Elucidating Galaxy Assembly Bias in SDSS
  We investigate the level of galaxy assembly bias in the Sloan Digital Sky
Survey (SDSS) main galaxy redshift survey using ELUCID, a state-of-the-art
constrained simulation that accurately reconstructed the initial density
perturbations within the SDSS volume. On top of the ELUCID haloes, we develop
an extended HOD model that includes the assembly bias of central and satellite
galaxies, parameterized as $\mathcal{Q}_\mathrm{cen}$ and
$\mathcal{Q}_\mathrm{sat}$, respectively, to predict a suite of one- and
two-point observables. In particular, our fiducial constraint employs the
probability distribution of the galaxy overdensity $\delta^g_8$ and the
projected correlation functions of quintiles of galaxies selected by
$\delta^g_8$. We perform extensive tests of the efficacy of our method by
fitting the same observables to mock data using both constrained and
non-constrained simulations. We discover that in many cases the level of cosmic
variance between the two simulations can produce biased constraints that lead
to an erroneous detection of galaxy assembly bias if the non-constrained
simulation is used. When applying our method to the SDSS data, the ELUCID
reconstruction effectively removes an otherwise strong degeneracy between
cosmic variance and galaxy assembly bias in SDSS, enabling us to derive an
accurate and stringent constraint on the latter. Our fiducial ELUCID
constraint, for galaxies above a stellar mass threshold $M_* =
10^{10.2}\,h^{-1}\,M_\odot$, is $\mathcal{Q}_\mathrm{cen} = -0.06\pm0.09$ and
$\mathcal{Q}_\mathrm{sat}=0.08\pm0.12$, indicating no evidence for a
significant galaxy assembly bias in the local Universe probed by SDSS. Finally,
our method provides a promising path to the robust modelling of the galaxy-halo
connection within future spectroscopic surveys like DESI and PFS.
