Building a digital twin of a luminous red galaxy spectroscopic survey:
  galaxy properties and clustering covariance
  Luminous red galaxies (LRGs) are one of the key tracers of the large-scale
structure of the Universe used by galaxy surveys. Hence, it is important to
make accurate predictions for their properties and clustering, including the
errors on these statistics. Here, we describe a novel technique which uses the
semi-analytical model of galaxy formation {\sc Galform}, embedded in the
high-resolution $N$-body Planck-Millennium simulation, to populate a thousand
halo catalogues generated using the Parallel-PM $N$-body {\sc glam} code. Our
hybrid scheme allows us to make clustering predictions on scales that cannot be
modelled in the original $N$-body simulation. LRGs are selected in the redshift
range $z=0.6-1$ from the {\sc Galform} output using similar colour-magnitude
cuts in the $r$, $z$ and $W1$ bands to those that will be applied in the Dark
Energy Spectroscopic Instrument (DESI) survey. We find that the LRG-halo
connection is non-trivial, leading to the prediction of a non-standard halo
occupation distribution; in particular, the occupation of central galaxies does
not reach unity for the most massive haloes, and drops with increasing mass.
The {\sc glam} catalogues reproduce the abundance and clustering of the LRGs
predicted by {\sc Galform}, and show good agreement with recent measurements of
the clustering of DESI-like LRGs using photometric redshifts. We use the
\glam{} mocks to compute the covariance matrices for the two-point correlation
function and power spectrum of the LRGs and their background dark matter
density field, revealing important differences. We also make predictions for
the linear-growth rate and the baryon acoustic oscillations distances at
$z=0.6$, $0.74$ and $0.93$. All DESI-like LRG catalogues are made publicly
available.
