The spectral study of the faint radio sources in the ELAIS N1 field

Understanding the spectral properties of sources is crucial for the characterization of the radio source population. In this work, we have extensively studied the ELAIS N1 field using various low-frequency radio observations. For the first time, we present the 1250\,MHz observations of the field using the upgraded Giant Meterwave Radio Telescope (uGMRT) that reach a central off-source RMS noise of $\sim 12\,\mu$Jy\,beam$^{-1}$. A source catalogue of 1086 sources is compiled at $5\sigma$ threshold ($>60\,\mu$Jy) to derive the normalized differential source counts at this frequency that is consistent with existing observations and simulations. We present the spectral indices derived in two ways: two-point spectral indices and by fitting a power-law. The latter yielded a median $\alpha = -0.57\pm 0.14$, and we identified nine ultra-steep spectrum sources using these spectral indices. Further, using a radio colour diagram, we identify the three mega-hertz peaked spectrum (MPS) sources, while three other MPS sources are identified from the visual inspection of the spectra, the properties of which are discussed. In our study of the classified sources in the ELAIS N1 field, we present the relationship between $\alpha$ and $z$. We find no evidence of an inverse correlation between these two quantities and suggest that the nature of the radio spectrum remains independent of the large-scale properties of the galaxies that vary with redshifts.