The 2175 {\AA} dust feature in star-forming galaxies at $1.3\le z\le 1.8$: the dependence on stellar mass and specific star formation rate

We present direct spectroscopic measurements of the broad 2175~{\AA} absorption feature in 505 star-forming main-sequence galaxies at $1.3\le z\le 1.8$ using individual and stacked spectra from the zCOSMOS-deep survey. Significant 2175~{\AA} excess absorption features of moderate strength are measured, especially in the composite spectra. The excess absorption is well described by a Drude profile. The bump amplitude expressed in units of $k(\lambda)=A(\lambda)/E(B-V)$, relative to the featureless Calzetti et al. law, has a range $B_k\approx0.2\textrm{--}0.8$. The bump amplitude decreases with the specific star formation rate (sSFR), while it increases moderately with the stellar mass. However, a comparison with local "starburst" galaxies shows that the high-redshift main-sequence galaxies have stronger bump features, despite having a higher sSFR than the local sample. Plotting the bump strength against the $\Delta\log\mathrm{sSFR}\equiv \log \left( \mathrm{SFR}/\mathrm{SFR_{MS}}\right)$ relative to the main sequence, however, brings the two samples into much better concordance. This may indicate that it is the recent star formation history of the galaxies that determines the bump strength through the destruction of small carbonaceous grains by supernovae and intense radiation fields coupled with the time delay of $\sim1~\mathrm{Gyr}$ in the appearance of carbon-rich asymptotic giant branch stars.