The Hawaii Infrared Parallax Program. VI. The Fundamental Properties of 1000+ Ultracool Dwarfs and Planetary-mass Objects Using Optical to Mid-IR SEDs and Comparison to BT-Settl and ATMO 2020 Model Atmospheres

We derive the bolometric luminosities ($L_{\mathrm{bol}}$) of 865 field-age and 189 young ultracool dwarfs (spectral types M6-T9, including 40 new discoveries presented here) by directly integrating flux-calibrated optical to mid-IR spectral energy distributions (SEDs). The SEDs consist of low-resolution ($R\sim$ 150) near-IR (0.8-2.5 $\mu$m) spectra (including new spectra for 97 objects), optical photometry from the Pan-STARRS1 survey, and mid-IR photometry from the CatWISE2020 survey and Spitzer/IRAC. Our $L_{\mathrm{bol}}$ calculations benefit from recent advances in parallaxes from Gaia, Spitzer, and UKIRT, as well as new parallaxes for 19 objects from CFHT and Pan-STARRS1 presented here. Coupling our $L_{\mathrm{bol}}$ measurements with a new uniform age analysis for all objects, we estimate substellar masses, radii, surface gravities, and effective temperatures ($T_{\mathrm{eff}}$) using evolutionary models. We construct empirical relationships for $L_{\mathrm{bol}}$ and $T_{\mathrm{eff}}$ as functions of spectral type and absolute magnitude, determine bolometric corrections in optical and infrared bandpasses, and study the correlation between evolutionary model-derived surface gravities and near-IR gravity classes. Our sample enables a detailed characterization of BT-Settl and ATMO 2020 atmospheric model systematics as a function of spectral type and position in the near-IR color-magnitude diagram. We find the greatest discrepancies between atmospheric and evolutionary model-derived $T_{\mathrm{eff}}$ (up to 800 K) and radii (up to 2.0 $R_{\mathrm{Jup}}$) at the M/L transition boundary. With 1054 objects, this work constitutes the largest sample to date of ultracool dwarfs with determinations of their fundamental parameters.