"Super-deblended" Dust Emission in Galaxies: II. Far-IR to
  (sub)millimeter photometry and high redshift galaxy candidates in the full
  COSMOS field
  We present a "super-deblended" far-infrared to (sub)millimeter photometric
catalog in the Cosmic Evolution Survey (COSMOS), prepared with the method
recently developed by Liu et al. 2018, with key adaptations. We obtain point
spread function (PSF) fitting photometry at fixed prior positions including
88,008 galaxies detected in either VLA 1.4~GHz, 3~GHz and/or MIPS 24~$\mu$m
images. By adding a specifically carved mass-selected sample (with an evolving
stellar mass limit), a highly complete prior sample of 194,428 galaxies is
achieved for deblending FIR/(sub)mm images. We performed ``active' removal of
non relevant priors at FIR/(sub)mm bands using spectral energy distribution
(SED) fitting and redshift information. In order to cope with the shallower
COSMOS data we subtract from the maps the flux of faint non-fitted priors and
explicitly account for the uncertainty of this step. The resulting photometry
(including data from Spitzer, Herschel, SCUBA2, AzTEC, MAMBO and NSF's Karl G.
Jansky Very Large Array at 3~GHz and 1.4~GHz) displays well behaved
quasi-Gaussian uncertainties, calibrated from Monte Carlo simulations and
tailored to observables (crowding, residual maps). Comparison to ALMA
photometry for hundreds of sources provide a remarkable validation of the
technique. We detect 11,220 galaxies over the 100--1200~$\mu$m range, extending
to $z_{\rm phot}\sim7$. We conservatively selected a sample of 85 $z>4$ high
redshift candidates, significantly detected in the FIR/(sub)mm, often with
secure radio and/or Spitzer/IRAC counterparts. This provides a chance to
investigate the first generation of vigorous starburst galaxies
(SFRs$\sim1000\mathrm{M}_\odot$~yr$^{-1}$). The photometric and value added
catalogs are publicly released.
