The Cloudy Universe

Mark Walker, Mark Wardle, PASA, 16 (3), 262.
Next Section: Observational tests
Title/Abstract Page: The Cloudy Universe
Previous Section: Compatibility with other data
Contents Page: Volume 16, Number 3

Subsections

Theoretical considerations

In §4 we described the immediate observational implications of a population of cold gas clouds contributing to the dark matter; it is important to recognise that none of these considerations excludes the model proposed in §3. We now turn to issues which are more theoretical, in the sense that they relate primarily to the physics of the putative clouds.

Cosmology

Theoretical cosmology is responsible for establishing the idea that dark matter is principally non-baryonic. This idea rests on two distinct lines of evidence, relating to primordial nucleosynthesis and to the formation of structure in the Universe.

When the Universe was only minutes old (redshift $z\sim10^9$), it passed through a period where nuclear reactions were effective in building-up the abundances of light elements from the initial building blocks of protons and neutrons. If the Universe is assumed to be homogeneous then the abundances of the various elements can be calculated with some precision, subject only to the unknown photon/baryon ratio (or equivalently the baryonic contribution, $\Omega_B$, to the closure parameter $\Omega$). For a small range of values

$0.005\mathrel{\hbox to 0pt{\lower 3pt\hbox{$\mathchar''218$}\hss} \raise 2.0pt\... ...\lower 3pt\hbox{$\mathchar''218$}\hss} \raise 2.0pt\hbox{$\mathchar''13C$}}0.03$, the calculated abundances of the light elements are roughly in accord with the observed abundances, giving confidence in the model and admitting an estimate of $\Omega_B$ -- see Schramm & Turner (1998). When combined with other pieces of evidence that indicate

$0.1\mathrel{\hbox to 0pt{\lower 3pt\hbox{$\mathchar''218$}\hss} \raise 2.0pt\hb... ...pt{\lower 3pt\hbox{$\mathchar''218$}\hss} \raise 2.0pt\hbox{$\mathchar''13C$}}1$ (e.g. Peebles 1993), these calculations demonstrate that most of the Universe (i.e. the dark matter) was not in the form of smoothly distributed baryons at the time of nucleosynthesis. This conclusion is usually stated more succinctly as a requirement for non-baryonic dark matter.

The second line of evidence for non-baryonic dark matter relates to the theory of growth of structure in the Universe. The fact that the Cosmic Microwave Background (CMB) is smooth to 10-5 K on large scales (Smoot et al 1992) tells us that the diffuse baryons possessed very little large-scale inhomogeneity at the epoch when electrons recombined with ions to form neutral atoms (at $z\simeq1500$). But today we see a great deal of structure: galaxies, clusters and even superclusters of galaxies appear organised in a network of vast filamentary features. This proliferation of structure can be explained by the effects of gravity acting on primordial (adiabatic) density fluctuations if the dark matter couples to the diffuse baryon-photon fluid only through gravity. If this condition is not met - e.g. if the dark matter is supposed to be in the form of diffuse baryons up to recombination - it proves difficult to explain the smoothness of the CMB, on the one hand, and the highly structured local Universe on the other (Peebles 1993). A known counterexample to this statement is the baryon isocurvature model - see Peebles 1993 - which invokes isothermal primordial density fluctuations. Unfortunately there is no fundamental theory for the origin of isothermal fluctuations, and the results for adiabatic fluctuations are usually given concomitantly greater weight.

These considerations have led to widespread acceptance of the idea that the bulk of the dark matter is non-baryonic. However, as emphasised by the phrasing of the preceding paragraphs, neither case is watertight. Very possibly the Universe was not homogeneous at the time of nucleosynthesis - in particular inhomogeneities could be introduced during the quark-hadron phase transition (Applegate & Hogan 1985) - and in this case the upper limit on baryons relaxes to

$\Omega_B\mathrel{\hbox to 0pt{\lower 3pt\hbox{$\mathchar''218$}\hss} \raise 2.0pt\hbox{$\mathchar''13C$}}0.3$ (Kurki-Suonio et al 1990). If we admit the possibility of isothermal fluctuations as the origin of present-day large-scale structure there is then no barrier, from cosmological considerations, to a purely baryonic universe. A baryonic universe might also be consistent with adiabatic fluctuations, but in this case we require the proto-clouds to have sufficiently high density that they decouple from the CMB well ahead of recombination.

Cloud formation

How might planetary-mass gas clouds form? The answer to this question depends on quite what mass needs to be explained. For clouds which lie at the upper end of the planetary range, a fairly straightforward answer can be given: they could form as the endpoint of hierarchical fragmentation of larger clouds undergoing collapse in the early Universe ($z\sim100$). There is a substantial literature on the topic of hierarchical fragmentation, beginning with Hoyle's (1953) classic paper, mostly employing spherically symmetric gas clouds in free-fall, in which ``fragment'' masses are equated with the Jeans mass for the gas. In most calculations the hierarchy is assumed to terminate when the cloud becomes optically thick - at which point cooling is impeded - and there are sound reasons why this usually results in sub-stellar masses for the smallest fragments (Rees 1976). By the same token, however, the smallest fragments are limited to masses

$M>{\rm a\;few\;\times10^{-3}\;M_\odot}$, so if the putative cold clouds are smaller than this then hierarchical fragmentation is not viable as a formation scenario.

There are some hints that the individual clouds may indeed have very small masses (§5.4), possibly as small as

$10^{-5}\;{\rm M_\odot}$. Moreover the arguments given in the preceding section suggest that the dark matter is not formed from baryons which were smoothly distributed at recombination, or even at nucleosynthesis. The implication is that the proto-clouds formed in the very early Universe (z>109, cf. Hogan 1978, 1993), and have maintained their identity right up to the present. (Two further indications that the clouds predate cosmic nucleosynthesis are the presence of metals in High Velocity Clouds, and the hints from quasar variability that the Universe might contain a critical density of planetary-mass objects -- see §5.4 and §4.4.1, respectively.) We envisage that the proto-clouds formed during the quark-hadron phase transition (cf. Applegate & Hogan 1985), and are thus fossils of that era. Although this is clearly speculative, it is the most economical hypothesis available.

Cloud stability

Supposing that we can find a sensible explanation for how the clouds might have formed, it remains to comprehend the observed/inferred properties of the clouds at the present time. A major part of this task is to understand the internal constitution of the clouds, and in particular their thermal balance (see also Gerhard & Silk 1996).

For equilibrium, the power radiated from each cloud must be balanced by some heat generated within. Unlike stars this heat is clearly not generated by nuclear fusion; there might plausibly be some exothermic chemical reactions occurring (e.g.

${\rm 2\,H+\,H_2\rightarrow2\,H_2}$), but the simplest hypothesis for Galactic clouds is that heat is deposited by energetic particles. In principle this could involve both photons and cosmic rays (their Galactic energy densities are similar); however, given that the clouds are transparent to optical photons (§4.3), but not to cosmic rays, it is likely that the cosmic rays dominate.

The local cosmic-ray heating rate for dense interstellar molecular gas is

$\sim3\times10^{-4}\;{\rm erg\,g^{-1}\,s^{-1}}$ (Cravens & Dalgarno 1978), and supposing the cloud temperature to be $T\sim10$ K this immediately implies a thermal (Kelvin-Helmholtz) time-scale of order 105 yr. This is much greater than the sound-crossing time-scale ($\sim10^2$ yr), so we see immediately that each cloud responds adiabatically to pressure perturbations and consequently dynamical stability is assured. Thermal stability is another matter.

Because the heating of each cloud is largely independent of its temperature, the radiative cooling must actually decrease, with increasing T, if it is to be thermally stable. If it were otherwise, the following scenario would take place. Suppose the cloud contracts slightly from an initial equilibrium condition, then its temperature increases, consequently it radiates more efficiently, but the heating rate remains the same, so cooling then outstrips heating and this causes further contraction. Evidently this contraction can continue without limit under the stated circumstances and such a cloud would be thermally unstable, collapsing (or expanding) on a thermal time-scale. As this is much less than the Hubble time, this is not an acceptable model. The difficulty we then face is that, in order to construct a thermally stable model, we need to identify a radiative cooling process which becomes less effective at higher temperatures.

While it is possible for this circumstance to arise, e.g. by virtue of a single spectral line becoming optically thick, it is a highly anomalous situation. In the particular case of the hypothesised cold, dense clouds there happens to be a remarkably simple solution to this conundrum (Wardle & Walker 1999). Conditions within the clouds are close to those required for the precipitation of solid hydrogen (Pfenniger & Combes 1994), and such particles efficiently cool the gas via their thermal continuum radiation. If this process dominates the radiative cooling of the clouds, then they can be thermally stable because an increase in temperature rapidly destroys the coolant, leading to less efficient cooling at higher temperatures. This concept is examined in detail by Wardle & Walker (1999).

Cloud survival

Beyond just the stability of the clouds, we need to understand their survival in the Galaxy for billions of years. This issue was first considered by Gerhard & Silk (1996), who arrived at simple criteria which the clouds must satisfy if they are not to be destroyed by evaporation or by collisions. Gerhard & Silk (1996) found the latter to be the more restrictive condition, implying a lower bound on the column density of individual clouds:

$N\mathrel{\hbox to 0pt{\lower 3pt\hbox{$\mathchar''218$}\hss} \raise 2.0pt\hbox{$\mathchar''13E$}}4\times10^{24}\;{\rm cm^{-2}}$. This constraint can be tightened quite considerably by going beyond just order-of-magnitude estimates and examining the evolution, under the influence of collisions, of a model halo.

Starting from a singular isothermal sphere, Walker (1999b) found that the dark halo developed a core of constant density, with the core radius increasing as a function of time, as a result of destructive collisions between clouds. In this model the size of the core, rc, is a function of the halo velocity dispersion, $\sigma$ - large velocity dispersions imply high collision rates - with

$r_c\propto\sigma^{3/2}$. There is some evidence that dark halos do indeed possess finite cores with the size of the core increasing as $\sigma^{3/2}$ (Kormendy 1990).

Collisions between clouds cause shock heating of their constituent material; these shocks typically dissociate the molecular gas and unbind the clouds, their material subsequently being assimilated into the ISM of their host galaxy. Walker & Wardle (1999) pointed out that the Galactic High Velocity Clouds (HVCs; Wakker & van Woerden 1997) might plausibly be identified with post-collision gas which has not yet been assimilated into the Galactic disk. If this identification is correct, the fact that HVCs contain metals is of particular interest because our naive expectation is that the composition of these clouds reflects the nucleosynthetic yields of the Big Bang. This is entirely unconventional, of course, but is in accord with the hypothesis that the clouds predate nucleosynthesis and introduce inhomogeneity at that epoch (§§5.1,5.2; Applegate & Hogan 1985).

In due course stars may form from the diffuse gas released by collisions, but either way the material is part of the visible pool of matter and consequently the visible mass within a dark halo can be predicted. Walker (1999b) discovered that data published by Broeils (1992) are in good agreement with this model; matching the theory to the data requires only that the surface density of individual clouds is

$\Sigma\simeq140\; {\rm g\,cm^{-2}}$ (assuming the age of the Universe to be 10 Gyr). Moreover it seems very likely that this relationship between visible galaxy mass and halo velocity dispersion,

$M_{vis}\propto\sigma^{7/2}$, underlies the well-known Tully-Fisher relation between galaxy luminosity and velocity dispersion. This is a remarkable success for such a simplistic model, and this result assumes particular importance because it occurs in the arena where we find the strongest evidence for dark matter, i.e. the dynamics of spiral galaxies.

With the above estimate for the mean cloud surface density we can immediately compute the sky-covering fraction for the clouds:

$f_{coll}\simeq2\times10^{-4}$ (Walker 1999b). This is considerably smaller than the estimate based on ESEs (

$f_{ESE}\sim5\times10^{-3}$; Fiedler et al 1994), and if we wish to reconcile these values it seems necessary to contemplate photo-ionised winds arising at radii

$(f_{ESE}/f_{coll})^{1/2}\sim5$ times larger than the underlying hydrostatic clouds. Presumably, if both models are valid, this difference implies that a neutral wind transports mass out to several cloud radii before it becomes ionised. Thus since Walker & Wardle (1998a) estimate an inner radius of order 2 AU for the photo-ionised wind, we can estimate the underlying cloud radii as roughly 0.4 AU

$=6\times10^{12}\;{\rm cm}$. In combination with the estimated mean surface density, this implies that a characteristic mass for the individual clouds is

$M\sim10^{-5}\;{\rm M_\odot}$. (A cloud with this mass/radius ratio has a virial temperature of a few Kelvin, cf. §5.3.) As the line of reasoning which leads to this figure is not yet secure, the estimate should be treated with some caution.

A further interesting aspect of collisions is that the shock-heated gas radiates strongly, and this radiation may be detectable. In the case of collisions in the Galactic halo one expects (unobservable) extreme ultraviolet flashes, with accompanying optical transients at a median magnitude of V<23, lasting a few days. For halos with larger velocity dispersions the thermal radiation moves into the X-ray band and is directly observable. Rather dramatically, the implied X-ray luminosity for a cluster of galaxies with

$\sigma=1000\;{\rm km\,s^{-1}}$ is (assuming polytropic clouds with n=3/2)

$L_X\simeq3\times10^{44}\;{\rm erg\,s^{-1}}$, comparable to what is actually observed from such clusters. Because this emission is thermal radiation from gas at roughly the virial temperature, it is difficult to distinguish it from thermal emission by diffuse, hot gas in the cluster (which is the standard interpretation of the observed emission). These issues are discussed by Walker (1999c).

Next Section: Observational tests
Title/Abstract Page: The Cloudy Universe
Previous Section: Compatibility with other data
Contents Page: Volume 16, Number 3

Welcome... About Electronic PASA... Instructions to Authors
ASA Home Page... CSIRO Publishing PASA
Browse Articles HOME Search Articles
© Copyright Astronomical Society of Australia 1997
ASKAP
Public