What can rotational splittings of low-luminosity subgiants actually tell us about the rotation profile?

Abstract

Context. Inversions of the rotation profile using rotationally induced splittings of low-luminosity subgiant stars suggest that angular momentum transport mechanisms must be 1-2 orders of magnitude more efficient than theory predicts. The lack of precise high resolution of measurements of the rotation profile limits our understanding of the physical mechanism inducing excess angular momentum transport. Rotational inversions are limited to some positions in a star and are restricted in accuracy and resolution by the number of observed splittings, the specific modes of the splittings that are observed, and their associated uncertainties. For example, state-of-the-art observations of rotational splittings of low-luminosity subgiants are limited to low degree = 1 and 2 modes, offering only limited precision measures of the core and surface rotation rates, not the shape of the rotation profile between these positions. Aims. We study the feasibility of making precise constraints to the rotation profile between the core and surface and the possibility of differentiating between rotation profile shapes using the observed rotational splittings of low-luminosity subgiant KIC 12508433. Methods. We use qualitative assumptions of extreme angular momentum transport mechanisms to prescribe the shape of the five synthetic profiles with the same core and surface rotation rates. We calculate the expected rotational splittings given these five profiles and analyse the differences between them. Markov chain Monte Carlo integration of the synthetic profiles using their associated splittings highlights the limited differentiability between rotation profiles that can currently be made. Results. Despite significant changes to the shape of the rotation profile, the rotational splittings deviate on a scale much smaller than the precision of splittings in current observations. We also find degeneracy between the surface rotation rate and position of strong differential rotation gradient of the inverted profiles. Conclusions. Constraining the physical mechanism contributing to more efficient angular momentum transport during the lowluminosity subgiant phase through the shape of the profile is impossible with current observations of = 1 and 2 rotationally split modes. We speculate that population inference using only the core and surface rotation rates from rotational splittings of a series of stars beginning to ascend the subgiant branch provides an alternative path to understanding the excess angular momentum transport.

Mode Mixing and Rotational Splittings. I. Near-degeneracy Effects Revisited

“…Moreover, our numerical construction recovers exactly as many π-mode kernels as there are p-dominated mixed modes, thereby maximizing the use of the available information. In the case of core rotation, Fellay et al (2021) assert to have constrained the shape of radial differential rotation localized to near the boundary of the radiative core-in tension with the claim made in Wilson et al (2021) that no meaningful constraints of this kind are possible. The use of γ-mode kernels here may refine these arguments and assist in resolving this tension, by eliminating any potential interference owing to envelope rotation.…”