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Astron. Astrophys. 333, 399-410 (1998)

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1. Introduction

It is generally believed that galaxies formed by gravitational collapse. Small fluctuations in the primeval density field grew through gravitational instabilities. When the mean density in a proto-galaxy reaches approximately twice the mean density of the Universe, the proto-galaxy breaks away from the general expansion of the Universe and collapses, and forms a gravitationally bound galactic halo. If the gas in a galactic halo is able to cool efficiently, it can dissipate kinetic energy and condense into a galactic object at the center of the halo.

The purpose of this paper is to study under what circumstances the gas in proto-galaxies is able to cool efficiently, and condense into objects with galactic densities. Particularly, we take a close look at the possible effects of a strong background UV radiation field and the dynamical effects of metal enrichment of halo gas. The results are based on three-dimensional hydrodynamical computer simulations, and a standard CDM cosmology is assumed throughout. The results should have some relevance for all hierarchical scenarios of galaxy formation.

In hierarchical models of galaxy formation, the statistical cosmological time of collapse for a proto-galaxy is an increasing function of mass. More massive galactic halos thus form later. This general picture is consistent with observations indicating that clusters are younger than the contained galaxies, and that the Universe is homogeneous on very large scales.

Any theory of galaxy formation must address fundamental properties of the observed galaxy population like characteristic masses and sizes. Rees & Ostriker (1977), and Silk (1977), showed that the characteristic masses and sizes of galaxies are just those to be expected of gas clouds that can cool in a Hubble time. This provides a natural explanation for the sharp upper cut-off in the galaxy luminosity function; more massive proto-galaxies can not cool in a Hubble-time. These calculations were based on simple models of homogeneous gas clouds, very unlike the highly inhomogeneous collapse of a proto-galaxy in a hierarchical model, where objects are formed by merging of smaller ones, where the gas have already had time to cool. If a substantial fraction of the gas is still heated to virial temperatures, these models still shows that limits due to gas cooling are likely to play an important role in the formation of galaxies.

Observations suggest that only a small fraction, around [FORMULA], of the closure density of the Universe is in the form of stars. It therefore seems likely that most of the baryonic matter has avoided falling into compact objects, where efficient star formation could take place. Hierarchical models (White & Frenk 1991, Cole et al. 1994), on the other hand, tend to lock up most of the baryonic mass in the universe in small galactic objects, at early times. If the gas in these halos is able to cool and condense into dwarf galaxies, hierarchical models seem to over-predict the current mass fraction of stars in the Universe. One possible explanation is that supernova driven winds are able to suppress the formation of dwarf galaxies (Dekel & Silk 1986). Another process that may be important involves the presence of a photo-ionizing UV background radiation field. A photo-ionizing background field would heat the gas, and, by keeping the gas at a high degree of ionization, it would suppress collisional line cooling from neutral atoms. Evidence for such a field is given by the lack of a Gunn-Peterson effect even at high redshifts [FORMULA] (Webb et al. 1992), indicating that the Universe was highly ionized at these redshifts.

Based on simple models of the collapse of gas clouds, Efstathiou (1992) argued that a strong background UV radiation field might indeed suppress the formation of dwarf galaxies. The gas is heated by photo-ionization, and the gas is also kept at a high degree of ionization that suppresses collisional line cooling. Efstathiou found that this might prevent the gas in galactic halos with circular velocities less than [FORMULA] from cooling.

The UV background photo-ionization heating is able to raise the equilibrium gas temperature to only about [FORMULA] K, for the typical range of densities in question, ([FORMULA]). Further, the photo-ionization process is proportional to the density, through relative abundances, but the excitation and collisional cooling processes are proportional to the density squared. Therefore, the effect of photo-ionization is larger for low densities, and becomes less significant for higher densities. Above [FORMULA] K photo-ionization effects also diminishes, due to first hydrogen, later helium, becoming completely ionized. It is therefore only likely to be important for the dynamics of small galaxies. But, large galaxies could also have been affected, since their lower mass progenitors may have been unable to cool.

Typical virial temperatures of galactic halos are [FORMULA] K. In this temperature range the cooling rate of interstellar gas is highly dependent on the metallicity. The cooling rate of a gas with solar metallicity can be more than one order of magnitude larger than for a gas of primordial composition (Sutherland & Dopita 1993). Observations of intra-cluster gas typically indicates metallicities of [FORMULA]. This metal enrichment can have a strong effect on the amount of gas that is able to cool at low redshifts.

Källander (K"allander (1996)) has performed simulations similar to the ones presented here, using a similar model for the metal enrichment of halo gas, (described in the next section), but twice as high metallicity yield. The numerical resolution was similar, but no UV field was included, and only galaxies with a total mass of [FORMULA] were studied. The increase in cooling rate, due to line cooling in metals, was in that case found to be enough to cause the hot halo gas to collapse in a cooling flow, in roughly one Hubble time. Without the increased cooling rate, significantly less cooling flow was present, and essentially no disk formed. Some experimentation seems to indicate that the magnitude of the gas dynamical effects of metal enrichment, are sensitive to the details of how the metal enrichment is modelled.

White and Frenk (1991) used an intricate semi-analytic framework to compare different models of hierarchical galaxy formation to observations, and found that the results were sensitive to the assumptions made for the metal enrichment of the gas.

Other simulations including the effects of photo-ionization have been presented by Vedel, Hellsten, & Sommer-Larsen (1994), Thoul & Weinberg (1996), Quinn, Katz, & Efstathiou (1996), Weinberg, Hernquist, & Katz (1997), Navarro & Steinmetz (1997). These authors uses different implementations, initial conditions and strengths of the photo-ionizing field. Vedel et al. uses three dimensional SPH simulations of a Milky Way sized object, but cannot draw conclusions on objects of other masses. Thoul & Weinberg uses one dimensional models, and have much higher resolution. The remaining uses 3D SPH simulations and emphasise on resolution effects, which are shown to be of critical importance to the results in these simulation. In spite of that these authors uses different implementations, the main conclusions are very similar. A background photo-ionizing field does have some effects on lower mass objects, but cannot alone be responsible for suppressing the formation of dwarf galaxies, and make the hierarchical CDM models consistent with observations. These authors does not include the effects of metal enrichment, but this does not alter the general result, however.

Hierarchical clustering is a highly inhomogeneous process. Direct three-dimensional simulations are therefore a vital complement to lower dimensional analytical models. Gas dynamics must be included because dissipation is a fundamental part of galaxy formation. In this article we present computer simulations of galaxy formation that provide further insight on hierarchical clustering models, with an emphasis on cooling arguments. Even though a CDM cosmological model is assumed throughout, the results should have some relevance for all hierarchical scenarios. The effects of a UV background is investigated by running otherwise identical simulations, with and without the effects of an ionizing field incorporated. To be able to address questions about the mass dependence of physical processes, simulations covering a wide range of galactic masses are presented.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998