Stochastic Properties of Ultralight Scalar Field Gradients

TL;DR

This paper develops a comprehensive stochastic model for ultralight axion-like particle gradients, crucial for interpreting direct detection experiments, especially when data collection spans less than the coherence time.

Contribution

It introduces the first complete stochastic treatment of axion field gradients, including efficient likelihood-based analysis methods applicable regardless of coherence time.

Findings

Stochastic fluctuations significantly impact axion gradient signals.

Ignoring stochasticity can lead to missed detections.

New methods improve data analysis robustness for axion searches.

Abstract

Ultralight axion-like particles are well-motivated dark matter candidates that are the target of numerous direct detection efforts. In the vicinity of the Solar System, such particles can be treated as oscillating scalar fields. The velocity dispersion of the Milky Way determines a coherence time of about 10^6 oscillations, beyond which the amplitude of the axion field fluctuates stochastically. Any analysis of data from an axion direct detection experiment must carefully account for this stochastic behavior to properly interpret the results. This is especially true for experiments sensitive to the gradient of the axion field that are unable to collect data for many coherence times. Indeed, the direction, in addition to the amplitude, of the axion field gradient fluctuates stochastically. We present the first complete stochastic treatment for the gradient of the axion field, including multiple computationally efficient methods for performing likelihood-based data analysis, which can be applied to any axion signal, regardless of coherence time. Additionally, we demonstrate that ignoring the stochastic behavior of the gradient of the axion field can potentially result in failure to discover a true axion signal.