Molecular gas in radio galaxies in dense Mpc-scale environments at
  $z=0.4-2.6$
  We investigate the role of dense Mpc-scale environment in processing
molecular gas in distant Low luminosity radio galaxies (LLRGs) in galaxy
(proto-)clusters. We have selected within the COSMOS and DES surveys a sample
of five LLRGs at $z=0.4-2.6$ that show evidence of ongoing star formation on
the basis of their far-infrared emission. We have assembled and modeled the
far-infrared-to-ultraviolet spectral energy distributions (SEDs) of the LLRGs.
We have observed the sources with the IRAM-30m telescope to search for CO
emission. We have then searched for dense Mpc-scale overdensities associated
with the LLRGs using photometric redshifts of galaxies and the Poisson
Probability Method, that we have upgraded using the wavelet-transform
($\mathit{w}$PPM), to characterize the overdensity in the projected space.
Color-color and color-magnitude plots have been derived for the fiducial
cluster members. We set upper limits to the CO emission of the LLRGs, at
$z=0.39, 0.61, 0.91, 0.97$, and $2.6$. For the most distant radio source,
COSMOS-FRI 70 at $z=2.6$, a hint of CO(7$\rightarrow$6) emission is found at
2.2$\sigma$. The upper limits found for the molecular gas content $M({\rm
H}_2)/M_\star<0.11$, 0.09, 1.8, 1.5, and 0.29, respectively, and depletion time
$\tau_{\rm dep}\lesssim(0.2-7)$ Gyr of the five LLRGs are overall consistent
with the values of main sequence field galaxies. Our SED modeling implies large
stellar masses for the LLRGs, in the range $\log(M_\star/M_\odot)=10.9-11.5$,
while the associated Mpc-scale overdensities show a complex morphology. The
color-color and color-magnitude plots suggest that the LLRGs are consistent
with being star forming and on the high-luminosity tail of the red sequence.
The present study increases the limited statistics of distant cluster core
galaxies with CO observations. The radio galaxies of this work are excellent
targets for ALMA and JWST.
