Dark Subhaloes and Disturbances in Extended HI Discs
  We develop a perturbative approach to study the excitation of disturbances in the extended atomic hydrogen (HI) discs of galaxies produced by passing dark matter subhaloes. The shallow gravitational potential of the dark matter subhaloes (compared to the primary halo) allows us to use the epicyclic approximation, the equations of which we solve by modal analysis, i.e., assuming a disc is composed of N radial rings with M modes. We show that properties of dark matter subhaloes can be inferred from the profile and amplitude of the modal energy of the disc. Namely, we find that the overall amplitude of the response gives the mass of the dark sub-halo. Motivated by this modal analysis, we then show that the density response shows similar features. Finally, we show that our results agree with those from full hydrodynamic simulation. We find a simple scaling relation between the satellite mass and Fourier amplitudes of the resultant surface density of the gas disc where the effective Fourier amplitude (essentially a sum over the low order modes) scales as $m_{s}^{1/2}$, where $m_{s}$ is the satellite mass. The utility of this relation is that it can be readily applied to an observed HI map to deduce the satellite mass without recourse to full numerical simulation. This will greatly aid us in analyzing large samples of spiral galaxies to constrain the population of dwarf satellites in the Local Volume. 
Philip Chang and Sukanya Chakrabarti
astro-ph.CO astro-ph.GA