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

Context. 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. 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 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. Results. 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◦ 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.