The standard lore envisions galaxies forming as a result of the dissipative
collapse of gas within an
evolving population of dark matter halos. In systems where the dynamical
timescale exceeds the cooling timescale the gas component can radiate away
efficiently its pressure support and collapse until it settles into a centrifugally
supported disk, where it starts forming stars. The gas fraction that participates
of this collapse and is eventually transformed into stars determines the
total luminosity of a galaxy. The angular momentum of the gas determines
the size and surface brightness of a disk galaxy. Combined with the total
mass and spatial structure of the halo, it also sets the rotation velocity
and the shape of the rotation curve of a galactic disk. Computing the amount
of gas that can cool and form stars within a dark matter halo as well as
its angular momentum is therefore of crucial importance for understanding
the origin of disk galaxies and the significance of scaling laws that relate
different properties of the galaxy population such as the Tully-Fisher
relation.
Our numerical experiments have provided interesting clues to the process
of hierarchical galaxy formation[4,5,9,10,15]
. Dissipative effects are extremely efficient at high redshift (when
all systems, and the universe as a whole, were in general denser than today)
and, in the absence of a reheating mechanism, most of the gas in the universe
collects at the center of protogalactic halos as so on as they collapse.
There, it settles into tightly bound, rotationally supported disks which,
as halos collide and merge, sink to the center of the new halos, eventually
merging into a single object (Figure 1).
Face-on View
Edge-on View
Figure 1: Particle plots of a gaseous disk formed through dissipational collapse within a dark matter halo. Gas particles are shown in green and dark matter particles in red.
Radial Velocity vs radius
Rotational Velocity vs radius
Figure 2: Radial and tangential velocity profiles of the gas and dark matter. Note that the gaseous disk is centrifugally supported and that the rotation curve is approximately flat out to about 20 kpc.
This efficient cooling and early collapse of baryons is very difficult to reconcile with the observation that galaxies contribute a very small fraction of the total baryonic density of the universe implied by primordial nucleosynthesis constraints and with the existence of massive amounts of X-ray emitting gas in clusters of galaxies.
A related problem that arises if disk galaxies assemble most of their mass through merging of the baryonic cores of protogalactic halos is that substantial angular momentum losses occur during the mergers of these cores. Although gaseous disks formed this way have several properties in common with spiral galaxies, such as flat rotation curves (Figure 2) and roughly exponential disks, excessive angular momentum transfer between gaseous disks and dark halos during mergers result in disks that are much more concentrated than real spirals. Figure 3 shows the specific angular momentum of dark matter halos (filled circles) and gaseous cores (open circles) as a function of mass for an ensemble of 30 simulations of galaxy formation in the standard CDM cosmogony. The specific angular momentum of gaseous disks is, on average, only a tenth of that of their surrounding halos, although tidal torques gave both components approximately the same spin during the expansion phase. Typical spiral galaxies have higher angular momenta than the gaseous disks formed in these simulations.
These are potentially serious problems for any hierarchical clustering scenario, and it is clearly important to investigate physical mechanisms that can reduce the efficiency of cooling, such as energy feedback from supernovae or the effect of a photoionizing background. It is possible that the same mechanism that prevents the baryons from condensing at the center of small halos at high redshift can change the dynamics of the collapse of the gas, allowing it to conserve a larger fraction of its initial angular momentum and leading perhaps to better agreement with observations.
We were able to show that the effect of a photoionizing background such
as that inferred from the proximity effect on QSO absorption lines is insufficient
to prevent the early collapse of large amounts of gas into low mass halos[23].
This implies that further progress towards understanding the formation
of disk galaxies requires a realistic treatment of the effects of star
formation and feedback from supernovae and evolving stars on the interstellar
medium.
Young star particles can also devolve energy and mass to their surrounding gas, an effect that attempts to mimic the energy and mass input by supernovae and evolving stars into the ISM. The energy released by each star particle can be invested in heating up the neighboring gas or in perturbing its kinetic energy. Preliminary experiments[5] indicate that the results of a simulation are extremely sensitive to the fraction of energy invested in modifying the gas bulk motions, fv. This is the single most important free parameter in the whole procedure and can in principle be constrained by analytic models of SN explosions and by 1-D simulations of the interaction of SN remnants with the ISM.
Because our numerical treatment is fully Lagrangian, we can follow the
process of metal enrichment in a spatially resolved manner. Our code
tracks ``metals'' dumped into the neighboring gas by young star particles.
These metals are assumed to be released with two distinct timescales, corresponding
roughly to the different evolutionary timescales of type I and type II
supernovae[20]. This procedure
allows us to study the global metal enrichment process of a galaxy, the
establishment of metal gradients within galaxies, and the amount and composition
of metals expelled from a galaxy.
By modeling galaxies selected to have different morphological types at z=0 we expect to gain insight into the interplay between the underlying cosmology and the structure, kinematic properties, and observability of the progenitor(s) of galaxies like our own. Also, by matching simulations to observational data at different redshifts we hope to constrain the star formation history of galaxies of various morphological types and to learn of possible signatures that may relate particular cosmological models with the appearance of galaxies at different redshifts.
We expect that the numerical study we intend to carry out will help identify the causes of these observed regularities between galaxies of a given morphology. We plan to simulate a large number of systems of different mass, and to analyze the sensitivity of the resulting scaling laws to the particular cosmological model adopted and to our assumptions about the star formation and feedback processes. Since our simulations contain spatially resolved information, we will be able to assess the importance of possible biases introduced by observational procedures. For example, we will be able to compute Tully-Fisher relations in different passbands, constructed from simulated HI velocity widths and from rotation curves (optical or HI) at different redshifts. A similar analysis will be applied to the progenitors of present-day elliptical galaxies. These results can be directly compared with ongoing surveys that address the shape and normalization of these scaling laws at different redshifts.
Early results are encouraging[7,11,14]
We have included the effects of star formation in a subsample of simulated
halos which have suffered recent major mergers and are therefore unlikely
to harbour stellar disks. Stellar systems formed this way are found
to be slowly rotating, mildly triaxial ellipsoids supported by an anisotropic
velocity dispersion tensor. They also appear to obey similar correlations
to those of real ellipticals, giving some insight into the origin of the
``fundamental plane'' and the Faber-Jackson relation. This is an example
of the way in which outstanding problems regarding the origin and evolution
of elliptical and spiral galaxies can be approached in the numerical study
we intend to carry out.
None of the simulations published so far include star formation, but future investigations are likely to benefit dramatically from its inclusion. The simulations we propose can track the metal enrichment and abundance patterns in gas that inhabits galaxy halos and that has been expelled from galaxies by supernova-driven winds. These simulations would thus provide clear interpretation for observations of the metal abundances in low column density systems. One issue of particular interest that could be addressed with our techniques concerns recent observations that indicate that all Ly-alpha alpha clouds with measured metal abundances seem to exhibit a minimum metallicity of about 0.01 Zsolar. This observation constrains very strongly the star formation process and the efficiency of feedback. Our simulations can help sort out whether this indicates that essentially all the intergalactic medium (IGM) has been polluted by Pop III stars that have since faded out of view or whether feedback is so strong that metal enriched gas can be expelled from galaxies and pollute the IGM far beyond the sites of galaxy formation. We are confident that our numerical simulations will show under which conditions (or for which cosmological models) such strong mass losses are expected or even allowed. Finally, full knowledge of the thermodynamic state of the gas provided by our simulations can be used to simulate spectra and to find reliable ways to limit uncertainties in estimates of metal abundances from analysis of absorption lines.
Another planned application of our simulations concerns the relationship between damped Ly-alpha systems and evolving galaxies. Simulations which neglect star formation are not ideal for this task because gas densities tend to be severely overestimated unless stars are allowed to form. We intend to use our simulations to characterize the optical and infrared properties of galaxies responsible for damped systems. This can be used to interpret the observations of the few cases in which galaxies responsible for the damped system have been identified and to improve the observing strategy of future search. We also expect to address issues such as the typical distance from a galaxy at which damped systems arise, and the extent to which actual kinematic and spatial information can be extracted from studies of unsaturated lines in these systems. We expect these numerical studies to have a strong impact in this very active area of research.