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Forty lines of evidence for condensed matter--the sun on trial: liquid metallic hydrogen as a solar building block.

The Sun is a world so different from our own ... However [relative to understanding its structure], one must not lose heart; over the past few years science has made a lot of progress, and those who come after us will not fail to make even more.

Father Angelo Secchi, S.J., 1875 [1, p. 300, V. I] *

1 Introduction

A long time ago, men like Gustav Kirchhoff, Johann Zollner, William Thomson (Lord Kelvin), and James Jeans viewed the photosphere (or the solar body) as existing in the liquid state [2, 3]. Despite their stature, scientists, since the days of Herbert Spencer and Angelo Secchi, slowly drifted towards the concept that the Sun was a ball of gas surrounded by condensed matter [2,3]. ([dagger])

Others, of equal or greater prominence, including August Ritter, Jonathan Lane, Franz Schuster, Karl Schwarzschild, Arthur Eddington, Subrahmanyan Chandrashekhar, and John Bahcall, would have their chance to speak [2, 3]. The Sun became a fully gaseous plasma.

As a consequence, the gaseous Sun has imbedded itself at the very foundation of astronomy. Few would dispute that the Sun is a gas and that our understanding of all other stars and the entire universe, is inherently linked to this reality. Therefore, any endeavor to touch the phase of the Sun must be viewed as an attempt to reformulate all of astronomy.

Yet, when astrophysics remained a young science, observational astronomers, such as James Keeler, Edwin Frost, and Charles Abbot [4], objected to the theoretical basis for a gaseous Sun. August Schmidt was the first to mathematically dismiss the solar surface as illusion. Speaking of him, Charles Abbot, the director of the Smithsonian Observatory would write, "Schmidt's views have obtained considerable acceptance, but not from observers of solar phenomena" [5, p. 232]. In 1913, Charles Maunder made the point even more forcefully, "But under ordinary conditions, we do not see the chromosphere itself, but look down through it on the photosphere, or general radiating surface. This, to the eye, certainly looks like a definite shell, but some theorists have been so impressed with the difficulty of conceiving that a gaseous body like the Sun could, under the conditions of such stupendous temperatures as there exist, have any defined limit at all, that they deny that what we see on the Sun is a real boundary, and argue that it only appears so to us through the effects of the anomalous refraction or dispersion of light. Such theories introduce difficulties greater and more numerous than those that they clear away, and they are not generally accepted by the practical observers of the Sun" [6, p. 28]. Alfred Fowler, the first Secretary of the International Astronomical Union, shared these views, "The photosphere is thus regarded as an optical illusion, and remarkable consequences in relation to spots and other phenomena are involved. The hypothesis appears to take no account of absorption, and, while of a certain mathematical interest, it seems to have but little application to the actual Sun" [7].

With time, however, the voices of the observational astronomers were silenced by the power and elegance of the mathematical arguments [2,3]. Those who could not follow sophisticated theory could no longer become professional astronomers. At Cambridge, the Mathematical Tripos became and remained an accepted path to a Ph.D. degree in astronomy [8]. Theory [9-14], * rather than observation, came to dictate the phase of the Sun and all solar phenomena were explained in terms of a gaseous entity.

As gases are unable to support structure, additional means were adopted to explain solar observations. Magnetic fields became the solution to every puzzle [12], even though gases are incapable of their generation. ([dagger]) Over time, theoretical approaches claimed one victory after the next, until it seemed as if the Standard Solar Models [11,13,14] were unshakable. Gases were inappropriately endowed with all of the properties of condensed matter.

In reality, a closer examination would have revealed that many theoretical achievements were inapplicable. Some of the difficulties stemmed from improper experimental conclusions. The universality of several laws [15-20], on which the entire solar framework rested [9, p. 27-58], was the product of faulty assumptions [21-24]. These errors were introduced when theoretical physics remained in its infancy. But now, they were governed by other branches of physics (i.e. blackbody radiation and condensed matter physics [15-20,25]), not by astronomy. The most pressing problems were never properly solved by the physics community [21-24].

Solar theory was replete with oversights and invalid assumptions, but the shortcomings would be extremely difficult to detect. Problems which were 'solved 100 years ago' still lurked in the background [19,20]. Too much forward progress was desired with too little attention paid to the road traveled. Most viewed that only a few minor problems remained with gaseous equations of state [13,14]. Evidence that the Sun was not a gas was dismissed with complex schemes often requiring the suspension of objectivity.

Nonetheless, many lines of evidence had revealed that the body of the Sun must be comprised of condensed matter (see Table I). Slowly, arguments initially advanced by men like Gustav Kirchhoff [26] and James Jeans [27, 28] began to reemerge. Moreover, they were joined by an arsenal of new observations. Today, at least forty proofs can be found disputing the gaseous nature of the Sun. There are surely more to be discovered. ([double dagger]) Conversely, not one direct proof exists that the body of the Sun must be considered a gaseous plasma.

It is clear that the lines of evidence for condensed matter which are contained herein ([section]) are worthy of a cohesive discussion. For the purpose of this presentation, they are subdivided and reorganized into seven broad categories: 1) Planckian, 2) spectroscopic, 3) structural, 4) dynamic, 5) helioseismic, 6) elemental, and 7) earthly. Each proof will be discussed relative to the liquid metallic hydrogen (LMH) model [36, 39, 47, 48] wherein condensed hydrogen, pressurized in the solar interior, assumes a graphite-like lattice on the photosphere [39,40,45,48], a more metallic nature in sunspots and faculae [40,45,52], a diffuse presence in a somewhat cool corona [57,58,60], and a solid character in the core [50]. *

Of these lines of evidence, the thermal proofs will always remain central to understanding the condensed nature of solar material. They are tied to the most important questions relative to light emission [15-20] and have the ability to directly link physical observation to the presence of a vibrational lattice, a key aspect of all matter in the condensed phase [21-24]. Hence, the discussion begins with the thermal lines of evidence, as inherently related to blackbody radiation [15-25,63] and to the earliest scientific history of the Sun [2, 3].

2 Planckian (or Thermal) Lines of Evidence

The Sun emits a spectrum in the visible and infrared region of the electromagnetic spectrum (see Fig. 1) whose detailed analysis provides a total of eight lines of evidence relative to the presence of condensed matter. ([dagger]) For gaseous models, solar emission must be explained using the most complex of schemes, resting both on the validity of Kirchhoff's law of thermal emission [15,16] and on the 'solar opacity problem' [42].

Agassi reminds us that "Browsing through the literature, one may find an occasional use of Kirchhoff"s law in some experimental physics, but the only place where it is treated at all seriously today is in the astrophysical literature" [63]. In reality, it would not be an overstatement to argue that Kirchhoff's law [15,16] constitutes the very core of accepted solar theory. Any problems with its formulation would send shock waves not only throughout stellar astrophysics, but to every corner of modern astronomy. Hence, the discussion with respect to the thermal lines of evidence commences with a review of Kirchhoff's law [15,16] and of blackbody radiation [17-25]. This will be followed by an overview of these principles, as applied to the Sun and the resulting solar opacity problem [42].

2.1 Blackbody Radiation and Kirchhoff's Law

The author has previously stated that, "Kirchhoff's law is one of the simplest and most misunderstood in thermodynamics" [24]. * Formulated in 1860 [15,16], the law was advanced to account for the light emitted from objects in response to changes in temperature. Typically, in the mid-1800s, the objects were black, as they were covered with soot, or black paint, for best experimental results [21, 23, 24]. Thus, this field of research became known as the study of 'blackbody radiation' [21, 23, 24]. Kirchhoff attempted to synthesize an overarching law into this area of physics in order to bring a certain unification to laboratory findings. At the time, physics was in its infancy and theorists hoped to formulate laws with 'universal' consequences. Such was Kirchhoff's goal when his law of thermal emission was devised.

The heart of Kirchhoff's law states that, "If a space be entirely surrounded by bodies of the same temperature, so that no rays can penetrate through them, every pencil in the interior of the space must be so constituted, in regard to its quality and intensity, as if it had proceeded from a perfectly black body of the same temperature, and must therefore be independent of the form and nature of the bodies, being determined by the temperature alone ... In the interior therefore of an opake red-hot body of any temperature, the illumination is always the same, whatever be the constitution of the body in other respects" [16, [section] 16]. ([dagger])

Blackbody radiation was governed strictly by the temperature and the frequency of interest. The nature of the walls was irrelevant. Kirchhoff introduced the idea that blackbody radiation somehow possessed a 'universal' significance and was a property of all cavities [15,16].

Eventually, Max Planck [19,20] provided a mathematical form for the spectral shape of blackbody emission sought by Kirchhoff [15,16]. Kirchhoff's law became ingrained in Planck's formulation [20, [section]24-[section]62]. By extension, it also became an integral part of the laws of Wien [17] and Stefan [18], as these could be simply derived from Planck's equation [20, [section]31-[section]60]. In turn, the laws of radiation, came to form the very foundation of the gaseous models (see e.g. [9, p. 27-58]).

Since blackbody radiation was thought to be of a 'universal ' nature and independent of the nature of the walls, Max Planck, was never able to link his equation to a direct physical cause [21, 23, 24]. ([double dagger]) He spoke of any such attempt as a 'hopeless undertaking' [20, [section]41]. In this respect, blackbody radiation became unique in physics. Planck's equation was not linked to anything in the material world, as Kirchhoff's law [15,16] had dictated that the process was detached from physical causality [20,21].

With his law, Gustav Kirchhoff was informing the physics community that the light emitted by an object will always correspond to the same 'universal' spectrum at a given temperature, provided that the object be enclosed and the entire system remain at thermal equilibrium. Any enclosure contained the same blackbody radiation. The nature of the enclosure was not relevant to the solution, given that it was truly opaque. Perfectly reflecting enclosures, such as those made from silver, should function as well as perfectly absorbing enclosures made from graphite or coated with carbon black.

In reality, Kirchhoff erred in believing that the nature of the enclosure did not matter [21-24]. Perfectly reflecting enclosures manifest the radiation of the objects they contain, not blackbody radiation (see [22] for a proof). To argue otherwise constitutes a violation of the First Law of Thermodynamics. Furthermore, if Kirchhoff's law was correct,

any enclosed material could serve as an experimental blackbody. But, laboratory blackbodies are known to be extremely complex devices, typically involving the use of specialized nearly perfectly absorbing' materials over the frequencies of interest. *

Max Planck believed that "... in a vacuum bounded by totally reflecting walls any state of radiation may persist" [20, [section]61]. In itself, this was contrary to what Kirchhoff had stated, as noted above, "... In the interior therefore of an opake red-hot body of any temperature, the illumination is always the same, whatever be the constitution of the body in other respects" [16, [section]16]. Throughout his text on thermal radiation [20], Max Planck repeatedly introduces a 'small carbon particle' to ensure that the radiation he was treating was truly black [21, 23]. He viewed the particle as a catalyst and believed that it simply accelerated the move towards black radiation. In reality, he had introduced a perfect absorber/emitter and thereby filled the cavity with the radiation desired (see [22] for a proof). If Kirchhoff's law was correct, this should not be necessary. The carbon particle was much more than a simple catalyst [21,23].

Another repercussion to Kirchhoff's statement was the belief that objects could radiate internally. In fact, Planck would use this approach in attempting to derive Kirchhoff's law (see [20, p. 1-45]). ([dagger]) Yet, conduction and/or convection properly govern heat transfer within objects, not internal radiation. Thermal radiation constitutes an attempt to achieve equilibrium with the outside world.

The idea that all opaque enclosures contain blackbody radiation was demonstrably false in the laboratory and Kirchhoff's law of thermal emission, invalid [21-24]. ([double dagger]) Rather, the best that could be said was that, at thermal equilibrium and in the absence of conduction or convection, the absorption of radiation by an object was equal to its emission. This was properly formulated by Balfour Stewart in 1858, one year before Kirchhoff developed his own law [22,25].

The universality which Kirchhoff sought was not present. Regrettably, Max Planck had embraced this concept and, as a direct consequence, blackbody radiation was never linked to a direct physical cause. Tragically, the astrophysical community would come to believe that blackbody radiation could be produced without the presence of condensed matter. Upon this exnihilo generation, it built the foundations of a gaseous Sun [9, p. 27-58] and the framework of the universe.

2.2 Kirchhoff's Law, Solar Opacity, and the Gaseous Models of the Sun

Given thermal equilibrium, Kirchhoff's belief that all opaque enclosures contained blackbody radiation had profound consequences for astronomy. If the Sun was considered to be an enclosure operating under thermal equilibrium, then by Kirchhoff's law, it was filled with blackbody radiation (e.g. [9, p. 27-58]). Nothing was required to produce the radiation, other than adherence to Kirchhoff's condition. Even so, use of the laws of thermal emission [15-20] explicitly required the presence of thermal equilibrium in the subject of interest (i.e. conduction and convection must not be present [21-24]).

As for the Sun, it operates far out of equilibrium by every measure, emitting a large amount of radiation, but absorbing essentially none. Furthermore, it sustains clear differential convection currents on its surface, as reported long ago by Carrington [67,68]. Consequently, how could the proponents of the gaseous models justify the use of the laws of thermal emission to treat the interior of the Sun[9,13,14]?How could an object like the Sun be considered enclosed?

Arthur Eddington viewed the Sun as filled with radiation which was essentially black. For him, the Sun acted like a slowly leaking sieve [9, p. 18]. In speaking of the application of Stefan's law [18] to the solar interior, Eddington argued, "To a very high degree of approximation the last two results are immediately applicable to the interior of a star. It is true that the radiation is not in an ideal enclosure with opaque walls at constant temperature; but the stellar conditions approach the ideal far more closely than any laboratory experiments can do" [9, p. 99-100]. He justified these statements based on the veryopaque nature of stellar material which he inferred by considering a distant star, Capella [9, p. 100].

Stefan's law codified a fourth power dependence on temperature ([T.sup.4]) [18]. At the same time, the gaseous Sun was thought to sustain a core temperature of roughly 1.6 X [10.sup.7] K [13, p. 9] while displaying an apparent surface temperature of only 6,000 K. Therefore, application of Stefan's law [18] to imaginary concentric spheres [13, p. 2] located in the interior of the Sun would result in a great deal more photons produced in the core than ever emitted by its surface. Through the application of such logic, the Sun could be viewed as a slowly leaking sieve and essentially perfectly enclosed. Eddington inferred that the opacity, or ability to absorb a photon, within the Sun was extremely elevated. Under these circumstances, light produced in the solar interior could not travel very far before being absorbed (see [9, p. 100] and [14, p. 185-232]). * Arthur Milne argued that the interior of a star could be viewed as being in local thermal equilibrium, thereby insisting that Kirchhoff's law could be applied within the Sun. Speaking of the solar interior, he stated, "If the atoms are sufficiently battered about by colliding with one another, they assume a state (distribution of stationary states) characteristic of thermodynamic equilibrium at temperature T" [69, p. 81-83]. Unfortunately, these words describe the conditions required for the onset of conduction [70]. Thermal equilibrium could never exist at the center of the Sun, as the setting prevailing at the core would facilitate a non-radiative process [21-24]. ([dagger])

Max Planck has clearly stated that thermal equilibrium can only exist in the absence of all conduction, "Now the condition of thermodynamic equilibrium requires that the temperature shall be everywhere the same and shall not vary with time ... For the heat of a body depends only on the heat radiation, since on account of the uniformity in temperature, no conduction of heat takes place." [20, [section]24]. That is why he insisted that the walls of the enclosure be rigid (e.g. [20, [section]24-25]), as no energy must be carried away through the action of the momentum transfer which accompanies collisions. Accordingly, Milne's arguments, though they rest at the heart of the gaseous solar models, are fallacious. It is inappropriate to apply Stefan's law to the interior of the Sun, as conductive forces violate the conditions for enclosure and the requirements for purely radiative heat transfer. ([double dagger])

In his treatise on heat radiation, Planck warned against applying the laws of thermal emission directly to the Sun, "Now the apparent temperature of the Sun is obviously nothing but the temperature of the solar rays, depending entirely on the nature of the rays, and hence a property of the rays and not a property of the Sun itself. Therefore it would be not only more convenient, but also more correct, to apply this notation directly, instead of speaking of a fictitious temperature of the Sun, which can be made to have meaning only by the introduction of an assumption that does not hold in reality" [20, [section]51]. Planck must have recognized that the Sun possessed convection currents on its surface [41], as Carrington's discovery [67] would have been well-established throughout scientifically educated society.

To further complicate matters, astrophysics must create sufficient opacity in the Sun. Opacity acts to contain and shift the internal radiation essential to the gaseous models. It has been said that absorption of radiation in the solar interior takes place through the summation of innumerable processes (including bound-bound, bound-free, free-free, and scattering reactions [14, p. 185-232]). Such a hypothesis constitutes the 'stellar opacity problem '. ([section]) The blackbody spectrum which could be produced in the laboratory using simple materials like graphite, soot, or metal-blacks [21-24], at once required the summation of a large set of processes which were not known to contribute to the production of the blackbody spectrum on Earth [41,42]. The central problem for gas models is not that the Sun sustains clear convection at the level of the photosphere, nor that inferred conduction exists at its core. Rather, it was that Kirchhoff's law was not valid and that Planck's equation had not been linked to the physical world [21-24]. The laws of thermal emission could not be applied to the Sun. It was not reasonable to account for the production of a blackbody spectrum using opacity calculations which depended on processes unrelated to thermal emission [42]. The production of blackbody radiation required much more than imaginary enclosures. It required the presence of nearly perfectly absorbing condensed matter, as well-demonstrated by all laboratory experiments over the course of more than 200 years (see [21-24] and references therein).

2.3 The Eight Planckian Lines of Evidence

The eight Planckian (or thermal) lines of evidence, on their own, provide sufficient proof that the Sun is comprised of condensed matter. Each of these proofs includes two components 1) a discussion of some aspect of thermal radiation, and 2) the associated structural implications. It has been well-established in experimental physics that the thermal emissivity of a material is directly linked to its structure [71]. Furthermore, condensed matter is known to possess varying directional emissivities which play a key role in understanding the structures associated with the Sun, including the degree to which one might infer that they are metallic [66, 72, 73].

2.3.1 Solar Spectrum #1

The blackbody lineshape of the solar spectrum (see Fig. 1) has been known since the days of Samuel Langley (see [74, Plate 12 and 21] and [75, Plate IV]). ([paragraph]) Still, though astrophysics has tried to explain the production of this light for nearly 150 years [2, 3], little real progress has been made in this direction. As demonstrated in Section 2.2, the gaseous models fail to properly account for the occurrence of the solar spectrum. Gases are unable to emit a continuous spectrum. Rather, they emit in bands (see [21,70] and references therein). Even when pressure broadened, these bands cannot produce the blackbody lineshape. Moreover, when gases are heated, their emissivity can actually drop [21,70], in direct contradiction of Stefan's law [18]. Under these circumstances, the answer cannot be found in the gaseous state. One must turn to condensed matter.

Throughout history, the production of a blackbody spectrum [21, 23, 24] has been facilitated by the use of graphite [76-84] or soot. For this reason, even after the formulation of Kirchhoff's law, astronomers envisioned that graphite particles floated on the surface of the Sun [2,3]. Hastings recognized that the solar surface was too hot to permit the existence of carbon in the condensed state [85]. He noted that "Granting this, we perceive that the photosphere contains solid or liquid particles hotter than carbon vapor, and consequently not carbon" [85]. As a result, in 1881, he suggested that "... the substance in question, so far as we know it, has properties similar to those of the carbon group" [85]. Hastings wanted something which had the physical characteristics of graphite, especially related to emissivity. Yet, the only aspect of graphite which could contribute to its emissive characteristics was its lattice structure. He was indirectly searching for a material which might share the lattice arrangement known to exist in graphite (see Fig. 2), but which might likewise be reasonably expected to exist on the surface of the Sun.

Eventually, Cecilia Payne determined that the stars were largely made of hydrogen [86] and Henry Norris Russell [87] extended the conclusion to the Sun. * Whatever was responsible for the thermal spectrum had to be composed of hydrogen.

Then, in 1935, a seminal work appeared which had the potential to completely alter our understanding of the stars [36,39]. Eugene Wigner (Nobel Prize, Physics, 1963) and H.B. Huntington [88], proposed that at sufficient pressures, hydrogen could become metallic. More importantly, they would make a direct link between the structure of metallic hydrogen and that of graphite itself, "The objection comes up naturally that we have calculated the energy of a body-centered metallic lattice only, and that another metallic lattice may be much more stable. We feel that the objection is justified. Of course it is not to be expected that another simple lattice, like the face-centered one, have a much lower energy, --the energy differences between forms are always very small. It is possible, however, that a layer-like lattice has a much greater heat of formation, and is obtainable under high pressure. This is suggested by the fact that in most cases of Table I of allotropic modifications, one of the lattices is layer-like (1) ..." [88]. The footnote in the text began, "Diamond is a valence lattice, but graphite is a layer lattice ..." [88].

With time, Brovman et al. [89] would propose that metallic hydrogen might be metastable. Like diamonds, it would require elevated pressures for formation, but remain stable at low pressures once synthesized. Neil Ashcroft and his group hypothesized that metallic hydrogen might be metastable between its solid and liquid forms [90,91].

Metallic hydrogen remains elusive in our laboratories (see [39, 92] for recent reviews). Nonetheless, this has not prevented astrophysics from invoking its existence within brown dwarfs and giant planets [93-95], or even in neutron stars [96]. In fact, based on expected densities, temperatures, and elemental abundances obtained using the gaseous models for the solar core, metallic hydrogen has been said to exist at the center of the Sun [97-99]. ([dagger])

In previous astrophysical studies [93-99], thermal emission has not guided the selection of the form which metallic hydrogen would adopt. As a result, they have sidestepped the layered graphite-like structure first suggested by Wigner and Huntington [88]. Nonetheless, it seems clear that metallic hydrogen, based on the inferred solar abundance of hydrogen [86,87] and extensive theoretical support (see [39,92] for reviews), constitutes an ideal building material for the entire Sun which is appropriate for 21st century thought.

Thus, theoretical condensed matter physics unknowingly provided astronomy with everything needed to explain the origin of the thermal spectrum (see Fig. 1). Payne and Russell had determined that the Sun was composed of hydrogen [86, 87]. Under the enormous pressures which existed in the solar interior, Wigner and Huntington [88] allowed that this hydrogen could be converted to the metallic state and adopt the lattice structure of graphite. Work by Brovman et al. [89] enabled metallic hydrogen, formed under high pressure conditions within the solar interior, to be metastable at the surface. Thermal emission could then result from lattice vibrations [21], occurring within layered metallic hydrogen, much like what occurs with graphite on Earth.

In contrast to the gaseous models, where photons take millions of years to escape from the solar core [9], in a liquid metallic hydrogen (LMH) Sun, light can be instantly produced at the level of the photosphere, using mechanisms identical to those found within graphite. Complex changes in internal solar opacities are not required [42]. The solar spectrum can be explained without recourse to unsuited gases [21, 70], imaginary enclosures [9], dismissal of observed conduction [69] and convection [67,68], the need for local thermal equilibrium [69], or Kirchhoff's erroneous law [15,16]. The conjecture that solar thermal emission is produced by hydrogen in the condensed state on the surface of the Sun is simpler than any scheme brought forth by the gaseous models. Furthermore, it unifies our understanding of thermal emission in the stars with that of laboratory models on Earth. But most importantly, it results in the incorporation of a structural lattice directly onto the photosphere, providing thereby a basis upon which every other physical aspect of the Sun can be directly explained--from the presence of a true surface to the nature of all solar structures. Hydrogen's ability to exist as condensed matter within the solar body, photosphere, chromosphere, and corona, appears all but certain. The remainder of this work should help to further cement this conclusion.

2.3.2 Limb Darkening #2

According to Father Angelo Secchi, while Galileo denied the existence of limb darkening (see Figs. 3, 4), the phenomenon had been well established by Lucas Valerius of the Lincei Academy, "... the image of the Sun is brighter in the center than on the edges." [1, p. 196, V. I]. *

In 1902, Frank Very demonstrated that limb darkening was a frequency dependent phenomenon [101] which he attributed to scattering in the solar atmosphere and reflection with carbon particles. ([dagger])

Very's study of solar emission [101] eventually led to the law of darkening initially developed by Karl Schwarzschild [102], whereby the observed phenomenon could be explained by relying on the assumption that radiative equilibrium existed within the stars. Once again, this was viewed as a great triumph for gaseous models (see [3] for additional details).

Arthur Eddington would come to adopt Milne's treatment [103] of the law of darkening [9, p. 320-324]. However, all of these approaches shared a common flaw: they were based on the validity of Kirchhoff's law [15,16]. Karl Schwarzschild's derivation began with the words, "If E is the emission of a black body at the temperature of this layer and one assumes that Kirchhoff's law applies, it follows that the layer will radiate the energy Eadh in every direction" [102, p. 280--in Meadows].

Beyond the validity of Kirchhoff's law, these derivations sidestepped the reality that clear convection currents existed on the exterior of the Sun [67, 68]. Remarkably, just a few years after publishing his classic derivation of the law of darkening [103], Milne himself argued that local thermal equilibrium did not apply in the outer layers of the stars [69]. Arthur Eddington also recognized that the laws of emission could not be used to treat the photosphere, "The argument cannot apply to any part of the star which we can see; for the fact that we see it shows that its radiation is not 'enclosed'" [9, p. 101]. As such, how could Kirchhoff's law be invoked to explain limb darkening?

To further complicate the situation, any explanation of limb darkening for gaseous models would once again resurrect the solar opacity problem [42]. How could the exterior of the Sun generate a perfect blackbody spectrum using an assembly of processes not seen within graphite?

Gas models accounted for limb darkening by insisting that the observer was sampling different depths within the Sun (see Fig. 5). When viewing the center of the disk, our eye was observing radiation originating further in the interior. This radiation was being released from a layer which was at a higher temperature. Hence, by the Wien's law [17] it appeared brighter. As for limb radiation, it was being produced at shallower depths, thereby appearing cooler and darker.

These ideas were reliant on the belief that the surface of the Sun was merely an illusion, * a conjecture which will be refuted in [section]3.1, [section]3.2, [section]3.7, [section]4.3, [section]4.5, [section]5.1, [section]5.2, [section]5.5, [section]5.7, [section]6.1, [section]6.2, and [section]6.3.

In the end, the simplest explanation for limb darkening lies in the recognition that directional spectral emissivity occurs naturally within condensed matter [66, 71-73]. Poor conductors tend to have elevated normal emissivities which gradually fall as the angle of observation is decreased (see Fig. 6). This is precisely what is being observed across the solar disk. Good conductors often display lower normal emissivities, which can gradually increase as the angle of observation is decreased, prior to decreasing rapidly as the viewing angle becomes parallel to the surface (see Fig. 6).

Limb darkening revealed that the solar photosphere was condensed, but not highly metallic. ([dagger]) Graphite itself behaves as an excellent emitter, but only a modest conductor. It can be concluded, based on Figs. 4 & 6, that the liquid metallic hydrogen which comprises the solar surface is not highly metallic. The inter-atomic distances in this graphite-like layered material (a Type-I lattice) would be slightly larger than those found in the more metallic sunspots (a Type II lattice), as previously described by the author [35,39,40].

2.3.3 Sunspot Emissivity #3

Galileo viewed sunspots (see Fig. 7) as clouds floating very near the solar surface [105]. ([double dagger]) His great detractor, Christoph Scheiner, initially saw them as extrasolar material [2], but eventually became perhaps the first to view them as cavities [1, p. 15, V. I]. This apparent depression of sunspots was confirmed by Alexander Wilson [2] who, in 1774 [106], used precise geometric arguments to establish the effect which now bears his name [1, p. 70-74]. In 1908, George Ellery Hale discovered that sunspots were characterized by intense magnetic fields [107]. This remains one of the most far reaching findings in solar science.

In addition to the Wilson effect, sunspot emissivity has been found to drop significantly with increasing magnetic field strength [108,109]. The magnetic fields within sunspot umbra are known to have a vertical orientation. Their intensity increases in the darkest regions of the umbra (e.g. [110, p. 75] and [111, p. 80]). Sunspot emissivity has also been hypothesized to be directional, with increasing emissivity towards the limb [111, p. 75-77]. In this regard, Samuel Langley had observed, "With larger images and an improved instrument, I found that, in a complete ring of the solar surface, the photosphere, still brilliant, gave near the limb absolutely less heat than the umbra of the spots" [112, p. 748]. Edwin Frost echoed Langley, "A rather surprising result of these observations was that spots are occasionally relatively warmer than the surrounding photosphere" [113]. Today, the apparent directional changes in the emissivity of sunspots has been dismissed as due to 'straylight' [111, p. 75-77].

Since a gaseous Sun is devoid of a real surface, the 'Wilson Effect' cannot be easily explained within these bounds. Once again, optical depth arguments must be made (e.g. see [110, p. 46] and [114, p. 189-190]). In order to account for the emissivity of sunspots, gaseous models propose that magnetic fields prevent the rising of hot gases from the solar interior [104]. Hence, the spot appears cool. But sunspots can possess light bridges (see Secchi's amazing Fig. 33 in [1, p. 69, V. I]). These are characterized by higher emissivities and lower magnetic fields [111, p. 85-86]. The problem for the gaseous models is that light bridges seem to 'float' above the sunspot. How could these objects be warmer than the material below? Must a mechanism immediately be found to heat light bridges? Sunspots are filled with substructure, including that which arises from Evershed flow. Such substructure is well visible in Fig. 7. However, gases are unable to support structure. How can a gaseous solar model properly account for Evershed flow, while dismissing the surface as an illusion? The problem, of course, remains that all these illusions actually are behaving in systematic fashion (see [section]5.1). Furthermore, in modern astronomy, the apparent change in sunspot emissivity towards the limb must be dismissed as a 'stray light' effect. But the most pressing complication lies in the reality that gases are unable to generate powerful magnetic fields (see [section]5.3). They can respond to fields, but have no inherent mechanism to produce these phenomena. Along these lines, how can magnetic fields be simultaneously produced by gases while at the same time prevent them from rising into the sunspot umbra? On Earth, the production of powerful magnets involves the use of condensed matter and the flow of electrons within conduction bands, not isolated gaseous ions or atoms (see [section] 5.3).

In contrast to the gaseous models, the idea that the Sun is comprised of condensed matter can address all of these complications. The 'Wilson Effect', one of the oldest and simplest of solar observations, can continue to be explained without difficulty by using elementary geometry [106], precisely because a true surface can be invoked [45]. The lowered emissivity of sunspot umbra, in association with increased magnetic field strengths, strongly suggests that sunspots are metallic in nature. Langley's observation that sunspots display increased limb emissivity relative to the photosphere can be explained as related to metallic effects. * The increased emissivity and lower magnetic field strength observed within light bridges could be explained by assuming that they, like the photosphere, are endowed with a Type I lattice [35, 39, 40] with lowered metallic properties. Conversely, the decreased normal emissivity of sunspot umbra along with their increased magnetic field strength suggests a more metallic Type II lattice [35,39,40] in these structures.

In sunspots, the electrons responsible for generating magnetic fields can be viewed as flowing freely within the conduction bands available in metallic hydrogen. This implies that the lattice within sunspot umbrae are positioned so that the hexagonal hydrogen planes (see direction A in Fig. 2) are nearly orthogonal to the solar surface (see Fig. 8). In the penumbra, they would be oriented more horizontally, as demonstrated by the magnetic field lines in this region. The accompanying emissivity would be slightly stronger, resulting in the penumbra appearing brighter. As such, the emissivity in layered metallic hydrogen appears to be highly dependent on the orientation of the hexagonal hydrogen planes.

Likewise, it has been observed that sound waves travel faster within sunspots than within the photosphere [116,117]. These findings are supportive of the idea that sunspots are denser and more metallic than the photosphere itself. The use of condensed matter brings with it both structure and function.

2.3.4 Granular Emissivity #4

When observed at modest resolution, the surface of the Sun is covered with granules (see Fig. 9). * The appearance of these structures caused considerable controversy within astronomy in the mid-1800s [40], but they have been well described and illustrated [118-122] since the days of Father Secchi [1, p.48-59, V.I]. Individual granules have limited lifetimes, can be arranged in mesogranules, supergranules, or giant cell [40,118-122], and seem to represent a convective process. ([dagger])

Though granules are dynamic convective entities which are constantly forming and dying on the surface of the Sun, they have been found to observe the laws of Aboav-Weaire and of Lewis [123-125], along with the perimeter law, for space filling structures in two dimensions [126]. That granules can be viewed as crystals was first hypothesized by Chacornac in 1865 [127]. Clearly, the laws of space filling cannot be applied to gases which expand to fill the space of containers. They cannot, on their own, restrict the spatial extent which they occupy. The laws of space filling can solely be observed by materials which exist in the condensed state. Adherence to these laws by granules [126] constitutes important evidence that these structures are comprised of condensed matter.

Studies reveal that granules can contain 'dark dots' at their center, linked to 'explosive'structural decay. Rast [128] has stated that this decay "can be better understood if granulation is viewed as downflow-dominated-surface-driven convection rather than as a collection of more deeply driven upflowing thermal plumes". These arguments depend on the presence of a true solar surface. Noever has linked the decay of granules associated with the appearance of 'dark dots' to the perimeter law alone [126], once again implying that structure determines dynamic evolution.

Granules are characterized by important emissive characteristics. These structure tend to be brighter at their center and surrounded by dark intergranular lanes (see Fig. 9) whose existence has been recognized by the mid-1800s [40].

In order to account for the emissive properties of granules, the gaseous models maintain that these structures represent convective elements. Hot gases, rising from deep within the Sun, emerge near the center of these formations, while cooler material, held in the dark intergranular lanes, slowly migrates towards the solar interior. In this case, emissivity is linked to temperature changes alone, as dictated by Wien's law [17]. This hypothesis rests on the validity of Kirchhoff's law [15, 16, 20-24] and depends upon subtle changes in solar opacity [42] in adjacent regions of the solar surface. As seen in [section]2.1 and [section]2.2, these arguments are invalid.

Within the context of the LMH model [35, 39], granules are viewed as an integral portion of the true undulating surface of the Sun. Their complex radiative properties can be fully explained by considering directional spectral emissivity. As sub-components of the photosphere, the same mechanism invoked to understand limb darkening [section]2.3.2 can be used to explain granular emissivity.

The normal emissivity of these bubble-like structures remains somewhat elevated. As the viewing angle moves away from the normal, * emissivity progressively drops in accordance with the known behavior of non-metals (see Fig. 6). Intergranular lanes appear dark, not because they are cooler (an unlikely scenario in the same region of the Sun), but rather, because less photons are observed when the surface being visualized becomes increasingly coincident with the direction of emission. In a sense, with respect to thermal emission, each granule constitutes a mini-representation of the macroscopic limb darkening observed across the disk of the Sun (see [section]2.3.2), an idea first expressed by Very [101].

In the LMH model, granules therefore possess a Type I lattice [35, 39], which is somewhat less metallic than the Type-II lattice found in sunspots. This is revealed by the lack of strong magnetic fields associated with granules and by the slowly decaying center-to-limb variation in directional emissivity observed on the solar surface (see [section]2.3.2). In a manner analogous to what is observed in sunspots, the emissivity of layered metallic hydrogen would imply that the hexagonal hydrogen planes are oriented parallel to the solar surface at the center of a granules providing higher emissivity, or brighter appearance, in this instance. The orientation should become more vertical in the intergranular lanes, thereby accounting for their darker appearance. The LMH model [35,39] dispenses with optical depth and variable temperature arguments. It elegantly accounts for solar emission using a single phenomenon (directional spectral emissivity in condensed matter) applicable across the full range of solar observations.

2.3.5 Facular Emissivity #5

In visible light, faculae are difficult to observe at the center of the solar disk, but often become quite apparent towards the limb. ([dagger]) Father Secchi noted the difficulty of observing faculae at the center of the disk [1, p. 49, V.I] and George Ellery Hale commented on the enhanced emissivity of faculae towards the limb, "The bright faculae, which rise above the photosphere, are conspicuous when near the edge of the Sun, but practically invisible when they happen to lie near the center of the disk ..." [129, p. 85-86]. Solar faculae appear to float on the photosphere itself. The structures have long been associated with sunspots [130]. Wang et al. recently postulated that these objects could result from the conversion of sunspots, wherein the horizontal magnetic field contained within penumbrae makes a transition to a vertical field in faculae [131]. Faculae are known to possess strong magnetic fields [132-134].

The emissivity of faculae as they approach the solar limb [135] cannot be reasonably explained within the context of the gaseous models. The accepted scheme, Spruit's hot wall' [136, 137] model is illustrated in Fig. 10. When the faculae are at the center of the disk, the observer is able to see deeper into the Wilson depression to the flux tube 'floor' [137, p. 926]. This floor is thought to be at a lower temperature and, according to the laws of blackbody emission [15-20], appears relatively dark. As for the 'walls' of the flux tube, they are said to sustain elevated temperatures and appear bright when compared to the deeper 'floor'. As the flux tube moves towards the limb, the observer can no longer observe the 'floor' and one of the hot walls' becomes increasingly visible. With time, even that hot wall' disappears. This agrees with observation: facular emissivity is initially indistinguishable from that of the photosphere at disk center. It then increases and becomes bright with respect to the rest of the solar surface, as theses objects move towards the limb. Finally, the emissivity decreases precipitously at the limb.

To help explain the emissivity of faculae, the gas models suggest macroscopic structures, 'cool floors' and 'hot walls'. Gases are incapable of generating such features. In faculae, flux tubes are said to be permitting heat from the solar interior to rise into the hot walls'. Yet, to account for the darkness within sunspots, the models had required that field lines inhibited the upward flow of hot gases beneath the umbra (see [section]2.2.3).

It is immediately apparent that the emissive behavior just described within faculae exactly parallels the known radiative properties of metals, as previously illustrated in Fig. 6. Faculae possess strong magnetic fields [132-134]. In combination with their directional emissivity, this all but confirms that they are metallic in nature.

In addition to faculae, an extension of Spruit's hot wall model has been invoked to explain the presence of magnetic bright points found within the dark intergranular lanes of the granules [138]. As the name implies, magnetic bright points are also believed to possess strong magnetic fields [12,138, 139]. Moreover, they display powerful center-to-limb variations in their emissivity [138], being most visible at the center of the solar disk within the dark intergranular lanes. In the case of magnetic bright points, it is the 'floor' which is viewed as bright, as light is said to originate from "deeper photospheric layers that are usually hotter" [138]. *

The problem rests in the realization that magnetic bright points are located within the dark intergranular lanes. As a result, in order to explain the presence of locally strong magnetic fields within these objects, it is hypothesized that an "efficient turbulent dynamo transforms into magnetic fields part of the kinetic energy of the granular convection" [138]. This serves to emphasize the problems faced by the gas models.

Within the context of the LMH model [35, 36, 39], the presence of faculae and magnetic bright points on the solar surface are elegantly explained by invoking lattice structure. Since faculae are associated with sunspots [130] and even thought to be ejected from these structures [131], it is reasonable to propose that they can be metallic in nature (see Fig. 6), that their structural lattice mimics the type II lattice found in sunspots, and that they have not yet relaxed back to the Type-I lattice found in granules. In this case, the brightness of faculae implies that their hexagonal hydrogen planes lie parallel to the solar surface. This should account for both emissivity and the presence of associated magnetic fields in these structures.

In the end, the simplest explanation for the origin for magnetic bright points may be that they are nothing more than facular elements. Rising from internal solar regions, they have not fully relaxed from a Type II to a Type I lattice, but have been transported through granular flow to deeper intergranular lanes. Their center-to-limb emissivity variations may well rest in the realization that they are hidden from view by the granules themselves as the limb is approached. Hence, their numbers appear to fall towards the edge of the solar disk [138].

2.3.6 Chromospheric Emissivity #6

While hydrogen-[alpha] emissions are responsible for the red glow of the chromosphere visible during an eclipse, this region of the Sun also emits a weak continuous spectrum [56] which has drawn the attention of solar observers for more than 100 years [140-147]. ([dagger]) Relative to this emission, Donald Menzel noted, "... we assumed that the distribution in the continuous chromospheric spectrum is the same as that of a black body at 5700[degrees], and that the continuous spectrum from the extreme edge is that of a black body at 4700[degrees]. There is evidence in favor of a lower temperature at the extreme limb in the observations by Abbot, Fowle, and Aldrich of the darkening towards the limb of the Sun" [142].

The gaseous models infer that the chromosphere has an average density of ~[10.sup.-12] g/[cm.sup.3] [115, p. 32]. ([double dagger]) Despite a [10.sup.5] drop in density with respect to the photosphere, these treatments continue to advance that the continuous emission in the chromosphere is being produced by neutral H, [H.sup.-], Rayleigh scattering, and electron scattering (see [145,146] and [150, p. 151-157]). But, none of these processes can be found in graphite (see [section] 2.1 and [section] 2.2).

Alternatively, within the context of the LMH model, the chromospheric continuous emission provides evidence that condensed matter exists in this region of the solar atmosphere [56]. This is in keeping with the understanding that continuous spectra, which can be described using blackbody behavior, must be produced by condensed matter [21-24]. In this regard, the chromosphere may be viewed as a region of hydrogen condensation and recapture within the Sun. Though generating condensed matter, the chromosphere is not comprised of metallic hydrogen. *

2.3.7 K-Coronal Emissivity #7

The white light emitted by the K-corona is readily visualized during solar eclipses. ([dagger]) Observing from Iowa in 1869, William Harkness "obtained a coronal spectrum that was continuous except for a single bright green line, later known as coronal line K1474" on the Kirchhoff scale [151, p. 199]. Eventually, it became clear that the continuous spectrum of the K-corona was essentially identical to photospheric emission [152-156], with the important distinction that the former was devoid of Fraunhofer lines. In addition, the spectrum of the K-corona appeared to redden slightly with increasing distance from the solar surface, "microphotograms for solar distances varying from R = 1.2s to R = 2.6s show that the coronal radiation reddens slightly as the distance from the Sun is increased" [156]. The reddening of the K-coronal emission suggested that the corona was cooling with increased distance from the solar surface. ([double dagger])

Within the context of the gas models, the corona is extremely hot and thus, cannot be self-luminous in the visible spectrum. Rather, these models maintain that coronal white light must represent photospheric radiation. But as the thermal spectrum from the photosphere is punctuated with Fraunhofer absorption lines (see [section]3.7), some mechanism must be devised to explain their absence in coronal light. As such, proponents of the gaseous models have proposed that coronal light is being scattered by highly relativistic electrons [115, 148, 157, 158]. The Fraunhofer absorption lines are hypothesized to become highly broadened and unobservable. Relativistic electrons require temperatures in the millions of degrees. These temperatures are inferred from the line emissions of highly ionized ions in this region of the Sun (see [section]3.8). Unfortunately, such a scheme fails to account for the reddening of the coronal spectrum [156].

In contrast, the LMH model [35, 39] states that the solar corona contains photospheric-like condensed matter (Type I) and is, accordingly, self-luminous [57]. It is well-known that the Sun expels material into its corona in the form of flares and coronal mass ejections. It is reasonable to conclude that this material continues to emit (see [section]2.3.8) and may eventually disperse into finely distributed condensed matter in this region of the Sun. The reddening of the coronal spectrum implies that the apparent temperatures of the corona are no greater than those within the photosphere. [section] The apparent temperature slowly decreases, as expected, with increased distance from the solar surface. The production of highly ionized ions in the corona reflects condensed matter in the outer solar atmosphere (see [section]2.3.8, [section]3.8, and [section]5.5). As for the Fraunhofer lines, they do not appear on the spectrum of the K-corona owing to insufficient concentrations of absorbing species exist in this region of the Sun. There is no need to invoke scattering by relativistic electrons.

2.3.8 Coronal Structure Emissivity #8

The corona of the active Sun is filled with structures easily observed using white-light coronographs [154,155]. ([paragraph]) Flares [159-162], prominences and coronal mass ejections [163-171], streamers [172-174], plumes [175], and loops [176-178], can all be visualized in white light.

The mechanism for generating white-light in this wide array of structures remains elusive for the gaseous models, in part because the densities, in which they are hypothesize to exist, are lower than ~[10.sup.-15] g/[cm.sup.3] [148]. Moreover, the release of white-light by these structures tends to be explosive in nature, particularly when flares are involved [179-186]. These phenomena cannot be adequately explained by relying on gradual changes in opacity [42] or the action of relativistic electrons to scatter photospheric light [160,161,164, 187,188]. Currently, many of these structures are believed to derive their energy from coronal magnetic sources overlying active regions [12]. That is a result having no other means of accounting for this extensive and abrupt release of energy in the gaseous Sun [179].

Within the context of the LMH model [35,39], the whitelight emitted by coronal structures is associated with their condensed nature. Since many of these formations originate from eruptions taking place at the level of the photosphere, such a postulate appears reasonable. As a result, coronal structures should be regarded as self-luminous. The explosive increase in white-light is related to powerful lattice vibrations associated with their formation [21]. Long ago, Zollner [189] had insisted that flares involved the release of pressurized material from within the Sun [3]. These mechanisms remain the most likely, as they properly transfer energy out of the solar body, not back to the surface from the corona (see [section]5.1).

3 Spectroscopic Lines of Evidence

Though Gustav Kirchhoff erred [21-24] relative to his law of thermal emission [15,16], his contributions to solar science remain unchallenged. Not only was he amongst the first to properly recognize that the Sun existed in liquid state [2, 26], but as the father of spectral analysis, along with Robert Bunsen, he gave birth to the entire spectroscopic branch of solar science [190,191]. Using spectroscopic methods, Kirchhoff successfully identified the lines from sodium on the Sun and this led to an avalanche of related discoveries, spanning more than a century [190,191]. Indeed, all of the thermal proofs discussed in [section]2, are the result of spectroscopic analysis, centered on the blackbody spectrum observable in visible and infrared light. It is fitting that the next series of proofs are spectroscopic, this time centering on line emission of individual atoms or ions. These eight lines of evidence highlight anew the power of Kirchhoff's spectroscopic approaches.

3.1 UV/X-ray Line Intensity #9

The Sun is difficult to study in the ultraviolet (UV) and X-ray bands due to the absorption of this light by the Earth's atmosphere. * As a consequence, instruments like the AIA aboard NASA's Solar Dynamic Observatory (see Fig. 11) are being used for these observations [192, p. ix]. When the Sun is observed at these frequencies, striking evidence is produced on the existence of a real solar surface. Harold Zirin describes the findings as follows, "The case in the UV is different, because the spectrum lines are optically thin. Therefore one would expect limb brightening even in the absence of temperature increase, simply due to the secant increase of path length. Although the intensity doubles at the limb, where we see the back side, the limb brightening inside the limb is minimal ... Similarly, X-ray images show limb brightening simply due to increased path length." [193]. Fig. 11 presents this phenomenon in X-Ray at 94[Angstrom], for a somewhat active Sun. ([dagger])

When the observer is directly examining the center of the opaque solar disk, weak spectral lines are obtained at these frequencies. The lines brighten slightly as observation moves towards the limb, owing to a slightly larger fraction of the solar atmosphere being sampled (line of sight 2 versus 1 in Fig. 12). However, immediately upon crossing the solar limb, a pronounced increase in spectroscopic intensity can be recorded. In fact, it approximately doubles, because a nearly two-fold greater line of sight is being viewed in the solar atmosphere. This can be understood if one would compare a line of sight very near line 3 in Fig. 12 (but still striking the solar disk) with line 3 itself.

In this manner, UV and X-ray line intensities can provide strong evidence that the Sun possesses an opaque surface at these frequencies which is independent of viewing angle. Limb darkening is not observed, as was manifested in the visible spectrum (see [section]2.3.2), in that condensed matter is not being sampled. Rather, the behavior reflects that gases are being monitored above a distinct surface through which UV and X-ray photons cannot penetrate. ([double dagger])

3.2 Gamma-Ray Emission #10

Occasionally, powerful gamma-ray flares are visible on the surface of the Sun and Rieger [194] has provided evidence that those with emissions >10 MeV are primarily visualized near the solar limb (see Fig. 13). * Speaking of Rieger's findings, Ramaty and Simnett noted that "Gamma-ray emitting flares are observed from sites located predominantly near the limb of the Sun ... This effect was observed for flares detected at energies >0.3 MeV, but it is at energies >10 MeV that the effect is particularly pronounced ... Since in both of these cases the bulk of the emission is bremsstrahlung from primaryelectrons, these results implythat the radiating electrons (are) stronglyanisotropic, with more emission in the directions tangential to the photosphere than in directions away from the Sun" [195, p. 237].

The production of anisotropic emission would typically imply that structural constraints are involved in flare production. Since the gaseous Sun cannot sustain structure, another means must be used to generate this anisotropy. Based on theoretical arguments, Ramaty and Simnett consequently advance that: "... the anisotropy could result from the mirroring of the charged particles in the convergent chromospheric magnetic fields" [195, p. 237]. The anisotropy of gamma-ray emission from high energy solar flares is thought to be generated by electron transport in the coronal region and magnetic mirroring of converging magnetic flux tubes beneath the transition region [195]. The energy required for flare generation could thereby be channeled down towards the solar surface from the corona itself. Conveniently, the chromosphere instantly behaves as an 'electron mirror'. Devoid of a real surface, another mechanism was created to act as a surface.

The inability to generate flare anisotropy using the most obvious means--the presence of a true photospheric surface --has resulted in a convoluted viewpoint. Rather than obtain the energy to drive the flare from within the solar body, the gaseous models must extract it from the solar atmosphere and channel it down towards the surface using an unlikely mechanism. It remains simpler to postulate that the anisotropy observed in high energy solar flares is a manifestation that the Sun has a true surface. The energy involved in flare generation can thereby arise from the solar interior, as postulated long ago by Zollner [189]. In this respect, the LMH model [35, 39] retains distinct advantages when compared to the gaseous models of the Sun.

3. 3 Lithium Abundances #11

Kirchhoff's spectroscopic approaches [190,191] have enabled astronomers to estimate the concentrations of many elements in the solar atmosphere. ([dagger]) Application of these methods have led to the realization that lithium was approximately 140-fold less abundant in the solar atmosphere than in meteors [196, 197].

In order to explain this discrepancy, proponents of the gaseous stars have advanced that lithium must be transported deep within the interior of the Sun where temperatures >2.6 x [10.sup.6] K are sufficient to destroy the element by converting it into helium [[sup.7]Li (p, [alpha])(4) He] [198]. To help achieve this goal, lithium must be constantly mixed [198-200] into the solar interior, a process recently believed to be facilitated by orbiting planets [201,202]. Though these ideas have been refuted [203], they highlight the difficulty presented by lithium abundances in the gaseous models.

As for the condensed model of the Sun [35, 39], it benefits from a proposal [54], brought forth by Eva Zurek, Neil Ashcroft, and others [204], that lithium can act to stabilize metallic hydrogen [88, 92]. Hence, lithium levels could appear to be decreased on the solar surface, as a metallic hydrogen Sun retains the element in its interior. At the same time, lithium might be coordinated by metallic hydrogen in the corona, therefore becoming sequestered and unavailable for emission as an isolated atom.

In this manner, lithium might be unlike the other elements, as these, including helium, are likely to be expelled from the solar interior (see [section]5.1) as a result of exfoliative forces [48]. Lithium appears to have a low abundance, but, in reality, it is not being destroyed. This would better reconcile the abundances of lithium observed in the solar atmosphere with that present in extrasolar objects. Clearly, if lithium is being destroyed within the stars, it becomes difficult to explain its abundance in meteors. This problem does not arise when abundances are explained using a LMH model, as metallic hydrogen can sequester lithium into its lattice.

3.4 Hydrogen Emission #12

The 'flash spectrum' associated with solar eclipses characterizes the chromosphere. * The strongest features within this spectrum correspond to line emissions originating from excited hydrogen atoms. As far back as 1931, the outstanding chromospheric observer, Donald H. Menzel, listed more than twenty-three hydrogen emission lines originating from this region of the Sun (see Table 3 in [205, p. 28]). It is the cause of these emissions which must now be elucidated. The most likely scenario takes advantage of the condensation appearing to occur in the chromospheric layer (see [section] 5.4 [section] 5.6 and [56,59]).

By modern standards, the nature of the chromosphere remains a mystery, as Harold Zirin reminds us, "The chromosphere is the least-well understood layer of the Sun's atmosphere ... Part of the problem is that it is so dynamic and transient. At this height an ill-defined magnetic field dominates the gas and determines the structure. Since we do not know the physical mechanisms, it is impossible to produce a realistic model. Since most of the models ignored much of the data, they generally contradict the observational data. Typical models ignore other constraints and just match only the XUV data; this is not enough for a unique solution. It reminds one of the discovery of the sunspot cycle. While most of the great 18th century astronomers agreed that the sunspot occurrence was random, only Schwabe, an amateur, took the trouble to track the number of sunspots, there by discovering the 11-year cycle" [193]. But if mystery remains, it is resultant of the denial that condensed matter exists in this layer of the Sun.

The chromosphere is characterized by numerous structural features, the most important of which are spicules (see Fig. 14) [59,150]. Even in the mid-1800s, Secchi would provide outstanding illustrations of these objects (see Plate A in [1, V. II]). He would discuss their great variability in both size and orientation, "In general, the chromosphere is poorly terminated and its external surface is garnished with fringes ... It is almost always covered with little nets terminated in a point and entirely similar to hair ... it often happens, especially in the region of sunspots, that the chromosphere presents an aspect of a very active network whose surface, unequal and rough, seems composed of brilliant clouds analogous to our cumulus; the disposition of which resembles the beads of our rosary; a few of which dilate in order to form little diffuse elevations on the sides" [1, p. 31-36, V. II].

At first glance, spicules are thought to have a magnetic origin, as these fields seem to flood the chromosphere [148, 150, 206-215]. In reality, matter within the chromosphere seems to form and dissipate quickly and over large spatial extent, with spicules reaching well into the corona [148,150, 206-215]. The random orientation which spicules display, as noted long ago by Secchi [1, p. 31-36, V. II], along with their velocity profiles (see [section]5.6), should have dispelled the belief that these structures are magnetic in origin. Rather, they appear to be products of condensation ([section]5.6). ([dagger])

If spicules and chromospheric matter are genuinely the product of condensation reactions, then their mechanism of formation might shed great light into the emissive nature of this solar layer.

3.4.1 The Liquid Metallic Hydrogen Solar Model

The search for answers begins by considering condensation processes known to occur on Earth [59].

In this respect, while studying the agglomeration of silver clusters, Gerhart Ertl's (Nobel Prize, Chemistry, 2007) laboratory noted that "Exothermic chemical reactions may be accompanied by chemiluminescence. In these reactions, the released energy is not a diabatically damped into the heat bath of the surrounding medium but rather is stored in an excited state of the product; decay from this excited state to the ground state is associated with light emission" [216].

The reactions of interest are seldom studied. Those which must arouse attention involve the condensation of two silver fragments and the formation of an activated cluster species: [Ag.sub.n] + [Ag.sub.m] [right arrow] [Ag.sup.*.sub.m+n] [216]. With respect to the chromosphere, the important features of these reactions involve the realization that condensation processes are exothermic.

When silver clusters condense, energy must be dissipated through light emission. This constitutes a vital clue in explaining why the chromosphere is rich in hydrogen emission lines [59, 205]. Once an activated cluster is formed, it can relax by ejecting an excited atom: [Ag.sup.*.sub.m+n] [right arrow] [Ag.sub.m+n-1] + [Ag.sup.*]. The reactions are completed when the ejected excited species emits light to reenter the ground state: [Ag.sup.*] [right arrow] Ag + hv.

Taking guidance from the work in metal clusters [216], hydrogen emission lines in the chromosphere might be seen as produced through the condensation of hydrogen fragments, [H.sub.n] + [H.sub.m] [right arrow] [H.sup.*.sub.m+n]. The resultant condensation product could then relax through the ejection of an excited hydrogen atom, [H.sup.*.sub.m+n] [right arrow] [H.sub.m+n-1] + [H.sup.*], which finally returns to a lower energy state with light emission, [H.sup.*] [right arrow] H + hv. This could give rise to all the Lyman lines ([N.sub.2] > 1 [right arrow] [N.sub.1] = 1). If one postulates that the excited hydrogen atom can hold its electron in any excited orbital [N.sub.2] > 2, [H.sup.**], then the remaining complement of hydrogen emission lines could be produced [H.sup.**] [right arrow] [H.sub.*] + hv (Balmer [N.sub.2] > 2 [right arrow] [N.sub.1] = 2, Paschen series [N.sub.2] > 3 [right arrow] [N.sub.1] = 3, and Brackett series [N.sub.2] > 4 [right arrow] [N.sub.1] = 4).

But since the chromosphere is known to possess spicules and mottles [148, 150, 206-215], it is more likely that hydrogen is condensing, not onto a small cluster, but rather, onto very large condensed hydrogen structures, CHS [59]. * The most logical depositing species in these reactions would be molecular hydrogen, as it has been directly observed in sunspots [217,218], on the limb [219], and in flares [218]. Importantly, the emission from molecular hydrogen is particularly strong in chromospheric plages [220], providing further evidence that the species might be the most appropriate to consider.

As a result, it is reasonable to postulate that molecular hydrogen could directly interact with large condensed hydrogen structures, CHS, in the chromosphere [59]. The reaction involved would be as follows: CHS + [H.sub.2] [right arrow] CHS-[H.sup.*.sub.2]. This would lead to the addition of one hydrogen at a time to large condensed structures and subsequent line emission from the ejected excited species, [H.sup.*] [right arrow] H + hv. Numerous reactions could simultaneously occur, giving rise to the rapid growth of chromospheric structures, accompanied with significant light emission in all spectral series (i.e. Lyman, Balmer, Paschen, and Brackett).

3.4.2 The Gaseous Solar Models

The situation being promoted in [section] 3.4.1, concerning hydrogen line emission in the chromosphere, is completely unlike that currently postulated to exist within the gaseous Sun [59]. In the gas models, line emission relies on the accidental excitation of hydrogen through bombardment with either photons or electrons [206, p. 2]. The process has no purpose or reason. Atoms are randomly excited, and then, they randomly emit.

Przybilla and Butler have studied the production of hydrogen emission lines and the associated lineshapes in the gaseous models. They reached the conclusion that some of the hydrogen emission lines "collisionally couple tightly to the continuum" [221]. Their key source of opacity rests with the [H.sup.-] ion, which has previously been demonstrated to be incapable of providing the desired continuous emission [42]. Of course, it is impossible to "collisionally couple tightly to the continuum" [221] in the gaseous models, as the continuum originates solely from opacity changes produced by an array of processes [42]. In the chromosphere, where average densities are postulated to be extremely low (~[10.sup.-15] g/[cm.sub.3] [148]), continuous emission is thought to be produced by neutral H, [H.sup.-], Rayleigh scattering, and electron scattering (see [145,146] and [150, p. 151-157]). Clearly, it is not possible to tightly couple to all of these mechanisms at once.

Przybilla's and Butler's computations [221] involve consideration of line blocking mechanisms and associated opacity distribution functions [222]. Stark line broadening mechanisms must additionally be invoked [223].

Beyond the inability of gases to account for the continuous spectrum and the shortcomings of solar opacity calculations [42], the central problem faced in trying to explain hydrogen emission and the associated line shapes rests in the Stark mechanisms themselves. Stark line broadening relies upon the generation of local electric fields near the emitting hydrogen atom. These fields are believed to be produced by ions or electrons which come into short term contact with the emitting species [223]. On the surface at least, the approach seems reasonable, but in the end, it relies on far too many parameters to be useful in understanding the Sun.

In the laboratory, Stark broadening studies usually center upon extremely dense plasmas, with electron numbers approaching [10.sup.17] [cm.sup.-3] [224]. Stehle, one of the world's preeminent scientists relative to Stark linewidth calculations [223, 225, 226], has analyzed lineshapes to infer electron numbers ranging from [10.sup.10] to [10.sup.17] [cm.sup.-3] [227]. ([dagger]) She initially assumes that plasmas existing within the chromosphere (T = 10,000 K) have electron numbers in the [10.sup.13] [cm.sup.-3] range [223]. Other sources call for much lower values. For instance, electron numbers of ~[10.sup.16] [m.sup.-3] (or ~[10.sup.10] [cm.sup.-3]) are obtained from radio measurements by Cairns et al. [229] and of no more than ~[10.sup.15] [m.sup.-3] (or ~[10.sup.9] [cm.sup.-3]) are illustrated in Dwivedi Fig. 3 [157, p. 285]. Stark experiments on Earth typically utilize electron numbers which are approximately 1-100 million times greater than anything thought to exist in the chromosphere.

A minor objection to the use of Stark broadening to explain the width of the hydrogen lines in the gaseous models rests on the fact that the appropriate experiments on hydrogen plasma do not exist. The plasma form of hydrogen (H II) is made of protons in a sea of electrons. It lacks the valence electron required for line emission. The closest analogue to excited hydrogen in the Sun would be ionized helium in the laboratory [224], although ionized Argon has been used for the H[beta] profile [227]. *

However, the most serious problem rests in the realization that these methods are fundamentally based on the presence of electric or electromagnetic fields in the laboratory. For instance, the inductively produced plasmas analyzed by Stehle [227] utilize discharges on the order of 5.8 kV [227]. Inductively produced plasmas involve directionally-oscillating electromagnetic fields. Spark or arc experiments utilize static electric fields to induce capacitive discharges across charged plates. In every case, the applied electric field has a distinct orientation. Such conditions are difficult to visualize in a gaseous Sun, particularly within the spicules (see [section]3.4 and [section]5.7), given their arbitrary orientations. Random field orientations are incapable of line broadening, as well understood in liquid state nuclear magnetic resonance.

Stark broadening requires constraints on the electric field. In the gaseous models, these must take the form of a charged particle which approaches, precisely at the correct moment, an emitting species. The use of such mechanisms to account for chromospheric line profiles is far from justified. But, as the gaseous models cannot propose another explanation, everything must rest on Stark mechanisms, however unlikely these are to be valid in this setting.

In the end, it is not reasonable that matter existing at the concentration of an incredible vacuum (~[10.sup.-15] g/[cm.sup.3] [148]) could be Stark broadened, given the extremely low electron numbers associated with the chromosphere [157,229]. Computations have merely extended our 'observationalrange'to electron numbers never sampled in the laboratory. According to the gas models, the chromosphere is a region of extremely low density, but high density plasmas must be studied to enable Stark analysis. Then, while the results of Stark broadening calculations appear rigorous on the surface, they contain experimental shortcomings. Spatially aligned electric fields cannot exist throughout the spicular region of a fully gaseous solar atmosphere, lone electrons are unlikely to produce the desired electric fields, and atoms such as argon have little relevance to hydrogen. In any case, given enough computational flexibility, any lineshape can be obtained, but opacity considerations remain [42].

3.4.3 Summary

As just mentioned in [section]3.4.2, Stark experiments involve electron densities far in excess of anything applicable to the solar chromosphere. Using the same reasoning, it could be argued that metallic hydrogen has not been created on Earth [39,92]. The criticism would be justified, but this may be simply a matter of time. Astrophysics has already adopted these materials in other settings [93-96] and experimentalists are getting ever closer to synthesizing metallic hydrogen [39, 92]. The Sun itself appears to be making an excellent case that it is comprised of condensed matter.

Unlike the situation in the gaseous solar models, where hydrogen emission becomes the illogical result of random reactions, within the context of the liquid hydrogen model, it can be viewed as the byproduct of systematic and organized processes (see [section]3.4.1). An underlying cause is associated with line emission, dissipation of the energy liberated during condensation reactions. The driving force is the recapture of hydrogen through condensation, leading ultimately to its re-entry into the solar interior. This tremendous advantage cannot be claimed by the gaseous models.

Pressure (or collisional) broadening can be viewed as the most common mechanism to explain line broadening in spectroscopy. This mechanism can be invoked in the condensed model, because the atmosphere therein is not devoid of matter (see [section]2.3.6, [section]5.4, [section]5.5, [section]5.6, [section]6.6 and [56,58,59]).

It is possible that line broadening is occurring due to direct interaction between the emitting species and condensed hydrogen structures in the chromosphere. In this case, emission would be occurring simultaneously with the ejection of hydrogen. Under the circumstances, hydrogen line shapes may be providing important clues with respect to the interaction between molecular hydrogen and larger condensed structures in the chromosphere. If Stark broadening mechanisms play any role in the Sun, it will only be in the context of condensed matter generating the associated electric field.

3.5 Elemental Emission #13

Beyond hydrogen, the solar chromosphere is the site of emission for many other species, particularly the metals of the main group and transition elements. ([dagger]) For gaseous models, these emissions continue to be viewed as the product of random events (see [section]3.4.2). However, for the LMH model, condensation remains the focus ([section]3.4.1), but this time with the assistance of the hydrides.

The solar disk and the sunspots are rich in hydrides including CaH, MgH, CH, OH, [H.sub.2]O, NH, SH, SiH, AlH, CoH, CuH, and NiH [230,231]. CaH and MgH have been known to exist in the Sun for more than 100 years [232]. Hydrogen appears to have a great disposition to form hydrides and this is important for understanding the role which they play in the chromosphere.

At the same time, the emission lines from CaII and MgII are particularly strong in the chromosphere [206, p. 361-369]. These represent emissions from the [Ca.sup.+] and [Mg.sup.+] ions. Yet, the inert gas configurations for these atoms would lead one to believe that the [Ca.sup.+2] (CaIII) and [Mg.sup.+]2 (MgIII) lines should have been most intense in the chromosphere. As such, why is the Sun amplifying the CaII and MgII lines? Surely, this cannot be a random phenomenon ([section]3.4.2), * as these should have led to the buildup of the most stable electronic configuration.

The answer may well lie in reconsidering the condensation reactions presented in [section]3.4.1, but this time substituting CaH for molecular hydrogen. It should be possible for CaH and a condensed hydrogen structure, CHS, to interact, thereby forming an activated complex, CHS + CaH [right arrow] CHS-H[Ca.sup.*]. This complex could then emit a CaII ion in activated state, [Ca.sup.+*], and capture the hydrogen atom: CHS-H[Ca.sup.*] [right arrow] CHS-H + [Ca.sup.+*]. Finally, the emission lines from CaII would be produced, as [Ca.sup.+*] ([CaII.sup.*]) returns to the ground state: [Ca.sup.+*] -[Ca.sup.+] + hv. As was the case when discussing the condensation of molecular hydrogen ([section]3.4.1), if one permits the electrons within the excited state of CaII to initially occupy any electronic orbital, [CaII.sup.**], then all possible emission lines from CaII could be produced: [Ca.sup.+**] [right arrow] [Ca.sup.+*] + hv. A similar scheme could be proposed for MgH and the other metal hydrides, depending on their relative affinity for CHS.

There is an important distinction between this scenario and that observed with molecular hydrogen ([section]3.4.1). When metal hydrides are utilized in this scheme, the condensation reactions are delivering both a proton and two electrons to the condensed hydrogen structure. The reactions involving molecular hydrogen delivered a single electron. This interesting difference can help to explain the varying vertical extent of the chromosphere when viewed in H[alpha], CaII, or HeII (see [section]3.6 and [section]4.7).

When sampling the solar atmosphere, electron densities appear to rise substantially as one approaches the photosphere (see [229] and [157, p. 285]). Hence, the lower chromosphere is somewhat electron rich with respect to the upper regions of this layer. Thus, in the lower chromosphere, condensation reactions involving the ejection of atomic hydrogen and neutral atoms can abound. As the altitude increases, a greater affinity for electrons arises and condensation can now be facilitated by species like as the metal hydrides, which can deliver two electrons per hydrogen atom. ([dagger]) This explains why CaII lines in the chromosphere can be observed to rise to great heights [193].

At the same time, lines from neutral metals, M, are more prevalent in the lower chromosphere [193]. Since this area is electron rich, a two electron delivery system is unnecessary and reactions of the following form can readily occur: 1) MH + CHS [right arrow] [CHS-HM.sup.*], 2) [CHS-HM.sup.*] [right arrow] CHS-H + [M.sup.*], and 3) [M.sup.*] [right arrow] M + hv. In this case, only a single electron has been transferred during hydrogen condensation.

Perhaps, it is through the examination of linewidths that the most interesting conclusions can be reached. The emission lines of H[alpha], Ca, and Mg from spicules are very broad, suggesting a strong interaction between CHS and the ejected atoms, in association with ejection and light emission [234-236]. In contrast, spicule emission linewidths from H[beta], H[gamma], H[epsilon], the D3 line from He, and the neutral line from oxygen are all sharp [234]. One could surmise that the interaction between these species and condensed hydrogen structures are weaker upon ejection.

It is reasonable to conclude that the hydrides play an important role in facilitating condensation within the chromosphere [59]. Hydrides enable the delivery of hydrogen in a systematic manner and, most importantly, either one or two electrons, depending on the electron densities present on the local level. Such an elegant mechanism to account for the prevalence of CaII and MgII in the chromosphere cannot be achieved by other models. Moreover, unlike the LMH model, the gaseous models take no advantage of the chemical species known to exist in the solar atmosphere.

3.6 Helium Emission #14

The analysis of helium emission in the chromosphere may well provide the most fascinating adventure with regard to the spectroscopic lines of evidence. ([double dagger]) This stands as fitting tribute to helium [47], as it was first observed to exist on the Sun [237,238]. These seminal discoveries exploited the presence of helium within prominences and the disturbed chromosphere [239, 240]. Astronomers would come to view solar helium as extremely abundant [241,242], but these conclusions have been challenged and may need to be revisited [47,48,61]. There is considerable reason to conclude that the solar body is actively ejecting He from its interior [47, 48].

Though helium can be found in spicules [193] and prominences, it is difficult to observe on the solar disk. It can be readily visualized in the chromosphere where the spatial extent of the 30.4 nm HeII emission lines can greatly exceed those from H[alpha] (see the wonderful Fig. 1 in [243]). With increased solar activity, helium emission can become pronounced in the solar atmosphere (see Fig. 15 and [244]).

In the chromosphere, the helium which gives rise to emission lines can possess both of its electrons (HeI) or lose an electron to produce an ion (HeII). HeII resembles the hydrogen atom in its electronic configuration. However, the situation concerning HeI can be more complex. When this species exists in the ground state, both of its electrons lie in the 1S orbital (N = 1) with their spins antiparallel, as dictated by Pauli's exclusion principle. In the excited state (i.e. 1 electron in the N = 1 shell, and the second electron in any of the N>1 shells), helium can exist either as a singlet (parahelium--spins remaining antiparallel to one another) or as a triplet (orthohelium --spins assume a parallel configuration). Interestingly, the line emissions from the triplet states of orthohelium can be quite strong on the limb of the Sun.

For instance, a well-known triplet HeI transition occurs at 1083 nm (10830[Angstrom]) which is barely visible on the disk, but it is nearly as intense as H[alpha] on the limb [245, p. 199-200]. At the same time, the HeI triplet D3 line at 588 nm can be enhanced 20 fold when visualization moves from the disk to the limb [245, p. 199-200]. *

During the eclipse of March 29, 2006, the triplet D3 line was carefully examined. It appeared to have a binodal altitude distribution with a small maximum at ~250 km and a stronger maximum between 1300-1800km (see Fig. 6 in [244]). This bimodal distribution was not always observed (see Fig. 7 in [244]). But generally, the D3 line is most intense at an altitude of ~2,000 km, with an emission width of approximately 1,600 km. The triplet D3 lines show no emission near the photosphere.

Within the context of gaseous models, it is extremely difficult to account for the presence of excited HeI triplet states in the chromosphere. Helium requires ~20 eV ([dagger]) to raise an electron from the N = 1 shell to the N = 2 shell. How can excitation temperatures in excess of 200,000 K be associated with a chromosphere displaying apparent temperatures of 5,00010,000K, values not much greater than those existing on the photosphere?

Therefore, since proponents of gaseous models are unable to easily account for the powerful D3 line emission, they have no choice but to state that helium is being excited by coronal radiation which has descended into the chromosphere [244, 246]. In a sense, helium must be 'selectively heated' by the corona. These proposals strongly suggest that the gaseous models are inadequate. It is not reasonable to advance that an element can be selectively excited by coronal radiation, and this over its many triplet states. At the extreme, these schemes would imply that coronal photons could strip away all electrons from chromospheric atoms. Yet, even lines from neutral atoms are observed. ([double dagger])

On the other hand, helium emissions can be easily understood in the LMH model [35, 36, 39], if attention is turned toward condensation reactions believed to occur within the chromosphere (see [section]3.4, [section]3.5 and [59,61]).

In this respect, it must be recognized that the famous helium hydride cation (He[H.sup.+]) "is ubiquitous in discharges containing hydrogen and helium" [247].

First discovered in 1925 [248], He[H.sup.+] has been extensively studied [249, 250] and thought to play a key role in certain astrophysical settings [251-253]. In the laboratory, its spectral lines were first observed by Wolfgang Ketterle (Nobel Prize, Physics, 2001) [254, 255]. The author has previously noted, "Although it exists only in the gas phase, its Br&nsted acidity should be extremely powerful. As a result, the hydrogen hydride cation should have a strong tendency to donate a proton, without the concerted transfer of an electron" [61].

Turning to Fig. 16, it appears that the action of the helium hydride cation, He[H.sup.+], can lead to a wide array of reactions within the chromosphere. These processes are initiated with its transfer to condensed hydrogen structures, CHS, believed to be be forming (see [section]2.3.6, [section]3.4, [section]3.5, [section]3.7, [section]5.4, [section]5.6, [section]6.6) in this region of the solar atmosphere. As was the case with hydrogen ([section]3.4) and elemental ([section]3.5) emission lines, everything hinges on the careful consideration of condensation.

First, He[H.sup.+] and CHS react to form an activated complex: CHS + He[H.sup.+] - CHS-H-[He.sup.+*]. If the expulsion of an excited helium ion ([He.sup.+*]) follows, full transfer of a proton and an electron to CHS will have occurred (top line in Fig. 16). The resulting [He.sup.+*] would be able to relax back to a lower energy state through emission, leading to the well known He II lines in the chromosphere (top right in Fig. 16).

Alternatively, when He[H.sup.+] reacts with CHS, the expulsion of an excited helium atom ([He.sub.*]) could follow (see Fig. 16) involving the transfer of a proton--but no electron--to the CHS. As a strong Bransted acid, He[H.sup.+] should permit these reactions (namely: CHS-H[He.sup.+*] [right arrow] CHS-[H.sup.+] + [He.sup.*]). Expulsion of an activated helium atom ([He.sup.*]) can lead to two conditions, depending on whether the electrons within this species are antiparallel (parahelium) or parallel (orthohelium). Within helium, the excited electron is allowed by selection rules to return to the ground state, if and only if, its spin is opposed to that of the ground state electron. As a result, only parahelium can relax back to the ground state: [He.sup.*] [right arrow] He + hv. This leads to the HeI lines from singlet helium.

As for the excited orthohelium, it is unable to relax, as its two electrons have the same spin (either both spin up or both spin down). Trapped in the excited state, this species can at once react with hydrogen, forming the excited helium hydride molecule, which, like the helium hydride cation, is known to exist [256,257]: [He.sup.*] + H [right arrow] He[H.sup.*].

Excited helium hydride can react with CHS in the chromosphere, but now resulting in a doubly activated complex: CHS + He[H.sup.*] [right arrow] CHS-H-[He.sup.**], wherein one electron remains in the ground state and the other electron is promoted beyond the 2S shell. * To relax, the doubly excited [He.sup.**] atom, must permit an electron currently in the 2P or higher orbital, to return to the 2S or 2P orbitals.

The helium [D.sub.3] line would be produced by a 3[sup.3]D [right arrow] 2[sup.3]P transition [245, p. 95]. The 2[sup.3]P [right arrow] 2[sup.3]S transition is associated with the strong triplet He I line at 10830 [Angstrom] [245, p. 95]. Alternatively, a 3[sup.3]P [right arrow] 2[sup.3]S transition produces the triplet HeI line at 3890 [Angstrom] [245, p. 95].

Importantly, since excited orthohelium cannot fully relax back to the ground state, it remains available to recondense with atomic hydrogen in the chromosphere. This results in its continual availability in the harvest of hydrogen. A cyclic process has been created using orthohelium ([He.sup.*]). The priming of this cycle had required but a single instance where hydrogen was transferred to CHS by He[H.sup.+], without the complementary transfer of an electron (top line in Fig. 16). ([dagger]) In this manner, much like what occurred in the case of molecular hydrogen ([section]3.4) and the metal hydrides ([section]3.5), the body of the Sun has been permitted to recapture atomic hydrogen lost to its atmosphere. It does not simply lose these atoms without any hope of recovery [59,61,62].

Within the LMH model, the prominence of the helium triplet lines can be elegantly explained. They result from the systematic excitation of helium, first delivered to condensed hydrogen structures by the helium hydride cation (He[H.sup.+]), a well-known molecule [247-254] and strong Bransted acid. The generation of triplet state excited helium can be explained in a systematic fashion and does not require unrealistic temperatures in the corona. It is not an incidental artifact produced by improbably selective excitations generated using coronal photons. Organized chemical reactions govern the behavior of helium in the Sun, not random events.

3.7 Fraunhofer Absorption #15

When examined under high spectral resolution, the visible spectrum of the Sun is punctuated by numerous absorption lines, which appear as dark streaks against a brighter background. * These lines were first observed by William Hyde Wollaston in 1802 [258]. They would eventually become known as Fraunhofer lines after the German scientist who most ably described their presence [259]. Fraunhofer lines can be produced by many different elements. They manifest the absorption of photospheric light by electrons, contained within gaseous atomic or ionic species above the photosphere, which are being promoted from a lower to a higher energy level.

In 1862, Kirchhoff was the first to argue that the Fraunhofer lines provided evidence for a condensed solar body, "In order to explain the occurrence of the dark lines in the solar spectrum, we must assume that the solar atmosphere incloses a luminous nucleus, producing a continuous spectrum, the brightness of which exceeds a certain limit. The most probable supposition which can be made respecting the Sun's constitution is, that it consists of a solid or liquid nucleus, heated to a temperature of the brightest whiteness, surrounded byan atmosphere of somewhat lower temperature." [190, p. 23].

Amongst the most prominent of the Fraunhofer lines are those associated with the absorption of photospheric light by the hydrogen atoms. The preeminent Fraunhofer lines are generated by the Balmer series. These lines are produced when an excited hydrogen electron (N=2) absorbs sufficient energy to be promoted to yet higher levels (H[alpha] N = 2 [right arrow] N = 3 656.3 nm; H[beta] N = 2 [right arrow] N = 4 486.1 nm; H[gamma] N = 2 [right arrow] N = 5 434.1 nm; H[delta] N = 2 [right arrow] N = 6 410.2nm; etc). They can be readily produced in the laboratory by placing hydrogen gas in front of a continuous light source.

In 1925, Albrecht Unsold reported that the solar Fraunhofer lines associated with hydrogen did not decrease as expected [260]. He noted intensities across the Balmer series ([H.sub.[alpha]] = 1; [H.sub.[beta]] = 0.73; [H.sub.[gamma]] = 0.91; [H.sub.[delta]] = 1) which where highly distorted compared to those expected in a hydrogen gas, as predicted using quantum mechanical considerations ([H.sub.[alpha]] = 1; [H.sub.[beta]] = 0.19; [H.sub.[gamma]] = 0.07; [H.sub.[delta]] = 0.03) [260].

Hydrogen lines were known to be extremely broad from the days of Henry Norris Russell and Donald H. Menzel, who had observed them in association with solar abundance [87] and chromospheric studies [205], respectively. Commenting on the strength of the hydrogen Balmer series, Henry Norris Russell would write, "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 ... 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 verystrongin the Sun, though the energyrequired to put an atom into condition to absorb these series is, respectively, 10.16 and 12.04 volts--higher than for anyother solar absorption lines. The obvious explanation --that hydrogen is far more abundant than the other elements--appears to be the onlyone" [87, p. 21-22].

In the photospheric spectrum, the hydrogen absorption lines are so intense that the observer can readily garner data from the Lyman (N=1 [right arrow] N=2 or higher), Balmer (N=2 [right arrow] N=3 or higher), Paschen (N=3 [right arrow] N=4 or higher), and Brackett (N=4 [right arrow] N=6 or higher) series [87,205,260-264].

The central questions are three fold: 1) Why are the hydrogen lines broad? 2) Why does hydrogen exist in excited state as reflected by the Balmer, Paschen, and Brackett lines? and 3) Why is the normal quantum mechanical distribution of the Balmer series distorted as first reported by Unsold [260]?

In the gaseous models, different layers of the solar atmosphere have to be invoked to account for the simultaneous presence of Lyman, Balmer, Paschen and Brackett line profiles in the solar spectrum [261-264]. Once again, as when addressing limb darkening (see [section]2.3.2), the models have recourse to optical depth [261-264]. These approaches fail to adequately account for the production of the excited hydrogen absorption.

As noted in [section]3.4, in the setting of the LMH model, excited hydrogen atoms can be produced through condensation reactions occurring in the solar chromosphere. These atoms could be immediately available for the absorption of photons arising from photospheric emission. Hence, condensation reactions provide an indirect mechanism to support the generation of many hydrogen Fraunhofer line. Since these lines are being produced in close proximity to condensed matter, it is reasonable to conclude that their linewidths are determined by their interaction with such materials and not from optical depth and Stark mechanisms (see [section]3.4). This may help to explain why the intensity of the Balmer lines, as first reported by Unsold [260], do not vary as expected in gases from quantum mechanical considerations. Unsold's findings [260] strongly suggest that the population of excited hydrogen atoms is being distorted by forces not known to exist within gases. Once again, this calls attention to condensed matter.

3.8 Coronal Emission #16

As was discussed in [section]2.3.7, the K-corona is the site of continuous emission which reddens slightly with altitude, but whose general appearance closely resembles the photospheric spectrum [57]. ([dagger]) This leads to the conclusion that condensed matter must be present within this region of the Sun [57]. Still, the nature of the corona is more complicated, as the same region which gives rise to condensed matter in the K-corona is also responsible for the production of numerous emission lines from highly ionized elements (e.g. FeXII-FeXXV [192]) in the E-corona [60]. *

When examined in light of the gaseous solar models, the production of highly ionized species requires temperatures in the million of degrees [192]. Temperatures as high as 30 MK have been inferred to exist in the corona [192, p. 26], even if the solar core has a value of only 16 MK [13, p. 9]. Flares have been associated with temperatures reaching [10.sup.8] K [273], and radio sampling has called for values between [10.sup.8] and [10.sup.10] K[245,p. 128].

Given the temperatures inferred in attempting to explain the presence of highly ionized atoms in the K-corona, proponents of the gaseous models deny that this region can be comprised of condensed matter. Harold Zirin summarizes the situation best, "... there is something erroneous in our basic concept of how ionization takes place" [245, p. 183].

Rather than cause a dismissal of condensed matter, such extreme temperature requirements should lead to the realization that the gaseous models are fundamentally unsound [62]. It is not reasonable to assume that the corona harbors temperatures which exceed those found in the core. Furthermore, to arrive at these extreme values, the corona must somehow be heated. The "zoo" [148, p. 278] of possible heating mechanisms is substantial [148, p. 239-251]. According to E.R. Priest, the hypothesized mechanisms are fundamentally magnetic in nature as "all the other possible sources are completely-inadequate" [273]. The problem for gaseous models can be found in the realization that their only means of producing highly ionized atoms must involve violent bombardment and the removal of electrons to infinity. These schemes demand impossible temperatures. ([dagger])

It is more reasonable to postulate that elements within the corona are being stripped of their electrons when they come into contact with condensed matter. The production of highly ionized atoms involves electron affinity, not temperature. The belief that the corona is a region characterized by extremely elevated temperatures is erroneous. The cool K-coronal spectrum is genuine. The associated photons are directly produced by the corona itself, not by the photosphere (see [section]2.3.7).

Moreover, condensed matter can have tremendous electron affinities. This is readily apparent to anyone studying lightning on Earth. Thunderhead clouds have been associated with the generation of 100 keV X-rays [274, p. 493-495], but no-one would argue that the atmosphere of the Earth sustains temperatures of [10.sup.9] K. Lightning can form "above volcanoes, in sandstorms, and nuclear explosions" [274, p. 67]. It represents the longest standing example of the power of electron affinity, as electrons are transferred from condensed matter in the clouds to the Earth's surface, or vise versa [274-276].

Metallic hydrogen should exist in the K-corona, as TypeI material has been ejected into this region (see [section]2.3.8) by activity on the photosphere [58]. Electrical conductivity in this region is thought to be very high [277, p. 174]. Thus, the production of highly ionized elements can be explained if gaseous atoms come into contact with this condensed matter. For example, iron (Fe) could interact with metallic hydrogen (MH) forming an activated complex: MH + Fe [right arrow] MH - [Fe.sup.*]. Excited Fe could then be ejected with an accompanying transfer of electrons to metallic hydrogen: MH - [Fe.sup.*] [right arrow] MH - n [bar.e] + [Fe.sup.+n*]. The emission lines observed in the corona are then produced when the excited iron relaxes back to the ground state through photon emission, [Fe.sup.+n*] [right arrow] [F.sup.e+n] + hv. Depending on the local electron affinity of the condensed metallic hydrogen, the number of electrons transferred, n, could range from single digits to ~25 [192] in the case of iron. ([double dagger])

The scheme formulated with iron can be extended to all the other elements, ([section]) resulting in the production of all coronal emission lines. The governing force in each case would be the electron affinity of metallic hydrogen which may increase with altitude. Highly ionized species are not produced through the summation of multiple electron ejecting bombardments. Rather, multiple electrons are being stripped simultaneously, in single action, by transfer to condensed matter. In this manner, the electron starved corona becomes endowed with function, the harvesting of electrons from elements in the solar atmosphere, thereby helping to maintain the neutrality of the solar body [60].

In this sense, the chromosphere and corona have complimentary action. The chromosphere harvests hydrogen atoms and protons. The corona harvests electrons. ([paragraph])

As for the transition zone (see Fig. 1.1 in [192]), it does not exist. This region was created by the gaseous models in order to permit a rapid transition in apparent temperatures between the cool chromosphere and hot corona (see [62] for a complete discussion). In the metallic hydrogen model, the apparent temperatures in both of these regions are cool, therefore a transition zone serves no purpose [62]. The changes in atomic and ionic compositions observed in the solar atmosphere can be accounted for by 1) the varying ability of molecular species to deliver hydrogen and protons to condensed hydrogen structures in the chromosphere as a function of altitude, and 2) to changes in the electron affinity of metallic hydrogen in the corona.

This scenario resolves, at long last, the apparent violation of the Second Law of Thermodynamics which existed in the gaseous model of the Sun. It is not realistic that the center of the Sun exists at 16 MK [13, p. 9], the photosphere at 6,000 K, and the corona at millions of degrees. A solution, of course, would involve the recognition that most of the energy of the photosphere is maintained in its convection currents and conduction bands [37], not in the vibrational modes responsible for its thermal spectrum and associated apparent temperature. But now, the situation is further clarified. The corona is not being heated--it is cool. No violation of the Second Law of Thermodynamics exists, even if photospheric convection and conduction are not considered.

4 Structural Lines of Evidence

The structural lines of evidence are perhaps the most physically evident to address, as they require only elementary mechanical principles to understand.

4.1 Solar Collapse #17

Should stars truly be of gaseous origin, then they are confronted with the problem of solar collapse. * Somehow, they must prevent the forces of gravity from causing the entire structure to implode upon itself.

Arthur Eddington believed that stellar collapse could be prevented by radiation pressure [9]. Photons could transfer their momentum to stellar particles and thereby support structure. These ideas depend on the existence of radiation within objects, a proposal which is counter to all laboratory understanding of heat transfer. Conduction and convection are responsible for the transfer of energy within objects [70]. It is only if one wishes to view the Sun as an assembly of separate objects that radiation can be invoked.

Eventually, the concept that the Sun was supported exclusively by radiation pressure was abandoned. Radiation pressure became primarily reserved for super-massive stars [13, p. 180-186]. Solar collapse was prevented using 'electron-gas pressure' [13, p. 132], with radiation pressure contributing little to the solution [13, p. 212].

But the idea that 'electron gas pressure' can prevent a star from collapsing is not reasonable [3,35,43,48]. The generation of gas pressure (see Fig. 17) requires the existence of true surfaces, and none can exist within a gaseous Sun. ([dagger]) When a particle travels towards the solar interior, it can simply undergo an elastic collision, propelling a stationary particle beneath it even further towards the core. Without a surface, no net force can be generated to reverse this process: the gaseous Sun is destined to collapse under the effect of its own gravity [48].

Donald Clayton, a proponent of the gaseous models, describes the situation as follows, "The microscopic source of pressure in a perfect gas is particle bombardment. The reflection (or absorption) of these particles from a real (or imagined) surface in the gas results in a transfer of momentum to that surface. By Newton's second law (F = dp/dt), that momentum transfer exerts a force on the surface. The average force per unit area is called the pressure. It is the same mechanical quantity appearing in the statement that the quantity of work performed by the infinitesimal expansion of a contained gas is dW = PdV. In thermal equilibrium in stellar interiors, the angular distribution of particle momenta is isotropic; i.e., particles are moving with equal probabilities in all directions. When reflected from a surface, those moving normal to the surface will transfer larger amounts of momentum than those that glance off at grazing angles' [14, p. 79]. The problem is that real surfaces do not exist within gaseous stars and 'imagined' surfaces are unable to be involved in a real change in momentum. 'Electron gas pressure' cannot prevent solar collapse.

Unlike the scenario faced by Eddington with respect to solar collapse, James Jeans had argued that liquid stars were immune to these complications, "And mathematical analysis shews that if the centre of a star is either liquid, or partially so, there is no danger of collapse; the liquid center provides so firm a basis for the star as to render collapse impossible" [278, p. 287]. By their very nature, liquids are essentially incompressible. Therefore, liquid stars are self-supporting and a LMH Sun faces no danger of collapse.

4.2 Density #18

Hot gases do not self-assemble * Rather, they are well-known to rapidly diffuse, filling the volume in which they are contained. As a result, hot gaseous 'objects' should be tenuous in nature, with extremely low densities. In this respect, hot gases offer little evidence that they can ever meet the requirements for building stars.

In an apparent contradiction to the densities expected in gaseous 'objects', the solar body has a substantial average density on the order of 1.4 g/[cm.sup.3] [279]. In gaseous models, the Sun is believed to have a density approaching 150 g/[cm.sup.3] in its core, but only ~[10.sup.-7] g/[cm.sup.3] at the level of the photosphere [148]. In this way, a gaseous star can be calculated with an average density of 1.4 g/[cm.sup.3]. But gaseous models would be in a much stronger position if the average density of the Sun was consistent with that in a sparse gas, i.e. ~[10.sup.-4] g/[cm.sup.3], for instance. It is also concerning that the average density of the Sun is very much coincident with that observed in the outer planets, even though these objects have much smaller total masses. ([dagger]) The giant planets are no longer believed to be fully gaseous, but rather composed of metallic hydrogen [93-95], suggestions which are contrary to the existence of a gaseous Sun.

The Sun has a density entirely consistent with condensed matter. If the solar body is assembled from metallic hydrogen [35, 39], it is reasonable to presume that it has a somewhat uniform distribution throughout its interior. ([double dagger]) This would be in keeping with the known, essentially incompressible, nature of liquids.

4.3 Radius #19

Within gaseous models, the Sun's surface cannot be real and remains the product of optical illusions [2,4,51]. ([section]) These conjectures were initially contrived by the French astronomer, Herve Faye. In 1865, Faye [280] had proposed that the Sun was gaseous [2,4] and would write, "This limit is in any case only apparent: the general milieu where the photosphere is incessantly forming surpasses without doubt, more or less, the highest crests or summits of the incandescent clouds, but we do not know the effective limit; the only thing that one is permitted to affirm, is that these invisible layers, to which the name atmosphere does not seem to me applicable, would not be able to attain a height of 3', the excess of the perihelion distance of the great comet of 1843 on the radius of the photosphere" [280]. With those words, the Sun lost its true surface. Everything was only 'apparent' (see [section]1). Real dimensions, like diameter or radius, no longer held any validity. Nonetheless, Father Secchi considered the dimensions of the Sun to be a question of significant observational importance, despite problems related to their accurate measure [1, p. 200-202, V.I].

Today, the radius of the Sun (~696,342 [+ or-] 65 km) continues to be measured [51] and with tremendous accuracy--errors on the order of one part in 10,000 or even 2 parts in 100,000 (see [281] for a table). Such accurate measurements of spatial dimensions typify condensed matter and can never characterize a gaseous object. ([paragraph]) They serve as powerful evidence that the Sun cannot be a gas, but must be composed of condensed matter.

The situation relative to solar dimensions is further complicated by the realization that the solar diameter may well be variable [282]. Investigations along these lines are only quietly pursued [283], as the gas models are unable to easily address brief fluctuations in solar dimensions. The stability of gaseous stars depends on hydrostatic equilibrium and relies on a perfect mechanical and thermal balance [13, p. 6-67]. Failing to maintain equilibrium, gaseous stars would cease to exist.

Conversely, fluctuating solar dimensions can be readily addressed by a liquid metallic hydrogen Sun, since this entity enables localized liquid/gas (or solid/gas) transitions in its interior (see [48,51,52] and [section]5.1).

4.4 Oblateness #20

James Jeans regarded the high prevalence of binaries as one of the strongest lines of evidence that the stars were liquids [27, 28]. ([parallel]) Indeed, it could be stated that most of his thesis rested upon this observation. As a spinning star became oblate, it eventually split into two distinct parts [27, 28]. Oblateness can be considered as a sign of internal cohesive forces within an object and these are absent within a gaseous star. As a result, any oblateness constitutes a solid line of evidence that a rotating mass is comprised of condensed matter.

The physics of rotating fluid masses has occupied some of the greatest minds in science, including Newton, Maclaurin, Jacobi, Meyer, Liouville, Dirichlet, Dedekind, Riemann, Poincare, Cartan, Roche, and Darwin [3]. The problem also captivated Chandrashekhar (Nobel Prize, Physics, 1983) for nine years of his life [284].

Modern studies placed the oblateness of the Sun at 8.77 x [10.sup.-6] [287]. Though the Sun appears almost perfectly round, it is actually oblate [50]. * To explain this behavior, astrophysicists invoked that the Sun possessed a constant solar density as a function of radial position [287]. This proposal is in direct conflict with the gaseous solar models [13,14] which conclude that most of the solar mass remains within the central core. An essentially constant internal density is precisely what would be required within the context of a liquid metallic Sun [35, 39].

At present, helioseismic measurements (see [section]6) indicate that the degree of solar oblateness may be slightly smaller [288, 289], but the general feature remains. The degree of solar oblateness may well vary with the solar cycle [290]. As was the case for variations in solar radius ([section]4.3), these changes pose difficulties for the gaseous models. That the Sun is slightly oblate provides excellent evidence for internal cohesive forces, as seen in condensed matter.
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Title Annotation:pp. 90-116
Author:Robitaille, Pierre-Marie
Publication:Progress in Physics
Date:Oct 1, 2013
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