Detection of radio-AGN in dust-obscured galaxies using deep uGMRT radio continuum observations

Radio observations being insensitive to the dust-obscuration, have been exploited to unveil the population of Active Galactic Nuclei (AGN) residing in galaxies with large dust content. In this paper, we investigate the radio characteristics of 321 dust-obscured galaxies (DOGs; S${}_{24\mu \mathrm{m}}$/S${}_{\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{n}\mathrm{d}}$ $\ge$1000) by using mainly deep band-3 (250$-$550 MHz) observations from the upgraded Giant Metrewave Radio Telescope (uGMRT) and 1.5 GHz Jansky Very Large Array (JVLA) observations. We find that, for our sample of DOGs, deep (median noise-rms $=$ 30 $\mu$Jy beam${}^{-1}$) 400 MHz band-3 uGMRT observations yield the highest detection rate (28 per cent) among those obtained with the JVLA, and the LOw Frequency ARray (LOFAR) radio observations and the $XMM-N$ X-ray observations. The radio characteristics of our sample sources, $i.e.,$ linear extent ($<$40 kpc at $z$ $<$1.2), bimodal spectral index (${\alpha }_{400\mathrm{M}\mathrm{H}\mathrm{z}}^{1.5\mathrm{G}\mathrm{H}\mathrm{z}}$) distribution and the radio luminosities (L${}_{1.5\mathrm{G}\mathrm{H}\mathrm{z}}$ $>$5.0 $\times$ 10${}^{23}$ W Hz${}^{-1}$), suggest them to be mainly consist of Compact$-$Steep$-$Spectrum (CSS) or Peaked-Spectrum (PS) sources representing an early phase of the AGN-jet activity in dust-obscured environments. With stacking we find the existence of faint radio emission (S${}_{400\mathrm{M}\mathrm{H}\mathrm{z}}$ = 72.9 $\mu$Jy beam${}^{-1}$ and S${}_{1.5\mathrm{G}\mathrm{H}\mathrm{z}}$ = 29 $\mu$Jy beam${}^{-1}$ with signal-to-noise ratio $\sim$ 20) in otherwise radio-undetected DOGs. Our study revealing the faint emission at a few tens of $\mu$Jy level in high$-z$ DOGs can be used as a test-bed for the deeper radio continuum surveys planned with the Square-Kilometer Array (SKA) and its pathfinders.