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

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3. Initial conditions

In setting up initial conditions for a simulation it is necessary to specify the cosmological model. Here a CDM model, with a baryon fraction of [FORMULA], a bias parameter of [FORMULA], [FORMULA], [FORMULA], and a Hubble constant [FORMULA] in units of 100 km/s/Mpc, is employed. The main significance of the cosmological model is in this case to provide a normalization, and shape, of the power spectrum of density fluctuations. The amplitude of the power spectrum on galactic scales is constrained by observations, choosing [FORMULA], (the rms field value, smoothed with a top hat filter on a scale of [FORMULA] Mpc). Choosing another hierarchical cosmological model is therefore likely to have only moderate effects on the results of these simulations.

The simulations presented here cover a mass range of objects, [FORMULA], in order to address questions about the mass dependence of different physical mechanisms. The gas is initially represented by 8000 particles and the dark matter by 4000 particles. Gas particles are under certain conditions allowed to merge with other nearby gas particles, and the number of gas particles is therefore a decreasing function of time, (see Hultman & Källander 1997 for details). The simulations start with a spherical region of the Universe at a redshift of [FORMULA].

We choose the simulation volumes as spheres, containing precisely the mass of the object in question. This minimizes the volume needed to be simulated, reducing costs in computational time, allowing for highest possible resolution, which is of critical importance in these type of simulations. The initial conditions used here are similar to the ones used by Katz & Gunn (1991), but there are some important differences, and improvements as will be explained below.

Selecting a limited spherical region to study the formation of a galaxy leads to two major complications, the neglect of the surroundings and the selection of a proper site.

Galaxies do not form at random locations. Finding good candidates for galactic seeds at high redshifts, using only the density distribution as a guide, is a difficult task. One possible procedure is to make a low resolution simulation of a large region, and thereby identify the sites where galactic halos of the desired type form. After that, such a region can be re-simulated with higher resolution. Although cumbersome, this is feasible and has been done (Navarro & White 1994).

We chose instead to rely on the "peaks formalism" (Bardeen et al. 1986) to identify likely sites of the formation of galactic halos. This enables us to use an explicit scheme where key properties of the proto-galaxy can be specified, "seeding" the formation of the galactic object to form at the desired location. The details of this are described in Appendix A.1.

By ignoring the surrounding regions outside the proto-galaxy, no account is taken of tidal interactions. Tidal interactions with the surrounding matter is believed to be what gives galaxies their spin. In its early pre-collapse phase, the proto-galaxy acquires angular momentum through gravitational interactions with surrounding matter. Density fluctuations grow by gravitational instabilities and at some time the proto-galaxy collapses. When it collapses, the quadrupole, and higher, moments of its mass distribution diminish as it shrinks in size. This drastically reduces any tidal interactions, and the angular momentum accumulated in the pre-collapse phase is effectively frozen in at this time. It is therefore believed that a galaxy that has not been involved in any major merger events has had an almost constant angular momentum since the main collapse of the proto-galaxy.

Thus, to approximate the neglected effects of the proto-galactic surroundings, the simulated spherical region is started in solid body rotation. The amount of angular momentum added corresponds to a spin parameter of [FORMULA] (Barnes & Efstathiou 1987).


[TABLE]

Table 1. Simulation parameters.


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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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