On wave equations and cutoff frequencies of plane atmospheres
Abstract
This paper deals with the onedimensional vertical propagation of linear adiabatic waves in plane atmospheres. In the literature there are various representations of the standard form of the wave equation from which different forms of the so called cutoff frequency are inferred. It is not uncommon that statements concerning the propagation behavior of waves are made which are based on the height dependence of a cutoff frequency. In this paper, first we critically discuss concepts resting on the use of cutoff frequencies. We add a further wave equation to three wave equations previously presented in the literature, yielding an additional cutoff frequency. Comparison among the various cutoff frequencies of the VALatmosphere reveals significant differences, which illustrate the difficulties of interpreting a height dependent cutoff frequency. We also discuss the cutoff frequency of the parabolic temperature profile and the behavior of the polytropic atmosphere. The invariants of the four wave equations presented contain first and second derivatives of the adiabatic sound speed. These derivatives cause oscillations and peaks in the space dependent part of the invariants, which unnecessarily complicate the discussion. We therefore present a new form of the wave equation, the invariant of which is extremely simple and does not contain derivatives of the thermodynamic variables. It is valid for any LTE equation of state. It allows us to make effective use of strict oscillation theorems. We calculate the heightdependent part of the invariant of this equation for the VALatmosphere including ionization and dissociation. For this real atmosphere, there is no obvious correspondence between the behavior of the invariant and the temperature structure or the sound speed profile. The invariant of the wave equation is nearly constant around the temperature minimum. In the chromosphere, the invariant is almost linear. The case of the wave equation with a linear invariant is studied analytically.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 September 1998
 Bibcode:
 1998A&A...337..487S
 Keywords:

 SUN: ATMOSPHERE;
 SUN: OSCILLATIONS;
 STARS: ATMOSPHERES