Seismic diagnostics for transport of angular momentum in stars^⋆

II. Interpreting observed rotational splittings of slowly rotating red giant stars

¹ LESIA, CNRS UMR 8109, Université Pierre et Marie Curie, Université Denis Diderot, Observatoire de Paris, 92195 Meudon, France
e-mail: mariejo.goupil@obspm.fr
² Georg-August-Universität Göttingen, Institut für Astrophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
³ Institut d’Astrophysique, Géophysique et Océanographie de l’Université de Liège, Allée du 6 Août 17, 4000 Liège, Belgium
⁴ Observatoire de Paris, GEPI, CNRS UMR 8111, 92195 Meudon, France

Received: 20 August 2012
Accepted: 5 November 2012

Abstract

Asteroseismology based on observations from the space-borne missions CoRoT and Kepler provides a powerful means of testing the modeling of transport processes in stars. Rotational splittings are currently measured for a large number of red giant stars and can provide stringent constraints on the rotation profiles. The aim of this paper is to obtain a theoretical framework for understanding the properties of the observed rotational splittings of red giant stars with slowly rotating cores. This allows us to establish appropriate seismic diagnostics for the rotation of these evolved stars. Rotational splittings were computed for stochastically excited dipolar modes by adopting a first-order perturbative approach for two 1.3 M_⊙ benchmark models that assume slowly rotating cores. For red giant stars with slowly rotating cores, we show that the variation in the rotational splittings of ℓ = 1 modes with frequency depends only on the large frequency separation, the g-mode period spacing, and the ratio of the average envelope to core rotation rates (ℛ). This led us to propose a way to infer directly ℛ from the observations. This method is validated using the Kepler red giant star KIC 5356201. Finally, we provide theoretical support for using a Lorentzian profile to measure the observed splittings for red giant stars.