On the use of the ratio of small to large separations in asteroseismic model fitting

Astronomy Unit, Queen Mary University of London Mile End Road London E1 4NS UK
e-mail: I.W.Roxburgh@qmul.ac.uk

Received: 21 February 2013
Accepted: 1 November 2013

Abstract

Aims. We aim to show that model fitting by searching for a best fit of observed and model separation ratios at the same radial orders n is in principle incorrect, and to show that a correct procedure is to compare the model ratios interpolated to the observed frequencies.

Methods. We compare models with different interior structures and outer layers, relate the separation ratios to phase shift differences, conduct model fitting experiments using separation ratios, and relate phase shift differences to internal phase shifts.

Results. We show that the separation ratios of stellar models with the same interior structure, but different outer layers, are not the same when compared at the same radial order n, but are the same when evaluated at the same frequencies by interpolation. The separation ratios trace the phase shift differences as a function of frequency, not of n, and it is the phase shift differences which are determined by the interior structure. We give examples from model fitting where the ratios at the same n values agree but the models have different interior structure, and where the ratios agree when interpolated to the same frequencies and the models have the same interior structure. The correct procedure is to compare observed ratios with model values interpolated to the observed frequencies.