Resolving the Tachocline using Inversion of Rotational Splitting Derived from Fitting Very Long and Long Time Series

Abstract

We use rotation splittings derived from very long and long time series, namely 25.2, 12.6 and 6.3 year long, computed by Korzennik (2023) independent methodology to characterize the solar tachocline and its variation with latitude and time. We use two different inversion methodologies and a model of the tachocline to derive its position, width and the amplitude of the radial shear. To validate our methodology we present results from simulated rotational splittings, whether including or not random noise commensurable with the current observational precision. We also describe how we leverage the fact that one of our methodologies uses an initial guess that can be chosen to include a priori information. In order to try to resolve the tachocline, we increased the radial density of the inversion grid and showed how it affect the inferences. We also show how the trade off between smoothing and noise magnification affects these, as well as the effectiveness of using an informed initial guess. Results derived from high-precision rotational splittings show clearly that the location of the tachocline at low latitudes is different for its position at high latitudes. The latitudinal variation of its width is not significantly constrained, but our results agree with estimates based on forward modeling. When using splittings derived from somewhat shorter time series, we find temporal variations that are neither definitive nor significant, since we see systematic differences when using different methodologies.