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

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany e-mail: jballot@mpa-garching.mpg.de
² Institut d'Astrophysique Spatiale, UMR 8617, Université Paris-Sud, Bât. 121, 91405 Orsay Cedex, France e-mail: thierry.appourchaux@ias.u-psud.fr
³ School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK e-mail: toutain@bison.ph.bham.ac.uk

Received: 31 December 2007
Accepted: 6 March 2008

Abstract

Context. Thanks to their high quality, new and upcoming asteroseismic observations, with CoRoT, Kepler, and from the ground, benefit from experience gained with helioseismology.

Aims. 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.

Methods. We used different, complementary approaches: we performed either semi-analytical computation of the Hessian matrix, fitting of single mean profiles, or Monte Carlo simulations.

Results. First, we give 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 the determination of a reliable rotational splitting difficult. 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° occurs. We also discuss this issue. Nevertheless, the central frequency and some derived parameters, such as the total power of the mode, are free of such biases.