Deep GMRT 610 MHz Observations of the ELAIS N1 Field : Catalogue and Source Counts

This is the first of a series of papers based on sensitive 610 MHz observations of the ELAIS N1 field using the Giant Metrewave Radio Telescope. We describe the observations, processing and source catalogue extraction from a deep image with area of 1.86\,deg$^{2}$ and minimum noise of $\sim$7.1\,$\mu$Jy/beam. We compile a catalogue of 4290 sources with flux densities in the range 28.9\,$\mu$Jy - 0.503\,Jy, and derive the Euclidean-normalized differential source counts for sources with flux densities brighter than $\rm{35.5\,\mu\,Jy}$. Our counts show a flattening at 610 MHz flux densities below 1 mJy. Below the break the counts are higher than previous observations at this frequency, but generally consistent with recent models of the low-frequency source population. The radio catalogue is cross-matched against multi-wavelength data leading to identifications for 92\% and reliable redshifts for 72\% of our sample, with 19\% of the redshifts based on spectroscopy. For the sources with redshifts we use radio and X-ray luminosity, optical spectroscopy and mid-infrared colours to search for evidence of the presence of an Active Galactic Nucleus (AGN). We compare our identifications to predictions of the flux density distributions of star forming galaxies (SFGs) and AGN, and find a good agreement assuming the majority of the sources without redshifts are SFGs. We derive spectral index distributions for a sub-sample. The majority of the sources are steep spectra, with a median spectral index that steepens with frequency; $\mathrm{\alpha^{325}_{610}\,=\,-0.80\,\pm\,0.29}$, $\mathrm{\alpha^{610}_{1400}\,=\,-0.83\,\pm\,0.31}$ and $\mathrm{\alpha^{610}_{5000}\,=\,-1.12\,\pm\,0.15}$.