Numerical Simulations Of Galaxy Formation Research Articles

Parameter tests within cosmological simulations of galaxy formation

ABSTRA C T Numerical simulations of galaxy formation require a number of parameters. Some of these are intrinsic to the numerical integration scheme (e.g., the time-step), while others describe the physical model (e.g., the gas metallicity). In this paper we present results of a systematic exploration of the effects of varying a subset of these parameters on simulations of galaxy formation. We use N-body and ‘Smoothed Particle Hydrodynamics’ techniques to follow the evolution of cold dark matter and gas in a small volume. We compare a fiducial model with 24 different simulations, in which one parameter at a time is varied, focusing on properties such as the relative fraction of hot and cold gas, and the abundance and masses of galaxies. We find that for reasonable choices of numerical values, many parameters have relatively little effect on the galaxies, with the notable exception of the parameters that control the resolution of the simulation and the efficiency with which gas cools.

Galaxy Formation from a Low-Spin Density Perturbation in a CDM Universe

In order to understand the formation process of elliptical galaxies which are not rotationally supported, we carried out numerical simulations of galaxy formation from a density perturbation with a rotation corresponding to a small spin parameter. The three-dimensional TREE N-Body/SPH simulation code used included dark matter and gas dynamics, radiative cooling, star formation, supernova feedback, and metal enrichment. The initial condition was a slowly rotating, top-hat over-dense sphere on which the perturbations expected in a cold dark matter (CDM) universe were superposed. By means of a stellar-population synthesis, we calculated the surface-brightness profile, the metallicity distribution, and the photometric properties of the end-product, and found that these properties quantitatively agree with the observed properties of bright elliptical galaxies. Thus, we conclude that, in a CDM universe, a proto-galaxy having a spin-parameter as small as 0.02 evolves into an elliptical galaxy.

The Global Schmidt Law in Star‐forming Galaxies

Measurements of H-alpha, HI, and CO distributions in 61 normal spiral galaxies are combined with published far-infrared and CO observations of 36 infrared-selected starburst galaxies, in order to study the form of the global star formation law, over the full range of gas densities and star formation rates (SFRs) observed in galaxies. The disk-averaged SFRs and gas densities for the combined sample are well represented by a Schmidt law with index N = 1.4+-0.15. The Schmidt law provides a surprisingly tight parametrization of the global star formation law, extending over several orders of magnitude in SFR and gas density. An alternative formulation of the star formation law, in which the SFR is presumed to scale with the ratio of the gas density to the average orbital timescale, also fits the data very well. Both descriptions provide potentially useful "recipes" for modelling the SFR in numerical simulations of galaxy formation and evolution.

Two-body heating in numerical galaxy formation experiments

We show that discreteness effects related to classical two-body relaxation produce spurious heating of the gaseous component in numerical simulations of galaxy formation. A simple analytic model demonstrates that this artificial heating will dominate radiative cooling in any simulation where the mass of an individual dark matter particle exceeds a certain critical value. This maximum mass depends only on the cooling function of the gas, on the fraction of the material in gaseous form, and (weakly) on typical temperatures in the gas. It is comparable to, or smaller than, the dark matter particle masses employed in most published simulations of cosmological hydrodynamics and galaxy formation. Any simulation which violates this constraint will be unable to follow cooling flows, although catastrophic cooling of gas may still occur in regions with very short cooling times. We use a series of N--body/smoothed particle hydrodynamics simulations to explore this effect. In simulations which neglect radiative cooling, two--body heating causes a gradual expansion of the gas component. When radiative effects are included, we find that gas cooling is almost completely suppressed for dark matter particle masses above our limit. Although our test simulations use smoothed particle hydrodynamics, similar effects, and a similar critical mass, are expected in any simulation where the dark matter is represented by discrete particles.

The Structure of Isothermal, Self‐gravitating, Stationary Gas Spheres for Softened Gravity

A theory for the structure of isothermal, self-gravitating gas spheres in pressure equilibrium is developed for softened gravity, assuming an ideal gas equation of state. The one-parameter spline softening proposed by Hernquist & Katz is used. We show that the addition of this extra scale parameter implies that the set of equilibrium solutions constitute a one-parameter family, rather than the one and only one isothermal sphere solution for Newtonian gravity, and we develop a number of approximate, analytical or semianalytical solutions. For softened gravity, the structure of isothermal spheres is, in general, very different from the Newtonian isothermal sphere. For example, for any finite choice of softening length and temperature T, it is possible to deposit an arbitrarily large mass of gas in pressure equilibrium and with a nonsingular density distribution inside of r0 for any r0 > 0. Furthermore, it is sometimes claimed that the size of the small-scale, self-gravitating gas structures formed in dissipative Tree-SPH simulations is simply of the order the gravitational softening length. We demonstrate, that this claim, in general, is not correct. The main purpose of the paper is to compare the theoretical predictions of our models with the properties of the small, massive, quasi-isothermal gas clumps (r ~ 1 kpc, M ~ 1010 M?, and T 104 K) which form in numerical Tree-SPH simulations of the formation of Milky Way-sized galaxies when effects of stellar feedback processes are not included. We find reasonable agreement, despite the neglect of effects of rotational support in the models presented in this paper. We comment on whether the hydrodynamical resolution is sufficient in our numerical simulations of galaxy formation involving highly supersonic, radiative shocks, and we give a necessary condition, in the form of a simple test, that the hydrodynamical resolution in any such simulations is sufficient. Finally, we conclude that one should be cautious, when comparing results of numerical simulations, involving gratitational softening and hydrodynamical smoothing, with reality.