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 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.
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