On deriving p-mode parameters for inclined solar-like stars

TL;DR

This paper provides a theoretical analysis of the errors, biases, and correlations in determining p-mode parameters of inclined solar-like stars, highlighting challenges in measuring inclination and rotational splitting.

Contribution

It introduces analytical approximations and simulation approaches to assess uncertainties and biases in p-mode parameter estimation for stars with unknown inclination angles.

Findings

Inclination determination is difficult for slow rotators like the Sun.

Biases can occur in parameter estimation due to inclination locking at 90 degrees.

Central frequency and mode power are reliably estimated without bias.

Abstract

Thanks to their high quality, new and upcoming asteroseismic observations - with CoRoT, Kepler, and from the ground... - can benefit from the experience gained with helioseismology. We focus in this paper on solar-like oscillations, for which the inclination of the rotation axis is unknown. We present a theoretical study of the errors of p-mode parameters determined by means of a maximum-likelihood estimator, and we also analyze correlations and biases. We have used different, complementary approaches: we have performed either semi-analytical computation of the Hessian matrix, fitting of single mean profiles, or Monte Carlo simulations. We give first analytical approximations for the errors of frequency, inclination and rotational splitting. The determination of the inclination is very challenging for the common case of slow rotators (like the Sun), making difficult the determination of a reliable rotational splitting. Moreover, due to the numerous correlations, biases - more or less significant - can appear in the determination of various parameters in the case of bad inclination fittings, especially when a locking at 90 degrees occurs. This issue concerning inclination locking is also discussed. Nevertheless, the central frequency and some derived parameters such as the total power of the mode are free of such biases.