Global Law for the Dust-to-Gas Ratio of Spiral Galaxies

Using a one-zone model for the evolution of dust in spiral galaxies andapplying the instantaneous recycling approximation to the model equations, weinvestigate dust-to-gas ratio of spiral galaxies. Four processes areconsidered; dust formation from heavy elements ejected by stellar mass loss,dust destruction in supernova remnants, dust destruction in star-formingregions, and accretion of heavy elements onto preexisting dust grains. Theequations describe a simplified relation between dust-to-gas ratio andmetallicity. The relation is independent of star formation rate. By comparingthe theoretical relation with the observational data of nearby spiral galaxies,we show (i) that the accretion process onto the preexisting dust particles mustbe taken into account for the spiral galaxies; (ii) that the efficiency of dustproduction from heavy elements ejected by stars can be constrained by thespiral galaxies with low metallicity; (iii) that the Salpeter and Scalo initialmass functions are both consistent with the data of the spiral galaxies.Comment: 9 pages LaTeX, 3 figures, to appear in ApJ Letter