The critical frequency in a given atmosphere layer of a stellar model is defined
as the frequency below which acoustic waves are reflected back towards the
resonant cavity. The acoustic cut-off frequency, the maximum value of the critical
frequency, is usually
determined in the outermost atmospheric regions, where the temperature
starts to rise and hence the critical frequency decreases again. In the case of our
Sun, this region is at the bottom of the chromosphere.
For a subgroup of the chemically peculiar stars, the magnetic
late Bp to early Fp stars (CP2 stars, Preston 1974), we observe pulsations.
Some of these rapidly oscillating CP2 (roAp) stars, have frequencies which are larger
than the theoretical acoustic cut-off frequency.
Waves beyond the cut-off frequency propagate into the
atmosphere, dissipate mechanical energy and become damped. Therefore, their decreasing
amplitude makes them very hard to detect.
As the cut-off frequency depends on the T(tau) relation in the
atmosphere, we have computed models and adiabatic frequencies for
pulsating CP2 stars with T(tau) laws based on Kurucz
model atmospheres, and on Hopf's purely radiative relation.
Since the existence of a temperature minimum in the upper
atmospheric layers of CP stars is not established by observations,
we have to speculate on the position of such a minimum,
which is a prerequisite for the existence of an acoustic cut-off frequency.
We compare the values of the cut-off frequency derived from the expression
of the potential by Vorontsov & Zarkhov (1989), by
Gough (1986), and from the approximation of an isothermal atmosphere.
These models predict a different reflexion efficiency for waves,
and hence marginally different values for the
cut-off frequency. The frequency-dependent treatment
of radiative transfer as well as a better calculation
of the radiative pressure in Kurucz model atmospheres
increase the theoretical acoustic cut-off frequency by about 200 \mu Hz, which
is closer to the observations, but still not in agreement.