The umbral--penumbral boundary in sunspsots in the context of magneto-convection

TL;DR

This paper investigates the magnetic field characteristics at the boundary between the umbra and penumbra in sunspots, proposing a magneto-convection-based explanation for the observed magnetic field threshold.

Contribution

It introduces a hypothesis linking the umbral-penumbral boundary to magneto-convection onset, based on empirical magnetic field measurements and theoretical models.

Findings

The UPB correlates with a vertical magnetic field of approximately 1867 G.

Magneto-convection onset is influenced by the magnetic field's effect on the temperature gradient.

The proposed hypothesis connects magnetic field strength to convection regulation at the UPB.

Abstract

Jurcak et al (2018) have reported that, in a sample of more than 100 umbral cores in sunspots, the umbral-penumbral boundary (UPB) is characterized by a remarkably narrowly-defined numerical value (1867 G) of the vertical component of the magnetic field. Gough and Tayler (1966), in their study of magneto-convection, showed that the onset of convection in the presence of a magnetic field is controlled by a parameter {\delta} which also depends on the vertical component of the field. Combining the Jurcak et al result with various empirical models of sunspots leads us to propose the following hypothesis: the UPB occurs where the vertical field is strong enough to increase the effective adiabatic temperature gradient by at least 100% above its non-magnetic value.