Disk-Star Alignment I: Pre-Main-Sequence Stellar Parameters and the Statistical Alignment Between Disks and Stellar Rotation

Astronomers generally assume planet-forming disks are aligned with the rotation of their host star. However, recent observations have shown evidence of warping in protoplanetary disks. One can measure the statistical alignment between the inclination angles of the disk and stellar spin using the projected rotational velocity, radius, and rotation period of the star and interferometric measurements of the protoplanetary disk. Such work is challenging due to the difficulty in measuring the properties of young stars and biases in methods to combine them for population studies. Here, we provide an overview of the required observables, realistic uncertainties, and complications when using them to constrain the orientation of the system. We show in several tests that we are able to constrain the uncertainties on the necessary stellar parameters to better than 5% in most cases. We show that by using a hierarchical Bayesian model, we can account for many of the systematic effects (e.g., biases in measured stellar and disk orientations) by fitting for the alignments of each system simultaneously. We demonstrate our hierarchical model on a realistic synthetic sample and verify that we can recover our input alignment distribution to $\leq$5$^{\circ}$ with a modest ($\simeq$30 star) sample. As the sample of systems with disk inclinations grows, future studies can improve upon our approach with a three-dimensional treatment of misalignment and better handling of non-Gaussian errors.