BANYAN. IX. The Initial Mass Function and Planetary-mass Object Space Density of the TW HYA Association

A determination of the initial mass function (IMF) of the current, incomplete census of the 10 Myr-old TW Hya association (TWA) is presented. This census is built from a literature compilation supplemented with new spectra and 17 new radial velocities from ongoing membership surveys, as well as a reanalysis of Hipparcos data that confirmed HR 4334 (A2 Vn) as a member. Although the dominant uncertainty in the IMF remains census incompleteness, a detailed statistical treatment is carried out to make the IMF determination independent of binning while accounting for small number statistics. The currently known high-likelihood members are fitted by a log-normal distribution with a central mass of {0.21}_-0.06^+0.11 M _⊙ and a characteristic width of {0.8}_-0.1^+0.2 dex in the 12 M _Jup-2 M _⊙ range, whereas a Salpeter power law with α ={2.2}_-0.5^+1.1 best describes the IMF slope in the 0.1-2 M _⊙ range. This characteristic width is higher than other young associations, which may be due to incompleteness in the current census of low-mass TWA stars. A tentative overpopulation of isolated planetary-mass members similar to 2MASS J11472421-2040204 and 2MASS J11193254-1137466 is identified: this indicates that there might be as many as {10}_-5⁺¹³ similar members of TWA with hot-start model-dependent masses estimated at ∼5-7 M _Jup, most of which would be too faint to be detected in 2MASS. Our new radial velocity measurements corroborate the membership of 2MASS J11472421-2040204, and secure TWA 28 (M8.5 γ), TWA 29 (M9.5 γ), and TWA 33 (M4.5 e) as members. The discovery of 2MASS J09553336-0208403, a young L7-type interloper unrelated to TWA, is also presented.