A Volume-limited Sample of Ultracool Dwarfs. II. The Substellar Age and Mass Functions in the Solar Neighborhood

Abstract We present the most precise constraints to date for the mass and age distributions of single ultracool dwarfs in the solar neighborhood, based on an updated volume-limited sample of 504 L, T, and Y dwarfs within 25 pc. We develop a Monte Carlo approach using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:mi>V</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">〉</mml:mo> </mml:math> statistic to correct for incompleteness and obtain a space density of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>1.83</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.15</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.16</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> pc −3 for spectral types L0–Y2. We calculate bolometric luminosities for our sample, using an updated “super-magnitude” method for the faintest objects. We use our resulting luminosity function and a likelihood-based population synthesis approach to simultaneously constrain the mass and age distributions. We employ the fraction of young L0–L7 dwarfs as a novel input for this analysis that is crucial for constraining the age distribution. For a power-law mass function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mrow> <mml:mi mathvariant="italic">dN</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">dM</mml:mi> </mml:mrow> </mml:mfrac> </mml:mstyle> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> </mml:math> , we find <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0.58</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.20</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.16</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , indicating an increase in numbers toward lower masses, consistent with measurements in nearby star-forming regions. For an exponential age distribution b ( t ) ∝ e − β t we find β = −0.44 ± 0.14, i.e., a population with fewer old objects than often assumed, which may reflect dynamical heating of the Galactic plane as much as the historical brown dwarf birthrate. We compare our analysis to that of Kirkpatrick et al., who used a similar volume-limited sample. Although our mass function measurements are numerically consistent, their assumption of a flat age distribution is disfavored by our analysis, and we identify several important methodological differences between our two studies. Our calculation of the age distribution of solar neighborhood brown dwarfs is the first based on a volume-limited sample.