Red Giant Rotational Inversion Kernels Need Nonlinear Surface Corrections

Asteroseismology is our only means of measuring the rotations of stars in their interiors, rather than at their surfaces. Some techniques for measurements of this kind-"rotational inversions"-require the shapes of linear response kernels computed from reference stellar models to be representative of those in the stars they are intended to match. This is not the case in evolved stars exhibiting gravitoacoustic mixed modes: we show that the action of the asteroseismic surface term-systematic errors in the modeling of near-surface layers-changes the shapes of their inversion kernels. Corrections for the surface term are not ordinarily considered necessary for rotational inversions. We show how this may have caused previous estimates of red-giant envelope rotation rates from mixed-mode asteroseismic inversions to have been unintentionally contaminated by core rotation as a result, with errors comparable to the entire reported estimates. We derive a mitigation procedure for this hitherto unaccounted systematic error, and demonstrate its viability and effectiveness. We recommend this mitigation be applied when revising existing rotational inversions. Finally, we discuss both the prospects for applying such mitigation to the harder problem of inversions for stellar structure (rather than rotation), as well as the broader implications of this systematic error with regard to the longstanding problem of internal angular momentum transport.