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MASS­FLOW EFFECTS ONWAVE HEATING BYRESONANT
ABSORPTION
R. ERD '
ELYI VON F '
AY­SIEBENB ¨
URGEN
Center for Plasma­Astrophysics, K.U. Leuven
Celestijnenlaan 200 B, B­3001 Heverlee, Belgium
1. Introduction
To heat the solar atmosphere by waves one requires some efficient dissipa­
tion mechanisms. Resonant absorption, suggested by Ionson (1978), might
be a candidate to explain the heating mechanism(s) in the solar corona.
In the former studies of resonant absorption one has mostly assumed static
equilibria. However, Hollweg et al. (1990) showed that resonant absorption
can be severely influenced by the presence of velocity shears. Erd'elyi et al.
(1995) studied analytically the resonant absorption in linear compressible
MHD for background equilibrium states with flow.
In this paper we show numerically the effect of background equilibrium
flows on resonant absorption. Lou's (1990) cylindrical equilibrium model is
extended with an equilibrium plasma flow, v 0
(r) = f \Theta v Alfv (r), where f
denotes the flow strength parameter.
2. Results
In Figure 1 we have plotted the absorption rate versus the flow strength
parameter, f . Fig. 1 shows that the flow has a very determinant effect on
the absorption rate. By increasing the flow strength parameter the absorp­
tion rate enhances very strongly. Increasing further the equilibrium flow
strength, the absorption rate shows a strong oscillatory behaviour between
ca. the value of total resonant absorption and the value of total reflection.
Increasing even further the equilibrium flow parameter, f , the absorption
rate smoothly decreases. Roberts et al. (1984) have shown that homoge­
neous, non­twisted magnetic flux tubes can have infinite eigenvalues. If one
drives a flux tube with a frequency close to one of its eigenfrequencies the

2 R. ERD '
ELYI VON F '
AY­SIEBENB ¨
URGEN
Figure 1. Absorption coefficient ff versus the equilibrium flow strength parameter, f
driving wave will be strongly absorbed (Goossens and Hollweg, 1993). We
guess this is the case when in Fig. 1 f 2 [0:25 \Gamma 0:31), the absorption rate
shows so many maxima. We cannot prove this statement now because we
have to solve the eigenvalue problem of our non­homogeneous driven prob­
lem, but this work is under investigation.
The presence of the equilibrium flow may therefore be very determinant for
resonant absorption and may significantly affect the resonant absorption
rate for acoustic oscillations in sunspots or for Alfv'en waves in the solar
corona.
Acknowledgements The author is grateful to M. Goossens and M. Ruder­
man for suggesting the work and for stimulating discussions.
References
Erd'elyi, R., Goossens, M. and Ruderman, M. S. (1995), Sol. Phys., in press
Goossens, M. and Hollweg, J. V. (1993), Sol. Phys.,145, pp. 19--44
Hollweg, J. V., Yang, G., Cadez, V. M. and Gakovic, B. (1990), ApJ., 349, pp. 335--344
Ionson, J. A. (1978), ApJ.,226, pp. 650--673
Lou, Y. Q. (1990), ApJ., 350, pp. 452--462
Roberts, B., Edwin, P. M. and Benz, A. O. (1984), ApJ., 279, pp. 857--865