Paramagnetic alignment of small grains: a novel method for measuring interstellar magnetic fields

We present a novel method to measure the strength of interstellar magnetic fields based on ultraviolet (UV) polarization of starlight, which is in part produced by weakly aligned, small interstellar grains. We begin with calculating degrees of alignment of small (size $a\sim 0.01\mu$m) and very small ($a\sim 0.001\mu$m) grains in the interstellar magnetic field due to the Davis-Greenstein paramagnetic relaxation and resonance paramagnetic relaxation. We compute the degrees of paramagnetic alignment with the ambient magnetic field $B$ using Langevin equations. In this paper, we take into account various processes essential for the dynamics of small grains, including infrared (IR) emission, electric dipole emission, plasma drag and collisions with neutral and ionized species. We find that the alignment of small grains is necessary to reproduce the observed polarization in the UV, although the polarization arising from these small grains is negligible at the optical and IR wavelengths. Based on fitting theoretical models to observed extinction and polarization curves, we find that the best-fit model requires a higher degree of alignment of small grains for the case with the peak wavelength of polarization $\lambda_{\max}<0.55\mu$m, which exhibits an excess UV polarization relative to the Serkowski law, compared to the typical case $\lambda_{\max}=0.55\mu$m. We interpret the correlation between the systematic increase of the UV polarization relative to maximum polarization (i.e. of $p(6\mu m^{-1})/p_{\max}$) with $\lambda_{\max}^{-1}$ by appealing to the higher degree of alignment of small grains. We identify paramagnetic relaxation as the cause of the alignment of small grains and utilize the dependence of the degree of alignment on the magnetic field strength $B$ to suggest a new way to measure $B$ using the observable parameters $\lambda_{\max}$ and $p(6\mu m^{-1})/p_{\max}$.[Abridged]