# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1902.09431