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We perform a stacking analysis of {\it Planck}, {\it AKARI}, InfraredAstronomical Satellite ($IRAS$), Wide-field Infrared Survey Eplorer ($WISE$),and {\it Herschel} images of the largest number of (candidate) protoclusters at$z\sim3.8$ selected from the Hyper Suprime-Cam Subaru Strategic Program(HSC-SSP). Stacking the images of the $179$ candidate protoclusters, thecombined infrared (IR) emission of the protocluster galaxies in the observed$12-850~\mu$m wavelength range is successfully detected with $>5\sigma$significance (at $Planck$). This is the first time that the average IR spectralenergy distribution (SED) of a protocluster has been constrained at $z\sim4$.The observed IR SEDs of the protoclusters exhibit significant excess emissionin the mid-IR compared to that expected from typical star-forming galaxies(SFGs). They are reproduced well using SED models of intense starburst galaxieswith warm/hot dust heated by young stars, or by a population of active galacticnuclei (AGN)/SFG composites. For the pure star-forming model, a total IR (from8 to 1000 $\mu$m) luminosity of $19.3_{-4.2}^{+0.6}\times10^{13}~L_{\odot}$ anda star formation rate (SFR) of $16.3_{-7.8}^{+1.0}\times10^3~M_{\odot}$yr$^{-1}$ are found whereas for the AGN/SFG composite model,$5.1_{-2.5}^{+2.5}\times10^{13}~L_{\odot}$ and$2.1^{+6.3}_{-1.7}\times10^3~M_{\odot}$ yr$^{-1}$ are found. Uncertaintyremaining in the total SFRs; however, the IR luminosities of the most massiveprotoclusters are likely to continue increasing up to $z\sim4$. Meanwhile, nosignificant IR flux excess is observed around optically selected QSOs atsimilar redshifts, which confirms previous results. Our results suggest thatthe $z\sim4$ protoclusters trace dense, intensely star-forming environmentsthat may also host obscured AGNs missed by the selection in the optical.

Planck far-infrared detection of Hyper Suprime-Cam protoclusters at $\bf z\sim4$: hidden AGN and star formation activity