[Paper Review] Microlensing Constraints on the Frequency of Jupiter Mass Planets

B. Scott Gaudi, Michael D. Albrow+18 more|arXiv (Cornell University)|Apr 19, 2000

Astro and Planetary Science3 citations

TL;DR

This study uses microlensing light curves from 23 high-quality events monitored by the PLANET collaboration to constrain the frequency of Jupiter-mass planets. Despite high-precision data, no planetary perturbations were detected, leading to a 95% confidence upper limit that less than 33% of stellar systems host Jupiter-mass planets at separations of 1.5–3 AU, with similar limits for 3 Jupiter-mass planets at 1–4 AU.

ABSTRACT

Microlensing is the only technique likely, within the next 5 years, to constrain the frequency of Jupiter-analogs. The PLANET collaboration has monitored nearly 100 microlensing events of which more than 20 have sensitivity to the perturbations that would be caused by a Jovian-mass companion to the primary lens. No clear signatures of such planets have been detected. These null results indicate that Jupiter mass planets with separations of 1.5-3 AU occur in less than 1/3 of systems. A similar limit applies to planets of 3 Jupiter masses between 1-4 AU.

Motivation & Objective

• To determine the frequency of Jupiter-mass planets in the 1.5–3 AU separation range using microlensing data.
• To assess the detectability of planetary companions via short-duration perturbations in microlensing light curves.
• To establish statistical upper limits on the occurrence rate of massive planets based on null detections across multiple high-quality events.
• To evaluate the sensitivity of microlensing to planets with masses comparable to Jupiter and beyond, particularly in the lensing zone.
• To provide constraints complementary to radial velocity surveys, focusing on systems with wider orbital separations relevant to our solar system.

Proposed method

• Analysis of 23 high-quality microlensing light curves from the 1998–1999 PLANET seasons, selected for photometric accuracy and temporal sampling.
• Application of a detection efficiency model ε_i(d, q) that accounts for the geometric probability of planetary perturbations based on planet-star separation d (in units of Einstein radius) and mass ratio q.
• Use of the likelihood function P = ∏[1 − f(d,q)ε_i(d,q)] to compute the probability of observing no detections across N events.
• Computation of 95% confidence level upper limits on the fraction f(d,q) of lenses hosting companions by solving P = 5%.
• Conversion of limits from d and q to physical separation (AU) and planet mass (M_J) using standard microlensing distance assumptions (D_L = 6 kpc, M_L = 0.3 M☉).
• Integration of angular separation limits into physical separation via r_E = θ_E × D_L, with θ_E derived from lens mass and distances.

Experimental results

Research questions

• RQ1 What is the upper limit on the frequency of Jupiter-mass planets with orbital separations of 1.5–3 AU based on microlensing null detections?
• RQ2 How does the detection efficiency for planetary companions vary with planet-star separation and mass ratio in microlensing events?
• RQ3 To what extent do high-magnification microlensing events (A_max > 10) enhance the sensitivity to planetary companions in the lensing zone?
• RQ4 What constraints can be placed on the occurrence rate of 3 Jupiter-mass planets at separations of 1–4 AU using current microlensing data?
• RQ5 How do the results compare with predictions from theoretical models of planet formation and radial velocity survey frequencies?

Key findings

• No planetary perturbations were detected in any of the 23 high-quality microlensing light curves analyzed, despite sufficient sensitivity to detect Jupiter-mass planets.
• The 95% confidence level upper limit on the fraction of stars hosting Jupiter-mass planets (M_p ≈ 1 M_J) at separations of 1.5–3 AU is less than 33%.
• Similarly, the upper limit for planets with mass ≥3 M_J at separations of 1–4 AU is also less than 33%.
• For planets at the separation of Jupiter (5.2 AU), the upper limit on the fraction of systems hosting 3 M_J planets is less than 50%.
• The analysis confirms that high-magnification events (A_max > 10) are highly efficient for planet detection, with near-100% detection probability for planets in the lensing zone.
• The results demonstrate that microlensing is a powerful, complementary method to radial velocity and transit surveys for constraining the frequency of massive planets at wider orbital separations.