Polarization from Aligned Dust Grains in the $\beta$ Pic Debris Disk

We present 870 $\mu$m ALMA polarization observations of thermal dust emission from the iconic, edge-on debris disk $\beta$ Pic. While the spatially resolved map does not exhibit detectable polarized dust emission, we detect polarization at the $\sim$3$\sigma$ level when averaging the emission across the entire disk. The corresponding polarization fraction is $P_\textrm{frac}$ = $0.51 \pm 0.19$%. The polarization position angle $\chi$ is aligned with the minor axis of the disk, as expected from models of dust grains aligned via radiative alignment torques (RAT) with respect to a toroidal magnetic field ($B$-RAT) or with respect to the anisotropy in the radiation field ($k$-RAT). When averaging the polarized emission across the outer versus inner thirds of the disk, we find that the polarization arises primarily from the SW third. We perform synthetic observations assuming grain alignment via both $k$-RAT and $B$-RAT. Both models produce polarization fractions close to our observed value when the emission is averaged across the entire disk. When we average the models in the inner versus outer thirds of the disk, we find that $k$-RAT is the likely mechanism producing the polarized emission in $\beta$ Pic. A comparison of timescales relevant to grain alignment also yields the same conclusion. For dust grains with realistic aspect ratios (i.e., $s > 1.1$), our models imply low grain-alignment efficiencies.