Using Old and New Approaches: Determining Physical Properties of Brown Dwarfs with Empirical Relations and Machine Learning Models

We investigate applications of machine learning models to directly infer physical properties of brown dwarfs from their photometry and spectra using $\textit{The Cannon}$. We demonstrate that absolute magnitudes, spectral types, and spectral indices can be determined from low-resolution SpeX prism spectra of L and T dwarfs without trigonometric parallax measurements and with precisions competitive with commonly used methods. For T dwarfs with sufficiently precise spectra and photometry, bolometric luminosities and effective temperatures can be determined at precisions comparable to methods that use polynomial relations as a function of absolute magnitudes. We also provide new and updated polynomial relations for absolute magnitudes as a function of spectral types L0-T8 in 14 bands spanning Pan-STARRS $r_{P1}$ to AllWISE $\textit{W3}$, using a volume-limited sample of 256 brown dwarfs defined entirely by parallaxes. These include the first relations for brown dwarfs using Pan-STARRS1 photometry and the first for several infrared bands using a volume-limited sample. We find that our novel method with $\textit{The Cannon}$ can infer absolute magnitudes with equal or smaller uncertainties than the polynomial relations that depend on trigonometric parallax measurements.