Abstract
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.
Highlights
The differential rotation of the solar interior is an important constraint for solar dynamo models (Charbonneau 2010)
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
Our findings suggest that inversions for the radial differential rotation of subgiant stars would benefit from more tightly constrained stellar models
Summary
The differential rotation of the solar interior is an important constraint for solar dynamo models (Charbonneau 2010). Inferring the radial differential rotation of stars requires measuring the splittings of modes and solving an inversion problem for the rotation using some stellar model. Inverting for the rotation given the rotational splittings is, mathematically, an ill-posed problem It is usually solved using some flavour of linear inversion technique, such as regularised least squares (RLS), which have proved successful for the case of the Sun Deheuvels et al (2014) inferred the radial differential rotation for a subgiant star with two stellar models computed by different stellar evolution codes (ASTEC and CESAM2K) They found no significant difference in the inversion results. We quantify the sensitivity of the RLS inversions for radial differential rotation to the use of rotation kernels constructed from an improper stellar model for a Sun-like star, HD 52265, and a subgiant star, KIC 7341231.
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