On the combined effect of atmospheric stratification and non-uniform magnetic field on magneto-sonic-gravity waves

Abstract

The linear magneto-acoustic-gravity (MAG) wave equation is considered for a non-isothermal atmosphere under a non-uniform external magnetic field. The starting point is a magnetohydrostatic equilibrium with an arbitrary profiles of temperature and horizontal magnetic field as a function of altitude; this specifies the profiles of gas pressure, mass density and sound and Alfvén speeds. The wave equation is solved exactly in the case of an isothermal atmosphere with horizontal magnetic field decaying exponentially with altitude on twice the scale height. The solution for the vertical velocity perturbation is represented by confluent hypergeometric functions specifying the effect of the magnetic field in modifying the amplitude and phase of acoustic-gravity waves. It is shown that (i) in the physical conditions corresponding to the solar corona, the decrease in Alfvén speed with height leads to a decreasing spacing of nodes; this agrees with observations of ratios of periods p 2 / p 1 less than two in solar arches or loops; also (ii) the dissipation of these magnetosonic-gravity modes in the solar transition region is sufficient to heat the corona by compensating for energy losses in solar radiation. (i) and (ii) are set in the context of a tentative global picture of the possible role of MAG waves in establishing the mass and energy balances in the solar atmosphere.

Magnetic waves in a stratified medium: dispersion relations and exact solutions

“…The case (a) above can also be considered as Alfven waves in a non-uniform magnetic field modified by the presence of stratification. Two earlier results by Nye & Thomas (1976) and Campos & Marta (2015), emerges as special cases of our solutions.…”

“…Again we need to consider two cases q = 2 and q = 2. The latter has already been solved exactly by Campos & Marta (2015). Below we present the solution for the former.…”

“…For waves traveling along the gravity, Campos & Marta (2015) presented an exact solution for a very special case of q = 2. In this paper, we consider the first and the second cases and present exact solutions for arbitrary values of q.…”

“…In both of these cases, it is possible to find an exact solution that uses the hypergeometric functions. Campos & Marta (2015) generalized the latter to the one where the magnetic field is also an exponential function of the vertical coordinate z, with a characteristic length scale ℓB, but its direction remains fixed -along the x direction. For the particular case where ℓB is twice the density scale height, ℓρ, Campos & Marta (2015) found an exact solution for waves propagating along the gravity field in terms of confluent hypergeometric functions.…”

“…Campos & Marta (2015) generalized the latter to the one where the magnetic field is also an exponential function of the vertical coordinate z, with a characteristic length scale ℓB, but its direction remains fixed -along the x direction. For the particular case where ℓB is twice the density scale height, ℓρ, Campos & Marta (2015) found an exact solution for waves propagating along the gravity field in terms of confluent hypergeometric functions. The problem remains unsolved for any value of ℓB/ℓρ, not equal to two as well as for waves propagating along the x direction -the direction of the magnetic field and along the y direction -the direction orthogonal to both the direction of the magnetic field and the direction of gravity.…”