No universal connection between the vertical magnetic field and the umbra-penumbra boundary in sunspots

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: loeptien@mps.mpg.de
² School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701, Republic of Korea

Received: 17 March 2020
Accepted: 3 June 2020

Abstract

Context. It has been reported that the boundary between the umbra and the penumbra of sunspots occurs at a canonical value of the strength of the vertical magnetic field, independently of the size of the spot. This critical field strength is interpreted to be the threshold for the onset of magnetoconvection.

Aims. Here we investigate the reasons why this criterion, also called the Jurčák criterion in the literature, does not always identify the boundary between the umbra and the penumbra.

Methods. We performed a statistical analysis of 23 sunspots observed with Hinode/SOT. We compared the properties of the continuum intensity and the vertical magnetic field between filaments and spines and how they vary between spots of different sizes.

Results. We find that the inner boundary of the penumbra is not related to a universal value of the vertical magnetic field. The properties of spines and filaments vary between spots of different sizes. Both components are darker in larger spots and the spines exhibit a stronger vertical magnetic field. These variations of the properties of filaments and spines with the spot size are also the reason for the reported invariance in the averaged vertical magnetic field at 50% of the mean continuum intensity.

Conclusions. The formation of filaments and the onset of magnetoconvection are not related to a canonical value of the strength of the vertical magnetic field. The seemingly unique magnetic field strength is rather an effect of the filling factor of spines and penumbral filaments.