The Initial Mass Function Based on the Full-sky 20 pc Census of ∼3600 Stars and Brown Dwarfs

Abstract A complete accounting of nearby objects—from the highest-mass white dwarf progenitors down to low-mass brown dwarfs—is now possible, thanks to an almost complete set of trigonometric parallax determinations from Gaia, ground-based surveys, and Spitzer follow-up. We create a census of objects within a Sun-centered sphere of 20 pc radius and check published literature to decompose each binary or higher-order system into its separate components. The result is a volume-limited census of ∼3600 individual star formation products useful in measuring the initial mass function across the stellar (&lt;8 M ⊙ ) and substellar (≳5 M Jup ) regimes. Comparing our resulting initial mass function to previous measurements shows good agreement above 0.8 M ⊙ and a divergence at lower masses. Our 20 pc space densities are best fit with a quadripartite power law, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ξ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi mathvariant="italic">dN</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi mathvariant="italic">dM</mml:mi> <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> , with long-established values of α = 2.3 at high masses (0.55 &lt; M &lt; 8.00 M ⊙ ), and α = 1.3 at intermediate masses (0.22 &lt; M &lt; 0.55 M ⊙ ), but at lower masses, we find α = 0.25 for 0.05 &lt; M &lt; 0.22 M ⊙ , and α = 0.6 for 0.01 &lt; M &lt; 0.05 M ⊙ . This implies that the rate of production as a function of decreasing mass diminishes in the low-mass star/high-mass brown dwarf regime before increasing again in the low-mass brown dwarf regime. Correcting for completeness, we find a star to brown dwarf number ratio of, currently, 4:1, and an average mass per object of 0.41 M ⊙ .