The Ultracool SpeXtroscopic Survey. I. Volume-limited Spectroscopic Sample and Luminosity Function of M7-L5 Ultracool Dwarfs

We present a volume-limited, spectroscopically verified sample of M7-L5 ultracool dwarfs (UCDs) within 25 pc. The sample contains 410 sources, of which 93% have trigonometric distance measurements (80% from Gaia DR2) and 81% have low-resolution (R similar to 120), near-infrared (NIR) spectroscopy. We also present an additional list of 60 sources that may be M7-L5 dwarfs within 25 pc when distance or spectral-type uncertainties are taken into account. The spectra provide NIR spectral and gravity classifications, and we use these to identify young sources, red and blue J-K-S color outliers, and spectral binaries. We measure very low gravity and intermediate-gravity fractions of 2.1(-0.8%)(+0.9%) and 7.8(-1.5%)(+1.7%), respectively; fractions of red and blue color outliers of 1.4(-0.5%)(+0.6%) and 3.6(-0.9%)(+1.0%), respectively; and a spectral binary fraction of 1.6(-0.5%)(+0.5%). We present an updated luminosity function for M7-L5 dwarfs continuous across the hydrogen-burning limit that agrees with previous studies. We estimate our completeness to range between 69% and 80% when compared to an isotropic model. However, we find that the literature late-M sample is severely incomplete compared to L dwarfs, with completeness of 62(-7%)(+8%) and 83(-9%)(+10%), respectively. This incompleteness can be addressed with astrometric-based searches of UCDs with Gaia to identify objects previously missed by color- and magnitude-limited surveys.