The sharp almost step like increase the temperature in the transition region (TR) between chromosphere and solar corona is well-known from decades; for first time we are giving a detailed magnetohydrodynamic (MHD) calculation of the height dependence of the temperature. The width of the transition region is evaluated by maximal value of the logarithmic derivative of the temperature. At fixed heating, only MHD can give such a narrow width and in such sense, even the qualitative agreement with the observational data, gives the final verdict what the heating mechanism of the solar corona is. Static profiles of the temperature and wind velocity are calculated for static frequency dependent spectral density of the incoming MHD waves; no time dependent computer simulations. At fixed spectral density of MHD waves, the MHD calculation predicts height dependence of the non-thermal broadening of spectral lines and its angular dependence. For illustration is used one dimensional approximation of completely ionized hydrogen plasma in weak magnetic field, but it is considered that the width of the TR is weakly dependent with respect of further elaboration. The analyzed MHD calculation is a numerical confirmation of the qualitative concept of self-induced opacity of the plasma with respect to MHD waves. The plasma viscosity strongly increases with the temperature. Heated by MHD waves, plasma increases the wave absorption and this positive feedback leads to further heating. The static temperature profile is a result of a self-consistent calculation of propagation of MHD wave through the static background of wind and temperature profile. The numerical method allows consideration of incoming MHD waves with an arbitrary spectral density. Further elaboration of the method are briefly discussed: influence of second viscosity in the chromospheric part of the TR, influence of the magnetic field on the coronal side of the TR and investigation of such type effects on the width of the TR.
Magnetohydrodynamic calculation of the temperature and wind velocity profile of the solar transition region. Preliminary results.
