Downsizing of Star Formation Measured from the Clustered Infrared
  Background Correlated with Quasars
  Powerful quasars can be seen out to large distances. As they reside in
massive dark matter haloes, they provide a useful tracer of large scale
structure. We stack Herschel-SPIRE images at 250, 350 and 500 microns at the
location of 11,235 quasars in ten redshift bins spanning $0.5 \leq z \leq 3.5$.
The unresolved dust emission of the quasar and its host galaxy dominate on
instrumental beam scales, while extended emission is spatially resolved on
physical scales of order a megaparsec. This emission is due to dusty
star-forming galaxies clustered around the dark matter haloes hosting quasars.
We measure radial surface brightness profiles of the stacked images to compute
the angular correlation function of dusty star-forming galaxies correlated with
quasars. We then model the profiles to determine large scale clustering
properties of quasars and dusty star-forming galaxies as a function of
redshift. We adopt a halo model and parameterize it by the most effective halo
mass at hosting star-forming galaxies, finding $\log(M_\mathrm{eff}/M_{\odot})
= 13.8^{+0.1}_{-0.1}$ at $z=2.21-2.32$, and, at $z=0.5-0.81$, the mass is
$\log(M_\mathrm{eff}/M_{\odot}) = 10.7^{+1.0}_{-0.2}$. Our results indicate a
downsizing of dark matter haloes hosting dusty star-forming galaxies between
$0.5 \leq z \leq 2.9$. The derived dark matter halo masses are consistent with
other measurements of star-forming and sub-millimeter galaxies. The physical
properties of dusty star-forming galaxies inferred from the halo model depend
on details of the quasar halo occupation distribution in ways that we explore
at $z>2.5$, where the quasar HOD parameters are not well constrained.
