Direct measurements of dust attenuation in z~1.5 star-forming galaxies
  from 3D-HST: Implications for dust geometry and star formation rates
  The nature of dust in distant galaxies is not well understood, and until
recently few direct dust measurements have been possible. We investigate dust
in distant star-forming galaxies using near-infrared grism spectra of the
3D-HST survey combined with archival multi-wavelength photometry. These data
allow us to make a direct comparison between dust around star-forming regions
($A_{V,\mathrm{HII}}$) and the integrated dust content ($A_{V,\mathrm{star}}$).
We select a sample of 163 galaxies between $1.36\le{}z\le1.5$ with H$\alpha$
signal-to-noise ratio $\ge5$ and measure Balmer decrements from stacked spectra
to calculate $A_{V,\mathrm{HII}}$. First, we stack spectra in bins of
$A_{V,\mathrm{star}}$, and find that
$A_{V,\mathrm{HII}}=1.86\,A_{V,\mathrm{star}}$, with a significance of
$\sigma=1.7$. Our result is consistent with the two-component dust model, in
which galaxies contain both diffuse and stellar birth cloud dust. Next, we
stack spectra in bins of specific star formation rate ($\log\,\mathrm{SSFR}$),
star formation rate ($\log\,\mathrm{SFR}$), and stellar mass ($\log{}M_*$). We
find that on average $A_{V,\mathrm{HII}}$ increases with SFR and mass, but
decreases with increasing SSFR. Interestingly, the data hint that the amount of
extra attenuation decreases with increasing SSFR. This trend is expected from
the two-component model, as the extra attenuation will increase once older
stars outside the star-forming regions become more dominant in the galaxy
spectrum. Finally, using Balmer decrements we derive dust-corrected H$\alpha$
SFRs, and find that stellar population modeling produces incorrect SFRs if
rapidly declining star formation histories are included in the explored
parameter space.
