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Asteroseismic inversions for radial differential rotation of Sun-like stars: Sensitivity to uncertainties

We quantify the effect of observational spectroscopic and asteroseismic uncertainties on regularised least squares (RLS) inversions for the radial differential rotation of Sun-like and subgiant stars. We first solved the forward problem to model rotational splittings plus the observed uncertainties for models of a Sun-like star, HD 52265, and a subgiant star, KIC 7341231. We randomly perturbed the parameters of the stellar models within the uncertainties of the spectroscopic and asteroseismic constraints and used these perturbed stellar models to compute rotational splittings. We experimented with three rotation profiles: solid body rotation, a step function, and a smooth rotation profile decreasing with radius. We then solved the inverse problem to infer the radial differential rotation profile using a RLS inversion and kernels from the best-fit stellar model.We found that the inversions for Sun-like stars with solar-like radial differential rotation profiles are insensitive to the uncertainties in the stellar models. We found that when the rotation rate below the convection zone is increased to six times that of the surface rotation rate the inferred rotation profile excluded solid body rotation. With the current observational uncertainties, we found that inversions of subgiant stars are sensitive to the uncertainties in the stellar model. Our findings suggest that inversions for the radial differential rotation of subgiant stars would benefit from more tightly constrained stellar models. In Sun-like stars, the insensitivity of the inversions to stellar model uncertainties suggests that it may be possible to perform ensemble inversions for the average radial differential rotation of many stars with a range of stellar types to better constrain the inversions.