Bayesian least squares deconvolution

¹ Instituto de Astrofísica de Canarias, 38205, La Laguna, Tenerife, Spain
e-mail: aasensio@iac.es
² Departamento de Astrofísica, Universidad de La Laguna, 38205, La Laguna, Tenerife, Spain
³ Université de Toulouse, UPS-OMP, Institut de Recherche en Astrophysique et Planétologie, 31400 Toulouse, France
⁴ CNRS, Institut de Recherche en Astrophysique et Planétologie, 14 avenue Édouard Belin, 31400 Toulouse, France

Received: 24 April 2015
Accepted: 12 September 2015

Abstract

Aims. We 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.