Rotational Evolution of Classical T Tauri Stars: Models and Observations

We developed a grid of stellar rotation models for low-mass and solar-type Classical T Tauri stars (CTTS) ($0.3M_{\odot}<M_{\ast}<1.2M_{\odot}$). These models incorporate the star-disk interaction and magnetospheric ejections to investigate the evolution of the stellar rotation rate as a function of the mass of the star $M_{\ast}$, the magnetic field ($B_{\ast}$), and stellar wind ($\dot{M}_{wind}$). We compiled and determined stellar parameters for 208 CTTS, such as projected rotational velocity $v\sin(i)$, mass accretion rate $\dot{M}_{acc}$, stellar mass $M_{\ast}$, ages, and estimated rotational periods using TESS data. We also estimated a representative value of the mass-loss rate for our sample using the $[\text{O}\text{ I}]$ spectral line. Our results confirm that $v\sin(i)$ measurements in CTTS agree with the rotation rates provided by our spin models in the accretion-powered stellar winds (APSW) picture. In addition, we used the Approximate Bayesian Computation (ABC) technique to explore the connection between the model parameters and the observational properties of CTTS. We find that the evolution of $v\sin(i)$ with age might be regulated by variations in (1) the intensity of $B_{\ast}$ and (2) the fraction of the accretion flow ejected in magnetic winds, removing angular momentum from these systems. The youngest stars in our sample ($\sim $1 Myr) show a median branching ratio $\dot{M}_{wind}/\dot{M}_{acc}\sim$ $0.16$ and median $B_{\ast}\sim$ 2000 G, in contrast to $\sim 0.01$ and 1000 G, respectively, for stars with ages $\gtrsim 3$ Myr.