Searching for Ultra-light Dark Matter in Spatial Correlations of White Dwarf Structure

Abstract If dark matter is ultra-light and has certain Standard Model interactions, it can change the mass–radius relation of white dwarf (WD) stars. The coherence length of ultra-light dark matter (ULDM) imparts spatial correlations in deviations from the canonical mass–radius relation, and thus, WDs can be used to reconstruct the coherence length, or equivalently the particle mass, of the dark matter field. We simulate the observability of such spatial correlations accounting for realistic complications like variable hydrogen envelope thickness, dust, binaries, measurement noise, and distance uncertainties in DA WDs. Using a machine learning approach on simulated data, we measure the dark matter field coherence length and find that large deviations from the mass–radius relation (∼10% change in radius) are needed to produce an observable signal given realistic noise sources. We apply our spatial correlation measurement routine to the Sloan Digital Sky Survey catalog of 10,207 DA WDs. We detect a positive spatial correlation among WDs at separations corresponding to a coherence length of 300 ± 50 pc, with an average Z -score of 85 for WDs separated by less than this coherence length. We conclude that this signal is due to observational bias. The signal can be explained by an offset between measurements and theory for nearby cool WDs, and the presence of few, low-temperature WDs with noisy measurements at farther distances. With future improvements in WD models and measurement techniques, particularly for cool WDs, this method can provide interesting constraints on ULDM models.