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The crude treatment of gas thermodynamics in most work to date is perhaps the greatest barrier to simulating star formation in interacting galaxies. As described in Section 2, radiative cooling is typically cut off at 104 K, and most of the gas remains close to this temperature. Stars, on the other hand, form at much lower temperatures; consequently, sites of star formation can't be directly located in the simulated gas.

Within the framework of most simulations, gas density is the only variable with an interesting range of values, so most treatments assume the star formation rate is a function of the gas density. This approach has some justification; studies of star formation in systems ranging from quiescent disk galaxies to violent starbursts find that star formation rates roughly follow a Schmidt (1959) law of the form Sigmadot
align=absmiddles propto Sigmagn, where Sigmas and Sigmag are the stellar and gaseous surface densities, respectively, and the index n appeq 1.4 ± 0.15 (eg., Kennicutt 1998). The usual approach is thus to adopt a star formation law of the form rhodots propto rhogn, where rhos and rhog are the stellar and gaseous volume densities, respectively.

The implementation of feedback effects due to stellar evolution and supernovae is particularly difficult. Cooling is so rapid that the otherwise plausible strategy of dumping thermal energy into the gas proves ineffective; the energy is radiated away before anything else can happen (Katz 1992, Summers 1993). Another trick is to impart some outward momentum to gas particles surrounding sites of star formation and/or supernovae; this seems more effective, but involves an arbitrary efficiency factor (Navarro & White 1993, Mihos & Hernquist 1994). It's unlikely that feedback can be properly implemented as long as the gas is effectively treated as a single-phase medium.

A promising alternative to density-driven star formation is now available (Gerritsen & Icke 1997). In this approach the gas is allowed to cool below 104 K, and sites of star formation are defined by a Jeans criterion. The stellar radiation field, calculated in the optically thin limit, is used to heat the gas. Star formation is thus a self-regulating process; negative feedback maintains the system in a quasi-stable state while slowly converting gas to stars. Competition between radiative heating and cooling creates a two-phase medium with temperatures of 102 K and 104 K; a third phase at 106 K appears when the effects of supernovae are included. As a bonus, the resulting star formation obeys a Schmidt law with index n appeq 1.3.

It may turn out that many of the desirable features of this approach are simple consequences of combining radiative cooling and negative feedback. Some details surely require modification; the treatment of the radiation field seems particularly suspect since galactic disks, edge-on, are not optically thin. But the general view of star formation as a self-regulating process and the re-introduction of gas temperature as a physically interesting variable are surely major improvements on previous treatments.

Does the treatment of star formation make a real difference in the outcome of simulations? In at least one respect, it does. Simulations using the Schmidt law predict that interacting late-type disk galaxies consume most of their gas shortly after their first passage; merger-induced starbursts only result if the disks are protected from bar formation by compact central bulges (Mihos & Hernquist 1996). In contrast, simulations using self-regulated star formation predict that bulgeless disk galaxies retain enough gas to fuel ultra-luminous starbursts during their final mergers; while star formation rates increase after the first passage, radiative heating delays violent star formation until the merger drives most of the gas into a compact central cloud (Gerritsen 1997).

To date, outflows like those seen in interacting starburst galaxies have not been reproduced with either treatment of merger-induced star formation. This,This remains an important challenge for the future.

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