AT2025ulz and S250818k: Leveraging DESI spectroscopy in the hunt for a kilonova associated with a sub-solar mass gravitational wave candidate

Supplementary material to DESI's publication AT2025ulz and S250818k: DESI Host Galaxy Properties to comply with the data management plan. Abstract On August 18th, 2025, the LIGO–Virgo–KAGRA collaboration reported a sub-threshold gravitational wave candidate detection consistent with a sub-solar-mass neutron star merger, denoted S250818k. An optical transient, AT2025ulz, was discovered within the localization region. AT2025ulz initially appeared to meet the expected behavior of kilonova (KN) emission, the telltale signature of a binary neutron star merger. The transient subsequently rebrightened after ~5 days and developed spectral features characteristic of a Type IIb supernova. In this work, we analyze the observations of the host galaxy of AT2025ulz obtained by the Dark Energy Spectroscopic Instrument (DESI). From the DESI spectrum, we obtain a secure redshift of z = 0.084840±0.000006, which places the transient within 2σ of the gravitational wave distance. Our analysis of the host galaxy's spectral energy distribution reveals a star-forming, dusty galaxy with stellar mass ∼10^10 M⊙, broadly consistent with the population of both short gamma-ray bursts and core-collapse supernova host galaxies. We also present our follow-up of DESI-selected candidate host galaxies using the Fraunhofer Telescope at the Wendelstein Observatory, and show the promise of DESI for associating or rejecting candidate electromagnetic counterparts to gravitational wave alerts. These results emphasize the value of DESI’s extensive spectroscopic dataset in rapidly characterizing host galaxies, enabling spectroscopic host subtraction, and guiding targeted follow-up. Data Here we give the data for all figure as well as the spectrum of the host AT2025ulz. We include the host photometry, the various images, the host spectrum of AT2025ulz, the fastspecfit results of other sGRBs. The data used to compare the SFR and masses of GRBs and CC SN.