ALMA reveals a warm and compact starburst around a heavily obscured
  supermassive black hole at z=4.75
  We report ALMA Cycle 0 observations at 1.3mm of LESS J033229.4-275619
(XID403), an Ultraluminous Infrared Galaxy at $z=4.75$ in the Chandra Deep
Field South hosting a Compton-thick QSO. The source is not resolved in our data
at a resolution of $\sim$0.75 arcsec, placing an upper-limit of 2.5 kpc to the
half-light radius of the continuum emission from heated-dust. After
deconvolving for the beam size, however, we found a $\sim3\sigma$ indication of
an intrinsic source size of $0.27\pm0.08$ arcsec (Gaussian FWHM), which would
correspond to $r_{half}\sim0.9\pm0.3$ kpc. We build the far-IR SED of XID403 by
combining datapoints from both ALMA and Herschel and fit it with a modified
blackbody spectrum. For the first time, we measure the dust temperature
$T_d=58.5\pm5.3$ K in this system, which is comparable to what has been
observed in other high-z submillimeter galaxies. The measured star formation
rate is SFR=$1020\pm150$ $M_{\odot}$ yr$^{-1}$, in agreement with previous
estimates at lower S/N. Based on the measured SFR and source size, we constrain
the SFR surface density to be $\Sigma_{SFR}>26\;M_{\odot}$yr$^{-1}$kpc$^{-2}$
($\sim200\;M_{\odot}$yr$^{-1}$kpc$^{-2}$ for $r_{half}\sim0.9$ kpc). The
compactness of this starburst is comparable to what has been observed in other
local and high-z starburst galaxies. If the gas mass measured from previous
[CII] and CO(2-1) observations at low resolution is confined within the same
dust region, assuming $r_{half}\sim0.9\pm0.3$ kpc, this would produce a column
density of $N_H\sim0.3-1.1\times10^{24}$cm$^{-2}$ towards the central SMBH,
similar to the column density of $\approx1.4\times10^{24}$cm$^{-2}$ measured
from the X-rays. Then, in principle, if both gas and dust were confined on
sub-kpc scales, this would be sufficient to produce the observed X-ray column
density without any need of a pc-scale absorber [abridged].
