  The cosmic infrared background (CIB) is the accumulated infrared (IR)
radiation mainly from interstellar dust heated up by early stars. In this work,
we measure the cross-correlation between galaxies from the unWISE catalog and
the CIB maps from the Planck satellite to simultaneously constrain the cosmic
star formation rate (SFR), dust spectral energy distribution (SED), and the
halo occupation distribution (HOD). The unWISE galaxy catalog is divided into
three tomographic bins centered at $z\sim 0.6, 1.1, 1.5$, and the CIB maps are
at 353, 545, and 857 GHz. We measure the cross-correlations between these
galaxy samples and CIB maps and get a 194$\sigma$ signal within an angular
scale $100<\ell<2000$, from which we constrain two CIB halo models from
previous literature and one new model. The SFR, SED, and HOD model parameters
are constrained consistently among the three models. Specifically, the dust
temperature at $z=0$ is constrained $T_0={21.14}^{+1.02}_{-1.34}$ K, which is
slightly lower than $T_0=24.4\pm1.9$ K measured by the Planck collaboration.
The halo mass that gives the most efficient star formation is around
$10^{{11.79}^{+0.73}_{-0.86}}M_{\odot}$. From the model parameters, combined
with the SFR density at $z=0$ synthesized from multi-wavelength observations,
we break the degeneracy between SED and SFR and recover the cosmic star
formation history that is consistent with multi-wavelength surveys. We also
constrain the graybody SED model in agreement with previous measurements from
infrared flux stacking. From the HOD constraints, we derive an increasing trend
of galaxy linear bias along redshifts that agrees with the results from cross-
and auto-correlation with unWise galaxies. This study indicates the power of
using CIB-galaxy cross-correlation to study star formation, dust, and abundance
of galaxies across cosmic time.
