Mathematical modeling of sunspot nucleation at the photospheric level of the Sun

In the present study, the initial stage of the generation of a group of sunspots at the photospheric level of the Sun is studied by computer simulation. The development of the nonlinear phase of the Parker instability of large-scale oscillations of magnetic fields in the middle layers of the convective zone is numerically modeled. The process of adiabatic cooling of a thin magnetic tube that floats from depths of the order of 100,000 km to the photospheric level is studied. The results of the calculations make it possible to analyze in detail the change in the magnetogasdynamic parameters of the tube at different depths of the convective zone, and to obtain the values of the physical parameters of emerging sunspots that can be compared with observational data.
The paper investigates the physical mechanism of the time delay in the formation of the head part of the active region compared with the formation of the sprayed tail part. The problem of stability of nascent active regions is also being investigated. The physical parameters determining the stability of the formed active regions at various phases of the solar activity cycle are highlighted. The physical mechanism of generation of a powerful shock wave flux in the initial stage of the nucleation of the active region, which makes a significant contribution to the abnormal heating of the solar atmosphere recorded in the observational data, has been determined.