On the Detectability of Compact Multi-Planet Systems via Gravitational Microlensing
Abstract
Compact multi-planet systems orbiting ultracool dwarfs, such as TRAPPIST-1, may be a major population of terrestrial worlds with poorly constrained demographics. Individual close-in planets are expected to escape microlensing detection, but whether a compact system can produce a detectable collective signal remains to be quantified. We calculate the microlensing signal from each TRAPPIST-1 planet, and of all seven combined, if the system were a lens toward the bulge. For a 0.09 M⊙ lens at 4 kpc, RE ≈ 1.21 AU, placing the planets at s = 0.010--0.051 θE, 12--63 times interior to the lensing zone. We measure each signal as the residual after fitting a single-lens model, which accounts for the barycentric dipole. Because the quadrupole term cancels between the two images to first order, the residual scales as the octupole (q s3), reaching |δA / A| ∼ 10−6. The seven planets combined yield Δχ2 ∼ 10−3 even at 1~mmag precision, five orders of magnitude below the standard detection threshold. Detection requires increasing all planet masses by a factor of ∼300, whereas the resonant chain loses its guarantee of Hill stability at a factor of ∼7. Only a lens within ∼15 pc of the source or the Sun places the outer planets in the lensing zone. The Nancy Grace Roman Space Telescope is therefore not expected to detect a TRAPPIST-1-like system through microlensing, whereas its transit channel in the same fields can detect such planets in large numbers, marking a sharp boundary in the Galactic census between microlensing and transit sensitivity.
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BibTeX
@misc{kane2026detectability,
title = {{On the Detectability of Compact Multi-Planet Systems via Gravitational Microlensing}},
author = {Stephen R. Kane},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05535},
eprint = {2611.05535},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05535},
}
RIS
TY - UNPB
TI - On the Detectability of Compact Multi-Planet Systems via Gravitational Microlensing
AU - Stephen R. Kane
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05535
UR - https://arxiv.org/abs/2611.05535
AB - Compact multi-planet systems orbiting ultracool dwarfs, such as TRAPPIST-1, may be a major population of terrestrial worlds with poorly constrained demographics. Individual close-in planets are expected to escape microlensing detection, but whether a compact system can produce a detectable collective signal remains to be quantified. We calculate the microlensing signal from each TRAPPIST-1 planet, and of all seven combined, if the system were a lens toward the bulge. For a 0.09 M_⊙ lens at 4 kpc, R_E ≈ 1.21 AU, placing the planets at s = 0.010--0.051 θ_E, 12--63 times interior to the lensing zone. We measure each signal as the residual after fitting a single-lens model, which accounts for the barycentric dipole. Because the quadrupole term cancels between the two images to first order, the residual scales as the octupole (q s^3), reaching |δA / A| ∼ 10^−6. The seven planets combined yield Δχ^2 ∼ 10^−3 even at 1~mmag precision, five orders of magnitude below the standard detection threshold. Detection requires increasing all planet masses by a factor of ∼300, whereas the resonant chain loses its guarantee of Hill stability at a factor of ∼7. Only a lens within ∼15 pc of the source or the Sun places the outer planets in the lensing zone. The Nancy Grace Roman Space Telescope is therefore not expected to detect a TRAPPIST-1-like system through microlensing, whereas its transit channel in the same fields can detect such planets in large numbers, marking a sharp boundary in the Galactic census between microlensing and transit sensitivity.
ER -