Free-floating Planet Mass Function from MOA-II 9 yr Survey toward the Galactic Bulge

Abstract

We present the first measurement of the mass function of free-floating planets (FFPs), or very wide orbit planets down to an Earth mass, from the MOA-II microlensing survey in 2006–2014. Six events are likely to be due to planets with Einstein radius crossing times t E < 0.5 days, and the shortest has t E = 0.057 ± 0.016 days and an angular Einstein radius of θ E = 0.90 ± 0.14 μas. We measure the detection efficiency depending on both t E and θ E with image-level simulations for the first time. These short events are well modeled by a power-law mass function, dN 4 / d log M = ( 2.18 − 1.40 + 0.52 ) × ( M / 8 M ⊕ ) − α 4 dex−1 star−1 with α 4 = 0.96 − 0.27 + 0.47 for M/M ⊙ < 0.02. This implies a total of f = 21 − 13 + 23 FFPs or very wide orbit planets of mass 0.33 < M/M ⊕ < 6660 per star, with a total mass of 80 − 47 + 73 M ⊕ star−1. The number of FFPs is 19 − 13 + 23 times the number of planets in wide orbits (beyond the snow line), while the total masses are of the same order. This suggests that the FFPs have been ejected from bound planetary systems that may have had an initial mass function with a power-law index of α ∼ 0.9, which would imply a total mass of 171 − 52 + 80 M ⊕ star−1. This model predicts that Roman Space Telescope will detect 988 − 566 + 1848 FFPs with masses down to that of Mars (including 575 − 424 + 1733 with 0.1 ≤ M/M ⊕ ≤ 1). The Sumi et al. large Jupiter-mass FFP population is excluded.

Are There Terrestrial Planets Lurking in the Outer Solar System?

“…Figure 3 shows the cumulative probability distribution of apparent magnitudes for each planet size (lower panel), as well as the expected number of planets (upper panel), calculated the same way as in Figure 2. Note that the upper panels of both Figures 2 and 3 adopt the best-fit values in Sumi et al (2023), which correspond to the solid blue curve in Figure 1.…”

“…The numerical approach adopted in Parker et al (2017) improves on the earlier calculations of planetary capture (Li & Adams 2016;Mustill et al 2016) in part by including Gaussian kinematic substructure, as opposed to assuming a Maxwellian distribution. We adopt the recently quantified mass function of free-floating planets (Sumi et al 2023) to estimate the mass of a captured free-floating planet with an expected abundance of unity in the solar system as a function of semimajor axis,…”

“…where the fraction of free-floating planets that are captured is f ffp ∼ 2%, 2 and where the cumulative fraction of captured planets out to a certain semimajor axis a, f ( < a), is adopted from Figure 2 of Parker et al (2017). We adopt the power-law slope of a = -+ 0.96 0.27 0.47 , which was applied by Sumi et al (2023) down to Mars-mass planets. In Equation (1) and throughout this Letter, unless otherwise stated, we adopt dN d M log , meaning that the quoted abundance of planets corresponds to planets masses within a logarithmic bin centered on the quoted mass.…”

“…We run this routine 10 8 times and record the heliocentric distance for each run. Figure 2 shows the cumulative probability distribution of heliocentric distances (lower panel), as well as this distribution multiplied by the capture fraction, f ffp ∼ 2%, and by the best-fit power-law for dN d M log from Sumi et al (2023) evaluated at the masses of the four terrestrial planets, to give the expected number of planets within logarithmic mass bins centered on the quoted mass (upper panel). To directly evaluate detectability, we calculate the distribution of apparent magnitudes using the distribution of heliocentric distances, the geometric cross sections of the four terrestrial planets, and a nominal albedo of 0.2.…”

“…In recent years, the first low-mass free-floating planets have been detected (Mróz et al 2020;Gould et al 2022). Most recently, Sumi et al (2023) measured the mass function of free-floating planets down to lowmass planets. Here, we use this mass distribution to ask the question: could there exist yet-undiscovered terrestrial planets in the outer solar system that were gravitationally captured by the solar system early in its history?…”