Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The umbral--penumbral boundary in sunspsots in the context of
  magneto-convection   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.

17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph