IN-SYNC I: Homogeneous Stellar Parameters from High Resolution APOGEE Spectra for Thousands of Pre-main Sequence Star

Over two years 8,859 high-resolution H-band spectra of 3,493 young (1 - 10 Myr) stars were gathered by the multi-object spectrograph of the APOGEE project as part of the IN-SYNC ancillary program of that SDSS-III survey. Here we present the forward modeling approach used to derive effective temperatures, surface gravities, radial velocities, rotational velocities, and H-band veiling from these near-infrared spectra. We discuss in detail the statistical and systematic uncertainties in these stellar parameters. In addition we present accurate extinctions by measuring the E(J-H) of these young stars with respect to the single-star photometric locus in the Pleiades. Finally we identify an intrinsic stellar radius spread of about 25% for late-type stars in IC 348 using three (nearly) independent measures of stellar radius, namely the extinction-corrected J-band magnitude, the surface gravity and the $R \sin i$ from the rotational velocities and literature rotation periods. We exclude that this spread is caused by uncertainties in the stellar parameters by showing that the three estimators of stellar radius are correlated, so that brighter stars tend to have lower surface gravities and larger $R \sin i$ than fainter stars at the same effective temperature. Tables providing the spectral and photometric parameters for the Pleiades and IC 348 have been provided online.