The Fundamental Properties of Young Stars

Accurate knowledge of the fundamental properties of stars--mass, temperature, and luminosity--is key to our understanding of stellar evolution. In particular, empirical measurements of stellar mass are difficult to make and are generally limited to stars that dynamically interact with a companion (e.g., eclipsing or astrometric binaries), a precious but ultimately small sample. We developed a technique that uses the rotation of the protoplanetary disk--a consequence of the star formation process still present around many pre-main sequence stars--to measure the stellar mass. To establish the absolute accuracy of this technique, in ALMA Cycle 1/2 we observed the few circumbinary disks around double-lined spectroscopic binary stars, enabling an independent confirmation of the total stellar mass. This comparison with radial-velocity results demonstrates that the disk-based dynamical mass technique can reliably achieve precise measurements of stellar mass on the order of 2-5\%, clearing the way for widespread application of this technique to measure the masses of \emph{single} stars. We discuss our calibration in the context of two sources, AK~Sco and DQ~Tau. Second, we developed novel statistical techniques for spectroscopic inference. Young stars exhibit rich and variable spectra; although interesting phenomena in their own right, accretion veiling and star spots complicate the retrieval of accurate photospheric properties. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints (pixels) into the residual spectrum. For the high signal-to-noise data with large spectral range that is commonly employed in stellar astrophysics, that covariant structure can lead to dramatically underestimated parameter uncertainties (and, in some cases, biases). We construct a likelihood function that accounts for the structure of the covariance matrix, utilizing the machinery of Gaussian process kernels. This framework specifically addresses the common problem of mismatches in model spectral line strengths (with respect to data) due to intrinsic model imperfections (e.g., in the atomic/molecular databases or opacity prescriptions) by developing a novel local covariance kernel formalism that identifies and self-consistently downweights pathological spectral line ``outliers." We demonstrate some salient features of the framework by fitting the high resolution $V$-band spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate resolution $K$-band spectrum of Gliese~51, an M5 field dwarf. Direct spectroscopic inference provides one means to avoid the systematic error that results from the uncertain spectral type--effective temperature scale for low mass pre-main sequence stars when placing a star on the Hertzsprung Russell diagram. Lastly, we discuss recent progress in measuring the masses of a large sample of single pre-main sequence stars observed with the Submillimeter Array, which will double the number of disk-based dynamical mass estimates of pre-main sequence stars. With ALMA, the disk-based technique holds enormous promise to become the primary means of stellar mass for statistically large samples of pre-main sequence stars, ushering in a new era of high precision in star and planet formation studies.Astronom