Asteroseismic inversions for radial differential rotation of Sun-like stars: ensemble fits

Context. Radial differential rotation is an important parameter for stellar dynamo theory and for understanding angular momentum transport.
Aims. We investigate the potential of using a large number of similar stars simultaneously to constrain their average radial differential rotation gradient: we call this “ensemble fitting”.
Methods. We use a range of stellar models along the main sequence, each with a synthetic rotation profile. The rotation profiles are step functions with a step of ΔΩ = −0.35 μHz, which is located at the base of the convection zone. These models are used to compute the rotational splittings of the p modes and to model their uncertainties. We then fit an ensemble of stars to infer the average ΔΩ.
Results. All the uncertainties on the inferred ΔΩ for individual stars are of the order 1 μHz. Using 15 stellar models in an ensemble fit, we show that the uncertainty on the average ΔΩ is reduced to less than the input ΔΩ, which allows us to constrain the sign of the radial differential rotation. We show that a solar-like ΔΩ ≈ 30 nHz can be constrained by an ensemble fit of thousands of main-sequence stars. Observing the number of stars required to successfully exploit the ensemble fitting method will be possible with future asteroseismology missions, such as PLATO. We demonstrate the potential of ensemble fitting by showing that any systematic differences in the average ΔΩ between F, G, and K-type stars larger than 100 nHz could be detected.