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

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 similar to 3600 individual star formation products useful in measuring the initial mass function across the stellar (<8M(circle dot)) and substellar (greater than or similar to 5M(Jup)) regimes. Comparing our resulting initial mass function to previous measurements shows good agreement above 0.8M(circle dot) and a divergence at lower masses. Our 20 pc space densities are best fit with a quadripartite power law, xi(M) = dN/dM proportional to M-alpha, with long-established values of alpha = 2.3 at high masses (0.55 < M < 8.00M(circle dot)), and alpha = 1.3 at intermediate masses (0.22 < M < 0.55M(circle dot)), but at lower masses, we find alpha = 0.25 for 0.05 < M < 0.22M(circle dot), and alpha = 0.6 for 0.01 < M < 0.05M(circle dot). 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-circle dot.