Measuring the total infrared light from galaxy clusters at z=0.5-1.6:
  connecting stellar populations to dusty star formation
  Massive galaxy clusters undergo strong evolution from z~1.6 to z~0.5, with
overdense environments at high-z characterized by abundant dust-obscured star
formation and stellar mass growth which rapidly give way to widespread
quenching. Data spanning the near- to far-infrared (IR) spectrum can directly
trace this transformation; however, such studies have largely been limited to
the massive galaxy end of cluster populations. In this work, we present ``total
light" stacking techniques spanning 3.4-500{\mu}m aimed at revealing the total
cluster IR emission, including low mass members and potential intracluster
dust. We detail our procedures for WISE, Spitzer, and Herschel imaging,
including corrections to recover the total stacked emission in the case of high
fractions of detected galaxies. We apply our stacking techniques to 232
well-studied massive (log M200/Msun~13.8) clusters across multiple z bins,
recovering extended cluster emission at all wavelengths, typically at >5sigma.
We measure the averaged near- to far-IR radial profiles and SEDs, quantifying
the total stellar and dust content. The near-IR radial profiles are well
described by an NFW model with a high (c~7) concentration parameter. Dust
emission is similarly concentrated, albeit suppressed at small radii
(r<0.2Mpc). The measured SEDs lack warm dust, consistent with the colder SEDs
expected for low mass galaxies. We derive total stellar masses consistent with
the theoretical Mhalo-M_star relation and specific-star formation rates that
evolve strongly with redshift, echoing that of massive (log Mstar/Msun>10)
cluster galaxies. Separating out the massive galaxy population reveals that the
majority of cluster far-IR emission (~70-80%) is provided by the low mass
constituents, which differs from field galaxies. This effect may be a
combination of mass-dependent quenching and excess dust in low mass cluster
galaxies.
