Simplifying asteroseismic analysis of solar-like oscillators

An application of principal component analysis for dimensionality reduction

¹ School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK
e-mail: m.b.nielsen.1@bham.ac.uk
² Advanced Research Computing, University of Birmingham, Birmingham B15 2TT, UK
³ Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

Received: 6 February 2023
Accepted: 11 June 2023

Abstract

Context. The asteroseismic analysis of stellar power density spectra is often computationally expensive. The models used in the analysis may require several dozen parameters to accurately describe features in the spectra caused by the oscillation modes and surface granulation. Many of these parameters are often highly correlated, making the parameter space difficult to quickly and accurately sample. They are, however, all dependent on a much smaller set of parameters, namely the fundamental stellar properties.

Aims. We aim to leverage this to develop a method for simplifying the process of sampling the model parameter space for the asteroseismic analysis of solar-like oscillators, with an emphasis on mode identification.

Methods. Using a large set of previous observations, we applied principal component analysis to the sample covariance matrix to select a new basis on which to sample the model parameters. Selecting the subset of basis vectors that explains the majority of the sample variance, we then redefined the model parameter prior probability density distributions in terms of a smaller set of latent parameters.

Results. We are able to reduce the dimensionality of the sampled parameter space by a factor of two to three. The number of latent parameters needed to accurately model the stellar oscillation spectra cannot be determined exactly but is likely only between four and six. Using two latent parameters, the method is able to produce models that describe the bulk features of the oscillation spectrum, while including more latent parameters allows for a frequency precision better than ≈10% of the small frequency separation for a given target.

Conclusions. We find that sampling a lower-rank latent parameter space still allows for accurate mode identification and parameter estimation on solar-like oscillators over a wide range of evolutionary stages. This allows for the potential to increase the complexity of spectrum models without a corresponding increase in computational expense.