Aligning Planet-Hosting Binaries via Dissipative Precession in Circumstellar Disks

Recent observations have demonstrated that some subset of even moderately wide-separation planet-hosting binaries are preferentially configured such that planetary and binary orbits appear to lie within the same plane. In this work, we explore dissipation during the protoplanetary disk phase, induced by disk warping as the system is forced into nodal recession by an inclined binary companion as a possible avenue of achieving orbit-orbit alignment. We analytically model the coupled evolution of the disk angular momentum vector and stellar spin vector under the influence of a distant binary companion. We find that a population of systems with random initial orientations can appear detectably more aligned after undergoing dissipative precession, and that this process can simultaneously produce an obliquity distribution that is consistent with observations. While dissipative precession proceeds efficiently in close binaries, favorable system properties (e.g., $r_{out} \gtrsim 100$ AU, $\alpha \gtrsim 0.05$, and/or $M_b/M_{*} \gtrsim 1$) are required to reproduce observed alignment trends at wider binary separations $a_\mathrm{b} \gtrsim450$ AU. Our framework further predicts that circum-primary planets in systems with high stellar mass ratios should be preferentially less aligned than planets in equal-mass stellar binary systems. We discover tentative evidence for this trend in \textit{Gaia} DR3 and TESS data. Our findings suggest that dissipative precession may play a significant role in sculpting orbital configurations in a sub-set of moderately-wide planet-hosting binaries, but is likely not solely responsible for their observed population-level alignment.