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

TL;DR

This work investigates whether ultra-light dark matter (ULDM) coupled to Standard Model fields can imprint spatial correlations in white dwarf (WD) radius deviations from the canonical mass-radius relation. By modeling ULDM as a three-dimensional, coherently oscillating field and quantifying deviations with Moran's I statistics across WD separations, the authors train a convolutional neural network to infer the ULDM coherence length from simulated data and apply the method to a large WD catalog. Real data show a positive WD deviation correlation at separations up to ~500 pc, but extensive tests reveal this signal is dominated by observational biases (notably for nearby, cool WDs) and distance-dependent systematics, preventing a robust ULDM constraint. The study provides a rigorous framework for ULDM searches with WD structure, highlighting the importance of improved WD models, dust handling, and bias control, and it outlines a pathway to constrain ULDM masses in the $m_{DM} \sim 6\times10^{-24}$–$6\times10^{-22}$ eV range via coherence-length measurements.

Abstract

If dark matter is ultra-light and has certain Standard Model interactions, it can change the mass-radius relation of white dwarf stars. The coherence length of ultra-light dark matter imparts spatial correlations in deviations from the canonical mass-radius relation, and thus white dwarfs 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 white dwarfs. 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 ($\sim10\%$ change in radius) are needed to produce an observable signal given realistic noise sources. We apply our spatial correlation measurement routine to the SDSS catalog of 10,207 DA white dwarfs. We detect a positive spatial correlation among white dwarfs at separations corresponding to a coherence length of $300\pm50$ pc, with an average Z-score of 85 for white dwarfs 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 white dwarfs, and the presence of few, low-temperature white dwarfs with noisy measurements at further distances. With future improvements in white dwarf models and measurement techniques, particularly for cool white dwarfs, this method can provide interesting constraints on ultra-light dark matter models.

Figures (9)

• Figure 1: A simulated sample of 10,207 WDs (black circles) with coordinates drawn from the clean catalog of Sec. \ref{['sec:catalog']}, overlaid on an idealized ULDM background scalar field with coherence length $\Delta x=200$ pc.
• Figure 2: The spatial autocorrelation signal from a simulated catalog of 10,207 WDs with no added sources of noise. The top, middle, and bottom panels show the Moran's I statistic, Z-score, and product of Moran's I and Z-score as a function of the maximum distance between two WDs included in the calculation. The left column shows these statistics for one value of the ULDM coherence length and various maximum observed radius deviations, and the right column shows these statistics for a particular maximum observed radius deviation and various ULDM coherence lengths. The shape of the (Moran's I)$\times$(Z-score) curve indicates the coherence length of the field, with the peak occurring at $\sim1/2-1/3$ the coherence length and the curve reaching a minimum at distances just smaller than the coherence length.
• Figure 3: Same as Fig. \ref{['fig:curves_no_noise']}, but with noise due to dust added. We reduce the strength of the dust effect by a factor of 10. For sufficiently small $\epsilon_\text{max}$, the ULDM signal is washed out by the effect of dust, resulting in a monotonic increase of the (Moran's I)$\times$(Z-score) curve with increasing distance cutoff.
• Figure 4: Same as Figs. \ref{['fig:curves_no_noise']} and \ref{['fig:curves_dust_10']}, but with noise due to thin hydrogen envelope contamination, dust, binary contamination, measurement noise, and distance uncertainty added. We improve measurement uncertainties and reduce the strength of the effect of dust by a factor of 10. For sufficiently small $\epsilon_\text{max}$, the ULDM signal is washed out by the effect of various noise sources, resulting in a monotonically increasing of the (Moran's I)$\times$(Z-score) curve.
• Figure 5: The spatial autocorrelation signal from a simulated catalog of 10,207 WDs with no ULDM effects. The left column shows the Moran's I and Z-score statistic when all noise sources are included, and the right column shows the same but has improvement_factor=effect_strength=10. We find that for some configurations of improvement_factor and effect_strength, we can produce an ULDM-like signal even when not including ULDM, but this signal is much weaker than in simulations including ULDM.