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.
