Liquid Metallic Hydrogen: Building Block of a Liquid Sun

Abstract

The establishment by Andrews of critical temperatures (T. Andrews, Phil.
Trans. 1869, v. 159, 575-590) soon became one of the great pillars in
support of the gaseous models of the Sun. Gases above these temperatures
simply could not be liquefied. Given that interior of the Sun was
already hypothesized in the 19th century to be at temperatures well
exceeding those achievable on Earth in ordinary furnaces, it became
inconceivable to think of the solar interior as anything but gaseous.
Hence, the models advanced by Secchi, Faye, Stoney, Lane, and Young,
could easily gain acceptance. However, modern science is beginning to
demonstrate that hydrogen (which under ordinary conditions has a
critical point at ˜33 K) can become pressure ionized such that its
electrons enter metallic conductions bands, given sufficiently elevated
pressures, as the band gap is reduced from 15 eV to ˜0.3 eV.
Liquid metallic hydrogen will possess a new critical temperature well
above that of ordinary hydrogen. Already, experiments suggests that it
can exist at temperatures of thousands of Kelvin and millions of
atmospheres (S. T. Weir et al., Phys. Rev. Let. 1996, 76, 1860). The
formation of liquid metallic hydrogen brings with it a new candidate for
the interior of the Sun and the stars. Its existence shatters the great
pillar of the gaseous models of the Sun which the critical point of
ordinary gases had erected.

Full text

Volume 3 PROGRESS IN PHYSICS July, 2011
Liquid Metallic Hydrogen: A Building Block for the Liquid Sun
Pierre-Marie Robitaille
Department of Radiology, The Ohio State University, 395 W. 12th Ave, Columbus, Ohio 43210, USA
E-mail: robitaille.1@osu.edu
Liquid metallic hydrogen provides a compelling material for constructing a condensed
matter model of the Sun and the photosphere. Like diamond, metallic hydrogen might
have the potential to be a metastable substance requiring high pressures for forma-
tion. Once created, it would remain stable even at lower pressures. The metallic
form of hydrogen was initially conceived in 1935 by Eugene Wigner and Hillard B.
Huntington who indirectly anticipated its elevated critical temperature for liquefaction
(Wigner E. and Huntington H. B. On the possibility of a metallic modification of hydro-
gen. J. Chem. Phys., 1935, v.3, 764–770). At that time, solid metallic hydrogen was
hypothesized to exist as a body centered cubic, although a more energetically accessible
layered graphite-like lattice was also envisioned. Relative to solar emission, this struc-
tural resemblance between graphite and layered metallic hydrogen should not be easily
dismissed. In the laboratory, metallic hydrogen remains an elusive material. However,
given the extensive observational evidence for a condensed Sun composed primarily of
hydrogen, it is appropriate to consider metallic hydrogen as a solar building block. It
is anticipated that solar liquid metallic hydrogen should possess at least some layered
order. Since layered liquid metallic hydrogen would be essentially incompressible, its
invocation as a solar constituent brings into question much of current stellar physics.
The central proof of a liquid state remains the thermal spectrum of the Sun itself. Its
proper understanding brings together all the great forces which shaped modern physics.
Although other proofs exist for a liquid photosphere, our focus remains solidly on the
generation of this light.
1 Introduction
Decidedly, the greatest single impetus for a fully gaseous Sun
[1, 2] was the elucidation of critical temperatures by Thomas
Andrews in 1869 [3, 4]. Since ordinary gases could not be
liquefied at the temperatures associated with the Sun, it was
inconceivable that the photosphere was made from condensed
matter: “It is, however, scarcely possible to regard as existing
in the interior of the Sun, matter in either the solid or in the
liquid condition. . . Since, however, it became apparent from
the classic research of Dr. Andrews in 1869, that there exists
for every element a critical temperature, above which it is
impossible for it under any conditions of pressure to assume
the liquid state, it has generally been regarded that a liquid
interior to the Sun is next to an impossibility” [5, p. 36-37].
As a result of such logic, the idea that the Sun was gaseous
flourished. Though Father Angello Secchi and Herv´
e Faye
had already proposed a gaseous solar model [1], Andrews’
discovery served to significantly validate their conjectures.
Given the logic of the period, the body and photosphere of
the Sun could not be liquid [1].
At the same time, scientists of the late 19th and early 20th
century remained puzzled with respect to the solar spectrum
[1, 2]. Because graphite was the prime source of blackbody
radiation on Earth [6], G. Johnstone Stoney placed liquid or
solid carbon on the surface of the Sun in 1867 [7]. It would
remain there for the next 50 years [2]. Armed with graphite, it
became simple to explain why the solar photosphere emitted
a thermal spectrum resembling a blackbody. Over time, the
enthusiasm for carbon began to wane. Charles Hastings ar-
gued that condensed carbon could not be present on the Sun.
The temperatures involved did not permit such a hypothesis.
Hastings required an alternative: “At any rate, we are sure
that the substance in question, so far as we know it, has prop-
erties similar to those of the carbon group” [8]. Hastings did
not elaborate on these properties, but it was clear that he was
searching for a substance with unbelievable refractory charac-
teristics, something with the structure of graphite. A material
capable of producing the thermal spectrum of the Sun had to
exist in the condensed state at tremendous temperatures.
Eventually, theoretical astrophysics dispensed of the need
for condensed matter. In so doing, the stellar opacity problem
was created [9]. It was Schuster’s Radiation through a Foggy
Atmosphere [10] which began to cast condensed matter out
of the photosphere [2]. Schuster postulated that all gases, if
sufficiently thick, emitted as blackbodies: “The radiation in
this case becomes equal to that of a completely black sur-
face, which agrees with the well-known law that absorption
irrespective of scattering tends to make the radiation of all
bodies equal to that of a black body when the thickness is in-
creased” [10, p. 6]. Schuster’s conclusion was not supported
by the gaseous nebula. These celestial objects had long been
known to emit line spectra [11, p. 87] and, though they were
assuredly thick, blackbody lineshapes were not produced. As
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July, 2011 PROGRESS IN PHYSICS Volume 3
previously outlined by the author [2], Schuster’s error con-
sisted in resting his derivation upon the premise that Kirch-
hoff’s law of thermal emission was valid [12].
Gustav Kirchhoffinsisted that, given thermal equilibrium
with an enclosure, a blackbody spectrum could be produced
by any object [12]. Yet, if Kirchhoff’s law was correct, his
contemporaries should not have refused to adopt a fully gas-
eous Sun throughout the 19th century [1, 2]. They would
not have insisted on the need for graphite. If graphite was
viewed as less than optimal, they would not have invoked
pressure broadening as a means to produce the solar spec-
trum [1]. Kirchhoff’s formulation, after all, was independent
of pressure. It would become evident that something was
not quite right with Kirchhoff’s deductions. The author has
outline why Kirchhoff’s law of thermal emission was erro-
neous [13, 14]. On the simplest level, it constituted a viola-
tion of the first law of thermodynamics. In addition, as was
outlined relative to the stellar opacity problem, gases remain
unable to emit a blackbody spectrum [9]. This was the surest
evidence that Kirchhoff’s law was invalid.
As a result, if gases could not produce the solar spectrum,
astrophysics should have returned to the condensed state. At
the beginning of the 20th century, Jeans promoted liquid stars
[15] based on stability arguments, only to discard them at the
end of his life [2]. If Jeans abandoned liquids, it was likely
due to his lack of a proper building block [2]. He conceived of
stars as composed of heavy elements such as uranium and ra-
dium [2]. When the Sun was shown to contain large amounts
of hydrogen [16–18], Jeans was left without a proper struc-
tural material. He did not anticipate that metallic hydrogen
could exist [19] and that the substance provided the perfect
candidate for a fully condensed Sun. In proposing the exis-
tence of metallic hydrogen [19], condensed matter physics
would unknowingly provide Jeans with a suitable material
for liquid stars [2]. Andrews’ critical temperature in ordinary
gases became inconsequential [20]. More intriguing was the
observation that the layered lattice of condensed metallic hy-
drogen possessed tremendous similarity with graphite [19].
Could the layered form of metallic hydrogen finally replace
Stoney’s solid carbon on the Sun [2,7]? Was this the strange
material sought by Hastings for generating the solar spec-
trum [2, 8]?
2 Metallic hydrogen
Eugene Wigner (1963 Nobel Prize in Physics [21]) and Hill-
ard B. Huntington [22] were the first to advance the exis-
tence of metallic hydrogen in 1935 [19]. They opened their
classic paper by stating that “Any lattice in which the hydro-
gen atoms would be translationally identical (Bravais lattice)
would have metallic properties” [19]. Their work focused
on the body centered lattice. Recognizing the difficulties in
obtaining the pressures required to form this lattice, they pro-
posed that the layered form of metallic hydrogen would be
more accessible. According to Wigner and Huntington “it
Fig. 1: Schematic representation of the layered lattice of graphite.
Wigner and Huntington [19] would propose that most energetically
favorable form of metallic hydrogen would assume this crystal struc-
ture.
was J. D. Bernal who first put forward the view that all sub-
stances go over under very high pressure into metallic or
valence lattices” [19]. For the body centered cubic form of
metallic hydrogen, they predicted a density of 0.8 g/cm3ver-
sus 0.087 g/cm3for molecular hydrogen in solid form [19].
This was nearly a tenfold increase in density. Wigner and
Huntington concluded their paper as follows: “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 sim-
ple lattice, like the face-centered one, have a much lower en-
ergy, — 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-
like19. . . ” [19]. The footnote in the text began: “Diamond is a
valence lattice, but graphite is a layer lattice... ” [19]. Thus,
in the first paper on metallic hydrogen, the layered structure
of graphite (see Figure 1), so critical to producing the black-
body spectrum on Earth, was promoted. A solar spectrum
explained through dense hydrogen was certain to eventually
rise to prominence.
2.1 Properties of metallic hydrogen
Initially, Wigner and Huntington estimated that the metallic
state of hydrogen, in its most energetically accessible form
(layered lattice), could be achieved at pressures in the 250,000
atm range (∼25 GPa) [19]. This value was much too opti-
mistic.
The most astounding property of metallic hydrogen
would be its tremendous critical temperature. It was well in
excess of anything Thomas Andrews and his contemporaries
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Volume 3 PROGRESS IN PHYSICS July, 2011
could have imagined in 1869 [3,4]. While the complete phase
diagram for hydrogen may never be fully known, several at-
tempts have been made to outline its general characteristics,
both in condensed matter physics [23–25] and as related to
astrophysics [26–28]. Franck [29] listed many of the early
contributions to the hydrogen phase diagram, including the
work by Alexey A. Abrikosov [30]. Abrikosov eventually
won the 2003 Nobel prize in physics while at Argonne Na-
tional Laboratories.
The critical point of metallic hydrogen has been constant-
ly revised towards ever higher values. Ebeling and Richert
[23] provided an overview of these estimates through the 20th
century. In 1980, Franck [29] arrived at a critical temperature
for metallic hydrogen in the 6,000–9,000 K range. In 1983,
Ronik and Kundt [26] gave a critical point at a unprecedented
19,100 K and 24 GPa. A slightly more conservative 16,500 K
and 22.5 GPa was soon published [23]. Beyond critical tem-
peratures, the transition pressures in moving from molecular
to metallic hydrogen have constantly been revised upwards.
At present, the values have moved to the 400–600 GPa range:
“Although quantum chemistry calculations have been devel-
oped to a high degree of sophistication, and in general, there
is a close correlation between theory and experiment, this is
not the case for hydrogen. Phase transition calculations that
seek the structure with the lowest lattice energy have difficulty
handling the zero-point energy contributions to the total en-
ergy and zero-point energy is very important for hydrogen.
As a result, the predicted critical transition pressures have
an enormous variation, from as low as 0.25 Mbar to over
20 Mbar, while recent predictions are in the 400 to 600 GPa
range” [25].
2.2 The theory of metallic hydrogen
Several authors have reviewed the metallic hydrogen litera-
ture [31, 32]. In a landmark 1968 publication, Neil Ashcroft
hypothesized that metallic hydrogen might be a high tempera-
ture superconductor [33]. Ashcroft consequently became one
of the most important theoretical physicists with respect to
understanding dense hydrogen in its molecular and metallic
forms [24,33–50]. Ashcroft’s prediction relative to high tem-
perature superconductivity was rapidly echoed by Schneider
and Stoll [51]. Depending on lattice configurations, they cal-
culated that metallic hydrogen would become superconduc-
tive with operational temperatures ranging from 67 to 200
K [51]. Barbee et al. confirmed these calculations, obtain-
ing a temperature of 230±85 K [52]. Metallic hydrogen had
the potential to be the highest temperature superconductor
known. The point was emphasized in 2001, when Maksi-
mov and Savrasov used ab initio calculations to conclude that
metallic hydrogen at high pressure might have a supercon-
ducting critical temperature of 600 K [53].
Ashcroft also examined the ground state of metallic hy-
drogen at zero temperature under conditions of changing spa-
tial densities achieved by varying pressures from ∼1 Mbar
to ∼75 Mbar [34, 35]. At the highest densities (rs=0.8, 1.2,
1.36, and 1.488), he discovered that crystalline phases were
preferred [35]. However, at the lowest lattice density studied
(rs=1.64), he found that metallic hydrogen was metastable
between the solid and liquid forms [34, 35]. He postulated
that the existence of a liquid ground state could not be ex-
cluded, but that it was not established [34]. Ashcroft contin-
ued this line of investigation in 1981 and 1982 [36, 37]. He
gathered that liquid metallic hydrogen might become essen-
tially devoid of structure and that the protons and electrons
would simply act as interpenetrating fluids [36]. The Cor-
nell scientist had theoretically constructed a two-component
Fermi-liquid from protons and electrons [36].
Still, there was no direct evidence that metallic hydrogen
at absolute zero would ever completely lose all structural in-
tegrity. As a theoretical physicist, Ashcroft could not really
establish if metallic hydrogen at absolute zero 1) acted as a
two component Fermi liquid, 2) behaved much like the un-
usual theoretical one-component plasma [54, 55], or 3) re-
tained the essential characteristic of a Bravais lattice, an or-
dered proton field with fully degenerate electrons. Nonethe-
less, in his 1981 communication, Ashcroft was careful to
mention that his conclusions were “assuming that it [the hy-
pothetical state of liquid metallic hydrogen] is normal” [36].
He highlighted: “that in assuming the existence of a liquid
phase, the very interesting question still remains of whether
or not it exhibits some form of magnetic, momental, or even
spatial (e.g. liquid crystal) ordering.. . We do not attempt at
this time to resolve the important questions of the existence
or properties of possible “ordered” liquid metallic phases of
hydrogen” [36]. In the ninth footnote to his 1982 treatment,
Ashcroft repeated the warning: “The possibility that liquid
metallic hydrogen exhibits some kind of momental (e.g. su-
perconductive), magnetic, or even spatial (e.g. liquid crystal)
ordering has not been ruled out” [37]. Only experimental
evidence could answer such questions, but none was avail-
able, as liquid metallic hydrogen remained an elusive mate-
rial [25, 31, 32, 56].
Astrophysics was quick to infer that Ashcroft had chosen
a path eventually leading to some form of degeneracy of mat-
ter [57]. In fact, careful reading of these articles suggested
otherwise. Ashcroft’s liquid was a reflection of what theoret-
ical condensed matter physicists were able to calculate at the
time. A liquid with spatial order, thoughtfully preserved in
the text [36] and in the footnotes [37] of his papers, was well
beyond the reach of computational approaches in the absence
of laboratory guidance.
Soon after Ashcroft published his groundbreaking papers
[34–37], MacDonald and Burgess also wondered about the
absence of crystallization in metallic hydrogen [58]. They
insisted that, since electronic screening was important in the
solid state but negligible in the liquid state, metallic hydrogen
would remain fluid at all pressures. Solid metallic hydrogen
could not be stable at any pressure [58]. Ashcroft answered
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July, 2011 PROGRESS IN PHYSICS Volume 3
that “The prospect of a relatively low-density quantum melted
phase of hydrogen, over a wide range of densities, is a fasci-
nating one. However, we would like to bring up the following
difficulties with concluding too definitely the existence of this
phase for all densities” [38]. Ashcroft then argued that such
a state would exist only over limited densities whose range
would be difficult to predict, as the solid and liquid phases
are both close in energy and widely separated in configura-
tion [38].
When Ashcroft returned to the ground state of metallic
hydrogen in 1984, he assumed that the protons occupied the
sites of a rigid Bravais lattice [39]. Using the Wigner-Seitz
approximation which he regarded as physically appealing,
Ashcroft calculated a lower bounds on the density of metallic
hydrogen at its transition pressure. This density would be on
the order 0.60 g/cm3corresponding to rs=1.65 [39]. Metal-
lic hydrogen, if it was stable at all, would have to possess a
greater density.
Given the nature of metallic hydrogen, both as a theoreti-
cal problem and as a prized material, significant Russian and
Ukranian contributions were made in this area [32,53,59–65],
beginning with Alexey Abrikosov [30]. In an important com-
munication, Abrikosov was one of the first to examine the
destruction of an atomic lattice under high compression [59].
He noted: “that at sufficiently small volumes the positive zero-
point oscillation energy exceeds the negative Coulomb en-
ergy, and this leads to a destruction of the crystal lattice”
[59]. Abrikosov remarked that “the inter-atomic distances
at the transition point are greater than the nuclear dimen-
sions only for the lightest elements, hydrogen and helium.
Thus, such a transition can take place only in these two el-
ements” [59]. It seemed as though elevated pressures might
lead to the destruction of the crystal lattice, but Abrikosov
never considered that fusion might act to relieve the stresses
of compression. Beyond a certain point, perhaps crystals be-
came incompressible. It was unclear if the small volumes
required to give prominence to the zero-point oscillations in
metallic hydrogen might ever be reached.
After Abrikosov’s classic paper was released [59], Brov-
man et al. were the first to hypothesize that metallic hydrogen
might be a metastable substance [61]. Kagan’s group [32, 61]
advanced that metallic hydrogen synthesized at elevated pres-
sures might be completely stable even at zero pressure. This
behavior would be much like diamond, the metastable form
of carbon. Brovman et al. [61] calculated that the most sta-
ble lattice of metallic hydrogen would be hexagonal with a
triangular string structure [60] . The conjecture would spawn
the possibility of industrial and propellant roles for metallic
hydrogen [25]. Many years later, Kaim et al. [64] would once
again address the metastable nature of metallic hydrogen and
essentially confirm Kagan’s findings [61].
However, the most interesting facet of Kagan’s work [61]
was the observation that metallic hydrogen displayed liquid
tendencies: “there occurs in metallic hydrogen a unique ten-
dency towards the formation of a family of structures with
very close energies.. . In a certain sense the picture recalls
the situation with graphite, but is apparently even more
strongly pronounced. . . the formation of the planar family is
evidence of the unique liquid-like tendencies that take place
in metallic hydrogen under pressure” [61]. They continued:
“As a result it is impossible to exclude beforehand, in prin-
ciple, the possibility that the transition from the molecular
phase to the metallic phase is a transition into the state of a
liquid metal. (It may turn out that the situation will be dif-
ferent in hydrogen than in deuterium.) The phase diagram
could have in this case a very special character. For exam-
ple, with increasing pressure, the liquid phase could go over
into the crystalline phase, but at extremely high densities a
liquid would again be produced, but now as a result of the
predominant role of the energy of the zero point oscillations
(see the paper by Abrikosov7). The metastable state could re-
main crystalline in this case” [61]. The footnote referred to
the work just discussed above by Abrikosov [59]. Relative to
the liquid metallic hydrogen model of the Sun, the work by
Brovman et al. [61] would remain landmark.
Barbee et al. [52, 66] continued the quest to calculate the
most stable structure for hydrogen in solid form. The work
supported Wigner and Huntington’s [19] contention that a
layered Bravais lattice form of metallic hydrogen was the
most stable in the 380±50 to 860±100 GPa range [66]. Above
such values, the body centered cubic was preferred. Below
380±50 GPa the molecular non-metallic hexagonal-close-
packed arrangement was most stable. The authors highlight
some of the difficulties faced by theoretical condensed matter
physics: “A metal-insulator phase is expected near 200 GPa,
in the m-hcp phase, but this transition pressure is harder to
predict because of the shortcomings of local-density theory
and the fact that structures with similar enthalpies (e.g. dia-
mond and graphite) may have completely different band
structures” [66].
At about the same time, an interest developed in theo-
retical physics for examining the mono-, di-, and trilayered
forms of atomic hydrogen [67–69]. While it could be argued
that such structures were not physically realistic, their study
generated additional insight into metallic hydrogen. Signif-
icantly, they demonstrated that very small changes in lattice
parameters could alter the conductive behavior substantially,
creating insulators from metals.
For his part, Neil Ashcroft maintained his interest in the
structure of hydrogen. In 1993, he once again examined the
metal-insulator transition in this element [40]. At this time,
Ashcroft moved increasingly towards the idea that dense hy-
drogen might lack local structure at the lower densities. It
seemed as if the stability of crystal forms was becoming ques-
tionable for him, even at the higher densities: “At sufficiently
high densities (rs61.5), the predicted states of H (eq. 1) cer-
tainly include monatomic crystalline arrangements [6], at
least where the dynamics of the protons can be ignored” [40].
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Volume 3 PROGRESS IN PHYSICS July, 2011
Though recognizing the presence of crystalline forms, he em-
phasized the dynamics of the protons. Observing that the
proton pairing in molecular hydrogen was robust, Ashcroft
eventually proposed that molecular metallic hydrogen might
be energetically preferred [42]. This was a material very dif-
ferent than first proposed by Wigner and Huntington [19]. At
low temperatures and at pressures less than 110 GPa, Ashcroft
argued that molecular hydrogen existed as a rotational crystal
[40,42]. At low densities (1.5<rs<2), he envisioned that hy-
drogen might become a low temperature quantum fluid [45].
Ashcroft moved further towards the idea that, at the
proper density, liquid hydrogen was a superfluid [47,48]. In
doing so, he revisited the ideas elucidated when first deal-
ing with two component Fermi liquids [36, 37] and expanded
on his work with Moulopoulos [41]. Ashcroft appropriately
highlighted that experiments up to 300 GPa proved that mol-
ecular H-H stretching modes continued to exist at these high
pressures [47]. He insisted that both proton-proton and
electron-electron pairing could become the dominant inter-
action, given the proper conditions [41]. The concept that
liquid metallic hydrogen was a two gap superconductor was
also promoted by Babaev [70]. In such a superfluid, both pro-
tons and electrons could flow in the same direction, providing
mass transfer without charge transfer. Alternatively, the sys-
tem could result in a superconducting mode wherein proton
and electrons flowed in opposite direction, resulting in the
flow of both mass and charge [48]. Ashcroft then emphasized
that “the neutral superfluid mode does not couple to an exter-
nal magnetic field, while the charged superconducting mode
does” [48]. The work did not address metallic hydrogen in its
densest form. Ashcroft mentions that: “Above any supercon-
ducting transition temperature (and above any Bose conden-
sation temperature) liquid metallic hydrogen and deuterium
should begin to adopt properties similar to those of conven-
tional liquid metals, at least in the structural characteristics
important to electron scattering” [47].
Ashcroft’s hypothesis that metallic hydrogen might ex-
ist as a quantum fluid immediately gained theoretical sup-
port [71]. Given increasing compression, Bonev et al. [71]
calculated that solid molecular hydrogen [72] would be trans-
formed into a quantum fluid state. Additional pressure would
then lead to the monatomic crystal [19, 71]. With increasing
pressure, it could be computed that hydrogen might undergo a
transition from a liquid-molecular state into a non-molecular
liquid [71]. This would become known as the liquid-liquid
transition [71]. By extending the work of Brovman et al.
[61], it was possible to visualize that hydrogen had a zero-
temperature structured liquid ground state. With enough pres-
sure, hydrogen could then move from the two component
Fermi liquid [36, 37, 41, 46–48, 70], to the crystalline solid
[19], and finally into a zero-temperature structured liquid
state [61]. Alternatively, metallic hydrogen might move from
a two component Fermi system directly either into a struc-
tured liquid metal [61] or into the solid classical form of
metallic hydrogen [19]. A wide array of theoretical possibili-
ties now existed for the state of hydrogen under dense condi-
tions.
While the theory of liquid metals [73] has remained a fas-
cinating branch of condensed matter physics, hydrogen liquid
metals, though they appear simple on the surface, continued
to offer unequalled challenges. With only sparse experimental
data (see Section 2.4), theoretical condensed matter physics
had little guidance from the laboratory. Even so, progress was
being made, if only in the realization that metallic hydrogen
was a material filled with mystery and promise. Modern con-
densed matter theory persisted in providing exciting results,
often from the most prestigious groups [74–81].
Relative to solar physics, it was clear that the superfluid
form of metallic hydrogen [36,37, 41,46–48, 70], devoid of all
structure, could never be found on the surface of the Sun. The
material required a very specific critical density along with
low temperatures not found on the solar surface. Superfluid
metallic hydrogen resembled nothing of the layered struc-
ture [19, 61] which mimicked graphite and was most likely
to generate the solar spectrum. Superfluid metallic hydro-
gen [36, 37, 41, 46–48, 70] might never be found anywhere.
Fillinov et al. [74] studied dense hydrogen states at
temperatures ranging from 10,000 to 100,000 K examining
plasma phase transitions. Interestingly, at 10,000 K, they no-
ticed droplet formation at certain densities (1023 cm−3). But
at the highest densities studied (1026 cm−3), they observed
an ordering of protons into a Wigner crystal. These were
tremendous densities on the order of ∼150 g/cm3. Militzer
and Graham extended theoretical calculations to the petapas-
cal range, a full eight orders of magnitude beyond the pres-
sures of the molecular phase [76]. Such computations were
appropriate only for the interior of astrophysical objects. Mil-
itzer and Graham [76] considered astounding hydrogen den-
sities (2100 g/cm3), but, in contrast to Abrikosov classic pa-
per [59], the lattice was not destroyed and the calculations
open serious questions as to the nature of the solid state.
Remaining in the realm of physically attainable pressures,
Attaccalite and Sorella [77] demonstrated that the molecular
liquid phase of hydrogen should be stable at pressures on the
order of 300 GPa at ∼400 K. The melting curves for hydro-
gen and its phase boundaries have likewise been addressed
[78, 79] revealing that theoretical approaches have remain-
ed difficult and open to new discoveries. Miguel Morales,
while working with David Ceperley and Carlo Pierle-
oni [80], recently addressed the problem of metallic hydrogen
by considering a range of temperatures and densities
(2,000 6T610,000 K; 0.76ρ62.4 g/cm−3). Such condi-
tions were appropriate for liquid metallic hydrogen devoid
of structure, much like the one-component plasma [54, 55].
At elevated temperatures and densities, the system was ob-
served to be a fully metallic liquid plasma [80]. However, a
combination of lower densities and temperatures resulted in
formation of an insulator [80]. Ceperley’s group also con-
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July, 2011 PROGRESS IN PHYSICS Volume 3
sidered electrical conductivity in high pressure liquid metal-
lic hydrogen [81]. The work was noteworthy, as it tried to
examine the liquid-semiconductor to liquid metal transition
first reported experimentally by Weir et al. [82, 83]. Using
either 32 or 54 atom cells, they calculated the transition den-
sity to be near rs∼1.65, a value very close to the experimen-
tally determined number (rs=1.62) [82, 83]. These calcu-
lations assumed that the liquid was devoid of any structure.
In addition, David Ceperley examined hydrogen at ultra high
pressures, P>20 TPa [84], a value considerably lower than
that of Militzer and Graham [76]. Furthermore, the Urbana-
Champaign scientist studied the phase diagram for hydrogen
in the ground state [85]. However, the theoretical procedure
utilized was best suited to tritium and deuterium, as infinitely
massive protons were hypothesized to be present. This work
presented an excellent literature review and a remarkable ar-
ray of potentially significant new structures for the ground
state of hydrogen as a function of increasing pressure up to
5 TPa [85].
2.3 Metallic hydrogen in astrophysics
Soon after Wigner and Huntington [19] published their clas-
sic paper, liquid metallic hydrogen entered the realm of astro-
physics. Its introduction as a constituent of the giant planets
and the white dwarfs far preceded any experimental confir-
mation. Liquid metallic hydrogen would eventually occupy a
peripheral position in astronomy, well removed from the Sun
and most stars of the main sequence.
In 1946, Kronig et al. [86] proposed that metallic hydro-
gen existed at the center of the Earth. Their work was mo-
tivated by a recent report postulating that the Earth’s center
was composed of residual solar matter containing up to 30%
hydrogen. Kronig et al. [86] calculated a density for metal-
lic hydrogen of 0.8 g/cm3. The result was apparently inde-
pendent of Wigner and Huntington [19] as they seemed un-
aware of this previous communication. Then in 1950, W.H.
Ramsey extended the study of metallic hydrogen to the plan-
ets and the white dwarfs [87]. According to Ramsey, at the
International Astronomical Union meeting in Paris of 1935,
H. N.Russell [88] had pointed out: “that both the planets and
the white dwarfs are cold in the sense that the density at any
interval point is determined by the pressure at that point. In
other words, the influence of temperature is so small that it
can be neglected to a good approximation. Thus, in the ac-
cepted theory of the white dwarfs it is assumed that the elec-
trons constitute a degenerate Fermi gas at absolute zero tem-
perature” [87]. The minutes of the meeting highlight how
Russell believed that the maximum radius of a cold body was
equal to one tenth of the solar radius, or about the diameter of
Jupiter [88, p. 260]. It was a crucial statement which linked
studies of the giant planets with those of the white dwarfs. At
the pressures inside white dwarfs and giant planets, all solids
were viewed as metallic [87]. Hydrogen was no exception. In
the end, Ramsey deduced that metallic hydrogen could not be
produced inside a small planet like the Earth [87]. Hence, it
was primarily because of this work [87] that the quest for liq-
uid metallic hydrogen would be extended simultaneously to
the celestial objects with features of mass and density lying
to either side of the Sun. In these objects, the study of liquid
metallic hydrogen [26–28, 89, 90] progressed quickly to the
fully degenerate liquid state (i.e. — states where both pro-
tons and electrons were unrestricted by lattice confinements).
Astrophysical bodies are not pure laboratory samples.
They are an assembly of mixtures and alloys. As such, once
scientists gained interest into the composition of the plan-
ets [91–95] and the white dwarfs (see [96] for a short review
relative to 22Ne), hydrogen/helium mixtures [97,98] and their
alloys [49, 50, 99] were certain to attract attention. Along
with Ashcroft, Eva Zurek and her coworkers [50] discovered
that lithium had the capability of greatly stabilizing the met-
allization of hydrogen. Even the phase diagram for carbon
under extreme conditions grew in importance, as potentially
relevant to understanding Neptune, Uranus, and the white
dwarf [100, 101]. A vast number of publications flourished,
but they shared one common factor: the paucity of laboratory
data. Nellis et al. extended results from the laboratory to in-
terior of Jupiter [94, 95], well before his findings [82] were
independently confirmed. Nellis’ work on the production of
liquid metallic hydrogen (see Section 2.4) at 140 GPa and
3,000 K was supported by conductivity measurements [82],
although the merits of these measurements were to remain
in doubt. In any case, astrophysics continued to insist that
the large planets and white dwarfs were constituted of liquid
metallic hydrogen devoid of structure and existing in fully de-
generate states. At pressure of ∼500 GPa (5 Mbar), William
Nellis maintained that materials were either semiconductors
or fully degenerate metals [102]. Experimental confirmation
of a fully degenerate state for liquid metallic hydrogen at such
pressures was unproven. In the laboratory, all forms of metal-
lic hydrogen remained ethereal with theoretical predictions
far surpassing experimental reality.
2.4 Laboratory quests for metallic hydrogen
Throughout the 20th century, the study of extraordinary states
of matter has represented one of the most fascinating aspects
of physics [102, 103]. The generation of extremes in tem-
peratures, pressures, and densities has always involved com-
plex and sophisticated experimental resources, often attain-
able only through national or multinational initiatives [103].
Nonetheless, with regards to metallic hydrogen [102], many
efforts have been conducted in university level laboratories.
Frederic Golden has provided an excellent review of the
search for metallic hydrogen which Ho-Kwang Mao dubbed
the “Holy Grail” of condensed matter physics [104]. Golden
touches on the early Russian and American attempts to syn-
thesize the material, along with a general description of meth-
ods [104]. Given the prize [56], experimental progress has
been limited.
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Volume 3 PROGRESS IN PHYSICS July, 2011
In June 1989, Ho-Kwang Mao and Russell Hemley, from
the Geophysical Laboratory of the Carnegie Institution, re-
ported evidence of metallization for hydrogen at 77 K and
250 GPa in the journal Science [105]. The key finding was
the near opaqueness of the sample at the highest pressures.
Isaac Silvera, working at the Lyman Laboratory of Physics
at Harvard, was studying the metallization problem in paral-
lel with Hemley [106–111]. He rapidly contested the validity
of Hemley’s claims and submitted a letter to Science [106]
to which Mao and Hemley responded [107]. Silvera argued
that visual darkening provided insufficient evidence for met-
allization and that further tests were needed [106]. Mao and
Hemley defended their result, but in the end, conceded that
“The observations and spectroscopic measurements clearly
indicate that significant changes in solid hydrogen occur with
increasing pressure, but further work is needed to charac-
terize in detail its optical, electrical, and structural proper-
ties under these conditions” [107]. Silvera soon reported that
there was no evidence of metallization up to 230 GPa from 77
to 295 K [110]. Metallic hydrogen had slipped away, but Ho-
Kwang Mao, Russell Hemley, and Isaac Silvera would come
to rank amongst the experimental leaders in the struggle to
synthesize the material.
A few years later, Weir, Mitchell, and Nellis reported
anew that metallic hydrogen had been produced [82]. Us-
ing shock compressed experiments [102, p. 1510–1514], the
metallization of fluid molecular hydrogen was thought to
have been achieved at 140 GPa and 3,000 K [82]. The com-
munication was supported through conductivity measure-
ments [82] a vital link in establishing metallization. The re-
sults were once again contested [112], though Nellis and Weir
maintained their position [113]. In arguing against metal-
lization, Besson brought in data with deuterium suggesting
that its samples might represent highly degenerate material,
something very different from molecular metallization in hy-
drogen [112]. Beyond this, Besson was concerned that the
Al2O3windows had affected the experiment [112]. Nellis
and Weir countered that “Our experiment and analysis yield
the simple picture of a dense metallic fluid comprised pri-
marily of molecular H2dimers and a relatively low disso-
ciation fraction of ∼5% of H monomers” [115]. The entire
sequence of observation was on the order of just a few hun-
dred nanoseconds [102, p. 1512], hardly time to conduct de-
tailed structural analysis, while introducing tremendous dif-
ficulties in properly measuring both pressures and conduc-
tivities. William Nellis once again addressed his metalliza-
tion experiments, but this time with Neil Ashcroft as a co-
author [114]. During the discussion which followed the pa-
per, Nellis admitted that “the exact nature of this unusual
fluid needs to be determined” [114, p. 135]. Though Nel-
lis eventually claimed that “Metallic fluid H is readily pro-
duced by dynamic high pressures” [102, p. 1564], only ques-
tionable evidence existed for this state [82]. The shock ex-
periments of metallic hydrogen from this group produced no
additional results and other groups never confirmed the find-
ings. The lack of lattice structure was debatable and mankind
was no closer to metallic hydrogen. For his part, William
Nellis moved to arguments of degeneracy, without solid ex-
perimental grounds [102].
In 1996, a collaboration between the University of Paris
and the Geophysical Laboratory at the Carnegie Institution
would make the next vital step forward [115]. Loubeyre et al.
[115] examined both solid hydrogen and deuterium with X-
ray diffraction at pressures just exceeding 100 GPa at 300 K.
They discovered that solid hydrogen “becomes increasingly
anisotropic with pressures” [115]. In like manner, the layered
structure of graphite was considered anisotropic. Loubeyre
et al. [115] tried to generate the equation of state for hydro-
gen as a function of temperature and pressure. They con-
cluded that their results differed substantially from ab ini-
tio calculations “indicating that theoretical understanding of
the behavior of dense hydrogen remains incomplete” [115].
Narayana et al. then studied solid hydrogen up to 342 GPa
at 300 K [116]. These were pressures similar to those at the
center of the Earth [117], but no evidence of metallization
was found. The findings confirmed Ramsey’s conclusion that
the interior of the Earth could not support the metallic state of
hydrogen [87]. In 2002, Loubeyre et al. again presented evi-
dence that solid hydrogen became black, this time at 320 GPa
and 100 K [118]. These values were not far removed from the
250 GPa used by Mao and Hemley in 1989 [105]. By observ-
ing the vibron mode, they maintain that molecular hydrogen
in the solid form existed at least until 316 GPa, but Narayana
had just reported that solid hydrogen remained transparent
up to 342 GPa at 300 K [116]. Two of the world’s major
groups were again at odds with one another. Perhaps the
discrepancies could be explained by difficulties in recording
proper pressures at such values [102, p. 1514–1533]. After
all, these studies were far from trivial in nature. Loubeyre
et al. [118] refrained from stating that metallization had been
achieved. Rather, they predicted that the process should occur
near 450 GPa [118].
Mankind has remained unable to synthesize metallic hy-
drogen in the laboratory. However, as pressures rose and ex-
perimental settings improved, the characteristics of dense hy-
drogen did become increasingly established [119–125]. Great
attention was placed on constructing phase diagrams for hy-
drogen (see [119] for a review). Determination of the peak
in the melt line of this element has consequently been the
subject of intense study (e.g. [121–124]). By this time, the
broken symmetry and hydrogen-A phase for dense hydrogen
were reasonably established, but neither form was metallic
(see [122] for a brief review). Blackbody radiation finally en-
tered such studies, with the goal to properly establish temper-
atures [122]. Along these lines, statements such as: “we have
shown that the emissivity of platinum is essentially indepen-
dent of temperature in the temperature region of our study”
[122] would only serve as a reminder that not all was correct
66 Robitaille P.-M. Liquid Metallic Hydrogen: A Building Block for the Liquid Sun

July, 2011 PROGRESS IN PHYSICS Volume 3
with our understanding of blackbody radiation [13, 14]. For
its part, metallic hydrogen continued to be ephemeral.
2.5 Commentary on liquid metallic hydrogen
As was seen in Section 2.3, within astrophysics, liquid metal-
lic hydrogen is believed to exist as fully degenerate matter
within the interior of white dwarfs and giant planets such as
Jupiter or Saturn. Some have suggested that these planets also
possessed liquid metallic helium, or a liquid metallic alloy of
hydrogen and helium. Solid metallic hydrogen would have
no role in astrophysics [27], as every hypothesis was either
a molecular or a fully degenerate liquid. The conjecture that
condensed matter could become degenerate in the large plan-
ets was far from what Chandrasekhar had envisioned when
he first promoted degeneracy [57]. As a fully degenerate ma-
terial, liquid metallic hydrogen could not sustain any useful
current or magnetic field. Positive charges in liberal motion
along with negative charges do not seem very amicable, either
to potential generation or net current flow. At the same time,
current flow with mass transfer seemed unreasonable in as-
trophysical objects. Direct laboratory observations remained
much too elusive to reach any confirmation of these theoret-
ical ideas. Some element of structure might always exist in
metallic hydrogen independent of temperature. The super-
fluid form could remain ever theoretical, as Ashcroft had first
carefully cautioned in the work with Oliva [36,37].
The application of fully degenerate matter to the large
planets and the white dwarfs was an unusual concept in light
of a fully gaseous Sun. If Jupiter contained metallic hydro-
gen as degenerate matter and the same was true for the white
dwarf, then it would not be unreasonable to place at least
some condensed hydrogen on the Sun. Solar temperatures
would prevent degenerate states and thus layered liquid
metallic hydrogen represented a remarkable constitutive el-
ement.
When it was first conceived, the most energetically ac-
cessible form of metallic hydrogen was the layered lattice ar-
rangement similar to that of graphite. Solid metallic hydro-
gen was viewed almost as a one component plasma [54, 55],
wherein all electrons were degenerate and distributed over a
hexagonal Bravais lattice formed from ordered protons [19].
In this sense, solid metallic hydrogen was considered as de-
generate only relative to the flow of its electrons. Today, the-
oretical astrophysics has abandoned early thoughts of solid
or liquid metallic hydrogen possessing a Bravais lattice [19],
opting instead for fully degenerate materials where both pro-
tons and electrons flow freely. Conversely, experimentalists
hope to harness metallic hydrogen for processes as varied as
earthly fusion and rocket propulsion [25]. Such processes
would not be easily approachable with a fully degenerate ma-
terial. Hence, many experimental physicists are likely to be
skeptical of a fully degenerate state for metallic hydrogen.
The progress towards dense hydrogen states has been an
intriguing aspect of condensed matter physics. Ashcroft’s
two component Fermi liquid has remained a fascinating sub-
stance. However, given the combination of low temperatures,
exact densities, and atypical conductive properties, it could
have little practical role in human advancement. Current flow
involving mass displacement was a concept which seemed to
oppose structural stability, even though it could sustain mag-
netic fields. Conversely, when proton and electron displace-
ment occurred in the same direction, there could be no current
or the generation of magnetically interesting properties.
Theoretical condensed matter physics promoted hydro-
gen at extreme densities [76, 84], but hydrogen might not be
compressible to such levels. In permitting essentially infinite
compression of the lattice, it was debatable whether or not
condensed matter physics had adopted a behavior similar to
the ideal gas. Moreover, if compression was great enough,
the solid might resist further attempts at reducing lattice di-
mensions. Fusion might relieve the stresses associated with
compression.
3 Lessons from the Sun
Though the Sun would always remain devoid of the great
advantage of our earthly laboratories, it has historically pro-
vided us with an amazing insight into nature. When Sir
Joseph Lockyer and Pierre Jules C´
esar Janssen independently
observed the lines of helium within solar spectra acquired in
1868 [126–130], they must have wondered if this unknown el-
ement would ever be discovered. Lockyer named this element
H¯
elios, the Greek name for the Sun god and the Sun [126].
Eventually, William Ramsay would isolate helium from cle-
veite [131–133], and the Sun would be credited for providing
the first indication that helium existed. The identification of
Coronium would follow a parallel story [134–136]. It took
nearly three quarters of a century for Bengt Edl´
en and Wal-
ter Grotrian to finally identify Coronium from transition lines
produced by highly oxidized iron, like Fe+13 and Fe+14 [136,
p. 170]. Hence, a combination of earthly science and celes-
tial observations became critical to the development of astron-
omy. This spirit of discovery has taught astronomers how to
tackle even the most perplexing problems. The understanding
of the solar spectrum should not be an exception.
3.1 Graphite, metallic hydrogen, and the solar spectrum
If graphite played a critical role, both in the construction of
blackbodies [14], and historically in the structure of the Sun
itself [2], it was because science has always recognized that
graphite possessed a unique ability towards the production
of Planck’s spectrum [6,13, 14]. Hastings was searching for
a material which would possess many of the properties of
graphite [8]. Graphite, the layered form of carbon, differed
significantly in optical properties from its cubic counterpart,
diamond. Structure was vital to the production of spectra.
That materials were condensed was not sufficient, but a dis-
tinct lattice arrangement seemed central [9]. As a conse-
quence, it would be expected that the layered form of metallic
Robitaille P.-M. Liquid Metallic Hydrogen: A Building Block for the Liquid Sun 67

Volume 3 PROGRESS IN PHYSICS July, 2011
hydrogen would resemble graphite itself in its optical prop-
erties. In contrast, fully degenerate forms of hydrogen [36,
37, 41, 46–48, 70–72] could never approach such optical be-
havior. Devoid of a true lattice, such a substance, if it truly
existed anywhere, would be completely unable to generate
a blackbody spectrum [6]. These are the lessons from our
earthly laboratories, after examining thousands of materials
over extreme ranges of frequencies and temperatures [13,14,
137]. The structural lattice of graphite and soot was to re-
main unique in its thermal properties [13, 14]. It should serve
as a guide for the nature of any condensed material placed
either on the photosphere or within sunspots. The generation
of a thermal spectrum with a blackbody lineshape has been
solely a quality of condensed matter, not of gases, degenerate
matter, or any other state which physicists might create.
Unlike the giant planets, the Sun possessed a unique fea-
ture: the ability to generate tremendous internal pressures
and temperatures. Based on the solar spectrum [138–140]
and other physical evidence [141], it was therefore reasonable
to postulate that liquid metallic hydrogen must constitute the
bulk of the solar mass and specifically the photospheric mate-
rial [20,142–149]. In considering a solar building block, ther-
mal emission required a distinct lattice [150], as the absence
of such structure would lead to the stellar opacity problem [9].
The author has previously made the point: “As a result, the
photosphere must be treated as condensed matter. Unfortu-
nately, it is counterintuitive than an object at extreme tem-
peratures can possess lattice structure. Nonetheless, given
the evidence for condensed matter4, the solar constitutive el-
ement (primarily H) must form a lattice. The presence of
powerful solar magnetic fields and gravitational forces make
liquid metallic hydrogen a distinct possibility for the con-
densed state of the photosphere. In this case, the hydrogen
nuclei can be viewed as arranged in an array forming an
essentially incompressible solar lattice. The hydrogen elec-
trons are contained within the metallic conduction bands. The
inter-nuclear distance is being maintained by the need to keep
the quantum conditions such that metallic conduction bands
can be produced. Hydrogen contains no inner shell electrons.
All the electrons are completely delocalized within the metal-
lic conduction bands. As such, hydrogen in this state is not
only a liquid metal (reminiscent of liquid sodium) but can also
be viewed as a liquid metallic plasma” [149]. The footnote
referred to reference [141] in this work.
In the solar framework, the electrons would translate
freely within the confines of conduction bands formed by the
Bravais lattice of the protons. Though not a one-component
plasma in a theoretical sense [54, 55], liquid metallic hydro-
gen could be considered as a one-component plasma in the
physical sense since the electrons were delocalized. But liq-
uid metallic hydrogen would possess a true Bravais lattice
and, perhaps, even liquid crystal behavior [151–153]. In this
regard, Ashcroft had left open the possibility that liquid
metallic hydrogen was a liquid crystal in 1981 and 1982 [36,
37]. Ashcroft had been unable to exclude the possibility when
he advanced the two-component Fermi liquid [36,37]. Liquid
metallic hydrogen could well have an ordered lattice which
oscillates between structural forms. The finding by Brov-
man et al. [61] that metallic hydrogen, much like graphite,
could adopt a family of structures with nearly the same en-
ergy should be considered in this regard.
In any event, it would be difficult to conceive that conduc-
tion bands could truly exist without a lattice and the impor-
tance of the Bravais lattice in the formation of metals should
not be dismissed. To a large extent, liquid metallic hydro-
gen should preserve the layered structure of solid metallic
hydrogen as anticipated by Wigner and Huntington [19]. But
the metallic character might be somewhat reduced in the low
pressures of the photosphere. In fact, this could be advan-
tageous for emission, better resembling graphite. Indeed, if
the graphitic spectrum was to be produced, the structure and
conductive properties of liquid metallic hydrogen should re-
semble graphite as much as possible. This is because graphite
represents the premier laboratory model.
3.2 Metallic hydrogen and solar structure
Metallic hydrogen, with its critical temperatures in the thou-
sands of degrees Kelvin [23–26], overcomes all concerns
raised regarding a liquid Sun based on Andrews [20] and his
findings in ordinary gases [3, 4]. A liquid Sun composed
of metallic hydrogen benefits from elevated critical temper-
atures for liquefaction, permitting hydrogen to adopt a con-
densed state even within an object like the Sun. Along these
lines, it is doubtful that metallic hydrogen could really be-
come infinitely compressed. Such a scenario appears un-
likely, as the presence of conduction bands involves quantum
restrictions on the lattice. If the internuclear distances are not
ideal, quantum mechanical conditions should fail to support
conduction. Two boundary conditions should exist. If the in-
teratomic distance becomes too large, the substance should
become an insulator. Similarly, if the interatomic distance
becomes too small, the crystal should collapse [59] and con-
duction cease. In this respect, it would be important to note
that the Sun has dynamo action and maintains large magnetic
fields. Both of these phenomena make destruction of the con-
ducting lattice unlikely [141].
It remains unclear why condensed structures resist com-
pression, but invoking fusion as a means of releasing the
strain of compressions should be a viable solution. This is
especially the case if compared to the destruction of the crys-
tal [59] and the creation of fully degenerate matter [36,37, 41,
46–48, 70]. Degeneracy removes all of the forces which lead
to fusion. As such, it should be more reasonable to maintain
the relative incompressibility of condensed matter. The Sun,
after all, has a very ordinary density of 1.4 g/cm3[141] and
the same is true for the giant planets. Thus, Jeans’ idea that
the Sun represents a rotating liquid mass of reasonably con-
stant density should not be dismissed [2]. Condensed mat-
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July, 2011 PROGRESS IN PHYSICS Volume 3
ter and metallic hydrogen provide a framework for ordinary
densities, even in light of enormous pressures. The reward
of such an approach is threefold leading to: 1) a reasonable
framework to generate the solar spectrum, 2) a decent ability
to impart structure, and 3) a practical path towards fusion.
A Sun composed of metallic hydrogen provides an in-
teresting model to explain sunspots and other structural el-
ements. The photospheric material in this case might be con-
sidered as liquid metallic hydrogen where the lattice dimen-
sions are relaxed at lowered pressures. Perhaps, the material
exists much like graphite at the limits of conductive behav-
ior. Conversely, within sunspots, pressures would be more
elevated, and liquid metallic hydrogen might assume a more
compact lattice, with increased metallic behavior. This would
help account for the stronger magnetic fields observed within
sunspots. As a result, scientists could be considering the con-
version from a Type I lattice in the photosphere to a Type II
lattice in the sunspots [141]. Such a scenario has great advan-
tages in terms of simplicity.
Gases have always been an unsustainable building mate-
rial for an object like the Sun. Gases know no surface and
cannot, even momentarily, impart structure. Hence, one can-
not be surprised to find that there is no physical evidence
which supports a gaseous Sun, while ample evidence [141]
has been revealed for its condensed state [20,142–149]. In or-
der to bring structure to the gas, astrophysics must depend on
the action of magnetic fields. However, strong magnetic fields
themselves are a property of condensed matter, not gases
[141]. In order to maintain a gaseous Sun and impart it with
structures, astrophysics must therefore have recourse to phe-
nomena best produced by condensed matter.
A simple illustration of these issues can be focused on the
understanding of solar prominences. Such objects appear as
sheet-like structures in images captured by NASA’s SOHO
satellite (see Figure 2). In a Sun built from layered metallic
hydrogen, it can be envisioned that a layer of material sim-
ply peeled away from the surface to form a prominence. In
contrast, within a gaseous body, the creation of such over-
whelming structures would remain difficult to explain, even
with magnetic fields forming and maintaining these entities.
Perhaps it would be more logical to presume that magnetic
fields were simply associated with the presence of metallic
hydrogen, whether on the surface of the Sun itself or within
the prominences.
Moreover, the active photosphere and chromosphere sup-
ports structural features [154]. Prominences contain fine
structure [155, 156], which would be easier to explain if a
condensed solar model was adopted. For more than one cen-
tury [157, p. 104], prominences have been known to emit con-
tinuous spectra in addition to the line spectra which character-
ize the quiescent state [158–161]. Eilnar Tandberg-Hanssen
has long studied prominences and has provided an excellent
review of the subject matter [160]. Like other solar physicists,
because the Sun was considered as a gas, he viewed promi-
Fig. 2: Sheet like appearance of solar prominences. NASA de-
scribes the image as follows: “A collage of prominences, which
are huge clouds of relatively cool dense plasma suspended in the
Sun’s hot, thin corona. At times, they can erupt, escaping the
Sun’s atmosphere. For all four images, emission in this spectral
line of EIT 304Å shows the upper chromosphere at a temperature
of about 60,000 degrees K. The hottest areas appear almost white,
while the darker red areas indicate cooler temperatures. Going
clockwise from the upper left, the images are from: 15 May 2001;
28 March 2000; 18 January 2000, and 2 February 2001”. Cour-
tesy of SOHO/[Extreme ultraviolet Imaging Telescope (EIT)] con-
sortium. SOHO is a project of international cooperation between
ESA and NASA. http://sohowww.nascom.nasa.gov/gallery/images/
promquad.html (accessed May 31, 2011).
nences as gaseous in nature [160]. Tandberg-Hanssen main-
tained that the continuous spectrum associated with some qui-
escent prominences was being generated by the scattering of
light emitted from the photosphere [161]. This was because
gaseous prominences could have no means of generating con-
tinuous spectra by themselves. They should have produced
only line spectra. Conversely, if the Sun was made from
condensed metallic hydrogen, the prominences could directly
produce the continuous spectrum. No scattering would need
to be invoked. If the density of the prominence material in
some cases could not sustain a continuous spectrum, then
only line spectra would be generated. Thus, as the promi-
nence dissipated with time, it would be expected that the con-
tinuous spectrum might weaken or become absent. It is possi-
ble to consider that prominences are formed by layered metal-
lic hydrogen separating from the inferior levels of the photo-
sphere. A slight change in density could account for such
actions reflecting an abrupt transformation from a more com-
pact lattice to a less dense form. This hypothesis might ex-
plain why entire sheets of material appear to be ejected, some-
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Volume 3 PROGRESS IN PHYSICS July, 2011
thing which would be difficult to understand otherwise.
It is possible, one further observation worth pondering in-
volves a figure presented by Fortov in his new text [103]. The
figure in question (Figure 7.7 in [103]) consists of a plot of the
log of object diameter versus the log of mass. On such a plot,
a straight line passes through all astrophysical objects within
our solar system, from the smallest comic dust, to the mete-
orites, to the comets, to the asteroids, to the satellites of plan-
ets, to the planets, and finally to the Sun [103, p. 192]. This
plot provides another line of evidence that the Sun should
be viewed as condensed matter. Every object on the graph
can be considered as condensed. Uranus and Neptune are
currently viewed as having metallosilicate cores and mantles
of ices [103, p. 193]. Jupiter and Saturn are largely liquid
metallic hydrogen or helium in either molecular or atomic
form [103, p. 193]. As the only remaining fully gaseous ob-
ject in the solar system, it may be reasonable to suggest that
the Sun should not stand alone on such a graph.
4 Conclusion
Relative to the Sun, a condensed approach brings interesting
contrasts and dilemmas versus the gaseous models. The latter
are endowed with tremendous mathematical flexibility [1,2],
but their physical relevance appears limited. Gases cannot
by themselves impart structure and the solar spectrum is not
easily explained in a gaseous framework [9]. The gaseous
stars suffer from the stellar opacity problem [9]. Conversely,
a liquid metallic hydrogen model imparts a wonderful abil-
ity to explain the origin of the solar spectrum relying on the
layered structure held in common with graphite [141–149].
Metallic hydrogen possesses a very high critical temperature
and can exist as condensed matter even on the solar surface
accounting for many features of the Sun best characterized
by material endowed with a lattice [141]. Most of the physi-
cal attributes of the Sun are more simply explained within the
framework of a liquid model [141]. However, a condensed
Sun is not as open to theoretical formulations. The advan-
tages of a liquid Sun are now so numerous [20,141–149] that
it is difficult to conceive why the model was not proposed
long ago. This speaks to the allure of the gaseous Sun and the
mathematical beauty of the associated equations of state.
In closing, it should be highlighted that there is currently
an effort to describe the Sun as “liquid-like” (e.g. [162]). In
the end, the author believes that such terminology should be
avoided. If the Sun is condensed, it should be viewed as
liquid, not “liquid-like”. Even gases could be “liquid-like”.
Such terms cannot be sufficient, since a real lattice is required
for production of the solar thermal spectrum. No compromise
can be made on this point for those who have studied thermal
emission in real materials. “Liquid-like” might refer to any-
thing from a gas, to a plasma, to fully degenerate matter, to
supercritical fluid and none are necessarily endowed with a
lattice. The contention of this work remains that the pho-
tosphere of the Sun is liquid, with true lattice structure and
ordered interatomic distances. The adoption of liquid metal-
lic hydrogen as a solar constituent brings with it a wealth of
possibilities in describing solar structures and understanding
the solar spectrum. Central to this advancement, the lattice
must remain the foremost element in all of condensed mat-
ter, whether here on Earth, within the Sun, and even, in the
firmament of the stars.
Acknowledgement
Luc Robitaille is acknowledged for producing a rendition of
graphite’s layered lattice.
Dedication
This work is dedicated to my son, Christophe, and his wife,
Lindsey.
Submitted on May 31, 2011 /Accepted on June 07, 2011
First published online on June 9, 2011
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