At the beginning of the 20th century, physicists were just beginning to understand matter.  Thompson discovered the electron in 1897 [1, 2].  Planck quantized physics in 1900 [3, 4, 5] and  Bohr presented his quantized theory of the atom in  1911 [6].   The laws of thermodynamics, which would form the basis of solar theory, were in the process of being formulated.  Even at the close of the 19th century, Planck was still advocating the irreversibility which is now at the center of the 2^nd law of thermodynamics (See The Little Heat Engine).  The 3^rd law of thermodynamics, which set absolute zero, did not yet exist.  The same can be said about the 0^th law (See The Little Heat Engine).  Little was really known about the fundamental internal differences between solids, liquids and gases.

            The fathers of thermodynamics, men like Carnot, Kirchhoff, Gibbs, Claussius, Wein and Stephan, had performed much of their work in the 18th and 19th centuries.  In order to analyze thermodynamic problems, they built their ideas on the fact that only the "thermodynamic system" as a whole was important.  The internal processes within the system were viewed as inconsequential.  Of course, these pioneers had no way of seeing the internal processes.  As such, it was perhaps logical for them to assume that these processes were unimportant.  The legacy of such men has been longstanding, and classical thermodynamics is still taught with a "systems approach" which for the most part ignores internal processes.

            It was under such influences, that Lane [7], first published his discussion of the gaseous nature of the sun.  At the time of course, Lane could have had little idea about whether or not the sun was a gas or a liquid.  However, the mass of the sun (1.9891 X10³⁰ kg) was known, as was its diameter (1,392,530 km).   

            In 1926, Sir A. S. Eddington [8, 9] would build on the ideas of Lane [7].   Eddington believed that the laws of physics and thermodynamics could be used to deduce the internal structure of the sun without any experimental verification [8, 9].  He would speak hypothetically about being able to live on an isolated planet completely surrounded by clouds.  In such a setting, he thought he would still be able to analyze the sun without any further knowledge than its mass, its size and the laws of physics [8, 9].   It was in this spirit that Eddington set out to expand on Lane's model of the sun.

            Assuming that Lane's gaseous model was correct [7], Eddington used simple deductive reasoning to set the internal temperature of the sun at 10,000,000 - 40,000,000 K [8, 9].  Today, this remains the range for the internal temperature of the sun (roughly ~15,000,000 K).  This accepted temperature is reinforced by man's knowledge of the temperatures associated with thermonuclear energy.

            In 1926, Eddington realized that a gaseous sun should collapse on itself [8, 9].  That is, the great forces of gravity present on the sun should pull all of the mass of the sun into a much smaller sphere.  Eddington pondered how it was that the gaseous sun did not collapse.  He solved the problem by invoking outward radiation pressure originating from within the sun.   He reasoned that if the inside of the sun was producing individual packets of light (or photons), that these photons could in turn produce the outward pressure he was seeking.   It was already known that light pressure (or radiation pressure) could be measured on earth.  For instance, a thin foil of platinum could be caused to rotate when exposed to light.  Therefore, light quanta clearly possessed momentum.

            It was this "external light pressure" that Eddington would invoke to keep the gaseous sun from collapsing on itself [8, 9].   Consequently, Eddington postulated that the inner portion of the sun produced photons.  He then deduced that these individual light quanta would sooner or later run into a gas ion or atom  and propel it up against the sun's forces of gravity.   He called the region of the sun were this occurs the "radiation zone".  This zone remains a central portion of solar theory to this day.  Importantly however, there is no scientific evidence for this zone.  It exists only as a result of Eddington's reasoning.

            Eddington believed that he properly understood a key aspect of solar theory with the creation of the "radiation zone".  However, he wanted to know exactly how many photons the sun could produce to support this hypothesis.  At the time, he also understood the consequences of Stephan's law of emission (see the essays on The Little Heat Engine and on Blackbody Radiation).

            Stephan's law of emission [10] states that the total amount of photons (or light) emitted from a perfectly emitting object (a blackbody) is directly proportional to the fourth power of the object's temperature (ε = σT⁴ , where ε represents total emission and Stephan’s constant, σ, is equal to 5.67051 X 10^-8 Watts/(m²K⁴)).

            In Stephan's law of emission, Eddington saw his answer.  Believing that the internal layers of the sun could be treated as individual blackbodies, Eddington could apply Stephan's law to internal solar structures.  He could construct hypothetical spheres within the sun and calculate the total amount of photons emitted from such spheres.  Given the dimensions and temperatures  involved, the total output of photons would be almost unimaginable!  Yet, Eddington believed that Stephan's law was universally applicable.  That is, he believe that all objects follow Stephan's law in the limit that they are blackbodies.

            Eddington's  application of Stephan's law would result in a tremendous output of photons from the sun.  Yet, the sun is known to have a much lower total energy output.

            At the same time, Eddington recognized from the laws of thermodynamics that an object at millions of degrees should produce its photons at X-ray frequencies.  This was preordained by Stephan's law of Emission [10],  Wein's law of Displacement [11] and Planck's blackbody radiation law [3].  However, Eddington also realized that the sun emitted very little X-rays.  Indeed, most of the solar output of energy occurs in the so called "visible region".  That is, the sun is producing its energy primarily at frequencies easily detected with the human eye.  This energy output is known to originate from an outer layer of the sun, called the "photosphere".

            In the mid 1880's, it was Langley [12, 13] who first recorded the output energy of the photosphere.  He thus pointed a detector directly at the sun, and recorded, for the first time, its emission spectrum. At the time that Langley obtained this emission spectrum of the sun he also sought to analyze it.  Langley immediately recognized that the solar spectrum had a thermal appearance (see The Little Heat Engine and Blackbody Radiation essays).  As such, Langley would seek to apply the laws of thermal radiation to the analysis of the solar spectrum.  First, he assumed that the sun was nearly a blackbody. Consequently,  and based on Kirchhoff's law of emission, he was able to set the temperature of the photosphere.   Without regard for the phases of matter, he therefore reported a temperature of nearly ~6,000 K.  As a result, even though the laws of thermal emission were developed in solids, the value of ~6,000 K remains the accepted temperature of the photosphere to this day.   

            It can be said that Langley's experiment was the beginning of a new age for astronomy [12, 13].  For the first time, the emission spectrum (plot of the intensity of light as a function of frequency) of a star had been recorded.

            When Eddington was working on his theory of the gaseous sun [8, 9], he was well aware of Langley's temperature for the photosphere (~6,000 K).   Yet, Eddington had deduced that the internal portion of the sun was at temperatures of millions of degrees.  Furthermore, these photons should be produced at X-ray frequencies.  In order to solve this dilemma, Eddington simply stated that when photons are produced in the radiation zone, they are initially produced at X-ray frequencies [8, 9].  However, when these photons are absorbed in the collisions associated with radiation pressure (see above), they slowly lose some of their energy.  In this manner, after millions of years, and many collisions, the photons emerge from the sun's photosphere shifted to the visible region.  Only a very small fraction of the total photons produced in the absorptive zone manage to escape at any time.  Thus, the radiation zone is acting as a very slowly leaking "sieve" [8, 9].

            It was in this manner that Eddington was able to solve some of the great problems in solar theory.  First, how to prevent the gaseous sun from collapsing on itself?  Second, how to set the internal temperature of the sun?  And finally, how to shift the frequency of photons produced at X-ray frequencies to the observed visible region?  The creation of the radiation zone had resulted in tremendous radiation pressure within the sun.  For Eddington, this radiative pressure exactly balanced with the gravitational forces resulting in our current gaseous model of the sun.  The gaseous sun had been prevented from collapsing and photons were now produced appropriately in the visible range [8, 9].  

              It can be argued even today that much of modern solar theory can be attributed to ideas first developed near the beginning of the 20th century by men like Lane [7], Langley [12, 13] and  Eddington [8, 9].  Little of significance has changed relative to solar theory since 1926 [8, 9].

            Today, Eddington’s radiation zone remains as a central feature of solar theory. The sun is viewed as composed of a very hot internal fraction (>10,000,000 K) surrounded by Langley’s photosphere at ~6,000 K (See Fig. 1). The density of the central core is thought to approach 90 g/cm³, while that of the lower photosphere is thought to be on the order of 10^-7 g/cm³ [14].  Neither of the numbers of course can be verified by direct experiment.

            In addition, the primary means of heat transfer within the sun, as proposed by Eddington, remains radiative in nature [8, 9].  That is, photons become the primary means of achieving internal thermal equilibrium in the sun (see essay on The Little Heat Engine).  The fact that for Eddington radiative heat transfer becomes a dominant means of achieving internal thermal equilibrium is not in accordance with our knowledge of the behavior of objects (see essay on The Little Heat Engine).  Rather, for all other objects internal thermal equilibrium is achieved through thermal conduction and convection.  In contrast, radiative heat transfer enables an object to equilibrate with the outside world.

            Thus, Eddington saw most of the sun as gaseous and at very high temperatures (millions of degrees).  Yet, this extremely hot object, was surrounded by a very cool photosphere only a few thousand kilometers thick and at a temperature of just ~6,000 K.  It is interesting that in Eddington's model, the inside of the sun is unable to heat the photosphere.  If the sun was a tennis ball, the entire ball would be sitting at millions of degrees.  Furthermore, it would be surrounded by a layer, thinner than skin, at  ~6,000 K.  How can the photosphere be so cold relative to the inside of the sun?  It is hard to conceive that such an object can really exist.

            The next big step in solar theory came in the 1950's.  At that time, scientists were beginning to obtain interesting data from the solar corona (the outer gaseous layer of the sun that is seen during eclipses).  The corona extends from the chromosphere (the layer just above the photosphere) to millions of kilometers away from the sun.      

            Soon, it was observed that the corona possessed within it highly ionized ions which can only be produced at temperatures well in excess of 1,000,000 K [15]. (The width of Lymanα lines further demonstrates that temperatures in the corona range from 2.6 x10⁶ K at 1.5 solar radius to 1.2 x10⁶ K at 4 solar radii [15]). 

            This finding of very hot temperatures in the corona presented a major problem for solar theory. Thus, a temperature within the corona (>1,000,000 K) which exceeded that of the photosphere (~6,000 K) indicated a violation of the 2^nd law of thermodynamics.  That is, heat could not be coming from inside the sun to heat the corona while remaining incapable of heating the photosphere. Thus, if the photosphere was really at ~6,000 K, there must be found an alternative means to heat the corona. It has now been widely accepted that the local heating in the corona occurs as a result of a process involving the flow of ions through the magnetic fields of the sun.

            Thus, our modern model of the sun must generate enough internal radiation pressure to prevent a gaseous sun from collapsing on itself. The model must also contain photons.  It must also shift the photons produced at X-ray frequencies to the visible region. Furthermore, in order to simultaneously preserve Langley’s temperature and respect the 2^nd law of thermodynamics, the model must provide two means of generating heat! The first of these must occur within the sun and is thought to be thermonuclear in origin. The second must occur in the corona and is thought to be of magnetic origin. Particles moving at enormous speeds must also be involved to ensure this second temperature. Furthermore, something very strange must be happening relative to the photosphere. Indeed, the model advances that this layer cannot be heated either by the interior of the sun or by the corona, both of which are at much higher temperatures.

             It is under this backdrop that the modern theory of the sun has developed and few if any have questioned the initial findings or assumptions. 

The Liquid Photosphere:

        The photosphere cannot be a gas. Gases simply cannot produce a Planckian shaped emission profile (See The Little Heat Engine and Photosphere Poster).  This is reserved for solids and liquids.  At the same time, the photosphere cannot be a solid as convection currents are clearly observed in this layer.  That is, there is clearly the flow of material in the photosphere.  This leaves the liquid state as a prime candidate for the photosphere.

            The sun has a total density of 1.4 g/cm³. This fact can easily support a liquid model.  By comparison, the density of water is 1 g/cm³.  In addition, a liquid structure eliminates the need for radiation pressure to prevent the sun from collapsing on itself through the forces of gravity. The liquid alone can support the upper layers.

            It is reasonable to postulate that a liquid is able to generate a Planckian emission spectrum.  It was seen in the essay on The Little Heat Engine that a liquid still possesses the vibrational degrees of freedom required for generating a Planckian emission profile.  In The Little Heat Engine it has been discussed that the temperature which is reported by a Planckian emission profile depends only on the amount of energy contained in the vibrational degrees of freedom, E_vib.  However, in a liquid, not all of the energy is contained within the vibrational degrees of freedom (E_vib).  Indeed, most of the energy (non-nuclear) may well be contained in the translational and rotational degrees of freedom (E_trans).  This leaves much less energy than expected at a given temperature in the vibrational degrees of freedom.  This fact causes a liquid to report a much lower temperature than its real temperature when Planck's, Wein's or Stephan's laws are utilized to monitor its emission spectrum.

            Since the frequency and amount of photons released by an object is related only to the amount of energy in the vibrational degrees of freedom E_vib , it is easy to see why Langley was tricked into thinking that the photosphere was sitting at a temperature of only ~6,000 K.   A liquid , instantaneously lowers the total output of photons at a given temperature and releases them at a frequency significantly lower than what would be predicted from the real temperature of the liquid.  Thus, a liquid photosphere with a temperature of ~7,000,000 degrees could be generating photons not at X-ray frequencies as expected, but rather, in the visible range.  This occurs because the photosphere is a liquid and has convection.  Since most of the energy of the photosphere is tied up in the translational (or rotational) degrees of freedom and its associated convection, it is simply not available for the generation of photons.  As such, the photosphere is "tricking us".  It is really much higher in temperature than it appears.

            Thus, the emissivity reflected in a liquid is not related directly to temperature (See The Little Heat Engine).  Since an "apparent temperature" is probably involved, Stephan’s [10],  Wein’s [11] and Planck’s [3] laws simply need to be modified.  In these equations, there is a temperature term (T),  included.  In order to apply these equations properly to a liquid, the temperature (T) term in these equations needs to be changed to an "apparent temperature",  T_app.   If this is done, everything will still work.   However, the apparent temperature will not be a real temperature.  Rather, the apparent temperature, T_app, is simply the real temperature, T, divided by a constant "alpha" (Tapp=T/alpha).  The constant alpha would be temperature dependent for most liquids.  For the photosphere alpha is ~1,000.  As such, the sun's photosphere is reporting a temperature which is nearly 1,000 times too low.  Thus, there is nearly 1,000 times more energy tide up into the translational degrees of freedom of the photosphere than in the vibrational degrees of freedom.  That is where the "trick" comes in and this is where Langley was fooled!

            The liquid phase could account for the tremendous convection currents found on the solar surface by invoking the translational and rotational degrees of freedom to deal with the heat separating the real temperature "T" and the apparent temperature "Tapp". The liquid phase is likely to provide the only means of producing a blackbody radiation curve for the sun at a lower apparent temperature than its real temperature. This remedies the problem with Langley’s temperature for the photosphere. Placing a real temperature of the photosphere at ~7,000,000 K eliminates the need to find exotic ways of heating the corona and permits the free flow of heat throughout the outer layers of the sun. As such, the 2^nd law of thermodynamics is no longer violated. Photons no longer take millions of years to leave the sun, but rather, are "instantly" released. 

            By invoking a liquid model with a shifted apparent temperature, the "radiation zone" is no longer required within the sun. This is because the massive amount of X-rays predicted by Eddington's application of Stephan’s law would never be produced. The second law of thermodynamics is no longer violated, since the photosphere is only reporting a lower apparent temperature and not a real temperature. The heating of the corona by complex magnetic field interactions is also no longer required. The primary means of internal heat transfer within the sun (like every other object known to man) once again becomes convection and conduction. A theory based on the release of superheated liquid from the convection zone could help explain much of the solar activity found on the surface of the sun (including flares and prominences).

            The liquid model for the photosphere is exceedingly simple. Moreover, the photosphere has a reasonably distinct surface. This can only occur when a liquid phase is invoked for the photosphere.

REFERENCES:

[1] http://www.aip.org/history/electron/

[2] http://www.nobel.se/physics/laureates/1906/index.html

[3]. Planck M., Ueber das Gesetz der Energieverteilung in Normalspectrum. Annalen der Physik. 1901; 4(3):553-563.

[4] http://www.thermalphysics.org/planck/planck.html

[5] http://www.nobel.se/physics/laureates/1918/index.html

[6] http://www.nobel.se/physics/laureates/1922/index.html

[7]. Lane J.H., On the Theoretical Temperature of the Sun, under the Hypothesis of a Gaseous Mass maintaining its Volume by its Internal Heat, and Depanding on the Laws of Gases as known to Terrestrial Experiments. Am. J. Sci. Arts, Series2, 4, 57.

[8]. Eddington A.S., The Internal Constitution of the Stars (Dover Edition). Dover Publications, Inc. New York, 1959.

[9]. Eddington, A.S., Stars and Atoms, Yale University Press, New Haven, 1927.

[10]. Stefan, J. Ueber die Beziehung zwischen der Warmestrahlung und der Temperatur. Wein. Akad. Sitzber. 1879; 79:391-428.

[11]. Wien W. Uber die Energieverteilung im Emissionspektrum eines schwarzen Korpers. Annalen der Physik. 1896; 58:662-669.

[12]. Langley S. P. Experimental Determination of Wave-Lengths in the Invisible Spectrum, Mem. Natl. Acad. Sci., vol. 2, pp. 147-162, 1883.

[13]. Langley S. P. On Hitherto Unrecognized Wave-lengths. Phil. Mag. 1886;22:149-173.

[14]. Gray, D.F., The Observation and Analysis of Stellar Photospheres. Cambridge University Press, 2^nd Edition, Cambridge, 1992, p.124.

[15]. Livingston W and Koutchmy S. Eclipse Science Results: Past and Present. ASP Conference Series, vol. 205, p. 3-10, 2000.

Published electronically on June 23rd, 2001

Presented in part at the American Physical Society Meeting Ohio Section May 2001

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