**Previous
abstract** **Next
abstract**

**Session 51 - Interstellar Medium II.**

*Display session, Thursday, January 08*

*Exhibit Hall, *

## [51.21] An Adiabatic Approximation for Grain Alignment Theory

*W. G. Roberge (Rensselaer)*
The alignment of interstellar dust grains is described by the
joint distribution function for certain ``internal''
and ``external'' variables, where
the former describe the orientation of a grain's axes with respect
to its angular momentum, \boldmathJ, and the latter describe the
orientation of \boldmathJ relative to the interstellar magnetic field.
I show how the large disparity between the dynamical timescales
of the internal and external variables--- which is typically
2--3 orders of magnitude--- can be exploited to
greatly simplify calculations of the required distribution.
The method is based on an ``adiabatic approximation'' which closely
resembles the Born-Oppenheimer approximation in quantum mechanics.
The adiabatic approximation prescribes an analytic distribution function
for the ``fast'' dynamical variables and a simplified Fokker-Planck
equation for the ``slow'' variables which can be solved straightforwardly
using various techniques.
These solutions are accurate to \calO(\epsilon), where \epsilon
is the ratio of the fast and slow dynamical timescales.
As a simple illustration of the method, I derive an analytic
solution for the joint distribution established when Barnett relaxation
acts in concert with gas damping.
The statistics of the analytic solution agree with the results of
laborious numerical calculations which do not exploit the adiabatic
approximation.

The author(s) of this abstract have provided an email address for comments about the abstract: roberw@rpi.edu

**Program
listing for Thursday**