Calibrating Ultracool Dwarfs: Optical Template Spectra, Bolometric Corrections, and $\chi$ Values

Abstract

We present optical template spectra, bolometric corrections, and $\chi$ values for ultracool dwarfs. The templates are based on spectra from the Sloan Digital Sky Survey (SDSS) and the Astrophysical Research Consortium 3.5-m telescope. The spectral features and overall shape of the L dwarf templates are consistent with previous spectroscopic standards and the templates have a radial velocity precision of $\sim$10--20 km s$^{-1}$. We calculate bolometric fluxes (accurate to 10--20\%) for 101 late-M and L dwarfs from SDSS, 2MASS, and WISE photometry, SDSS spectra, and BT-Settl model spectra. We find that the $z$- and $J$-band bolometric corrections for late-M and L dwarfs have a strong correlation with $z-J$ and $J-K_S$ colors respectively. The new $\chi$ values, which can be used to convert H$\alpha$ equivalent widths to activity strength, are based on spectrophotometrically calibrated SDSS spectra and the new bolometric fluxes. While the measured $\chi$ values have typical uncertainties of $\sim$20\%, ultracool dwarf models show the continuum surrounding H$\alpha$ can vary by up to an order of magnitude with changing surface gravity. Our semi-empirical $\chi$ values are one to two orders of magnitude larger than previous $\chi$ values for mid- to late-L dwarfs, indicating that the upper limits for H$\alpha$ activity strength on the coolest L dwarfs have been underestimated.