The Cloudy Universe
Mark Walker, Mark Wardle, PASA, 16 (3), 262.

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Compatibility with other data

In order that the mass in neutral gas clouds not exceed the dynamically determined value (i.e that deduced from the rotation curve) for the Galaxy, the individual cloud masses must be very small:

$M<10^{-3}\;{\rm M_\odot}$ . Assuming cloud masses comparable to this limit, and radii of a few AU implies that they have internal densities

$n\sim10^{12}\;{\rm cm^{-3}}$ , very dense in comparison with any other component of the interstellar medium. Three-body reactions (e.g.

${\rm 3\,H\rightarrow H+H_2}$ ; Palla, Salpeter & Stahler 1983) consequently proceed rapidly and the hydrogen is expected to be in molecular form.

Unfortunately there is very little else that one can deduce a priori about the putative neutral gas clouds, and it is necessary to contemplate a broad range of possibilities. With this in mind we now address the issue of detectability of the clouds themselves: ought they to be manifest in other ways?

Thermal emission

The most obvious expectation of the model is that there ought to be thermal emission from these dense clouds, and the Galactic population as a whole should therefore introduce an extra background of thermal radiation. The expected background spectrum is dictated by the temperature, density and composition of the clouds; we know that the temperature is low, and the density high, but the cloud chemistry is poorly constrained. We can nevertheless arrive at some crude estimates as follows.

Let us approximate any line emission as optically thick within the Doppler core, of velocity width c_s, implying a brightness temperature equal to the kinetic temperature (T) of the cloud, with negligible optical depth (and therefore brightness temperature) outside this region. When viewed as a background - i.e. without resolving the individual clouds - the observed brightness temperature contribution at line centre is then

$\Delta T_B \simeq f\,T (c_s/\sigma)$ , where f is the fraction of the sky covered by clouds, and $\sigma$ is their velocity dispersion. The quasar monitoring data (Fiedler et al 1994) suggest that

$f\sim5\times10^{-3}$ , while

$c_s\ll\sigma\sim150\;{\rm km\,s^{-1}}$ , and we see that $\Delta T_B$ is very small. If the instrument we are using cannot resolve the line (i.e. 2 x the channel width is greater than $\sigma$ ), then the recorded brightness temperature perturbation is even smaller:

$\Delta T_B\sim{\cal R}T^{3/2}$ nK, in a single spectral channel, where ${\cal R}$ is the spectral resolving power and T is in Kelvin. Inserting parameters appropriate to the COBE FIRAS instrument, which had brightness temperature sensitivity of order 0.1 mK, and

${\cal R}\sim10^2$ (Fixsen et al 1994) we see that FIRAS would not have detected the line unless

$T\mathrel{\hbox to 0pt{\lower 3pt\hbox{$\mathchar''218$}\hss} \raise 2.0pt\hbox{$\mathchar''13E$}}100$ K. The foregoing discussion is straightforwardly extended to a small number of spectral lines. While these estimates are rather crude they are not specific to any particular coolant: the key point is that the microwave/FIR data give only weak limits on possible cloud temperatures if there is negligible continuum opacity.

The limits on broad-band radiation are much more restrictive. COBE FIRAS data revealed a Galactic component of continuum emission which could be interpreted in terms of dust with temperatures in the range 4-7 K, and mean optical depth

$\langle\tau\rangle\sim10^{-4}$ (at

$\lambda = 0.33$ mm) at high latitude (Reach et al 1995; see Lagache et al 1998 for an alternative interpretation). In the cold cloud model

$\langle\tau\rangle=f\,\tau$ , where $\tau$ is the optical depth of a single cloud. Requiring the thermal continuum emission from any cloud population to be smaller than the COBE measurements, we then demand

$\tau<2\times10^{-2}$ if T=7 K, say. (Using the smaller value of f, i.e. f_coll, derived in §5.4, this limit relaxes to $\tau<0.5$ .) In turn, this limit on the optical depth implies that the clouds contain essentially no dispersed dust. This is expected if their composition reflects the standard Big Bang abundances, and likely even if the clouds do contain metals, because any dust grains will settle into the centre of the cloud, forming a ``dirty snowball'' there. In §5.3 we shall present theoretical arguments that there must in fact be some continuum opacity in these clouds - not from dust as such, but from particles of solid hydrogen. The limit on $\tau$ just quoted applies equally well to these particles.

Non-thermal emission

The most striking feature of the $\gamma$ -ray sky is the luminous interstellar medium in the Galactic plane. This emission arises as a consequence of cosmic rays interacting with the gas, principally by nuclear interactions (i.e. cosmic-ray protons + target nuclei) leading to pion production, with subsequent decay (

$\pi^0\rightarrow2\gamma$ ); relativistic electron bremsstrahlung also contributes (e.g. Bloemen 1989). If we suppose that the dark matter is simply cold gas then it too will be luminous in $\gamma$ -rays, as a result of these processes (de Paolis et al 1995). In principle this provides a strong constraint on the amount of dark matter in cold gas, but in practice the constraint is quite weak because the Galactic distribution of cosmic rays is poorly known; in particular the scale-height of the cosmic ray disk of the Galaxy is uncertain (Webber, Lee & Gupta 1992). In addition the column density of individual dark clouds may be sufficiently high that they are not entirely transparent to $\gamma$ -rays and cosmic rays. As a result of this freedom in modelling, the $\gamma$ -ray data must be regarded as inconclusive at present. However, we note that Dixon et al (1998) discovered an unmodelled Galactic ``halo'' component in the $\gamma$ -ray background, and the simplest explanation for this is that it is due to unseen (cold, dense) gas.

In addition to cosmic rays interacting within each cloud, we have already noted (§3) that UV photons are absorbed by the cloud and drive a wind from its surface. Radiation from this wind, in particular the optical/IR line transitions of molecular and atomic hydrogen, might be detectable. (This is, of course, thermal emission, but it seems more appropriate to cover it here than in §4.1 because the wind is so much hotter than the underlying cloud.) Noting that the Galactic halo ionising radiation has an intensity of order

$2\times10^6/\pi\;\,{\rm cm^{-2}\,s^{-1}\,sr^{-1}}$ (Dove & Shull 1994), and that all of the ionising photons incident upon a cloud will be absorbed, one can estimate (e.g. Bland-Hawthorn & Maloney 1997) that each cloud should have an Emission Measure of

${\rm EM\sim2\;\, pc\,cm^{-6}}$ . Averaging over the population of clouds, which collectively cover only a small fraction of the sky, then leads to a mean surface brightness (EM) a factor

$f\sim5\times10^{-3}$ smaller. This emission therefore contributes a tiny fraction ( $\sim$ 1%) of the observed EM at high Galactic latitudes (Reynolds 1992), and the data do not currently provide strong limits on the proposed cloud population. This situation could be improved with studies of the low-level emission-line wings, as the clouds are expected to have a velocity dispersion (

$\sigma\simeq150\;{\rm km\,s^{-1}}$ ) which is much greater than the width of the dominant observed component.

We can also consider the possibility of detecting individual clouds passing through regions where the radiation field is high, i.e HII regions, but the prospects seem remote. Here we differ from the conclusions of Gerhard & Silk (1996), who considered clouds having radii some four orders of magnitude larger (hence solid angles, and ${\rm H\alpha}$ fluxes, eight orders of magnitude larger) than in our model.

Extinction events

If the Galactic dark matter is composed of clouds which cover a fraction

$f\sim5\times10^{-3}$ of the sky then, because the total column of dark matter is known from dynamics (e.g. Binney & Tremaine 1987) to be

$\sim100\;{\rm M_\odot}$ , one can immediately infer that the column density of each cloud is

$N\sim10^{24}\;{\rm cm^{-2}}$ . If these clouds followed the same relationship between extinction and column density as the known molecular gas in the Galaxy, this would correspond to several hundred magnitudes of visual extinction; in turn this would mean that 0.5% of extragalactic stars (e.g. in the LMC) would be completely extinguished, with these events lasting tens of days. This phenomenon is readily detectable but has not been reported, and we are obliged to conclude that the clouds cannot be suffused with dust (see also §4.1).

In the UV - X-ray bands each cloud must be opaque because the fundamental constituents (H₂ and He) themselves provide substantial opacities in these regions of the spectrum (cf. Combes & Pfenniger 1997). The main sources of opacity are: Rayleigh scattering (near UV); the Lyman and Werner transitions of H₂; photoelectric absorption; and electron scattering at high energies. Monitoring extragalactic sources in these wavebands should, therefore, unambiguously reveal the presence of such a cloud population via the extinction events they introduce. Insufficient data have been recorded to date to usefully constrain a cold-cloud population, so this remains an interesting experiment for the future.

Lensing events

There are several distinct phenomena, relevant to cold clouds, which fall under the general heading of ``lensing'': plasma lensing (refraction by ionised gas, giving rise to ESEs), gas lensing (refraction by neutral gas), and gravitational lensing (refraction by the gravitational field). The last of these is widely acknowledged as a tool for investigating dark matter, and it is appropriate to deal with it first.

Gravitational lensing

Searches for gravitational microlensing of stars in the Large Magellanic Cloud (e.g. Alcock et al 1997) are designed to detect flux increases of 30% or more, and consequently these experiments are sensitive only to strong gravitational lenses, i.e. objects with column density of

$10^4\;{\rm g\,cm^{-2}}$ or greater. This is very much greater than the column density inferred for the cold clouds (

$\sim 10^2\;{\rm g\,cm^{-2}}$ ; see §5.4), and so the limits on low mass MACHOs in the Galactic halo (Alcock et al 1998) are, by definition, irrelevant, even though they cover the critical planetary mass range.

Clouds located at greater distances, e.g. at cosmological distances, may be strong gravitational lenses because the column density required to make a strong lens is smaller in this case, and we expect that quasars will be gravitationally microlensed by intervening clouds. Several authors have argued that quasars are indeed microlensed by planetary-mass objects, including lensing of quasars by cosmologically distributed objects (Hawkins 1993, 1996), and microlensing of quasars which are macrolensed by foreground galaxies (e.g. Schild 1996). The evidence is equivocal at present, and there is a pressing need to clarify this situation; clarification could be achieved by monitoring quasars which are viewed through the halos of low redshift galaxies or clusters (Walker 1999a; Walker & Ireland 1995; Tadros, Warren & Hewett 1998). Notice that if Hawkins is correct, that all quasars exhibit variability as a consequence of microlensing by planetary mass objects, then it follows (Press & Gunn 1973) that a large fraction of the cosmological critical density is in the form of these lenses. This has implications for cosmic nucleosynthesis (§5.1) and, in turn, the origin of the clouds (§5.2).

Gas lensing

The concept of ``gas lensing'' was introduced by Draine (1998), who pointed out that the refractive index of neutral hydrogen/helium gas clouds would be interestingly large if they had the mass and radius proposed by Walker & Wardle (1998a). More specifically: the refractive index could be comparable to the angular size of Galactic clouds, implying that strong focussing/de-focussing might occur. Supposing that no such effects are manifest in the microlensing monitoring data for the Magellanic Clouds (cf. Alcock et al 1998), Draine (1998) then used this concept to restrict the acceptable combinations of cloud masses and radii, under assumed polytropic equations of state. The principal difficulty in applying this work is our current lack of information on the density profile of the individual clouds. In turn this reflects our primitive understanding of the physics relevant to these clouds (particularly the heating/cooling balance: §5.3).

Plasma lensing

In §3 we presented the arguments which lead from the observation of ESEs to the conclusion that the dark matter is composed of cold clouds. The ESE phenomenon is, however, not the only piece of evidence which points to the existence of a large population of dense plasma clouds -- this population is also revealed by observations of periodic fringes in the spectra of pulsars (Rickett 1990). These periodicities were discovered many years before ESEs, and their interpretation requires similarly dense clouds of ionised gas, a few AU in radius. In principle these observations of pulsars are much more informative, in respect of the plasma lenses, than observations of ESEs in quasars, but this advantage has not yet been exploited. Pulsars clearly offer an opportunity to greatly advance our understanding of the ionised gas clouds responsible for ESEs, but this requires systematic studies of the various multiple imaging phenomena.

Next Section: Theoretical considerations
Title/Abstract Page: The Cloudy Universe
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Contents Page: Volume 16, Number 3

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