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 applying the instantaneous recycling approximation to the model equations, we investigate the dust-to-gas ratio of spiral galaxies. Four processes are considered: dust formation from heavy elements ejected by stellar mass loss, dust destruction in supernova remnants, dust destruction in star-forming regions, and accretion of heavy elements onto preexisting dust grains. The equations describe a simplified relation between the dust-to-gas ratio and the metallicity. The relation is independent of the star formation rate. By comparing the theoretical relation with the observational data of nearby spiral galaxies, we show (i) that the accretion process onto the preexisting dust 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.