Publication
Context. Low luminosity radio galaxies (LLRGs) typically reside in dense megaparsec-scale environments and are often associated with brightest cluster galaxies (BCGs). They are an excellent tool to study the evolution of molecular gas reservoirs in giant ellipticals, even close to the active galactic nucleus. Aims. We investigate the role of dense megaparsec-scale environment in processing molecular gas in LLRGs in the cores of galaxy (proto-)clusters. To this aim we 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 (FIR) emission. Methods. We assembled and modeled the FIR-to-UV spectral energy distributions (SEDs) of the five radio sources to characterize their host galaxies in terms of stellar mass and star formation rate. We observed the LLRGs with the IRAM-30m telescope to search for CO emission. We then searched for dense megaparsec-scale overdensities associated with the LLRGs using photometric redshifts of galaxies and the Poisson Probability Method, which we have upgraded using an approach based on the wavelet-transform (wPPM), to ultimately characterize the overdensity in the projected space and estimate the radio galaxy miscentering. Color-color and colormagnitude plots were then derived for the fiducial cluster members, selected using photometric redshifts. Results. Our IRAM-30m observations yielded 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 -> 6) emission is found at 2.2 sigma. The upper limits found for the molecular gas content M(H-2) = M-star< 0 : 11, 0.09, 1.8, 1.5, and 0.29, respectively, and depletion time tau(dep) less than or similar to (0.2-7) Gyr of the five LLRGs are overall consistent with the corresponding values of main sequence field galaxies. Our SED modeling implies large stellar-mass estimates in the range log(M-star/M-Theta) = 10.9-11.5, typical for giant ellipticals. Both our wPPM analysis and the cross-matching of the LLRGs with existing cluster/group catalogs suggest that the megaparsec-scale overdensities around our LLRGs are rich (less than or similar to 10(14) M-Theta) groups and 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 thus increases the still limited statistics of distant cluster core galaxies with CO observations. Conclusions. The radio galaxies of this work are excellent targets for ALMA as well as next-generation telescopes such as the James Webb Space Telescope.