Stellar Populations of over one thousand $z\sim0.8$ Galaxies from
  LEGA-C: Ages and Star Formation Histories from D$_n$4000 and H$\delta$
  Drawing from the LEGA-C dataset, we present the spectroscopic view of the
stellar population across a large volume- and mass-selected sample of galaxies
at large lookback time. We measure the 4000\AA\ break (D$_n$4000) and Balmer
absorption line strengths (probed by H$\delta$) from 1019 high-quality spectra
of $z=0.6 - 1.0$ galaxies with $M_\ast = 2 \times 10^{10} M_\odot - 3 \times
10^{11} M_\odot$. Our analysis serves as a first illustration of the power of
high-resolution, high-S/N continuum spectroscopy at intermediate redshifts as a
qualitatively new tool to constrain galaxy formation models. The observed
D$_n$4000-EW(H$\delta$) distribution of our sample overlaps with the
distribution traced by present-day galaxies, but $z\sim 0.8$ galaxies populate
that locus in a fundamentally different manner. While old galaxies dominate the
present-day population at all stellar masses $> 2\times10^{10} M_\odot$, we see
a bimodal D$_n$4000-EW(H$\delta$) distribution at $z\sim0.8$, implying a
bimodal light-weighted age distribution. The light-weighted age depends
strongly on stellar mass, with the most massive galaxies
$>1\times10^{11}M_\odot$ being almost all older than 2 Gyr. At the same time we
estimate that galaxies in this high mass range are only $\sim3$ Gyr younger
than their $z\sim0.1$ counterparts, at odd with pure passive evolution given a
difference in lookback time of $>5$ Gyr; younger galaxies must grow to
$>10^{11}M_\odot$ in the meantime, and/or small amounts of young stars must
keep the light-weighted ages young. Star-forming galaxies at $z\sim0.8$ have
stronger H$\delta$ absorption than present-day galaxies with the same
D$_n$4000, implying larger short-term variations in star-formation activity.
