Estimating gas accretion in disc galaxies using the Kennicutt-Schmidt   law
  We show how the existence of a relation between the star formation rate and the gas density, i.e. the Kennicutt-Schmidt law, implies a continuous accretion of fresh gas from the environment into the discs of spiral galaxies. We present a method to derive the gas infall rate in a galaxy disc as a function of time and radius, and we apply it to the disc of the Milky Way and 21 galaxies from the THINGS sample. For the Milky Way, we found that the ratio between the past and current star formation rates is about 2-3, averaged over the disc, but it varies substantially with radius. In the other disc galaxies there is a clear dependency of this ratio with galaxy stellar mass and Hubble type, with more constant star formation histories for small galaxies of later type. The gas accretion rate follows very closely the SFR for every galaxy and it dominates the evolution of these systems. The Milky Way has formed two thirds of its stars after z=1, whilst the mass of cold gas in the disc has remained fairly constant with time. In general, all discs have accreted a significant fraction of their gas after z=1. Accretion moves from the inner regions of the disc to the outer parts, and as a consequence star formation moves inside-out as well. At z=0 the peak of gas accretion in the Galaxy is at about 6-7 kpc from the centre. 
Filippo Fraternali and Matteo Tomassetti
astro-ph.CO