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) M-+0.11(circle dot) Me and a characteristic width of 0.8(-0.1)(+0.2) dex in the 12M(Jup)-2M(circle dot) range, whereas a Salpeter power law with alpha= 2.2(-0.5)(+1.1) best describes the IMF slope in the 0.1-2M(circle dot) 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 similar to 5-7M(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 gamma), TWA. 29 (M9.5 gamma), 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.