Correlating Changes in Spot Filling Factors with Stellar Rotation: The Case of LkCa 4

We present a multi-epoch spectroscopic study of LkCa 4, a heavily spotted non-accreting T Tauri star. Using SpeX at NASA's Infrared Telescope Facility (IRTF), 12 spectra were collected over five consecutive nights, spanning $\approx$ 1.5 stellar rotations. Using the IRTF SpeX Spectral Library, we constructed empirical composite models of spotted stars by combining a warmer (photosphere) standard star spectrum with a cooler (spot) standard weighted by the spot filling factor, $f_{spot}$. The best-fit models spanned two photospheric component temperatures, $T_{phot}$ = 4100 K (K7V) and 4400 K (K5V), and one spot component temperature, $T_{spot}$ = 3060 K (M5V) with an $A_V$ of 0.3. We find values of $f_{spot}$ to vary between 0.77 and 0.94 with an average uncertainty of $\sim$0.04. The variability of $f_{spot}$ is periodic and correlates with its 3.374 day rotational period. Using a mean value for $f^{mean}_{spot}$ to represent the total spot coverage, we calculated spot corrected values for $T_{eff}$ and $L_\star$. Placing these values alongside evolutionary models developed for heavily spotted young stars, we infer mass and age ranges of 0.45-0.6 $M_\odot$ and 0.50-1.25 Myr, respectively. These inferred values represent a twofold increase in the mass and a twofold decrease in the age as compared to standard evolutionary models. Such a result highlights the need for constraining the contributions of cool and warm regions of young stellar atmospheres when estimating $T_{eff}$ and $L_\star$ to infer masses and ages as well as the necessity for models to account for the effects of these regions on the early evolution of low-mass stars.