A&A 410, 415-424 (2003)

DOI: 10.1051/0004-6361:20031197

## Linear damping and energy dissipation of shear Alfvén waves in the interstellar medium

**M. Lazar**

^{1}, F. Spanier^{2}and R. Schlickeiser^{2}^{1}Alexandru Ioan Cuza University, Faculty of Physics, Bd. Carol I Nr. 11, 6600 Iasi, Romania

^{2}Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany

e-mail: r.schlickeiser@tp4.rub.de, fspanier@tp4.rub.de

(Received 6 January 2003 / Accepted 31 July 2003)

** Abstract **

The heating of the diffuse interstellar medium by the
dissipation of interstellar shear Alfvén waves is an important
process for the temperature balance of this gas phase. Following
our earlier analysis for fast magnetosonic waves we calculate here
the heating rate from the damping of interstellar shear Alfvén
waves, because interstellar plasma turbulence most probably is a
mixture of fast magnetosonic waves and shear Alfvén
waves. Relating the Alfvénic magnetic field fluctuation power
spectrum to the observed interstellar electron density fluctuation
power spectrum we derive the heating rate allowing for a scale
independent anisotropy of the power spectrum. Because the diffuse
intercloud medium is a partially ionised medium, the shear
Alfvén waves undergo different types of dissipation. Besides
collisionless Landau damping we considered various damping
mechanisms from collision-effects such as Joule dissipation,
electron and ion viscosity and ion-neutral friction. For all
individual damping processes we derive the respective damping
rates as a function of wavenumber and propagation angles of the
Alfvén waves. These damping rates then serve as input in the
calculation of the associated heating rates of the interstellar
medium which results from the integral over the product of the
damping rate times the magnetic field fluctuation power spectrum
allowing for a scale independent anisotropy of the power spectrum.
We demonstrate that for isotropic turbulence and typical diffuse
intercloud medium parameters ion-neutral friction provides the
dominant contribution to the heating rate of about
10^{-29} erg cm
^{-3} s
^{-1}, which is about four orders of magnitude smaller
than the cooling rate of the diffuse intercloud medium. Heating by
collisionless Landau damping is 13 orders of magnitude smaller
than dissipation by ion-neutral friction, heating by Joule and
viscosity dissipation is 10 orders of magnitude smaller. Apart
from factors of order unity these heating rates also hold for
predominantly parallel turbulence (
). In case of
predominantly perpendicular turbulence (
) the
heating rates from collisionless Landau damping and Joule and
viscosity dissipation decrease
, whereas
the heating rate from ion-neutral friction increases
as long as
. However,
compared to the heating rate by collisionless Landau damping of
fast magnetosonic waves the heating rate of Alfvén waves is
negligibly small. Hence, for the temperature balance of the warm
intercloud medium heating from shear Alfvén waves is negligible
compared to the heating by collisionless damping of fast
magnetosonic waves.

**Key words:**magnetohydrodynamics (MHD)

**--**plasmas

**--**turbulence

**--**waves

**--**ISM: general

**--**ISM: magnetic fields

Offprint request: R. Schlickeiser, rsch@tp4.ruhr-uni-bochum.de

**©**

*ESO 2003*