# Microlensing Constraints on the Stellar and Planetary Mass Functions

**Authors:** Jennifer C. Yee, Scott J. Kenyon  
**arXiv:** [2503.11597](https://arxiv.org/abs/2503.11597)  
**Date:** 2025-03-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2503.11597v1/

## Key points

- The mass function (MF) of isolated objects measured by microlensing consists of both a stellar and a planetary component.
- Comparison of microlensing MFs from Gould et al (2022) and Sumi et al (2023) with other measurements of the MF.
- Abundance of brown dwarfs in the Sumi et al (2023) stellar MF consistent with local solar neighborhood measurements by Kirkpatrick et al (2024).
- Microlensing free-floating planets ($\mu$FFPs) important for understanding populations of free-floating planetary-mass objects and wide-orbit planets.
- $\mu$FFPs may be free-floating or orbit host stars with semimajor axes $a\gtrsim 10~\mathrm{au}$.
- Most $\mu$FFP population with masses $>1~M_{\rm Jup}$ bound to hosts more massive than M dwarfs, but some could come from low-mass tail of stellar population.
- $\mu$FFP population constraints on planets inferred from debris disks and gaps in protoplanetary disks observed by ALMA, indicating potential issues with assumed physics regarding gap formation.
- Data from various observational methods show declining frequency of planets with increasing mass, mirroring trend observed among stars.
- Further investigations into mass function distribution can provide valuable insights into planetary formation processes and exoplanet populations within our galaxy.

## Summary

The mass function (MF) of isolated objects measured by microlensing consists of both a stellar and a planetary component. In this study, we compare the microlensing MFs of Gould et al (2022) and Sumi et al (2023) to other measurements of the MF. The abundance of brown dwarfs in the Sumi et al (2023) stellar MF is found to be consistent with measurements from the local solar neighborhood as reported by Kirkpatrick et al (2024). Microlensing free-floating planets ($\mu$FFPs) play a crucial role in understanding the populations of both free-floating planetary-mass objects and wide-orbit planets. These $\mu$FFPs may either be free-floating or orbit host stars with semimajor axes $a\gtrsim 10~\mathrm{au}$. Comparisons to radial velocity and direct imaging planet populations suggest that most of the $\mu$FFP population with masses $>1~M_{\rm Jup}$ is bound to hosts more massive than M dwarfs. However, there is also a possibility that some fraction of the observed bound population actually comes from the low-mass tail of the stellar population. Furthermore, the $\mu$FFP population places strong constraints on planets inferred from debris disks and gaps in protoplanetary disks observed by ALMA. The tension between these observations could indicate potential issues with assumed physics regarding gap formation by planets in these studies. It is possible that there is not a one-to-one correspondence between planets and gaps, or that theories about the physical mechanisms controlling gap formation are incomplete. Regardless, this tension highlights the significant ability of the $\mu$FFP population to constrain existing theories and assumptions in planetary formation studies. In conclusion, data from various observational methods such as microlensing, radial velocities, and transits show that planets with masses comparable to Saturn and Jupiter are less common compared to those with masses similar to Earth and Neptune. This declining frequency of planets with increasing mass mirrors a similar trend observed among stars. Additionally, further investigations into the mass function distribution can provide valuable insights into planetary formation processes and shed light on our understanding of exoplanet populations within our galaxy.