A Diagnostic for Localizing Red Giant Differential Rotation

TL;DR

This paper introduces a diagnostic method using mixed mode rotational splittings to determine where differential rotation occurs in red giants, providing insights into internal angular momentum transport mechanisms.

Contribution

The authors develop a simple diagnostic leveraging mixed mode splittings to localize differential rotation in red giants, applicable even with limited data.

Findings

Most differential rotation resides in the radiative interior of red giants.

The diagnostic is effective with modest rotational splitting measurements.

Results support local fluid instabilities as the main angular momentum transport process.

Abstract

We present a simple diagnostic that can be used to constrain the location of the differential rotation in red giants with measured mixed mode rotational splittings. Specifically, in red giants with radii $\sim 4R_\odot$, the splittings of p-dominated modes (sound wave dominated) relative to those of g-dominated modes (internal gravity wave dominated) are sensitive to how much of the differential rotation resides in the outer convection zone versus the radiative interior of the red giant. An independently measured surface rotation rate significantly aids breaking degeneracies in interpreting the measured splittings. We apply our results to existing observations of red giants, particularly those of Kepler-56, and find that most of the differential rotation resides in the radiative region rather than in the convection zone. This conclusion is consistent with results in the literature from rotational inversions, but our results are insensitive to some of the uncertainties in the inversion process and can be readily applied to large samples of red giants with even a modest number of measured rotational splittings. We argue that differential rotation in the radiative interior strongly suggests that angular momentum transport in red giants is dominated by local fluid instabilities rather than large-scale magnetic stresses.