The Langevin Equation and Its Application to Grain Alignment in Molecular Clouds

Details The Langevin Equation and Its Application to Grain Alignment in Molecular Clouds The Langevin Equation and Its Application to Grain Alignment in Molecular Clouds

Nov 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...418..287r&link_type=abstract

Astrophysical Journal v.418, p.287

Astronomy and Astrophysics

Astronomy

47

Ism: Dust, Extinction, Ism: Clouds, Ism: Molecules, Polarization

Scientific paper

We describe a new computational method for solving problems in grain alignment theory which uses numerical integration of the Langevin equation for Brownian rotation. The new method is completely general in the sense that it generates the solution to a Fokker-Planck equation with arbitrary diffusion coefficients. We derive accurate expressions for the diffusion coefficients of refractory grains with ice mantles, on the ad hoc hypothesis that the grains rotate with thermal kinetic energies. We include the effects of internal dissipation by Barnett relaxation or rotational anelasticity, Larmor precession, gas-grain collisions, thermal evaporation, and paramagnetic or superparamagnetic absorption. We develop a quantitative theory for the effects of thermal emission and infrared absorption on the alignment of nonspherical grains and assess the relevance of these processes to polarization in molecular clouds. We document the accuracy of our computational method by comparing numerical solutions for the Rayleigh reduction factor of magnetically aligned grains with exact solutions for spheres and thin disks.

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