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.