Modeling the Subsurface Structure of Sunspots

TL;DR

This paper reviews sunspot models, discusses numerical wave propagation methods, and analyzes helioseismic data of a specific sunspot, suggesting a shallow wave-speed perturbation and horizontal outflow in the moat.

Contribution

It provides a critical review of existing sunspot models, evaluates numerical methods for wave propagation, and offers new helioseismic analysis of a sunspot with implications for its subsurface structure.

Findings

Sunspot likely has a shallow, positive wave-speed perturbation.

Travel-time measurements indicate a horizontal outflow in the moat.

The analysis challenges traditional two-layer models.

Abstract

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this paper, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out an helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by \citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.