A diagnostic for localizing red giant differential rotation

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 ~4 R_⊙, 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.