Heating of Galaxy Disks by Dark Satellites

Abstract. We develop an analytic model to calculate the rate at whichgalaxy disks are heated by dark matter substructures orbiting in their halos.Applying these calculations within a model for the growth of disk galaxies ina Λ-dominated cold dark matter universe, we predict the distribution of diskscale heights, and find that 25% of bright galaxies should have a scale heightin excess of 10% of their radial scale length (the height corresponding to theMilky Way’s thin disk), if substructure is the only source of heating. Includingthe heating due to gravitational scattering of stars by molecular clouds increasesthis fraction to 63%. 1. IntroductionA generic prediction of hierarchical models of structure formation, such as thecold dark matter (CDM) model, is that the dark matter halos of galaxies andclusters should contain large amounts of substructure in the form of small, grav-itationally bound subhalos orbiting within the larger potential. A strong test ofthis scenario is to search for gravitational signatures of these subhalos, bypassingtheproblemsofrelatingsubhalostothevisiblematerialinsatellitegalaxies. Per-haps the most direct method of searching for substructure in dark matter halosis to look for gravitational microlensing signatures. This particular constraint isnow reasonably well studied theoretically (as discussed by Dalal & Kochanek inthese proceedings, p. 201). Although the interpretation of the current datasetsleaves some uncertainty, all studies so far find the observed microlensing ratesto be consistent with the abundance of substructure predicted by CDM.An alternative constraint on the amount of substructure in halos can be ob-tained by considering the thicknesses of the stellar disks of galaxies. Subhaloson orbits which pass through a galactic disk will gravitationally perturb the diskand deposit energy into it, gradually heating it and increasing its scale height.The observed thicknesses of galaxy disks therefore set an upper limit on theabundance of substructures. This heating mechanism has been considered be-fore, notably by T´oth & Ostriker (1992) who argued that the thinness of theMilky Way’s disk is inconsistent with a high density (Ω = 1) CDM universe.An accurate calculation of disk heating by halo substructure requires an ac-curate knowledge of the initial orbits of the subhalos, of how these orbits evolve125