LIGHTS. Survey Overview and a Search for Low Surface Brightness Satellite Galaxies

We present an overview of the LIGHTS (LBT Imaging of Galactic Halos and Tidal Structures) survey, which currently includes 25 nearby galaxies that are on average $\sim$ 1 mag fainter than the Milky Way, and a catalog of 54 low central surface brightness (24 $< \mu_{0,g}$/mag arcsec$^{-2} < 28$) satellite galaxy candidates, most of which were previously uncatalogued. The depth of the imaging exceeds the full 10-year depth of the Rubin Observatory's Legacy Survey of Space and Time (LSST). We find, after applying completeness corrections, rising numbers of candidate satellites as we approach the limiting luminosity (M$_r \sim -8$ mag) and central surface brightness ($\mu_{0,g} \sim 28$ mag arcsec$^{-2}$). Over the parameter range we explore, each host galaxy (excluding those that are in overdense regions, apparently groups) has nearly 4 such candidate satellites to a projected radius of $\sim$ 100 kpc. These objects are mostly just at or beyond the reach of spectroscopy unless they are H I rich or have ongoing star formation. We identify 3, possibly 4, ultra-diffuse satellite galaxies (UDGs; effective radius $> 1.5$ kpc). This incidence rate falls within expectations of the extrapolation of the published relationship between the number of UDGs and host halo mass. Lastly, we visually identify 12 candidate satellites that host a nuclear star cluster (NSC). The NSC occupation fraction for the sample (12/54) matches that published for satellites of early-type galaxies, suggesting that the parent's morphological type plays at most a limited role in determining the NSC occupation fraction.