Global law for the dust-to-gas ratio of spiral galaxies

Using a one-zone model for the evolution of dust in spiral galaxies and app lying the instantaneous recycling approximation to the model equations, we investigate the dust-to-gas ratio of spiral galaxies. Four processes are co nsidered: dust formation from heavy elements ejected by stellar mass loss, dust destruction in supernova remnants, dust destruction in star-forming re gions, and accretion of heavy elements onto preexisting dust grains. The eq uations describe a simplified relation between the dust-to-gas ratio and th e metallicity. The relation is independent of the star formation rate. By c omparing the theoretical relation with the observational data of nearby spi ral galaxies, we show (i) that the accretion process onto the preexisting d ust particles must be taken into account for the spiral galaxies, (ii) that the efficiency of dust production from heavy elements ejected by stars can be constrained by the spiral galaxies with low metallicity, and (iii) that the Salpeter and Scale initial mass functions are both consistent with the data of the spiral galaxies.