These simulations clarify some points of previous arguments about galaxy formation that are based on simple analytic models, and estimates of the efficiency of gas cooling. It is clear that the inclusion of a background radiation field, consistent with the observed Gunn-Petersson effect, can strongly suppress the formation of galaxies with total mass less than (circular velocity km/s). Furthermore, the formation of galaxies with total mass less than (circular velocity km/s) may be significantly delayed. These results of course depend on the assumed temporal and spectral form of the background radiation field. Nevertheless, the results are in reasonable agreement with previous analytic estimates (Efstathiou 1992), and in good agreement with recently published results based on simulations (Quinn et al. 1996, Navarro & Steinmetz 1997, Weinberg et al. 1997).
Hierarchical models of galaxy formation tend to over-produce galaxies with circular velocities less than 100 km/s. Our results indicate that photo-ionization alone is not sufficient to suppress the formation of these galaxies, since the effects on galaxies with circular velocities larger than 60 km/s is very limited.
The galactic objects that form in three-dimensional hydrodynamical simulations, are too compact when compared with observed disk galaxies. The reason for this is that most of the angular momentum in the gas component is transferred to the dark matter. Navarro & Steinmetz (1997) find that collapsed objects acquire even less angular momentum, when the effects of a UV field is included. Comparing Fig. 5 and Fig. 8, these simulations show that the angular momentum transfer, from the gas to the dark matter, decreases in magnitude when a UV field is included. This is not a contradiction. When a UV field is included, most of the gas angular momentum at is contained in a hot pressure supported halo. The angular momentum content of the collapsed gas cores does in fact decrease also in our simulations, in agreement with the results of Navarro & Steinmetz (1997).
Metal enrichment of the interstellar gas increases the gas cooling rate at late times, and may have significant effects on the amount of gas that may cool and sink to the center of a galactic halo in a Hubble time. The inclusion of a background radiation field leads to more massive hot halos in large galaxies, and , as seen when comparing Fig. 6 with Fig. 3. These hot halos contain most of the gas angular momentum. Metal enrichment increases the gas cooling rate at late times, and could potentially lead to the collapse of the hot halo gas, to the center of the galactic dark matter halo, in a cooling flow. However, as seen in Fig. 11, the increase in cooling rate is not enough for this to happen. See however Appendix A.2for potential two body heating effects. Increased cooling due to metal enrichment does decrease the mass of the hot halo that forms, (Fig. 11), but most of the gas angular momentum still resides in the remaining hot halo.
If inhomogeneities in the gas are smoothed out by the limited resolution used, the average cooling rate in the region will change. This is a problem common to all hydrodynamical simulations of galaxy formation. Some implicit assumption must be made, e.g., that the density field is smooth on unresolved scales due to physical processes not incorporated into the simulation or, that the density in regions where this could have an effect is already so high that the cooling is extremely efficient both with and without unresolved density fluctuations. Previous simulations without UV background ionization and heating, did not suffer from resolution effects, as badly as one might (naively) expect from the squared density dependence of the cooling function. The reason being that the cooling function is divided by the density, i.e. the gas cooling rate, per unit mass, is (roughly) proportional to the density, when thermal energy is integrated. For example, Navarro & White (1994) varied the gas mass- resolution by a factor of two, and Hultman & Källander (1997), by a factor of ten, both showing comparatively small effects.
Then, when a UV background field is included, there is a competition between density vs. density squared dependencies, being explicitly sensitive to resolution. Indeed, this was observed by Weinberg et al. (1997). Varying the mass-resolution by a factor of eight, had severe effects on the outcome of their results. Navarro & Steinmetz (1997) performed similar simulations varying the mass-resolution of identical runs with a factor of six. They found much smaller effects, that in addition decreased with redshift. However, the mass- resolution was much higher than in Weinberg et al. (In fact, even the lower resolution runs of Navarro & Steinmetz had slightly higher resolution as compared to the "high resolution" runs of Weinberg et al.) For the simulations presented here, the absolute resolution varies, since it is proportional to the total mass, but for comparison the runs are of comparable resolution to those of Navarro & Steinmetz. All in all, this is reassuring but not conclusive evidence that effects from limited numerical resolution are small. Ultimately, the tenacity of the underlying assumptions must be judged by comparisons with observations, and with other models that make different simplifying assumptions.
© European Southern Observatory (ESO) 1998
Online publication: April 20, 1998