# On the Mass Function, Multiplicity, and Origins of Wide-Orbit Giant Planets

## TL;DR

This study investigates the formation and characteristics of wide-orbit giant planets, revealing a steeply rising mass distribution towards smaller masses and suggesting they form mainly through core accretion, similar to close-in planets.

## Contribution

It introduces a statistical framework to derive the mass function and multiplicity fraction of wide-orbit giant planets from direct imaging data, highlighting their likely formation process.

## Key findings

- Mass distribution rises steeply toward smaller masses (N ∝ M^{-1.3±0.3}).
- Many systems probably host additional undetected sub-stellar companions.
- Results support core accretion as the primary formation mechanism for wide-orbit giants.

## Abstract

A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation of wide-orbit planets: 1) the relative mass function and 2) the fraction of systems hosting multiple companions. In this study, we focus on systems with directly imaged substellar companions, and the detection limits on lower-mass bodies within these systems. First, we uniformly derive the mass probability distributions of known companions. We then combine the information contained within the detections and detection limits into a survival analysis statistical framework to estimate the underlying mass function of the parent distribution. Finally, we calculate the probability that each system may host multiple substellar companions. We find that 1) the companion mass distribution is rising steeply toward smaller masses, with a functional form of $N\propto M^{-1.3\pm0.3}$, and consequently, 2) many of these systems likely host additional undetected sub-stellar companions. Combined, these results strongly support the notion that wide-orbit giant planets are formed predominantly via core accretion, similar to the better studied close-in giant planets. Finally, given the steep rise in the relative mass function with decreasing mass, these results suggest that future deep observations should unveil a greater number of directly imaged planets.