Dust-to-Gas Ratio and Metal Abundance in Dwarf Galaxies

We have compared the metallicity (represented by oxygen abundance), X_o, and the dust-to-gas ratio, \Dscr, in a sample of dwarf galaxies. For dwarf irregulars (dIrrs) we find a good correlation between the two quantities, with a power-law index of 0.52 +/- 0.25. Blue compact dwarf (BCD) galaxies do not show such a good correlation; in addition, both the dust-to-gas ratio and the metallicity tend to be higher than for dIrrs. We have then developed a simple but physical analytical model for the above relation. Comparing the model results with the data, we conclude that (i) for low values of \Dscr, the \Dscr-X_o relation is quasi-linear, whereas for higher values, the curve strongly deviates from the linear behavior, implying that the commonly used power-law approximation is very poor; (ii) the deviation from the linear behavior depends critically on the parameter χ, the ``differential'' mass outflow rate from the galaxy in units of the star formation rate, ψ (iii) the shape of the \Dscr-X_o curve does not depend on ψ, but only on χ however, the specific location of a given galaxy on the curve does depend on ψ and (iv) the BCD metallicity segregation is the result of a higher ψ, together with a significant differential mass outflow. Thus, the lack of correlation can be produced by largely different star formation rates and values of χ in these objects.