Inequalities on stellar rotational splittings derived from assumptions on the rotation profile

¹ School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
e-mail: dreese@bison.ph.bham.ac.uk
² Stellar Astrophysics Centre (SAC), Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark

Received: 15 July 2014
Accepted: 9 March 2015

Abstract

Context. A number of pulsating stars with rotational splittings, in particular subgiants and giants, have been observed thanks to the CoRoT and Kepler missions. This has led various groups to investigate their rotation profiles via different methods.

Aims. We would like to set up some criteria that will help us to know whether a decreasing rotation profile, or one that satisfies Rayleigh’s stability criterion, is compatible with a set of observed rotational splittings for a given reference model.

Methods. We derive inequalities on the rotational splittings using a reformulated version of the equation that relates the splittings to the rotation profile and kernels.

Results. These inequalities are tested out on some simple examples. The first examples show how they are able to reveal when a rotation profile is increasing somewhere or inconsistent with Rayleigh’s criterion in a main sequence star, depending on the profile and the ℓ values of the splittings. The next example illustrates how a slight mismatch between an observed evolved star and a reference model can lead to erroneous conclusions about the rotation profile. We also show how frequency differences between the star and the model, which should normally reveal this mismatch, can be masked by frequency corrections for near-surface effects.