Forming stars on a viscous timescale: the key to exponential stellar profiles in disk galaxies?

Abstract

We argue for implementing star formation on a viscous timescale in hydrodynamical simulations of disk galaxy formation and evolution. Modelling two-dimensional isolated disk galaxies with the Bhatnagar-Gross-Krook (BGK) hydrocode, we verify the analytic claim of various authors that if the characteristic timescale for star formation is equal to the viscous timescale in disks, the resulting stellar profile is exponential on several scale lengths whatever the initial gas and dark matter profile. This casts new light on both numerical and semi-analytical disk formation simulations which either (a) commence star formation in an already exponential gaseous disk, (b) begin a disk simulation with conditions known to lead to an exponential, i.e. the collapse of a spherically symmetric nearly uniform sphere of gas in solid body rotation under the assumption of specific angular momentum conservation, or (c) in simulations performed in a hierarchical context, tune their feedback processes to delay disk formation until the dark matter halos are slowly evolving and without much substructure so that the gas has the chance to collapse under conditions known to give exponentials. In such models, star formation follows a Schmidt-like law, which for lack of a suitable timescale, resorts to an efficiency parameter. With star formation prescribed on a viscous timescale however, we find gas and star fractions after $\sim$ 12 Gyr that are consistent with observations without having to invoke any ``fudge factor'' for star formation. Our results strongly suggest that despite our gap in understanding the exact link between star formation and viscosity, the viscous timescale is indeed the natural timescale for star formation.