3. Dispersion relation for the static () atmosphere
To obtain the dispersion relation for the static () atmosphere we Fourier analyze the perturbation variables as:
where , k is the horizontal wavenumber and is the frequency of the f -mode. represents a fluid variable such as , and p.
From this dispersion relation it follows that the f -mode frequency depends on the density and mode profiles either side of the interface, the wavevector k and the gravity g.
3.1. An instructive example: The case of isothermal plasma
Similarly to Gruzinov (1998), we consider the case of uniform temperatures inside the solar corona and the solar interior. However, there is a temperature jump at the interface . Then, the density profiles can be written as
where and are the isothermal pressure scale heights, . Here, and are the sound speeds. Consequently, there is a jump in the mass density () and the sound speed () at the interface .
In the case when this condition is not satisfied, waves cease to be localized, they propagate and the corona and the convection zone act as sinks for such perturbations.
where the density contrast is given by
© European Southern Observatory (ESO) 2000
Online publication: August 17, 2000