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 ∼ 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.