The LOFAR LBA Sky Survey: Deep Fields I. The Bo\"otes Field

We present the first sub-mJy ($\approx0.7$ mJy beam$^{-1}$) survey to be completed below 100 MHz, which is over an order of magnitude deeper than previously achieved for widefield imaging of any field at these low frequencies. The high resolution ($15 \times 15$ arcsec) image of the Bo\"otes field at 34-75 MHz is made from 56 hours of observation with the LOw Frequency ARray (LOFAR) Low Band Antenna (LBA) system. The observations and data reduction, including direction-dependent calibration, are described here. We present a radio source catalogue containing 1,948 sources detected over an area of $23.6$ deg$^2$, with a peak flux density threshold of $5\sigma$. Using existing datasets, we characterise the astrometric and flux density uncertainties, finding a positional uncertainty of $\sim1.2$ arcsec and a flux density scale uncertainty of about 5 per cent. Using the available deep 144-MHz data, we identified 144-MHz counterparts to all the 54-MHz sources, and produced a matched catalogue within the deep optical coverage area containing 829 sources. We calculate the Euclidean-normalised differential source counts and investigate the low-frequency radio source spectral indices between 54 and 144 MHz, both of which show a general flattening in the radio spectral indices for lower flux density sources, from $\sim-0.75$ at 144-MHz flux densities between 100-1000 mJy to $\sim-0.5$ at 144-MHz flux densities between 5-10 mJy, due to a growing population of star forming galaxies and compact core-dominated AGN.