Dwarf (Cold) Galaxy Formation

Since dwarf galaxies form a large part of the subject of this meeting, the rest of my remarks are addressed to their formation. Although it needs modification to allow for dark matter, the argument of Rees & Ostriker (1977) is still essentially valid. It shows that shock heating during the collapse of small galaxies is transient at best. Thus, the collapse of a small protogalaxy results in cold gas within a dark matter halo. I will use the term ``dwarf'' loosely to refer to any system resulting from such a cold collapse.

The collapse of the dark matter associated with the dwarf is dissipationless and leads to a halo of the form proposed by Navarro, Frenk & White (1997). This may be modified by gas processes, as discussed below. Its only significant function for the current purpose is that it provides a potential that confines the cold gas, squeezing it to high density.

Consider the early collapse of a halo with a total mass of $10^{10} M_{10} {\rm\ M_\odot}$ . Using standard arguments from semi-analytical models for galaxy formation (e.g. Nulsen, Barcons & Fabian 1998), such a halo would have a velocity dispersion of about

$\begin{displaymath} \sigma \simeq 46 M_{10}^{1/3} t_9^{-1/3} {\rm\ km\ s^{-1}}, \end{displaymath}$

(2)

if it collapsed at 10⁹ t₉ y. If the gas fraction in the collapse is 0.2 (section 2), then the protogalactic halo will contain about $2\times10^9 {\rm\ M_\odot}$ of cold gas. While star formation in dwarfs, even those with substantial gas fractions, can be slow now, it is hard to see how such a large mass of gas in such a deep potential well could be prevented from undergoing a massive star burst.

Since the last remark contradicts the evidence from local conditions, it worth considering more closely. For example, it is well known that according to the Jeans criterion, giant molecular clouds are unstable, yet they do not undergo rapid star formation. Apart from the fact that a very large mass of gas is trapped in a small region, why should we expect something different when galaxies are forming? The galaxies we observe at the present day are old, so we should expect them to have reached a relatively steady state, in which changes take place on a timescale defined by their age (since the last major disturbance). The only exceptions are systems where the time required to reach a steady state is longer than their ages, as may be the case for dwarf spheroidal galaxies (e.g. Gallagher & Wyse 1994). Thus, while it may be slightly surprising that giant molecular clouds do not collapse more quickly, it is no surprise that the overall star formation rate today is modest. There are numerous feedback processes that can help to maintain such conditions (e.g. Silk 1997). However, there is also ample evidence that disturbing a galaxy, e.g. by gravitational interaction with another galaxy, will significantly alter the star formation rate (e.g. Kennicutt et al. 1998). The conditions during collapse of a protogalaxy are about as far as it is possible to get from the near equilibrium that we see today. Some time is required (perhaps, of the order of the time until the first supernovae, a few million years) for feedback processes to begin to limit the first wave of collapse that results in star formation. Thus, there is no inconsistency between the expectation of a massive star burst during the collapse of a protogalaxy, but only a relative trickle of star formation today.

Nulsen & Fabian (1997) argue that an initial burst of star formation proceeds on the dynamical timescale (or faster). Feedback from supernovae can limit the burst only if it is at least as fast, requiring the speed of the expanding blast (driven by overlapping supernova explosions) to be at least comparable to the escape speed from the potential well. As a result, supernovae can only limit the star burst by ejecting a substantial part of the remaining gas. Gas may be completely ejected from the halo, or it may reaccrete some time later. The ejected gas can account for the bulk of the damped Ly $\alpha$ absorption line systems in quasar spectra (Nulsen et al. 1998). Observations of the Hubble Deep Field show clear evidence for the massive star bursts required by this model (Sawicki & Yee 1998; Lilly et al. 1998). Note that such massive star bursts are only expected in those collapses where star formation is not impeded for some other reason (e.g. because the gas is stable according to the Toomre criterion). This is why they tend to occur in early collapses of relatively massive systems.

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