A Pearl in the Shell: an ultra-compact dwarf within the tidal debris surrounding spiral galaxy NGC 7531

Stellar substructures within tidal debris preserve information about their progenitor galaxies' properties, offering insights into hierarchical mass assembly. We examine a compact stellar system (CSS) around the nearby spiral galaxy NGC 7531, including the shell-like tidal debris. Our goals are to determine the nature of the CSS, reconstruct the accretion history, and understand how the large, diffuse shell-like structure formed. We present photometric measurements of the shell-like debris and CSS using DESI Legacy Imaging Survey (LS) data. We obtained Keck/LRIS spectroscopic data for the CSS to confirm its association with NGC 7531 and to derive its star formation history (SFH). Deep ($\sim$27.9 mag/arcsec$^{2}$) amateur telescope images enabled complete characterization of the tidal debris structure. We confirm the CSS is associated with NGC 7531. We rename it NGC 7531-UCD1, since its stellar mass ($3.7_{-0.7}^{+1.0}\times 10^6$ $\mathrm{M}_\odot$), half-light radius ($R_{h} = 0.13 \pm 0.05$ arcsec) and SFH place it as an ultra-compact dwarf galaxy (UCD). NGC 7531-UCD1 was likely a nuclear star cluster (NSC) that was tidally stripped into a UCD- this is further supported by the presence of tidal tails. We quantify the shell-like debris' mass as $M_\star\sim 3$--$11\times 10^8 M_\odot$, implying a merger mass ratio of ~300:1 to 10:1. Our amateur telescope images confirm new pieces of debris, previously unclear in the DESI LS images. N-body simulations reproduce the tidal features, requiring a near radial orbit of the progenitor with two pericentric passages. The first passage coincides with the measured star formation enhancement ~1 Gyr ago. Our findings agree with predictions about the NSC to UCD formation pathway via tidal stripping, and further confirm the presence of these objects outside of our Milky Way.