The ODYSSEUS Survey. Using accretion and stellar rotation to reveal the star-disk connection in T Tauri stars

Classical T Tauri stars (CTTS) exhibit strong variability over timescales of minutes to decades. However, much theoretical work assumes that CTTS are in stable spin states. Here, we test expectations for CTTS angular momentum regulation by comparing star and disk rotation. We measure stellar rotation periods and disk corotation radii ($R_{\rm co}$) for 47 CTTS from the HST ULLYSES sample. We compare $R_{\rm co}$ to the magnetospheric truncation radii ($R_{\rm i}$) and show that most CTTS are in the spin-up regime based on model predictions, which may indicate efficient angular momentum loss processes. We find evidence of magnetospheric outflows and episodic accretion, and our observations are consistent with the presence of accretion-powered stellar winds. We confirm predictions that $R_{\rm i}$ is variable over timescales of days, causing some CTTS to cross accretion stability regime boundaries. We characterize light curve morphologies and confirm that our inclined CTTS with $R_{\rm i}\sim R_{\rm co}$ show dipper light curves, consistent with expectations from disk warp models. However, dippers occur at all values of $R_{\rm i}/R_{\rm co}$, suggesting that they do not need to be near the propeller regime. Finally, we show that our measured $R_{\rm i}$ locations are consistent with observed ultra-short-period planet (USP) semi-major axes. If USPs are stable against tidal dissipation, as has been suggested in the literature, then our work provides a plausible USP formation channel. These results show that the star-disk connection produces a large variety of accretion and stellar spin configurations, most of which are likely not in equilibrium.