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7.4. Suppression of star formation: external agents

7.4.1. Photoionization

Rapid cooling of proto-dwarf galaxies could be prevented if the gas is kept photoionized by the metagalactic radiation field. Babul and Rees (1992) and Efstathiou (1992) argue that the ionizing background at z > 1 is high enough to keep the gas in dwarf galaxy halos confined and stable, neither able to escape, nor able to collapse and form stars. The extent to which this effect is important depends on the shape of the ionizing spectrum and its evolution, neither of which are well quantified. The lack of a detectable Gunn-Peterson Lyman-alpha absorption trough in the spectra high-redshift QSO's (Steidel and Sargent 1987; Webb et al. 1992) suggests the IGM is highly ionized. The ionizing radiation field estimated from the proximity effect (Jnu approx 1021 erg cm-2 s-1 Hz-1; Lu et al. 1991) appears sufficient to prevent the gas from cooling in halos of velocity dispersion less than ~ 35 km s-1 until z approx 1. The advantage of the model is that it provides a clear connection between dwarf galaxies and QSO Lyalpha absorbers (the latter being dwarf galaxies in their latency period before cooling), and it provides a source of faint blue galaxies at 0.5 < z < 1. If AGN are the dominant source of ionizing radiation, a further prediction of the model is that the spatial distribution of dwarf galaxies could be modulated by the distribution of AGN.

7.4.2. Reheating

If AGN do not provide sufficient flux to photoionize the IGM (Shapiro and Giroux 1987), an alternative solution to satisfying the Gunn-Peterson test is to suppose that the intergalactic medium was reheated during the epoch of galaxy formation. Mechanisms include heating by supernova winds from protogalaxies (Tegmark et al. 1993), Compton heating from energetic objects at very high redshift (Collin-Souffin 1991), or a variety of other possibilities (Blanchard et al. 1992). In any case, if the IGM is maintained at a constant temperature TIGM, the only galaxies that can collapse are those with virial temperatures higher than the temperature of the IGM. Blanchard et al. (1992) argue that this consideration leads to a mass-function slope close to the observed one. Outside of the deep potentials of groups and clusters, the reheated IGM cools adiabatically, with temperature T propto (1 + z)2. The minimum velocity dispersion for a galaxy therefore evolves as sigmamin propto 1 + z. The mass function of halos in the CDM model scales as

Equation 13 (13)

However, all objects collapsing at a given redshift z have the same density rho propto (1 + z)3. The velocity dispersion scales as sigma2 propto M / R propto rho1/3 M2/3, so

Equation 14 (14)

which is proportional to (1 + z)3/2 when we constrain sigmamin to follow the IGM temperature. Combining these equations leads to a mass function

Equation 15 (15)

consistent with the cluster observations summarized in Sect. 5, if M / L is roughly independent of L. However, this argument only applies outside of groups and clusters, where the observed luminosity function slope is flat to the limits of the observations. The alpha = -1.3 slope for the luminosity function of cluster dE's must be due to some other cause.

7.4.3. Merging and shocks

The epoch of dwarf galaxy formation may also be the epoch of rapid merging, at least for a CDM power spectrum in an Omega = 1 cosmology. Shock heating during the mergers can partially counteract the cooling according to eqn. 12. However, Blanchard et al. (1992) conclude that this effect alone cannot suppress cooling enough to avoid overproducing dwarf galaxies.

7.4.4. Instabilities

The standard cooling-time calculation assumes that gas in a protogalaxy starts out in a singular isothermal sphere, in thermal equilibrium with the dark matter. Radiative cooling then proceeds smoothly from the inside out. Reality is unlikely to be so straightforward, and it is probable that cooling takes place in a turbulent, inhomogeneous medium. Gas at 106 K will be thermally unstable and will likely develop into a two-phase medium due to rapid cooling in the densest subclumps (Fall and Rees 1985), combined with heating from the first generation of stars. Murray et al. (1993) explore the effects of Kelvin-Helmoltz instabilities on clouds moving through a hot medium. Such an effect could truncate the galaxy mass function in clusters of galaxies at velocity dispersions sigma < 10 km s-1, but is unlikely to have a direct effect on the galaxy mass function at higher masses. Nevertheless, instabilities during the cooling phase may play an indirect role in shaping the galaxy luminosity function by influencing the stellar initial mass function, and hence the number of OB stars and supernovae per unit mass formed.

7.4.5. Sweeping

Sweeping of gas by an external medium is a widely cited mechanism for cutting off star formation, and transforming dwarf irregular galaxies into dE's (Lin and Faber 1983; Kormendy 1985; Binggeli 1986). Sweeping is unlikely to have been effective at high redshift. While the mean density of the intergalactic medium was presumably higher - approaching densities of the centers of present-day rich clusters (nH approx 10-3 cm-3) at redshifts z gtapprox 7 - random velocities of galaxies through this medium would have been sufficiently low that stripping timescales would be longer than a Hubble time. Sweeping during the epoch of dwarf galaxy formation is thus not a viable solution to the overcooling problem, although it may nevertheless account for the lack of gas in cluster dE's if some other process does not remove the gas prior to cluster collapse. Sweeping processes are discussed in detail in Sect. 7.6.

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