ALMA 873 $\mu$m Polarization Observations of the PDS~70 Disk

At a 112.4 pc distance, the PDS70 protoplanetary disk is a rare case that has been confirmed to host two accreting planets. This makes it the most important laboratory for studying dust growth in the context of planet formation. Here we present the first deep, full polarization observations at 873 $\mu$m wavelength. We detected $\sim$1%-2.5% linear polarization over the bulk of the $\sim$55-100 AU (sub)millimeter ring. The polarization position angles align preferentially with the projected minor axis of the disk. The standard interpretation is that the observed polarization is caused by dust self-scattering, with a maximum dust grain size of $\sim$100 $\mu$m. On $\gtrsim$10 AU scales, which can be resolved by the presented 873-3075 $\mu$m observations, the ring is marginally optical thick at 873 $\mu$m wavelength. Using Monte Carlo radiative transfer simulations, we found that an azimuthally asymmetric, marginally optically thick ring with a maximum dust grain size of $\sim$87 $\mu$m can reproduce the observed 873 $\mu$m polarization position angles and percentages. This study indicates that the coagulation of ice-coated dust in the protoplanetary disk may be limited by fragmentation or bouncing.