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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 $1.3 M_odot$ 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 (${cal R}$). This leds us to propose a way to infer directly ${cal R}$ 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.
Rotational splittings are currently measured for several main sequence stars and a large number of red giants with the space mission Kepler. This will provide stringent constraints on rotation profiles. Our aim is to obtain seismic constraints on the
Since the end of 2018, the Transiting Exoplanet Survey Satellite (TESS) provides high-quality space data on stellar photometry to the astronomical community. We present the results of an analysis of TESS photometric data for known slowly rotating mag
Transport of angular momentum is a long-standing problem in stellar physics which recently became more acute thanks to the observations of the space-borne mission emph{Kepler}. Indeed, the need for an efficient mechanism able to explain the rotation
According to standard stellar evolution, lithium is destroyed throughout most of the evolution of low- to intermediate-mass stars. However, a number of evolved stars on the red giant branch (RGB) and the asymptotic giant branch (AGB) are known to con
It is thought that magnetic fields must be present in the interiors of stars to resolve certain discrepancies between theory and observation (e.g. angular momentum transport), but such fields are difficult to detect and characterise. Asteroseismology