Bayesian least squares deconvolution

TL;DR

This paper introduces a Bayesian least squares deconvolution method with a Gaussian Process prior, enabling reliable detection of magnetic signals in noisy stellar spectropolarimetric data efficiently and with uncertainty quantification.

Contribution

It presents a novel Bayesian framework for LSD with a flexible GP prior, improving signal detection and uncertainty estimation in stellar spectropolarimetry.

Findings

Successfully detects magnetic signals with few spectral lines

Provides uncertainty estimates for each velocity bin

Operates efficiently on large spectral datasets

Abstract

Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider LSD under the Bayesian framework and we introduce a flexible Gaussian Process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results. We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.