Dust, Gas, and Metallicities of Cosmologically Distant Lens Galaxies

We homogeneously analyzed the \chandra\ X-ray observations of 10 gravitational lenses, HE 0047-1756, QJ 0158-4325, SDSS 0246-0805, HE 0435-1223, SDSS 0924+0219, SDSS 1004+4112, HE 1104-1805, PG 1115+080, Q 1355-2257, and Q 2237+0305, to measure the differential X-ray absorption between images, the metallicity, and the dust-to-gas ratio of the lens galaxies. We detected differential absorption in all lenses except SDSS 0924+0219 and HE 1104-1805. This doubles the sample of dust-to-gas ratio measurements in cosmologically distant lens galaxies. We successfully measured the gas phase metallicity of three lenses, Q 2237+0305, SDSS 1004+4112, and B 1152+199 from the X-ray spectra. Our results suggest a linear correlation between metallicity and dust-to-gas ratio (i.e., a constant metal-to-dust ratio), consistent with what is found for nearby galaxies. We obtain an average dust-to-gas ratio $E(B-V)/N_H=1.17^{+0.41}_{-0.31} \times 10^{-22}\rm mag\,cm^2\,atom^{-1}$ in the lens galaxies, with an intrinsic scatter of $\rm0.3\,dex$. Combining these results with data from GRB afterglows and quasar foreground absorbers, we found a mean dust-to-gas ratio $\mdtg,$ now significantly lower than the average Galactic value, $1.7\,\times 10^{-22}\,\rm mag\, cm^{2}\, atoms^{-1}.$ This suggests evolution of dust-to-gas ratios with redshift and lower average metallicities for the higher redshift galaxies, consistent with current metal and dust evolution models of interstellar medium. The slow evolution in the metal-to-dust ratio with redshift implies very rapid dust formation in high redshift ($z>2$) galaxies.