Seismic diagnostics for transport of angular momentum in stars 2. Interpreting observed rotational splittings of slowly-rotating red giant stars

Abstract

Asteroseismology with the space-borne missions CoRoT and Kepler provides a powerful mean 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 rotation of these evolved stars. Rotational splittings for stochastically excited dipolar modes are computed adopting a first-order perturbative approach for two $1.3M_{\odot }$ benchmark models assuming slowly rotating cores. For red giant stars with slowly rotating cores, we show that the variation of the rotational splittings of $\ell =1$ 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 ($\mathcal{R}$). This leds us to propose a way to infer directly $\mathcal{R}$ from the observations. This method is validated using the Kepler red giant star KIC 5356201. Finally, we provide a theoretical support for the use of a Lorentzian profile to measure the observed splittings for red giant stars.

arXiv comment15 pages, 15 figures, accepted for publication in A&A

References in corpus (21)

• Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars
• Fast core rotation in red-giant stars revealed by gravity-dominated mixed modes
• Spin down of the core rotation in red giants
• ADIPLS -- the Aarhus adiabatic oscillation package
• Seismic evidence for a rapidly rotating core in a lower-giant-branch star observed with Kepler
• Seismic diagnostics for transport of angular momentum in stars 1. Rotational splittings from the PMS to the RGB
• Probing the core structure and evolution of red giants using gravity-dominated mixed modes observed with Kepler
• Red-giant seismic properties analyzed with CoRoT
• The underlying physical meaning of the ${\nu }_{\max }-{\nu }_{\mathrm{c}}$ relation
• Theoretical amplitudes and lifetimes of non-radial solar-like oscillations in red giants
• Angular momentum transport in stellar interiors constrained by rotational splittings of mixed modes in red giants
• Mixed modes in red-giant stars observed with CoRoT
• The universal red-giant oscillation pattern; an automated determination with CoRoT data
• Characteristics of solar-like oscillations in red giants observed in the CoRoT exoplanet field
• Acoustic oscillations of rapidly rotating polytropic stars. II. Effects of the Coriolis and centrifugal accelerations
• Solar-like Oscillations (Invited Review)
• Oscillations of alpha UMa and other red giants
• Seismic diagnostics of red giants: first comparison with stellar models
• Gravity modes in rapidly rotating stars. Limits of perturbative methods
• Pulsations of rapidly rotating stars: I. The ACOR numerical code
• Amplitudes of solar-like oscillations in red-giant stars: Evidences for non-adiabatic effects using CoRoT observations

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