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

Radial differential rotation is an important parameter for stellar dynamo theory and for understanding angular momentum transport. 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'. 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 -350 nHz, 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 step size. All the uncertainties on the inferred step size for individual stars are of the order 1 micro Hz. Using 15 stellar models in an ensemble fit, we show that the uncertainty on the average step size is reduced to less than the input step size, which allows us to constrain the sign of the radial differential rotation. We show that a solar-like step size (approximately 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 step size between F, G, and K-type stars larger than 100 nHz can be detected.