Mathematical modeling of pre-llare signal formation in the solar atmosphere

This study is devoted to the development of Parker instability in the short-wavelength range of large-scale magnetic field oscillations (wavenumber $m>20$) within the upper layers of the solar convective zone. The strongly nonlinear ascent of the magnetic arc's apex forms a needle-like structure that penetrates the solar atmosphere at hypersonic velocities. During the magnetic field's rise, photospheric and chromospheric layers experience an abrupt vertical impact, generating a train of circular diverging shock waves propagating along the solar surface. This phenomenon, reliably detected by modern observational instruments, is called as a “sunquake”. The onset of diverging shock wave generation serves as a precursor to flare activity within the active region. The paper provides numerical estimates for the spatial and temporal resolution requirements of observational instrumentation needed to study hypersonic magnetic flux emergence in the solar chromosphere.