Implementing Feedback in Simulations of Galaxy Formation: A Survey of Methods

We present a detailed description, and examine the performance of, a number of different approaches to modeling feedback in simulations of galaxy formation. Gasdynamic forces are evaluated using smoothed particle hydrodynamics (SPH). Star formation and supernova feedback are included using a three-parameter model which determines the star formation rate (SFR) normalization, feedback energy, and lifetime of feedback regions. The star formation rate is calculated for all gas particles which fall within prescribed temperature, density, and convergent flow criteria, and for cosmological simulations we also include a self-gravity criterion for gas particles to prevent star formation at high redshifts. A Lagrangian Schmidt law is used to calculate the star formation rate from the SPH density. Conversion of gas to stars is performed when the star mass for a gas particle exceeds a certain limit, typically half that of the gas particle. Feedback is incorporated by returning a precalculated amount of energy to the ISM as thermal heating. We compare the effects of distributing this energy over the smoothing scale or depositing it on a single particle. Radiative losses are prevented from heated particles by adjusting the density used in radiative cooling so that the decay of energy occurs over a set half-life, or by turning off cooling completely and allowing feedback regions a brief period of adiabatic expansion. We test the models on the formation of galaxies from cosmological initial conditions and also on isolated disk galaxies. For isolated prototypes of the Milky Way and the dwarf galaxy NGC 6503 we find feedback has a significant effect, with some algorithms being capable of unbinding gas from the dark matter halo ("blow-away"). As expected feedback has a stronger effect on the dwarf galaxy, producing significant disk evaporation and also larger feedback "bubbles" for the same parameters. In the critical-density CDM cosmological simulations, evolved to a redshift z = 1, we find that, barring extreme models, feedback has little effect. Further, feedback only manages to produce a disk with a specific angular momentum value approximately twice that of the run with no feedback, the disk thus has an specific angular momentum value that is characteristic of observed elliptical galaxies. We argue that this is a result of the extreme central concentration of the dark halos in the standard CDM model and the pervasiveness of the core-halo angular momentum transport mechanism (even in light of feedback). A simulation with extremely violent feedback, relative to our fiducial models, leads to a disk that resembles the other simulations at z = 1 and has a specific angular momentum value that is more typical of observed disk galaxies. At later times, z = 0.5, a large amount of halo gas which does not suffer an angular momentum deficit is present; however, the cooling time is too long to accrete on to the disk. We further point out that the disks formed in hierarchical simulations are partially a numerical artifact produced by the minimum mass scale of the simulation acting as a highly efficient "support" mechanism. Disk formation is strongly affected by the treatment of dense regions in the SPH method. The problems inherent in the treatment of high-density regions in SPH, in concert with the difficulty of representing the hierarchical formation process, means that realistic simulations of galaxy formation require far higher particle resolution than currently used.