Observational tests

Having established that cold clouds could make up the dark matter, i.e. there is no evident inconsistency with observations, we can turn to the task of isolating some critical tests of the picture. Unlike the non-baryonic dark matter candidates, cold clouds interact with their environment in a rich variety of ways, admitting direct tests of the theory.

Lensing phenomena

A clear prediction of the model is that cosmologically distant sources should be strongly gravitationally lensed by intervening clouds. This possibility can be investigated relatively cleanly if one studies a large sample of quasars located behind low-redshift over-densities such as galaxy halos or clusters of galaxies (Walker 1999a; Walker & Ireland 1995; Tadros, Warren & Hewett 1998). In a collaborative effort led by Robert Smith (ANU), we are working towards this goal, making use of the large sample of objects identified in the 2dF Quasar Survey (Boyle et al 1996).

For clouds located in the Galactic halo, gravitational lensing is insignificant, but gas lensing may introduce measurable flux changes (Draine 1998). In the absence of a reliable structural model for the clouds there is great uncertainty in the predicted (de)magnification, making it difficult to use as a test. Nevertheless the requisite data have already been accumulated in the search for gravitational lensing events against LMC stars, and these data could usefully be searched for gas lensing events. Such a search should employ different criteria to those used to find gravitational microlensing (e.g. Alcock et al 1998): for gas lensing quite large differences in magnification can occur for different colours, and the light curves can be quite dissimilar to those for gravitational lensing by a compact object. We note also that the arguments presented in §5.4, suggesting a relatively small radius for the hydrostatic cloud, imply (high magnification) event time-scales of less than a day (cf. Draine 1998), and light-curves which are profoundly influenced by source size.

Plasma lensing (ESEs and related phenomena) is an area where further observational work would be extremely helpful. Pulsars offer the best targets for such work: they are much more informative than quasars in respect of the properties of the lens; multiple imaging is more common at low frequencies, where pulsars are brightest; and pulsars are very small in angular size, admitting sensitivity to distant lenses. Even rather basic information about the properties of the plasma lenses could discriminate between the various models. For example: if the lenses could be shown to be approximately axisymmetric and possessing an off-axis peak in electron column density, this evidence would very strongly favour the cold-cloud model. We also note that a 21 cm absorption line should arise during an ESE, but the strength of this line is difficult to predict because it depends on the tiny fraction of atomic hydrogen present within the cloud.

Extinction events

Throughout the far UV and X-ray bands the clouds must be completely opaque, implying that a small fraction of all compact extragalactic sources should be extinguished in these wavebands. However, these bands require space-based instrumentation and intensive monitoring experiments are consequently difficult to pursue. The best prospect for discovering clouds through their extinction therefore seems to be an accurate monitoring program at the blue end of the optical band, looking for Rayleigh scattering by the H₂. Modelling the cloud-cloud collision process (§5.4; Walker 1999b) provides an estimate of the mean cloud surface density

$\Sigma\simeq140\; {\rm g\,cm^{-2}}$ , which translates to a mean column density in H₂ of

$3.1\times10^{25}\;{\rm cm^{-2}}$ . Using the scattering cross-section of Dalgarno & Williams (1965) this implies an average extinction of

$\Delta B\simeq0.073$ magnitudes, while

$\Delta V\simeq0.032$ and

$\Delta R\simeq0.012$ . (Gas lensing [§§4.4.2, 6.1] also affects the received flux; however, for most of the time during a gas lensing event the received flux is lower than if the lens were absent, so that gas lensing typically reinforces the effects of extinction.) At shorter wavelengths, scattering quickly becomes a large effect: 0.25 mag at 336 nm, and 0.85 mag at 255 nm. Extinction events should last only a week or two, and should be manifest in a fraction

$\simeq2\times10^{-4}$ of Magellanic Cloud stars, say, at any one time.

Local H $\alpha$ sources

By virtue of their small mass, the nearest dark clouds ought to be quite close to the sun - perhaps within 0.1 pc - and it may be possible to detect these objects through their H $\alpha$ emission. In the solar neighbourhood the mean intensity of ionising photons appears to be very low (Vallerga & Welsh 1995) and will not lead to a detectable emission measure, even for a cloud which is so close that it is resolved by the telescope. However, the cosmic rays which pass through the cloud create some ionisation throughout its volume, and a small fraction of these ionisations lead to the production of H $\alpha$ photons.

More specifically, cosmic-ray ionisation of He gives He⁺ which reacts with H₂ to give He, H and H⁺, the last of which recombines with an electron, yielding emergent Balmer photons. (By contrast, ionisation of H₂ leads to the formation of H₂⁺, which reacts with H₂ to give H₃⁺; this subsequently recombines with an electron to yield H₂ and H.) Assuming that roughly 60% of H⁺ recombinations yield an H $\alpha$ photon - as for Case B conditions - and adopting an ionisation rate of

$3\times10^{-17}\;{\rm s^{-1}}$ (e.g. Webber 1998), the implied H $\alpha$ luminosity is

$2\times10^{35}M_{-4} \;{\rm s^{-1}}$ , where M_-4 is the cloud mass in units of

$10^{-4}\mathrm{M}_\odot$ . Now from the results of Walker (1999b) we can infer a local cloud density of

$80/M_{-4}\;{\rm pc^{-3}}$ , so if we survey a solid angle of $\omega$ sr, the brightest cloud within the survey area is expected to have a flux of

$1.5\times10^{-2} M_{-4}^{1/3}\omega^{2/3}\;{\rm cm^{-2}\,s^{-1}}$ .

By good fortune it happens that the Anglo-Australian Observatory has recently commissioned an H $\alpha$ filter for use with its Schmidt telescope. In three hours this combination reaches a depth approximately equivalent to R=21 (Parker 1998), and using the magnitude-flux transformation of Bessell (1983) we find that this corresponds to

$2.0\times10^{-4}\;{\rm cm^{-2}\,s^{-1}}$ . In collaboration with Quentin Parker (ROE) and Mike Irwin (IoA), we are currently using this telescope/filter combination to search for local examples of the cold cloud population. The technique we are using is to observe eight high-latitude fields (total

$\omega=3.1\times10^{-2}\;{\rm sr}$ ), in both H $\alpha$ and R to similar depth, then re-observing these fields one year later in order to identify any high proper-motion emission-line sources. Sciama (1999) has pointed out that the local cloud population should also be detectable with future satellite missions (MAP and Planck) designed to study the Cosmic Microwave Background. These missions are, however, some years away.

Collisions

The theory described in §5.4 implies that optical transients will arise from cloud-cloud collisions occurring within the halo of our Galaxy. We estimate that the median of the distribution of peak visual magnitudes will be V<23; the total event rate will be roughly

$0.7/M_{-4}\;{\rm deg^{-2}\,yr^{-1}}$ ; and typical durations will be a few days. The estimated magnitude assumes that the internal density profile is approximately that of a convective (n=3/2) polytrope; more centrally concentrated profiles result in fainter (median) transients (e.g. fainter by 3.6 mag if n=3). Although the properties of the transients are at present only crudely predicted by the theory, we know of no similar physical phenomenon and it seems unlikely that, if discovered, the origin of such events would be incorrectly attributed. Discovery would require a fairly deep, wide-area monitoring program with daily visits and rapid spectroscopic follow-up. Because the radiating gas reaches temperatures of approximately $5\times10^5$ K, optical spectra will presumably display emission lines superimposed on a continuum dominated by free-free emission and ${\rm He^{++}}$ recombination.

A further implication of the physics described in §5.4 is that a large fraction of the X-ray emission observed from clusters of galaxies must be attributed to cloud-cloud collisions. If this is really the case, then it follows (Walker 1999c) that the X-ray satellite Chandra will resolve the nearby Virgo cluster into a large number of point-like, transient X-ray sources.

$\gamma$ -ray background

A direct view of the bulk of the clouds is afforded by their $\gamma$ -ray emission, and it would be helpful to study the spectral properties and angular distribution of the $\gamma$ -ray background. Unfortunately there appears to be no immediate prospect for such studies. The Compton GRO satellite was able to detect the Galactic component of the high energy $\gamma$ -ray background (Dixon et al 1998), but lacked the sensitivity necessary to conduct studies on angular scales much less than a radian. Future gamma-ray missions - notably NASA's GLAST satellite (http://glast.gsfc.nasa.gov) - will have much greater sensitivity than CGRO, but are currently some years away from realisation. In the meantime it would be profitable to calculate the spectrum which is expected from cosmic-ray interactions with clouds of high column density. This may be relevant to the existing EGRET data on diffuse emission, whose spectra are not understood (Mori 1997).