New constraints on the 1.4 GHz source number counts and luminosity functions in the Lockman Hole field

We present a study of the 1173 sources brighter than $S_{1.4\,\rm GHz}= 120\,\mu$Jy detected over an area of $\simeq 1.4\,\hbox{deg}^{2}$ in the Lockman Hole field. Exploiting the multi-band information available in this field for $\sim$79% of the sample, sources have been classified into radio loud (RL) active galactic nuclei (AGNs), star forming galaxies (SFGs) and radio quiet (RQ) AGNs, using a variety of diagnostics available in the literature. Exploiting the observed tight anti-correlations between IRAC band 1 or band 2 and the source redshift we could assign a redshift to 177 sources missing a spectroscopic measurement or a reliable photometric estimate. A Monte Carlo approach was used to take into account the spread around the mean relation. The derived differential number counts and luminosity functions at several redshifts of each population show a good consistency with models and with earlier estimates made using data from different surveys and applying different approaches. Our results confirm that below $\sim300\,\mu$Jy SFGs$+$RQ AGNs overtake RL AGNs that dominate at brighter flux densities. We also confirm earlier indications of a similar evolution of RQ AGNs and SFGs. Finally, we discuss the angular correlation function of our sources and highlight its sensitivity to the criteria used for the classification.