The Environments of Luminous Radio - WISE Selected Infrared Galaxies
  We have observed the environments of a population of 33 heavily dust
obscured, ultra-luminous, high-redshift galaxies, selected using WISE and NVSS
at $z>$1.3 with the Infra-Red Array Camera on the $Spitzer$ Space Telescope
over $\rm5.12\,'\times5.12\,'$ fields. Colour selections are used to quantify
any potential overdensities of companion galaxies in these fields. We find no
significant excess of galaxies with the standard colour selection for IRAC
colours of $\rm[3.6]-[4.5]>-0.1$ consistent with galaxies at $z>$1.3 across the
whole fields with respect to wide-area $Spitzer$ comparison fields, but there
is a $\rm>2\sigma$ statistical excess within $\rm0.25\,'$ of the central
radio-WISE galaxy. Using a colour selection of $\rm[3.6]-[4.5]>0.4$, 0.5
magnitudes redder than the standard method of selecting galaxies at $z>$1.3, we
find a significant overdensity, in which $\rm76\%$ ($\rm33\%$) of the 33 fields
have a surface density greater than the $\rm3\sigma$ ($\rm5\sigma$) level.
There is a statistical excess of these redder galaxies within $\rm0.5\,'$,
rising to a central peak $\rm\sim2$--4 times the average density. This implies
that these galaxies are statistically linked to the radio-WISE selected galaxy,
indicating similar structures to those traced by red galaxies around radio-loud
AGN.
