Magnetic and Thermal Phase Shifts in the Local Helioseismology of Sunspots

TL;DR

This paper investigates how magnetic and thermal anomalies in sunspots affect helioseismic wave travel times, revealing that magnetic effects dominate in penumbrae while thermal effects are more significant in umbrae.

Contribution

It provides a numerical analysis of the combined magnetic and thermal effects on helioseismic phase shifts in sunspots, highlighting their different roles in penumbrae and umbrae.

Findings

Magnetic effects are largest in penumbrae and scale with field strength.

Travel-time perturbations are generally negative in penumbrae.

Thermal effects mainly influence umbrae, especially at low magnetic fields.

Abstract

Phase perturbations due to inclined surface magnetic field of active region strength are calculated numerically in quiet Sun and simple sunspot models in order to estimate and compare the direct and indirect (thermal) effects of the fields on helioseismic waves. It is found that the largest direct effects occur in highly inclined field characteristic of penumbrae, and scale roughly linearly with magnetic field strength. The combined effects of sunspot magnetic and thermal anomalies typically yield negative travel-time perturbations in penumbrae. Travel-time shifts in umbrae depend on details of how the thermal and density structure differs from the quiet Sun. The combined shifts are generally not well approximated by the sum of the thermal and magnetic effects applied separately, except at low field strengths of around 1 kG or less, or if the thermal shift is small. A useful rule-of-thumb appears to be that travel-time perturbations in umbrae are predominantly thermal, whereas in penumbrae they are mostly magnetic.