclear fragmentation. Direct assays of the solar winds
are currently viewed as incapable of providing definitive information regarding solar
helium abundances. As a result, insight relative to helium remains strictly based on theoretical estimates which couple helioseismological approaches to metrics derived from
solar models. Despite their “state of the art” nature, helium estimates based on solar
models and helioseismology are suspect on several fronts, including their reliance on
solar opacities. The best knowledge can only come from the solar winds which, though
highly variable, provide a wealth of data. Evaluations of primordial helium levels based
on 1) the spectroscopic study of H-II regions and 2) microwave anisotropy data, remain highly questionable. Current helium levels, both within the stars (Robitaille J. C.
and Robitaille P.-M. Liquid Metallic Hydrogen III. Intercalation and Lattice Exclusion
versus Gravitational Settling, and Their Consequences Relative to Internal Structure,
Surface Activity, and Solar Winds in the Sun. Progr. Phys., 2013, v. 2, in press) and
the universe at large, appear to be overstated. A careful consideration of available observational data suggests that helium abundances are considerably lower than currently
believed.
At the age of five Cecilia [Payne] saw a meteor, and
thereupon decided to become an Astronomer. She
remarked that she must begin quickly, in case there
should be no research left when she grew up.
Betty Grierson Leaf, 1923 [1, p. 72–73]
1 Introduction
Knowledge that helium [2,3] was first observed in the Sun by
Pierre Jules C´esar Janssen [4] and Joseph Norman Lockyer
[5], before being discovered on Earth by William Ramsay [6],
might prompt the belief that the element was abundant on the
solar surface. In fact, helium has never been identified in the
absorption spectra of the quiet Sun. Janssen and Lockyer’s
fortunate discovery was restricted to helium lines appearing
within the prominences of the corona and within the disturbed
chromosphere [4,5]. While the element was easily detectable
in these regions [7], helium has remained relatively spectroscopically silent on the Sun. Conversely, the stars and the
Sun display signs of extreme hydrogen abundance, as first observed by Cecilia Payne [8], Albrecht Uns¨old [9], and Henry
Norris Russell [10]. Few would take issue with the conclusion that the visible universe is primarily comprised of hydrogen. Helium abundances present a more arduous question.
Despite all the difficulties, several lines of reasoning sustain the tremendous attention that solar helium levels have
received in astronomy. First, helium is the end product of
the nuclear reactions currently believed to fuel many of the
stars, either in the pp process or the CNO cycle [11–15]. Second, solar helium levels are inherently linked to the gaseous
models of the Sun [16–18] and the application of theoretical
findings to the interpretation of helioseismic results [19–23].
Finally, helium is thought to be a key primordial element in
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 35
Volume 2 PROGRESS IN PHYSICS April, 2013
Big Bang cosmology [3, 24–30]. As a result, the evaluation
of helium levels in the Sun brings a unified vision of astrophysics, wherein accepted solar values lend credence to our
current concept of the formation of the universe. Still, questions remain relative to the accuracy of modern helium determinations.
A flurry of initial studies had suggested that helium abundances in the stars approached 27% by mass (see [3] for a
review). The findings provided support for those who proposed primordial formation of helium prior to the existence of
the objects which populate the main sequence [3, 24]. However, these ideas were challenged when it was discovered that
certain B-type stars, which should have been rich in helium
lines, were almost devoid of such features [3]. As a result,
in certain stars, helium was said to be gravitationally settling
towards the interior [3,31]. The desire to link helium levels in
the Sun with those anticipated from the primordial synthesis
continues to dominate modern solar theory [18]. Nonetheless, it can be demonstrated that the methods used to estimate
primordial helium levels in the universe [24] are either highly
suspect or implausible. Given these complexities, it is appropriate to compose a critical review of how helium abundances
have been historically obtained and how they are currently determined, both in the Sun and in the universe at large.
2 Assessing elemental abundances in stellar spectra
2.1 The Saha Equations
Reasoning, like Lindemann [32] and Eggert [33] before him,
that the fragmentation of an atom into an ion and an electron
was analogous to the dissociation of a molecule, Megh Nad
Saha [34, 35] formulated the ionization equations [36, 37] in
the early 1920s. In so doing, he called upon the Nernst equation [38] and suggested that the free electron could be viewed
as an ideal gas. He also relied on thermal equilibrium and
the ionization potentials of the elements. Since Saha’s equation was inherently related to parameters associated with the
ideal gas (i.e. [39, p. 29–36] and [40, p. 107–117]) he demonstrated that the level of ionization could be increased either
with elevated temperature or decreased pressure. Saha hypothesized that the pressure of the reversing layer approached
0.1–1 atm [36, p. 481] and was the first to utilize this assumption to account for the appearance of spectral lines across
stellar classes as simple functions of temperature [36, 37].
He was concerned with the marginal appearance of spectral
lines [36,37], that point at which these features first appeared
on a photographic plate. Cecilia Payne [1, 41] would soon
estimate the abundance of the elements in the universe using
the same criterion [8].
In his initial work, Saha would comment on the impossibility of solar temperatures increasing as one moves from
the photosphere to the upper chromosphere: “Lockyer’s theory. . . [that elements become more ionized as higher elevations are reached within the chromosphere] . . . would lead us
to the hypothesis that the outer chromosphere is at a substantially higher temperature than the photosphere, and the
lower chromosphere; and that the temperature of the sun increases as we pass radially outwards. This hypothesis is,
however, quite untenable and is in flagrant contradiction to
all accepted theories of physics” [36, p. 473]. Saha had not
suspected that 20th century solar theorists would maintain
such a position. Lockyer’s analysis was correct: ionization
increased with elevation in the chromosphere. This was an
important lesson relative to thermal equilibrium. In any case,
Saha did observe that hydrogen was not fully ionized in the
chromosphere, since the lines from Hα and Hβ were evident at
this level. He also recognized that hydrogen should be essentially ionized in O class stars and that the lines coincident with
the Balmer series in these stars had originated from ionized
helium. At the same time, he outlined that the same spectral lines for classes later than B2A were completely due to
hydrogen [37, p. 151].
Subrahmanyan Chandrasekhar’s (Nobel Prize, 1983 [42])
thesis advisor, Sir Ralph H. Fowler [43], had provided significant insight and criticisms into Saha’s second manuscript [37,
p. 153] and the resulting text was masterful. In 1927, Megh
Nad Saha was elected a Fellow of the Royal Society [34].
In the meantime, Fowler [43] and Edward Arthur Milne
[44] would collaborate and construct a wonderful extension
[45,46] of Saha’s seminal papers [36,37]. They improved the
treatment of ionization to consider not only principle lines
arising from atoms in their lowest energy states, but also the
subordinate lines produced by excited atoms and ions [45,46].
For his part, Saha had concentrated on the excitation and ionization of the neutral atom [36, 37]. Fowler and Milne understood that the marginal appearance of a spectral line could
be used in determining relative concentrations and provided
some indication of the minimum number of atoms necessary
for appearance [45, 46]. They emphasized the idea that: “the
intensity of a given absorption line in a stellar spectrum is
proportional to the concentration of atoms in the stellar atmosphere capable of absorbing the line” [45, p. 404]. Their
first paper also highlighted the value of the maximum of a
spectral line in assessing the temperature and pressure of the
reversing layer and outlined that this problem was not affected
by the relative abundance of the element studied [45]. Using
stellar data from the lines of Ca, Mg, Sr, and Ba they determined that the electron pressure of the reversing layer was
on the order of 10−4
atm [45]. Fowler and Milne understood
that electron pressure, Pe, of the reversing layer was not determined by a single ionization process, but by the ionization
of many elements: “In thus regarding Pe as fundamental we
are in effect assuming that, due to the presence of more easily ionised atoms, there are so many electrons present that
the partial electron pressure is practically independent of the
degree of ionization of the element under discussion” [45,
p. 409]. They expressed concern that their results led to the
assumption that absorbing species had very large absorption
36 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
coefficients [45]. Milne had already determined that the absorption coefficients should be very large [47] and would later
devote another theoretical paper to their determination [48].
In their work together, Fowler and Milne explicitly assumed
that the reversing layer could be treated as existing under
conditions of thermal equilibrium, as Saha’s treatment required [36]. The validity of such assumptions is not simple to
ascertain.
At Cambridge, Milne met Cecilia Payne [1, p. 121], a student at Newnham College [1, p. 112] and learned of her impending access to the vast collection of photographic plates
used to generate the Henry Draper Catalogue at the Harvard
Observatory [1, p. 144–153]. Prior to the advent of the modern MKK classification [49], the Henry Draper Catalogue was
the largest stellar library collection, with over 200,000 classified stars [1, p. 144–153]. Milne suggested that “if he had. . .
[Payne’s] . . . opportunity, he would go after the observations
that would test and verify the Saha theory” [1, p. 155]. Cecila
Payne soon left Cambridge and sailed to America.
2.2 Cecilia Payne: What is the universe made of?
“I remember when, as a student at Cambridge, I decided I wanted to be an astronomer and asked the
advice of Colonel Stratton, he replied, “You can’t
expect to be anything but an amateur”. I should have
been discouraged, but I wasn’t, so I asked Eddington the same question. He (as was his way) thought
it over a very long time and finally said: “I can see
no insuperable obstacle” [50, xv].
Nineteenth century scientists had little on which to base their
understanding of the composition of the universe. Their clues
could only come from the Earth itself and from the meteorites
which occasionally tumbled onto its surface. Consequently, it
was not unreasonable to expect that the universe’s composition matched the terrestrial setting. However, stellar spectra,
already stored on photographic plates throughout Europe and
especially in the vast Henry Draper Collection, were hiding
a drastically altered viewpoint. With the arrival of yet another woman at the Harvard Observatory [51–60], the stars
could not much longer conceal their story. Surrounded by
Pickering’s Harem [51–60], Cecilia Payne [1, 41] completed
her classic report on the abundance of the elements [8] and
became the first to underscore the importance of hydrogen as
the constitutive atom of universe. Her thesis had been carefully prepared and presented supportive laboratory evidence,
not only of ionization potentials, but of the validity of Saha’s
treatment [8, p. 105–115].
Stellar spectra signaled hydrogen [61] was so abundant
that several scientists, including Henry Norris Russell, could
not fully accept the conclusion. Payne had written an early
manuscript detailing the tremendous presence of hydrogen [1,
p. 19]. Her thesis advisor, Harlow Shapley, forwarded the
work to Russell who commented: “It is clearly impossible
that hydrogen should be a million times more abundant than
the metals” [1, p. 19]. That early manuscript was never published and has since been lost [1, p. 20]. Tempered by Russell and Shapley, Cecilia Payne finally produced her famous
PhD dissertation: Stellar Atmospheres: A Contribution to the
Observational Study of High Temperature in the Reversing
Layers of Stars [8]. She would comment on hydrogen in this
manner: “Although hydrogen and helium are manifestly very
abundant in stellar atmospheres, the actual values derived
from the estimates of marginal appearance are regarded as
spurious” [8, p. 186]. A little later she would add: “The outstanding discrepancies between the astrophysical and terrestrial abundances are displayed for hydrogen and helium. The
enormous abundance derived for these elements in the stellar atmospheres is almost certainly not real” [8, p. 188] and
“The lines of both atoms appear to be far more persistent,
at high and low temperatures, than those of any other element” [8, p. 189].
For her part, Payne privately maintained that hydrogen
was tremendously abundant in the stars: “When I returned to
visit Cambridge after I finished this first essay in astrophysics,
I went to see Eddington. In a burst of youthful enthusiasm, I
told him that I believed that there was far more hydrogen in
the stars than any other atom. ‘You don’t mean in the stars,
you mean on the stars’, was his comment. In this case, indeed,
I was in the right, and in later years he was to recognize it
too” [1, p. 165].
Payne’s work also highlighted the importance of helium
in the O and B class stars [8]. For the first time, hydrogen
and helium became the focus of scrutiny for their role as potential building blocks of the stars and the cosmos [8]. She
emphasized that: “there is no reason to assume a sensible departure from uniform composition for members of the normal
sequence” [8, p. 179] and “The uniformity of composition of
stellar atmospheres is an established fact” [8, p. 189]. She
also held, as Eddington and Zeipel had advanced, that given
their gaseous nature: “an effect of rotation of a star will be
to keep the constituents well mixed, so that the outer portions
of the sun or of a star are probably fairly representative of
the interior” [8, p. 185]. Still, Payne was cautious relative to
extending her results as reflecting the internal composition of
the stars: “The observations on abundances refer merely to
the stellar atmosphere, and it is not possible to arrive in this
way at conclusions as to internal composition. But marked
differences of internal composition from star to star might be
expected to affect the atmosphere to a noticeable extent, and
it is therefore somewhat unlikely that such differences do occur” [8, p. 189].
Payne would conclude her thesis with a wonderful exposition of the Henry Draper Classification system [8, p. 190–
198]. Otto Struve would come to regard the study as “the most
brilliant Ph.D. thesis ever written in astronomy” [41]. Edwin
Hubble would comment relative to Payne: “She’s the best
man at Harvard” [1, p. 184]. As Milne suggested, the first
dissertation of the Harvard College Observatory was founded
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 37
Volume 2 PROGRESS IN PHYSICS April, 2013
upon the application of the ionization equations [36,37,45,46]
to the detailed analysis of spectral lines across stellar classes.
It did not specifically address elemental abundances in the
Sun. Nonetheless, Payne’s 1925 dissertation heralded the application of quantitative spectral analysis in astronomy [8].
2.3 Albrecht Unsold, hydrogen abundance, and evi- ¨
dence for a solar surface
Albrecht Uns¨old extended Payne’s studies with a focus on
the solar spectra [9]. Following in her footsteps [8], in 1928
[9], he applied the ionization formula [36, 37] to the chromosphere and estimated the levels of sodium, aluminum, calcium, strontium, and barium. In addition, Uns¨old determined
that the electron gas pressure in the chromosphere stood at
∼ 10−6
atm [9]. He also concluded that hydrogen must be
about one million times more abundant than any other element in the Sun [9, 62]. William McCrea was soon to echo
Uns¨old, finding that hydrogen was a million times more abundant than Ca+ within the chromosphere [62, 63].
Importantly, Uns¨old also documented that the absorbance
of the hydrogen β, γ, and δ lines did not decrease across
the Balmer series (Hα =1; Hβ = 0.73; Hγ = 0.91; Hδ = 1.0) as
expected from quantum mechanical considerations (Hα =1;
Hβ = 0.19; Hγ =0.07; Hδ =0.03) [9]. This was an important
finding relative to the nature of the Sun. Recently, the behavior of hydrogen emission lines has been analyzed with
non-LTE methods [64]. It has been concluded that the “n =3
and higher levels are in detailed balance deep in the photosphere, but they develop a non-LTE underpopulation further
out. However, the levels with higher n-values stay in detailed
balance relative to each other at these atmospheric depths,
and they also collisionally couple tightly to the continuum”
[64]. Yet, in the gaseous models of the Sun, the continuum is
not composed of condensed matter [65]. It represents an area
of profoundly increased solar opacity [65]. Nevertheless, the
behavior of the Balmer series in the solar atmosphere strongly
supports the idea that the Sun is comprised of condensed matter. Only a physical entity of sufficient density, such as a
surface, can permit tight collisional coupling to the continuum, as it is impossible to couple to the opacity changes
which characterize the continuum in gaseous models [65].
These findings comprise the sixteenth and seventeenth lines
of evidence that the Sun is comprised of condensed matter.
The others are outlined by the author in recent publications
(e.g. [66]).
2.4 Henry Norris Russell: Inability to estimate Helium
from spectral lines
Soon Henry Norris Russell [67] surpassed Uns¨old in his analysis of solar spectral lines and provided a detailed compositional analysis of the Sun. Relative to the occupied energy
levels within atoms on the Sun, Russell affirmed that: “It must
further be born in mind that even at solar temperatures the
great majority of the atoms of any given kind, whether ionized
or neutral, will be in the state of lowest energy” [10, p. 21]. At
the same time, Russell realized that this rule was not observed
by hydrogen, leading him to the conclusion that the element
was extremely abundant in the Sun: “One non-metal, however, presents a real and glaring exception to the general rule.
The hydrogen lines of the Balmer series, and, as Babcock
has recently shown, of the Paschen series as well, are very
strong in the Sun, though the energy required to put an atom
into condition to absorb these series is, respectively, 10.16
and 12.04 volts - higher than for any other solar absorption
lines. The obvious explanation — that hydrogen is far more
abundant than the other elements — appears to be the only
one” [10, p. 22]. In fact, even the hydrogen Brackett lines
can be visualized in the infrared spectrum of the Sun [68].
Russell also highlighted Uns¨old’s observation [9] that the hydrogen β, γ, and δ lines did not decrease as expected. That
the hydrogen lines were extremely broad in the Sun had already been well established. Russell echoed some of his contemporaries and suggested that this might result from a Stark
effect [10, p. 50].
Finally, Russell accepted Payne’s findings relative to hydrogen and reported her numbers for the elements without
comment in his table XVI [10, p. 65]. He stated that: “The
most important previous determination of the abundance of
the elements by astrophysical means is that by Miss Payne. . . ”
[10, p. 64]. Russell found the correlation between their works
to display “a very gratifying agreement” [10, p. 65]
Like Payne, Russell had relied on the work of Fowler and
Milne [45, 46] to set the composition of the Sun. He implemented their suggestion that electron pressures, Pe, could be
gathered by considering the spectra and the ionization potential for elements like Ca, Sc, Ti, Sr and Yt. From these, he deduced a Pe of 3.1 ×10−6
atm, in close agreement with Milne
(2.5 ×10−5
atm), and Payne and Hogg (2.54 ×10−6
atm) in
class G0 stars [10, p. 54–55]. Along with John Quincy Stewart, Russell had previously considered various means of determining the pressures at the Sun’s surface and had determined
that the pressure of the reversion layer could not be more than
10−4
atm [69]. But Russell reported a factor of at least 10 in
discordance in calculating electron pressures based on either
the ionization formula or the numbers of metallic atoms and
ions [10, p. 70–71]. He would resolve the difficulty at the end
of his treatise when setting the final elemental composition
for the Sun [10, p. 72].
At the same time, while Payne had understood the importance of local thermal equilibrium (LTE) for the proper application of Saha’s equation [8, p. 92–101], she did not attempt
to make an explicit correction for the lack of equilibrium.
Conversely, Russell placed a correction factor in his work for
departure from LTE: “We have finally to take into consideration the fact that the atmosphere may not be in thermodynamic equilibrium. The comparison of solar and stellar spectra affords evidence that this is the case” [10, p. 52]. Relative
38 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
to his final abundances he commented: “The main source of
uncertainty which affects them is the magnitude of the correction for departure from thermodynamic equilibrium” [10,
p. 58] and “If the correction for departure from thermodynamic equilibrium should be wholly disregarded, the calculated abundance of hydrogen — already very great — would
be increased thirty fold” [10, p. 62]. In the 1920s, of course,
there was hesitancy concerning the tremendous levels of hydrogen observed in the solar atmosphere.
For Russell, oxygen appeared as abundant as all other
metals combined. He also argued against, although did not
fully dismiss, gravitational settling in the Sun for the heaviest
metals: “It does not appear necessary, therefore, to assume
that downward diffusion depletes the sun’s atmosphere of the
heavier elements, though the possibility of such an influence
remains” [10, p. 59]. Importantly, he noted: “The statement
that enhanced lines are found in the sun for those elements
which have lines of low excitation potential in the accessible
region has therefore few exceptions” [10, p. 35]. At the same
time, he advanced that for those elements “which fail to show
enhancement lines in the sun, the excitation potentials for the
accessible lines are high in every case for which they have
been determined” [10, p. 35]. Furthermore Russell hypothesized that: “It appears, therefore, that the principle factor
which is unfavourable to the appearance of a spectral line in
the sun is a high excitation potential” [10, p. 35]. This was
precisely the case relative to helium.
With respect to the second element, Russell wrote: “There
is but one element known to exist in the sun for which no estimate of abundance has now been made - and this is He. The
intensity of its lines in the chromosphere shows that it must be
present in considerable amount, but no quantitative estimate
seems possible” [10, p. 62]. Here was an explicit admission
that solar helium abundances could not be ascertained using
spectral data.
Helium was abundantly visible in early type stars, as Cecilia Payne had already discovered [8] and Paul Rudnick [70]
and Anne Underhill continued to confirm [71–73]. Estimates
of the number of hydrogen to helium atoms in O and B type
stars varied from values as low as 3.2 to more than 27 [73,
p. 156]. A factor of nearly 10 in relative abundances from
spectral lines in such stars was hardly reassuring. Nonetheless, Underhill still surmised that the number of helium atoms
was at the 4–5% level [73]. Yet for the Sun, data about helium
abundance remained wanting.
2.5 Local Thermal Equilibrium
Milne was perhaps the greatest authority relative to local thermal equilibrium (LTE) in astronomy [74–77] and many of
the most salient aspects of his arguments have been reviewed
[78]. Milne advocated that LTE existed in the center of a
star and that his treatment permitted “us to see in a general way why the state of local thermodynamic equilibrium
in the interior of a star breaks down as we approach the surface” [77, p. 81–83]. In 1928, Milne would express concern
relative to the appropriateness of the inferred thermal equilibrium in the reversing layer, as required by the Saha equations [36, 37], although he believed that studies based on the
validity of the ionization equations should be pursued: “The
recent work of Adams and Russell brings forward evidence
that the reversing layers of stars are not in thermodynamic
equilibrium. This suggests a degree of caution in applying the
fundamental method and formulae of Saha to stellar spectra.
Nevertheless, departure from thermodynamic equilibrium can
only be found by pushing to as great a refinement as possible
the theory which assumes thermodynamic equilibrium” [48].
Gerasimovic had already advanced corrections for small deviations from thermal equilibrium [79] and Russell applied
corrections directly in his work [10]. By 1925, the Saha equations had been generally confirmed under experimental conditions (e.g. [8, p. 111–112] and [80]), but only in the broadest sense. Over time, the ionization equations continued to be
widely studied and the problems considered were extended
to include two-temperature plasmas (e.g. [81]), high pressures (e.g. [82]), varying opacities (e.g. [83]), and non-LTE
(e.g. [84–88]). The Saha equations eventually became a useful staple in the treatment of plasma physics [89, p. 164] and
stellar atmospheres [90–92].
As Auer highlighted relative to solar models [88], under
non-LTE, a set of rate equations enters into the problem of
determining the abundance of any given electronic state. Furthermore, the radiation field is introduced directly into the
equations [88] utilized to calculate both opacities and populations. The problem therefore becomes dependent on “simultaneous knowledge of the radiation field at all frequencies
and all depths” [88, p. 576].
While ionization appeared tractable given modern computing, the solution became linked to the knowledge of stellar opacities, an area of theory whose weaknesses have already been outlined [78]. Nonetheless, non-LTE approaches
have been successful in addressing the spectra of early type
stars [93–95]. Today, such methods also account for electronic, atomic, and ionic collision processes [64]. Non-LTE
approaches have provided considerable insight into the Balmer and Paschen series associated with the hydrogen spectrum of the Sun [64].
Finally, it appears that the treatment adopted by Cecilia
Payne might not have been too far afield [8]. For many of
the cooler stars, simple LTE seems sufficient to address ionization problems [94]. Non-LTE methods become most important for the O and A class stars [93–95]. In any case,
helium cannot be assessed on the Sun using the ionization
equations due to the lack of appropriate spectral lines. As a
result, while the LTE and non-LTE settings may be fundamental to the proper treatment of spectral lines, the methods
have little bearing on the proper evaluation of helium levels
in the Sun.
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 39
Volume 2 PROGRESS IN PHYSICS April, 2013
3 Helium from solar theory
3.1 Henry Norris Russell
Since Russell was not able to extract helium abundances directly from spectral lines, he did so, without further scientific
justification, by assuming that the Sun had an mean molecular weight of ∼2 [10, p. 72–73]. Such a value had also been
suggested by Saha [36, p. 476], who had in turn adopted it
from Eddington [96, p. 596]. As for Eddington, he had previously examined the radiation equilibrium of the stars using
a mean molecular weight of 54 [97]. In 1916, this value had
been selected based on the belief that the stars were principally composed of elements such as oxygen, silicon, and iron
prior to full ionization [1, viii]. Eddington lowered the mean
molecular weight to a value of 2 in 1917 [96, p. 596], based
on the idea that the elements would be fully ionized in the
stars. In the fully ionized state, hydrogen has a mean molecular weight of 0.5, helium of ∼1.3, and iron of ∼ 2 (see [40,
p. 102–104] for a full discussion of mean molecular weights
in astrophysics). It was this value which Russell was to adopt
in his calculations.
Using a mean molecular weight corresponding to a metal
rich star, Russell concluded that helium was 13% as abundant as hydrogen by weight [10, p. 73]. He then computed
that the Sun had equal percentages of oxygen and other metals (∼24% each) and that hydrogen comprised just under half
of the constitution (∼ 45%) by weight (see table XX in [10,
p. 73]. If Russell had selected a mean atomic weight of ∼0.5,
there would be dramatic changes in the calculated helium
levels.
3.2 Early abundance calculations
In arbitrarily selecting mean molecular weights [96, 97], Eddington determined the mean central stellar temperatures and
pressures along with the acceleration due to gravity at the surface (e.g. [97, p. 22]). In turn, these parameters altered the
calculated absorption coefficient, and hence opacity, of stellar interiors [97, p. 22]. Consequently, the setting of mean
atomic weight had a profound implication on nearly every
aspect of stellar modeling, but opacity would always remain
paramount. In 1922, Eddington had derived a relationship
between opacity and temperature [98] which would become
known as Kramer’s law [99].
Soon, Str¨omgren introduced an interesting twist to Eddington’s approach [100, 101]. Rather than assuming a mean
atomic weight, Str¨omgren began his calculations by computing opacity values, and from there, estimating the fractional
composition of hydrogen within several stars [100], relying
in part on Russell’s elemental composition [10]. He concluded that the fractional abundance of hydrogen was ∼ 0.3
and maintained that the presence of helium would have little
effect on these calculations since “hydrogen and helium do
not contribute to the opacity directly” [100, p. 139]. Str¨omgren would write: “we have neglected the influence of helium.
The helium proportion is rather uncertain and the error introduced by neglecting helium altogether small [100, p. 142].
Modern stellar theory would come to rely greatly on the opacity contributions of the negative hydrogen ion (H−
) [102].
Str¨omgren’s assumptions were premature. Still, he championed the idea of initially computing opacity, and from these
values obtaining both solar parameters and elemental abundances [100, 101].
Following the publication of a key modeling paper by
Cowling [103], Martin Schwarzschild was to take the next
theoretical step [104]. First, he made use of the massluminosity relation while expressing mean molecular weight
and opacity as a function of elemental composition (X = hydrogen, Y = helium) [104]. Then, reasoning that the energy
output in the Sun from the CNO cycle [13] was directly related to elemental composition, he derived a fractional elemental composition for hydrogen, helium, and the metals
equal to 0.47, 0.41, and 0.12, respectively [104]. The results
were once again critically dependent on estimated opacities,
which Schwartzchild, like Str¨omgren before him [100, 101],
assumed to display Eddington’s [98] −3.5 power dependence
on temperature (see Eq. 9 in [104]). In fact, Schwarzschild
utilized an even greater dependence on temperature for energy production, allowing a 17th power in the exponential
(see Eq. 11 in [104]). Yugo Iinuma then advanced a broader
approach to the stellar composition problem [105]. He was
concerned with ranges of reasonable starting points, both for
hydrogen concentration and average molecular weight. His
treatment remained dependent on opacity computations,
though less rigid in its conclusions [105]. Schwarzschild et
al. [106] then introduced the effects of inhomogeneity in the
solar interior and convective envelopes along with solar age
into the abundance problem. They reached the conclusion
that the temperatures at the core of the Sun were such that
the carbon cycle should start to contribute to the problem.
Hydrogen abundances were assumed in order to arrive both
at a convection parameter and at helium values [106]. The
critical link to opacity remained [106]. Weymann, who like
Schwarzschild, was also at the Institute for Advanced Study,
built on his findings [107]. Taking account of the carbon cycle, Weymann found that the core of the Sun was not convective [107]. Powers of 4 and 20 for temperature were assumed in the energy generation laws associated with the pp
and CNO cycles [107]. The hydrogen fractional composition
of the Sun was assumed and ranged from 0.60 to 0.80 (see
Table 3 in [107]). This resulted in helium and metallic fractional compositions of 0.19–0.32 and 0.01–0.08, respectively
(see Table 3 in [107]).
In 1961, Osterbrock and Rogerson would elegantly summarize the situation relative to estimating helium abundances
in the Sun: “Though helium is observed in the upper chromosphere and in prominences, the physical conditions in these
regions are too complicated and imperfectly understood for
the abundance ratio to be determined from measurements of
40 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
these emission lines. Hence the only reliable way to find the
helium abundance in the Sun is by analysis of its internal
structure” [108]. Yet, given the progress to date, the determination of elemental compositions within the Sun had been
a complex adventure involving either assumed values of average molecular weights, hydrogen abundances, energy generation reactions, and opacity. The latter would eventually
present the greatest difficulties [78]. Osterbrock and Rogerson would utilize Weymann’s calculation, along with making
an assumption by setting the Z/X ratio at 6.4 ×10−2
[108],
to estimate interior solar fractional abundances at X = 0.67,
Y = 0.29, and Z = 0.04. They were guided in this estimation
by the belief that: “the solar, planetary nebula, and interstellar abundances are all essentially the same” [108, p. 132].
For the planetary nebula NGC 7027 they set the fractional
abundances at X = 0.64, Y = 0.32, and Z = 0.04 [108]. Solar
elemental composition became decidedly linked to estimates
from remote objects. The stage was set for conclusively linking solar elemental composition to stellar evolution and primordial nucleosynthesis.
3.3 Modern abundance calculation
Eventually, the solar neutrino problem entered theoretical
modeling [16, 109]. In his simulations, John Bahcall would
utilize fractional abundances of relatively narrow range (X =
0.715 − 0.80, Y = 0.19 − 0.258 and Z = 0.01 − 0.027), setting the central densities and temperatures near 150 g/cm3
and 15 million Kelvin, respectively [16]. The results, as before, were reliant on the use of solar opacity estimates [78].
By the beginning of the 1970s, fractional abundances for helium and the metals were settling on values near 0.28 and
0.02 [25]. Solar models became increasingly complex, relying on stellar opacity tables [110–118], energy generation
equations, neutrino flux, and solar age to arrive at internally
consistent results [17, 18]. Complexity was also introduced
by considering helium and heavy element diffusion throughout the solar body [17, 18, 119, 120]. It became important to
establish not only modern helium content, but also the initial
helium abundance in the Sun [17,21,121]. Gough had already
suggested that helioseismology could be used to help establish fractional abundances: “Thus one might anticipate inferring the hydrogen-helium abundance ratio by comparing the
measured values with a sequence of model solar envelopes”
[19, p. 21]. Helioseismological results became strongly incorporated into solar modeling [20–23] and “helioseismic techniques . . . [became] . . . the most accurate way to determine
the solar helium abundance” [20, p. 235]. The techniques remained linked to the equations of state which contained six
unknowns including: elemental composition, density, temperature, and pressure [20, p. 224]. Moreover, the problems
required an explicit knowledge of opacity [20, p. 224] from
its associated tables [110–118].
Relative to solar models, the central problem remains
linked to the determination of internal solar opacity. The
questions are complex and have been addressed in detail already by the author [78]. In the end, opacity tables [110–118]
have no place in the treatment of stellar problems, precisely
because they are incapable of reproducing the thermal emission spectrum required [78]. They simply mask ignorance
of a fundamental problem in astronomy: the mechanism for
the production of a thermal spectrum. Their inability to account for the production of a single photon by graphite on
Earth [78], establishes that stellar opacity derived from isolated atoms and ions can play no role in the proper understanding of thermal emissivity in the stars. As a result, helium levels can never be established using theoretical modeling based on the gaseous equations of state and their inherent
association with stellar opacity tables [78].
4 Primordial helium abundances
The quest to understand helium levels in the stars has been
further complicated by the inferred association of this element with primordial nucleosynthesis in Big Bang cosmology [24–30]. Early on, Alpher, Bethe, and Gamow postulated
that the elements had been synthesized in a primordial fireball [122]. This nucleosynthesis was proposed to include the
entire periodic table and even unstable elements, with short
lifetimes, of greater atomic number [122]. Soon, the idea that
the composition of the stars was largely related to primordial
conditions was born, especially relative to hydrogen and helium [24, 123]. No other scheme appeared likely to explain
the tremendous He levels in stellar atmospheres, which approached 27% by weight [3,24]: “It is the purpose of this article to suggest that mild ‘cooking’ [such as found in stars]
is not enough and that most, if not all, of the material of
our everyday world, of the Sun, of the stars in our Galaxy
and probably of the whole local group of galaxies, if not the
whole Universe, has been ’cooked’ to a temperature in excess
of 1010K” [123, p. 1108]. By then, the astrophysical community had already accepted that the heavy elements, which constituted trivial amounts of matter compared to hydrogen and
helium, had largely been synthesized in the stars [14]. Only
1H, 2H, 3He, 4He, and 7Li became candidates for synthesis
through a primordial process [124, 125].
The postulate that “helium abundance is universal and
was generated in a Big Bang” [125] eventually came to wide
acceptance. The entire theory was hinged on elevated helium
abundances: “We can now say that if the Universe originated
in a singular way the He/H ratio cannot be less than about
0.14. This value is of the same order of magnitude as the
observed ratios although it is somewhat larger than most of
them. However, if it can be established empirically that the
ratio is appreciably less than this in any astronomical object
in which diffussive seperation is out of the question, we can
assert that the Universe did not have a singular origin” [123,
p. 1109]. Elevated helium levels, along with the discovery
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 41
Volume 2 PROGRESS IN PHYSICS April, 2013
of the microwave background [126] and the red-shifts of distant galaxies [127, 128] became one of the three great pillars
of Big Bang cosmology [24, 129, 130]. This explained why
gravitational settling had become critical in discounting low
helium abundances of certain B type stars [3, 30, 31]. If empirical helium levels fell into question and a mechanism existed to accept the tremendously decreased helium levels in
these special B type stars [3, 31] by preventing gravitational
settling [131], Big Bang cosmology could not survive. Stellar and solar helium abundances cannot be allowed to drop in
modern cosmology.
Today, the quest to link helium abundances and primordial nucleosynthesis has continued [26–30] using two lines
of reasoning: 1) the analysis of anisotropy in the microwave
background [132, 133] and 2) the observation of helium and
hydrogen lines from low-metallicity extragalactic HII regions
[26, 134–137].
Unfortunately, the use of anisotropy data [132,133] to analyze primordial helium abundances are highly suspect. First,
insurmountable problems exist with the WMAP data sets, as
already highlighted by the author [138]. WMAP suffers from
significant galactic foreground contamination which cannot
be properly removed [138]. In addition, the WMAP team
cannot distinguish between signal arising from a hypothetically primordial origin from those produced throughout the
universe as a result of normal stellar activity [138]. While
evident ’point sources’ are taken into account, it remains impossible to determine, on a pixel by pixel basis, whether the
signal has a primordial origin, or originates from an unidentified non-cosmological object [138]. Furthermore, WMAP
raw data has proven to be unstable from year to year in a
manner inconsistent with the hypothesized cosmological origins of these signals [138]. The data suffers from poor signal
to noise and the ILC coefficients used for generating the final
anisotropy maps do not remain constant between data releases
[138]. Most troubling, the data sets cannot be combined using a unique combination of spectral channels [138]. As a
result, since no unique anisotropy data set can be extracted
[138], the data has no scientific value in analyzing helium
abundances. Similar problems will occur when data from the
Planck satellite finally becomes available [139]. As a result,
all helium abundances derived from microwave anisotropy
data sets must be viewed with a high degree of suspicion.
On the surface, the extraction of primordial helium abundances from H II regions appears more feasible [26, 134–
137]. H II regions are rich in both hydrogen and helium but
have low heavy element abundances (∼1/40 solar) [140]. Unlike H I regions (∼60K), H II regions exist at temperatures
between 7,500 and 13,000 K [141]. In H II regions “the 4He
abundance is derived from the recombination lines of singly
and doubly ionized 4He; neutral 4He is unobserved” [140,
p. 50]. Unfortunately, experiments which utilized H II regions to assess primordial helium cannot easily ascertain that
the sample has a uniform elemental composition. Furthermore, the use of H II regions for this purpose discounts the
idea that helium has been synthesized locally. Such a suggestion should not be easily dismissed, as the temperatures
of observation [141] are well above those in equilibrium with
the hypothesized residual temperature of the Big Bang (∼3K)
[130]. Only low metallicity supports the idea that these helium concentrations are primordial. Nothing should prevent
stellar systems from creating regions of low metallicity outside of a cosmological context. In this regard, the elevated
temperatures of H II regions suggest that a process well beyond primordial considerations is now influencing elemental
abundances in these regions. As such, it is imprudent to derive primordial helium abundances from H II regions.
We do not know, and will probably never be able to ascertain, primordial helium abundances. In order to observe helium in astronomy, elevated temperatures are required. These
immediately imply that the processes observed are no longer
in thermal equilibrium with those of interest in cosmology
[130].
5 Solar winds: The key to understanding helium
Helium abundances can also be monitored in the solar wind
[143–152]. Presumably, the results are so dynamic that they
cannot be utilized to establish helium levels in the Sun itself.
However, solar winds [143–152] have presented astronomy
with a wealth of scientific information, which could be used
to profoundly alter our understanding of the Sun [131].
Already in 1971, it was recognized that solar wind helium
abundance measurements gave values which were lower than
those ascertained from theoretical experiments [143, p. 369].
The study of solar winds became linked to models of the
corona. Although the relative abundance and velocities of hydrogen to helium were advanced as profoundly dependent on
location [143], it remained evident that solar winds harbored a
great deal of reliable information. Early on, it was known that
helium to hydrogen density ratios in the solar wind could experience dramatic fluctuations [144], especially in slow winds
[147], though values appeared more stable at high solar wind
speeds [145]. Extremely low ratios of 0.01, rising to 0.08,
with an average of 0.037, were reported [144]. Clearly, such
values were in direct conflict with the elevated helium levels expected in the Sun from primordial arguments [123]. As
such, solar wind measurements became viewed as unreliable
relative to estimating helium abundances in the Sun [148].
Nonetheless, something truly fascinating was present in
solar wind data. The Sun appeared to be expelling helium
(J. C. Robitaille, personal communication [131]) with increased activity. The helium to hydrogen ratio was observed
to increase in association with the onset of geomagnetic
storms [144] and was highly responsive to the solar cycle
[146, 149, 151]. The helium abundance could rise from average values of less than 2% at the solar minimum to around
4.5% at maximum [149]. After the early 1970s, the vari42 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
ation in solar wind helium abundance became increasingly
pronounced. By 1982, helium abundances in the solar wind
came to vary from values as low as 0.001 to as elevated as
0.35 [147]. A single value as high as 0.40 was reported [147].
At least half of all elevated helium abundance events were
related to a transient interplanetary shock wave disturbance
[147], though a significant portion were not associated with
such events. Each of these extremes highlighted something
phenomenal relative to solar winds. To explain the variability, theoretical models turned to the large scale structure of
plasma. It was assumed that elevated helium abundance originated in regions of high magnetic field activity in the corona
[131]. It was found that helium abundance “enhancements often have unusually high ionization temperatures, indicative of
an origin in active solar processes. . . Collectively, these observations suggest that. . . [helium abundance] . . . enhancements in the solar wind signal the arrival of plasma ejected
from low in the corona during a disturbance such as a large
solar flare or an eruptive prominence” [147]. While solar
winds had a close link to the “composition of the source material” it could then “be modified by the processes which operate in the transition zone and in the inner corona” [148].
Primordial helium abundances within the Sun could be saved
by discounting that solar wind helium abundances had any
meaning whatsoever relative to the composition of the Sun
itself. The idea that solar activity reflected the expulsion of
helium from the Sun (J. C. Robitaille, personal communication [131]) was never advanced. While the scientific community maintained that helium abundances were not reliable,
they claimed that it was possible to ascertain the fractional
isotopic composition of the elements in the solar wind and relate them directly to the solar convective zone: “The variability of the elemental abundances in the solar wind on all time
scales and the FIP. . . [first ionization potential] . . . effect,
and its variability, will make it difficult to derive accurate
solar abundances from solar wind measurements, with the
exception of isotopic determinations” [150]. Of course, isotope analysis could never constitute a challenge to the existence of large amounts of primordial helium in the Sun [123].
Solar wind helium abundances had to be simply correlated
to the coronal magnetic field, although the correlation coefficient was not powerful (σ∼0.3) [152]. Nonetheless, helium
abundance depressions could not be explained under such a
scenario [152]. At the same time, it is currently believed that
“solar wind abundances are not a genuine, unbiased sample of solar abundances, but they are fractionated. One such
fractionation depends on the first ionization potential (FIP):
When comparing solar wind to solar abundances, elements
with low FIP (<10 eV) are enriched by a significant factor, the
FIP bias, over those with a high FIP . . . Another fractionation
process affects mainly helium, causing its abundance in the
SW to be only about half of the solar abundance. . . It is most
likely due to insufficient Coulomb drag between protons and
alpha particles in the accelerating solar wind” [154, p. 16].
Herein was an explicit admission that the cause of extremely
low helium levels in the solar wind could not be adequately
understood. Conversely, fractionation models continued to
insist that elevated helium abundances were linked to the fractionation of large atoms by collisions with protons [152,153].
Nothing could be gathered about solar helium abundances
from solar winds precisely because theoretical constructs forbade such conclusions.
6 Conclusions
Modern day reports of elemental abundances in the Sun [154–
156] maintain that the Sun has a relatively large proportion of
helium with Y values typically near 0.248 and primordial values of 0.275. These values come from theoretical modeling,
as helium remains spectroscopically silent in the photosphere
and solar winds are viewed as unreliable [155, p. 166]. Therefore, claims that helium has “very high abundance” [155,
p. 166] in the Sun are not supported by observational fact.
In the end, mankind understands much less about this central element than a cursory review of the literature might suggest. Careful consideration of solar modeling establishes that
all theoretical estimates of helium levels in the Sun cannot
be relied upon, given their dependence of solar opacity tables [78]. This also applies to theoretical results which attempt to extract helium levels from helioseismology [156].
For this reason, it is simply not possible to establish elevated
helium levels in the Sun from theory. As helium levels cannot be established spectroscopically, we are left with the solar
winds for guidance.
Currently, solar winds are viewed as too complex to yield
information relative to solar abundances. In large measure,
this is because scientists are trying to understand this data in
the context of an object whose helium abundance has been
largely set in primordial times [24, 123, 155]. The idea that
the Sun and the stars are actively working to control their helium levels has never been previously considered [131]. Nevertheless, the association of solar activity and elevated helium
levels [146, 149, 151] strongly suggests that the active Sun is
expelling helium and excluding it from its hydrogen based lattice (J. C. Robitaille, personal communication [131]). Herein
can be found the cause of extremely low helium abundance
often obtained in the slow solar wind: the Sun works to keep
its helium levels low and solar activity represent a direct manisfestation of this fact. In the quiet Sun the slow solar winds
can report fractional abundances of less than 2% and these
should be viewed as steady state helium removal from the
convective zone of the Sun. Such an idea strongly supports
the contention that the Sun and the stars are primarily comprised of hydrogen in the liquid metallic state [131, 157].
In advancing that the universe is largely composed of hydrogen and that helium is being excluded from the stars
(J. C. Robitaille, personal communication [131]), perhapsit is
appropriate to turn once again to Cecilia Payne, as the first asP.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 43
Volume 2 PROGRESS IN PHYSICS April, 2013
tronomer to highlight the tremendous abundance of hydrogen
in the universe [8]. As a child, she had been eager to become
an astronomer “in case there should be no research left when
she grew up” [1, p. 72–73]. Yet, her position changed dramatically with age: “Looking back on my years of research,
I don’t like to dwell only on my mistakes; I am inclined to
count my blessings, and two seem to me to be very especially
valuable. The first blessing is that the process of discovery
is gradual — if we were confronted with all the facts at once
we should be so bewildered that we should not know how to
interpret them. The second blessing is that we are not immortal. I say this because, after all, the human mind is not pliable
enough to adapt to the continual changes in scientific ideas
and techniques. I suspect there are still many astronomers
who are working on problems, and with equipment, that are
many years out of date. Now that I am old, I see that it is dangerous to be in too much of a hurry, to be too anxious to see
the final result oneself. Our research does not belong to us, to
our institution, or to our country. It belongs to mankind. And
so I say to you, the young generation of astronomers: more
power to you. May you continue to expand the picture of the
universe, and may you never lose the thrill it gave you when it
first broke on you in all its glory” [Cecilia Payne-Gaposchkin,
April 10, 1968 [50, p. xv]].
Dedication
This work is dedicated to my oldest son, Jacob.
Submitted on: December 25, 2012 / Accepted on: December 31, 2012
First published in online on: January 6, 2012
References
1. Haramundanis K. Cecilia Payne-Gaposchkin: An autobiography and
other recollections (2nd Edition). Cambridge University Press, Cambridge, U.K., 1996.
2. Kragh H. The solar element: A reconsideration of helium’s early history. Ann. Science, 2009, v. 66(2), 157–182.
3. Taylor R.J. The helium problem. Quart. J. Roy. Astron. Soc., 1967, v. 8,
313–333.
4. Janssen J. Indications de quelques-uns des r´esultats obt´enus `a Guntoor,
pendant l’´eclipse du mois d’aoˆut dernier. Comptes Rendus, 1868, v. 67,
838–39.
5. Lockyer J.N. Notice of an observation of the spectrum of a solar prominence. Proc. Roy. Soc. London, 1868, v. 17, 91–92.
6. Ramsey W. On a gas showing the spectrum of helium, the reputed cause
of D3, one of the lines in the coronal spectrum. Preliminary note. Proc.
Roy. Soc. London, 1895, v. 58, 347–352.
7. Hirayama T. The abundance of helium in the prominences and in the
chromosphere. Solar Physics, 1971, v. 19, 384–400.
8. Payne C.H. The relative abundances of the elements. Stellar Atmospheres. Harvard Observatory Monograph no. 1 (Harlow Shapley, Editor), Harvard University Press, Cambridge, MA, 1925 (reprinted in part
in Lang K.R. and Gingerich O. A source book in astronomy and astrophysics, 1900–1975, Harvard University Press, Cambridge, MA, 1979,
p.245–248).
9. Uns¨old A. Uber die Struktur der Fraunhofersehen Linien und die quan- ¨
titative Spektralanalyse der Sonnenatmosph¨are. Zeitschrift f¨ur Physik,
1928, v.46(11–12), 765–781.
10. Russell H.N. On the composition of the Sun’s atmosphere. Astrophys. J., 1929, v.70, 11–82.
11. Bethe H.A. and Critchfield C.L. The formation of deuterons by proton
combination. Phys. Rev., 1938, v. 54, 248–254.
12. Bethe H.A. Energy production in stars. Phys. Rev., 1939, v. 55(1), 103.
13. Bethe H.A. Energy production in stars. Phys. Rev., 1939, v. 55(1), 434–
456.
14. Burbidge E.M., Burbidge G.R., Fowler W.A. and Hoyle F. Synthesis of
the elements in the stars. Rev. Modern Phys., 1957, v. 29(4), 547–650.
15. Wallerstein G., Icko I., Parker P., Boesgaard A.M., Hale G.M., Champagne A.E., Barnes C.A., K¨appeler F., Smith V.V., Hoffman R.D.,
Timmes F.X., Sneden C., Boyd R.N., Meyer B.S. and Lambert D.L.
Synthesis of the elements in stars: forty years of progress. Rev. Modern
Phys., 1997, v. 69(4), 995–1084.
16. Bahcall J.N., Bahcall N.A. and Shaviv G. Present status of the theoretical predictions for the 37Cl solar-neutrino experiment. Phys. Rev. Lett.,
1968, v. 20(21), 1209–1212.
17. Bahcall J.N. and Pinsonneault M.H. Standard solar models, with and
without helium diffusion, and the solar neutrino problem. Rev. Mod.
Phys., 1992, v. 64(4), 885–926.
18. Bachall J.N., Pinsonneault M.H. and Wasserburg G.J. Solar models
with helium and heavy-element diffusion. Rev. Mod. Phys., 1995, 67(4),
781–808.
19. Gough D.O. Towards a solar model. Mem. Soc. Astron. Ital., 1984, v. 1–
2, 13–35.
20. Basu S. and Antia H.M. Helioseismology and solar abundances. Phys.
Rep., 2008, v. 457, 217–283.
21. Serenelli A.M. and Basu S. Determining the initial helium abundance
of the Sun. Astrophys. J., 2010, v. 719(1), 865–872.
22. Delahaye F. and Pinsonneault M.H. The solar heavy-element abundances. I. Constraints from stellar interiors. Astrophys. J., 2006, v. 649,
529–540.
23. van Saders J.L. and Pinsonneault M.H. The sensitivity of convection
zone depth to stellar abundances: An absolute stellar abundance scale
from asteroseismology. Astrophys. J., 2012, v. 746, 16 (16 pages).
24. Peebles P.J.E. Primordial helium abundance and the primordial fireball.
II. Astrophys. J., 1966, v. 146, 542–552.
25. Danzinger I.J. The cosmic abundance of helium. Ann. Rev. Astron. Astrophys., 1970, v. 8, 161–178.
26. Izotov Y.I. and Thuan T.X. The primordial abundance of 4He revisited.
Astrophys. J., 1998, v. 500, 188–216.
27. Olive K.A., Steigman G. and Walker T.P. Primordial nucleosynthesis:
Theory and observations. Phys. Rep., 2000, v. 333–334, 389–407.
28. Pagel B.E.J. Helium and Big Bang Nucleosynthesis. Phys. Rep., 2000,
v. 333–334, 433–447.
29. Steigman G. Primordial nucleosynthesis: Successes and challenges.
Int. J. Mod. Phys. E, 2006, v. 15, 1–36.
30. Peimbert M. The primordial helium abundance. Curr. Sci., 2008, v. 95,
1165–1176; arXiv: astro-ph/0811.2980.
31. Greenstein G.S., Truran J.W. and Cameron A.G.W. Helium deficiency
in old halo B type stars. Nature, 1967, v. 213, 871.
32. Lindemann F.A. LXX. Note on the theory of magnetic storms. Phil.
Mag., 1919, v. 38(228), 669–684.
33. Eggert. J. Uber den Dissoziationszustand der Fixsterngase. ¨ Physikalische Zeitschrift, 1919, v. 20, 570–574.
34. Kothari D.S. Meghnad Saha. 1893–1956. Biogr. Mems. Fell. R. Soc.,
1960, v. 5, 216–236.
35. Chatterjee S. Meghnad Saha — The scientist and the institution builder.
Ind. J. Hist. Sci., 1994, v. 29(1), 99–110; http://www.new.dli.ernet.
in/rawdataupload/upload/insa/INSA 1/20005b68 99.pdf
44 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
36. Saha M.H. LIII. Ionization in the solar chromosphere. Phil. Mag.
Series 6, 1920, v. 40, 472–488.
37. Saha M.H. On the physical theory of stellar spectra. Proc. Roy. Soc.
London A, 1921, v. 99, 135–153.
38. Nernst W. Die theoretische un experimentellen Grundlagen des neuen
W¨armesatzes. Verlag von Wilhelm Knapp, Halle, 1918, p.154.
39. Clayton D.D. Principles of stellar evolution and nucleosynthesis.
Mcgraw-Hill, New York, N.Y., 1968.
40. Kippenhahn R. and Weigert A. Stellar structure and evolution.
Springer-Verlag, Berlin, 1990.
41. Gingerich O. Obituary — Payne-Gaposchkin Cecilia. Quart. J. Roy.
Astron. Soc., 1982, v. 23, 450–451.
42. McCrea W. Obituary: Subramanyan Chandrasekhar. The Observatory,
1996, v. 116, 121–124.
43. Chandrasekhar S. Ralph Howard Fowler. Astrophys. J., 1945, v.101(1),
1–5.
44. Taylor R.J. E.A. Milne(1896-1950) and the structure of stellar atmospheres and stellar interiors. Quart. J. Roy. Astron. Soc., 1996, v. 37,
355–363.
45. Fowler R.H. and Milne E.A. The intensities of absorption lines in stellar
spectra, and the temperature and pressures in the reversing layers of
stars. Mon. Not. Roy. Astron. Soc., 1923, v. 83, 403–424.
46. Fowler R.H. and Milne E.A. The maxima of absorption lines in stellar
spectra (Second Paper). Mon. Not. Roy. Astron. Soc., 1923, v. 83, 403–
424.
47. Milne E.A. XVIII. Statistical equilibrium in relation to the photoelectric effect, and its application the determination of the absorption
coefficients. Phil. Mag. Ser. 6, 1924, v. 47, 209–241.
48. Milne E.A. Ionization in stellar atmospheres. Part 1. Generalised Saha
formulae, maximum intensities, and the determination of the coefficient
of opacity. Mon. Not. Roy. Astron. Soc., 1928, v. 89, 17–49.
49. Morgan W.W., Keenan P.C. and Kellman E. An atlas of stellar spectra.
University of Chicago Press, Chicago, Il, 1943.
50. Gingerich O. Theory and observation of normal stellar atmospheres:
Proceedings of the third Harvard-Smithsonian conference on stellar atmospheres. The M.I.T. Press, Cambridge, M.A., 1969.
51. Mitchell H.B. Henrietta Leavitt and the Cepheid variables. The Physics
Teacher, 1976, v. 14(3), 162-–167.
52. Bok P.F. Annie Jump Cannon 1863–1941. Publ. Astron. Soc. Pac.,
1941, v. 53, 168–170.
53. Merrill P. Annie Jump Cannon. Mon. Not. Roy. Astron. Soc., 1942,
v. 102(2), 74–76.
54. Gaposchkin C.P. Annie Jump Cannon. Science, 1941, v. 93(2419), 443–
444.
55. Hoffleit D. Antonia C. Maury. Sky & Telescope, 1952, v. 11(5), 106.
56. Cannon A.J. Williamina Paton Fleming. Science, 1911, v. 33(861),
987–988.
57. Cannon A.J. Williamina Paton Fleming. Astrophys. J., 1911, v. 34, 314–
317.
58. Spradley J.L. The Industrious Mrs. Fleming. Astronomy, 1990, v. 18(7),
48–51.
59. Spradley J.L. Two centennials of star catalogs compiled by women.
Astron. Quart., 1990, v. 7(3), 177–184.
60. Lankford J. and Slavings R.L. Gender and Science: Women in American Astronomy, 1859–1940. Phys. Today, 1990, v. 43(3), 58–65.
61. Merton T.R. and Barratt S. Bakerian Lecture: On the spectrum of hydrogen. Phil. Trans. Roy. Soc. London, 1922, v. 222, 369–400.
62. Lang K.R. and Gingerich O. A source book in astronomy and astrophysics, 1900–1975. Harvard University Press, Cambridge, MA, 1979,
Chap. 39, p.244.
63. McCrea W.H. The hydrogen chromosphere. Mon. Not. Roy. Astron.
Soc., 1929, v. 89, 483–497.
64. Przybilla N. and Butler K. The solar hydrogen spectrum in non-local
thermodynamic equilibrium. Astrophys. J., 2004, v. 610, L61–L24.
65. Robitaille P.-M. On the Presence of a Distinct Solar Surface: A Reply
to Herv´e Faye. Prog. Phys., 2011, v. 3, 75–78.
66. Robitaille P.-M. Magnetic Fields and Directional Spectral Emissivity in
Sunspots and Faculae: Complimentary Evidence of Metallic Behavior
on the Surface of the Sun. Prog. Phys., 2013, v. 1, 19–24.
67. Moore C.E. Henry Norris Russell. The Observatory, 1957, v. 77, 67–
68.
68. de Jager C., Migeotte M., and Neven L. The profile of the Brackett
alpha line in the solar spectrum. Ann. Astrophys., 1956, v. 19, 9–18.
69. Russell H.N. and Stewart J.Q. Pressures at the Sun’s surface. Astrophys.
J., 1924, v. 59, 197–209.
70. Rudnick P. A quantitative investigation of spectral line intensities in Oand B-type stars. Astrophys. J., 1936, v. 83, 439–475.
71. Underhill A.B. and Petrie W. The stark effect of helium in some B type
stars. J. Roy. Astron. Soc. Canada, 1944, v. 38, 385–394.
72. Underhill A.B. The relative abundance of hydrogen to helium in stars.
J. Roy. Astron. Soc. Canada, 1953, v. 47, 153–159.
73. Underhill A.B. On the strength of the helium line in O-type stars. Les
Processus Nucl´eaires dans les Astres. Communications pr´esent´ees au
cinqui`eme Colloque International d’Astrophysique tenu `a Li`ege les 10-
12 Septembre, 1953, 374–386.
74. Milne E.A. Selective radiation-pressure and the structure of a stellar
atmosphere. Mon. Not. Roy. Astron. Soc., 1927, v. 87, 697–708.
75. Milne E.A. The effect of collisions on monochromatic radiative equilibrium. Mon. Not. Roy. Astron. Soc., 1928, v. 88, 493–502.
76. Milne E.A. Bakerian Lecture: The structure and opacity of a stellar
atmosphere. Phil. Trans. Roy. Soc. London, 1929, v. 228, 421–461.
77. Milne E.A. Thermodynamics of the stars. Handbuch der Astrophysik,
1930, v.3, Part 1, 65–255 (also in Menzel D.H. Selected Papers on the
Transfer of Radiation: 6 papers by Arthur Schuster, K. Schwarzschild,
A.S. Eddington, S. Rosseland, E.A. Milne. Dover Publications, Inc.,
New York, 1966, 77–269).
78. Robitaille P.M. Stellar opacity: The Achilles’ heel of the gaseous Sun.
Progr. Phys., 2011, v. 3, 93–99.
79. Gerasimovic B.P. On the correction to Saha’s formula for small deviations from thermodynamic equilibrium. Proc. Nat. Acad. Sci. USA,
1927, v. 13(4), 180–185.
80. Noyes A.A. and Wilson H.A. The thermal ionization of gaseous elements at high temperatures: a confirmation of Saha theory. Astrophys. J., 1923, v. 57, 20–32.
81. van der Mullen J.A.M., Benoy D.A., Fey F.H.A.G. and van der Sijde
B. Saha equation for two-temperature plasmas: Theories, experimental
evidence, and interpretation. Phys. Rev. B, 1994, v. 50(5), 3925–3934.
82. Sweeney M.A. Thermodynamic inconsistency of the modified Saha
equation at high pressures. Astrophys. J., 1978, v. 220, 335–338.
83. Pottasch S.R. and Thomas R.N. Departures from the Saha equation
under varying conditions of Lyman continuous opacity. Astrophys. J.,
1959, v. 130, 941–953.
84. Krawec R. Steady-state composition of low-density nonequilibrium hydrogen plasma. NASA Technical Note D-3457, Washington, D.C., October 1966.
85. Kurochka L.N. Saha’s equation under deviation from thermodynamic
equilibrium. Bull. Astron. Inst. Czechoslovakia, 1973, v. 24(4), 210–
212.
86. Avrett E.H. Solution of non-LTE transfer problems. J. Quant. Spectrosc. Radiat. Trans., 1971, v. 11(6), 511–529.
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 45
Volume 2 PROGRESS IN PHYSICS April, 2013
87. Canal G.P., Luna H., Galv˜ao R.M.O. and Castell R. An approach to a
non-LTE Saha equation based on Druyvesteyn energy distribution function: A comparison between electron temperature obtained from OES
and the Langmuir probe analysis. J. Phys. D: Appl. Phys., 2009, v. 42,
135202 (6 pages).
88. Auer L.H. The stellar atmosphere problem. J. Quant. Spectrosc. Radiat.
Transfer, 1971, v. 11, 573–587.
89. Fridman A.A. and Kennedy L.A. Plasma physics and engineering. Taylor & Francis, New York, N.Y., 2004.
90. Mihalas D. Stellar atmospheres (2nd Edition). W.H. Freeman and Company, San Francisco, CA, 1978
91. Hubeny I. Theory and modeling of stellar atmospheres. AIP Conf.
Proc., 2010, v. 1268, 73–115.
92. Werner K. and Dreizler S. The classical stellar atmosphere problem. J.
Comp. Appl. Math., 1999, v. 109(1–2), 65-93.
93. Lecar M. Departures from local thermodynamic equilibrium in an A0
stellar atmosphere. NASA Technical Note, D 2110, 1964.
94. Przybilla N., Nieva M.-F. and Butler K. Testing common classical LTE
and NLTE model atmosphere and line-formation codes for quantitative spectroscopy of early-type stars. J. Phys. Conf. Ser., 2011, v. 328,
012015 (12 pages).
95. Nieva M.F. and Przybilla N. Hydrogen and helium line formation in
OB dwarfs and giants: A hybrid non-LTE approach. Astron. Astrophys.,
2007, v. 467, 295–309.
96. Eddington A.S. Further notes on the radiative equilibrium of the stars.
Mon. Not. Roy. Astron. Soc., 1917, v. 77, 596–612.
97. Eddington A.S. On the radiative equilibrium of the stars. Mon. Not.
Roy. Astron. Soc., 1916, v. 77, 16–35.
98. Eddington A.S. On the absorption of radiation inside a star. Mon. Not.
Roy. Astron. Soc., 1922, v. 83, 32–46.
99. Kramers H.A. XCIII. On the theory of x-ray absorption and of the continuous x-ray spectrum. Phil. Mag., 1923, 46(275), 836–871.
100. Str¨omgren B. The opacity of stellar matter and the hydrogen content of
the stars. Zeitschrift f¨ur Astrophysik, 1932, v. 4, 118–152.
101. Str¨omgren B. On the interpretation of the Hertzaprung-RussellDiagram. Zeitschrift f¨ur Astrophysik, 1933, v. 7, 222–248.
102. Wildt R. Electron affnity in astrophysics. Astrophys. J., 1939, v. 89,
295–301.
103. Cowling T.G. The stability of gaseous stars. Mon. Not. Roy. Astron.
Soc., 1935, v. 96, 42–60.
104. Schwarzschild M. On the helium content of the Sun. Astrophys. J.,
1946, v. 104, 203–207.
105. Iinuma Y. On the determination of chemical composition of stars. Publ.
Astron. Soc. Japan, 1949, v. 1(1–2), 18–23.
106. Schwarzschild M., Howard R. and H¨arm R. Inhomogeneous stellar
models. V. A solar model with convective envelope and inhomogeneous
interior. Astrophys. J., 1957, v. 125, 233–241.
107. Weymann R. Inhomogeneous stellar models. VI. An improved solar
model with the carbon cycle included. Astrophys. J., 1957, v. 126, 208–
212.
108. Osterbrock D.E. and Rogerson J.B. The helium and heavy-element
content of gaseous nebulae and the Sun. Publ. Astron. Soc. Pac., 1961,
v. 73, 129–134.
109. Bahcall J.N., Fowler W.A., Iben I. and Sears R.L. Solar neutrino flux.
Astrophys. J., 1963, v. 137, 344–346.
110. Carson T.R. Stellar opacity. Ann. Rev. Astron. Astrophys., 1976, v. 14,
95–117.
111. Rozsnyai B.F. Solar opacities. J. Quant. Spec. Rad. Trans., 2001, v. 71,
655–663.
112. The Opacity Project Team. The Opacity Project. Institute of Physics
Publishing, Bristol, UK, 1995, v.1.
113. The Opacity Project Team. The Opacity Project. Institute of Physics
Publishing, Bristol, UK, 1996, v.2.
114. Rogers F.J. and Iglesias C.A. Stellar opacity. Lawrence Livermore National Laboratory, Preprint UCLRL-JC-137066.
115. Iglesias C.A. and Rogers F.J. Opacities for the solar radiative interior.
Astrophys. J., 1991, v. 371, 408–417.
116. Iglesias C.A. and Rogers F.J. Radiative opacities for carbon- and
oxygen-rich mixtures. Astrophys. J., 1993, v. 412, 752–760.
117. Rogers F.J. and Iglesias C.A. Rosseland mean opacities for variable
compositions. Astrophys. J., 1992, v. 401, 361–366.
118. Iglesias C.A. and Rogers F.J. Updated OPAL opacities. Astrophys. J.,
1996, v. 464, 943–953.
119. Aller L.H. and Chapman S. Diffusion in the Sun. Astrophys. J., 1960,
v. 132, 461–472.
120. Noerdlinger P.D. Diffusion of helium in the Sun. Astron. Astrophys.,
1977, v. 57, 407–415.
121. Aldo M. Serenelli A.M. and Basu S. Determining the initial helium
abundance of the Sun. Astrophys. J., 2010, v. 719(1), 865–872.
122. Alpher R.A., Bethe H., and Gamow G. The origin of chemical elements. Phys. Rev., 1948, v. 73(7), 803–804.
123. Hoyle F. and Taylor R.J. The Mystery of the Cosmic Helium Abundance. Nature, 1964, v. 203(4950), 1108–1110.
124. Wagoner R.V., Fowler W.A. and Hoyle F. On the synthesis of elements
at very high temperatures. Astrophys. J., 1967, v. 148, 3–49.
125. Burbidge G. Cosmic helium. Comm. Astrophys. Space Phys., 1969,
v. 1, 101–106.
126. Penzias A. A. and Wilson R.W. A measurement of excess antenna temperature at 4080 Mc/s. Astrophys. J., 1965, v. 1, 419–421.
127. Hubble E. A relation between distance and radial velocity among extragalactic nebulae. PNAS, 1929, v. 15(3), 168–173.
128. Rabounski D. On the Exact Solution Explaining the Accelerate Expanding Universe According to General Relativity. Progr. Phys., 2012,
v. 2, L1–L6.
129. Lemaˆıtre G. Un Univers homog`ene de masse constante et de rayon
croissant rendant compte de la vitesse radiale des n´ebuleuses extragalactiques. Annales de la Societ´e Scientifique de Bruxelles, ser.A,
1927, v. 47, 49–59.
130. Dicke R.H., Peebles P.J.E., Roll P.G., and Wilkinson D.T. Cosmic
black-body radiation. Astrophys. J., 1965, v. 1, 414–419.
131. Robitaille J.C. and Robitaille P.M. Liquid metallic hydrogen III. Intercalation and lattice exclusion versus gravitational settling, and their
consequences relative to internal structure, surface activity, and solar
winds in the Sun. Progr. Phys., 2013, v. 2, in press.
132. Komatsu E., Smith K.M, Dunkley J., Bennett C.L., Gold B., Hinshaw
G., Jarosik N., Larson D., Nolta M.R., Page L., Spergel D.N., Halpern
M., Hill R.S., Kogut A., Limon M., Meyer S.S., Odegard N., Tucker
G.S., Weiland J.L., Wollack W. and Wright E.L. Seven-year wilkinson microwave anisotropy probe (WMAP*) observations: Cosmological interpretation. Astrophys. J. Suppl. Ser., 2011, v. 192, 18 (47 pp).
133. Hinshaw G., Larson D., Komatsu E., Spergel D.N., Bennett C.L.,
Dunkley J., Nolta M.R., Halpern M., Hill R.S., Odegard N., Page L.,
Smith K.M., Weiland J.L., Gold B., Jarosik N., Kogut A., Limon M.,
Meyer S.S., Tucker G.S., Wollack E. and Wright E.L. Nine-year wilkinson microwave anisotropy probe (WMAP) observations: Cosmological
parameter results. arXiv: astro-ph.CO/1212.5226.
134. Pagel B.E.J, Simonson E.A., Terlevich R.J. and Edmunds M.J. The
primordial helium abundance from observations of extragalactic H II
regions. Mon. Not. Roy. Astron. Soc., 1992, v. 255, 325–345.
135. Peimbert M., Peimbert A. and Ruiz M.T. The chemical composition of
the Small Magellanic Cloud H II region NGC 346 and the primordial
helium abundance. Astrophys. J., 2000, v. 541, 688–700.
46 P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun
April, 2013 PROGRESS IN PHYSICS Volume 2
136. Luridiana V., Peimbert A., Peimbert M. and Cervi˜no M. The effect of
collisional enhancement of Balmer lines on the determination of the
primordial helium abundance. Astrophys. J., 2003, v. 592, 846–865.
137. Izotov Y.I. and Thuan T.X. Systematic effects and a new determination
of the primordial abundance of 4He and dY/dZ from observations of
blue compact galaxies. Astrophys. J., 2004, v. 602, 200–230.
138. Robitaille P.M. WMAP: A radiological analysis. Progr. Phys., 2006,
v. 1, 3–18.
139. Planck Satellite website: http://www.rssd.esa.int/index.php?project=
planck
140. Olive K.A. and Steigman G. On the abundance of primordial helium.
Astrophys. J. Suppl. Ser., 1995, v. 97, 49–58.
141. Spitzer L. and Savedoff M.P. The temperature of interstellar matter III.
Astrophys. J., 1950, v. 111, 593–608.
142. Dicke R.H., Peebles P.J.E., Roll P.G., and Wilkinson D.T. Cosmic
black-body radiation. Astrophys. J., 1965, v. 1, 414–419.
143. Formisano V. and Moreno G. Helium and heavy ions in the solar winds.
Revista del Nuovo Cimento, 1971, v. 1(3), 365–422.
144. Robbins D.E., Hundhausen A.J. and Bame S.J. Helium in the solar
wind. J. Geophys. Res., 1970, v. 75(7), 1178–1187.
145. Ogilvie K.W. and Hirshberg J. The solar cycle variation of the solar
wind helium abundance. J. Geophys. Res., 1974, v. 79(31), 4595–4602.
146. Bame S.J., Asbridge J.R., Feldman W.C. and Gosling J.T. Evidence for
a structure-free state at high solar wind speeds. J. Geophys. Res., 1977,
v. 82(10), 1487–1492.
147. Borrini G., Gosling J.T., Bame S.J., and Feldman W.C. Helium
abundance enhancements in the solar wind. J. Geophys. Res., 1982,
v. 87(A9), 7370–7378.
148. Bochsler P. Structure of the solar wind and compositional variations.
Space Sci. Rev., 1998, v. 85, 291–302.
149. Aellig M.R., Lazarus A.J. and Steinberg J.T. The solar wind helium
abundance: Variations with wind speed and solar cycle. Geophys. Res.
Let., 2001, v. 28(14), 2767–2770.
150. Wurz P. Solar Wind Composition. In: The Dynamic Sun: Challenges
for Theory and Observations, ESA SP-600, 2005, v. 5.2, 1–9.
151. Kasper J.C., Stevens M.L., Lazarus A.J. and Ogilvie K.W. Solar wind
and helium abundance as a function of speed and heliographic latitude:
Variation through a solar cycle. Astrophys. J., 2007, v. 660, 901–910.
152. Wang Y.M. Relating the solar wind helium abundance to the coronal
magnetic field. Astrophys. J., 2008, v. 683, 499–509.
153. Geiss J. and Bochsler P. Long time variations in solar wind properties: possible causes versus observations. In: The Sun in Time (Sonett
C.P., Giampapa M.S., Matthews M.S., eds.), The University of Arizona
Press, Tucson, AZ, 1991, p.98-117.
154. von Steiger R., Vial J.C., Bochsler P., Chaussidon M., Cohen C.M.S.,
Fleck B., Heber V.S., Holweger H., Issautier K., Lazarus A.J., Ogilvie
K.W., Paquette J.A., Reisenfeld D.B, Teriaca L., Wilhelm K., Yusainee
S., Laming J.M., and Wiens R.C. Measuring solar abundances. AIP
Conf. Proc., 2001, v. 598, 13–22.
155. Grevesse N. and Sauval A.J. Standard solar composition. Space Science Reviews, 1998, v. 85, 161–174.
156. Asplund M., Grevesse N., Sauval A.J. and Scott P. The chemical composition of the Sun. Ann. Rev. Astron. Astrophys., 2009, v. 47, 481–522.
157. Robitaille P.M. Liquid Metallic Hydrogen: A Building Block for the
Liquid Sun. Progr. Phys., 2011, v. 3, 60–74.
P.-M. Robitaille. A Critical Assessment of Current and Primordial Helium Levels in the Sun 47

from: https://www.researchgate.net/publication/257931269_Liquid_Metallic_Hydrogen_II_A_Critical_Assessment_of_Current_and_Primordial_Helium_Levels_in_the_Sun/fulltext/57ab150d08ae3765c3b70637/Liquid-Metallic-Hydrogen-II-A-Critical-Assessment-of-Current-and-Primordial-Helium-Levels-in-the-Sun.pdf

Regards, Dan, a. k. a. smAshomAsh

#8 · February 2, 2020, 11:11 pm

So i read the the paper,,,,, a gaseous star doesnt make sense, just thinking about density,,, black box radiation neither, it just looks more complex.....

The full spectrum of light the sun gives off also would assume many different photons from different reaction.

But helium is the dead give away to me since during minimum there is less emited. Also from my personal non provable perspective ,,,,then sun looks different the past year. Not as bright and more orange i think,,,

Thanks it was a good read

#9 · February 4, 2020, 9:44 am

Less helium emitted at solar minimum?

I was not aware of that. Could you cite your source of this information?

I say it regularly- the Sun is the Rosetta Stone of cosmology. The height of arrogance is the idea that we understand the mass/ structure/ inner workings of distant stars, galaxies, massive radio sources, etc...

The Sun needs to be the focus of astronomy, until the observations match the theories!

Regards, Dan, a. k. a. smAshomAsh

#10 · February 6, 2020, 12:10 am

Look at paragraph 3.6 helium emission #14. Right above fig 15. It say with increased solar activity, helium emission can become prounced in the solar atmosphere