The clustering of galaxies in the DESI imaging legacy surveys DR8: I.
  the luminosity and color dependent intrinsic clustering
  In a recent study, we developed a method to model the impact of photometric
redshift uncertainty on the two-point correlation function (2PCF). In this
method, we can obtain both the intrinsic clustering strength and the
photometric redshift errors simultaneously by fitting the projected 2PCF with
two integration depths along the line-of-sight. Here we apply this method to
the DESI Legacy Imaging Surveys Data Release 8 (LS DR8), the largest galaxy
sample currently available. We separate galaxies into 20 samples in 8 redshift
bins from $z=0.1$ to $z=1.0$, and a few $\rm z$-band absolute magnitude bins,
with $M_{\rm z} \le -20$. These galaxies are further separated into red and
blue sub-samples according to their $M^{0.5}_{\rm r}-M^{0.5}_{\rm z}$ colors.
We measure the projected 2PCFs for all these galaxy (sub-)samples, and fit them
using our photometric redshift 2PCF model. We find that the photometric
redshift errors are smaller in red sub-samples than the overall population. On
the other hand, there might be some systematic photometric redshift errors in
the blue sub-samples, so that some of the sub-samples show significantly
enhanced 2PCF at large scales. Therefore, focusing only on the red and all
(sub-)samples, we find that the biases of galaxies in these (sub-)samples show
clear color, redshift and luminosity dependencies, in that red brighter
galaxies at higher redshift are more biased than their bluer and low redshift
counterparts. Apart from the best fit set of parameters, $\sigma_{z}$ and $b$,
from this state-of-the-art photometric redshift survey, we obtain high
precision intrinsic clustering measurements for these 40 red and all galaxy
(sub-)samples. These measurements on large and small scales hold important
information regarding the cosmology and galaxy formation, which will be used in
our subsequent probes in this series.
