The LEGA-C of nature and nurture in stellar populations of galaxies at
  z~0.6-1.0: D4000 and H-delta reveal different assembly histories for
  quiescent galaxies in different environments
  Galaxy evolution is driven by a variety of physical processes which are
predicted to proceed at different rates for different dark matter haloes and
environments across cosmic times. A record of this evolution is preserved in
galaxy stellar populations, which we can access using absorption-line
spectroscopy. Here we explore the large LEGA-C survey (DR3) to investigate the
role of the environment and stellar mass on stellar populations at z~0.6-1.0 in
the COSMOS field. Leveraging the statistical power and depth of LEGA-C, we
reveal significant gradients in D4000 and H-delta equivalent widths (EWs)
distributions over the stellar mass vs environment 2D spaces for the massive
galaxy population (M>10^10 M$_{\odot}$) at z~0.6-1.0. D4000 and H-delta EWs
primarily depend on stellar mass, but they also depend on environment at fixed
stellar mass. By splitting the sample into centrals and satellites, and in
terms of star-forming galaxies and quiescent galaxies, we reveal that the
significant environmental trends of D4000 and H-delta EW when controlling for
stellar mass are driven by quiescent galaxies. Regardless of being centrals or
satellites, star-forming galaxies reveal D4000 and H-delta EWs which depend
strongly on their stellar mass and are completely independent of the
environment at 0.6<z<1.0. The environmental trends seen for satellite galaxies
are fully driven by the trends that hold only for quiescent galaxies, combined
with the strong environmental dependency of the quiescent fraction at fixed
stellar mass. Our results are consistent with recent predictions from
simulations that point towards massive galaxies forming first in over-densities
or the most compact dark matter haloes.
