AC23
A dark planet bends starlight
Start with a star that briefly brightens. Draw its images, give the star a finite disk, then ask which properties a real light curve can constrain.
L1
How a dark planet makes a distant star brighten
A planet bends the images of a background star. Follow their changing area to understand planetary microlensing and a brief brightening.
L1
From a bent light ray to two stellar images
Derive the point-mass lens equation, locate its two images, and calculate their parity and combined magnification.
L2
What happens when a stellar disk crosses a caustic?
Add two deflections, find critical image directions, and integrate a finite, limb-darkened stellar disk into its light curve.
L3
What can a microlensing light curve tell us about its lens?
Build a blended-light likelihood, distinguish fitted geometry from physical mass, and see how source size and parallax supply missing scales.
L4
Read a dark planet’s mass from Earth and space
Read the finite-source and Gaia-parallax evidence, inspect a separate host-star search, and distinguish Roman forecasts from detections.
L4
Fit the published OGLE-2005-BLG-390 photometry
Download five original files, fit finite-source planetary models, and test which conclusions survive alternative solutions and weak parallax.
Drag the star through a planetary lens
Sources and calculation scope
- Beaulieu et al. (2006), OGLE-2005-BLG-390 discovery, astro-ph/0601563v1
Read the main text, Table 1 and Figure 1: finite-source planetary anomaly, source limb coefficients, 650 original points and population-conditioned physical mass. Our independently rerun five-file subset contains 308 points.
- Bozza et al. (2018), VBBinaryLensing finite-source methods
Sections 2–4 and equations 14–20, 25–26 explain contour area, error refinement and radial source profiles. The pinned LGPL code remains a separately downloaded offline reference.
- Bozza et al., VBMicroLensing, arXiv:2410.13660v1; A&A 694 A219 (2025)
Read equations 1–16 and section 6 before interpreting binary roots, parity, critical curves or a missing image pair. This is a methods reading, not a replication of its benchmark suite.
- OGLE published OGLE-2005-BLG-390 project files
Five fixed photometry URLs are named in observation-sources.json. The tutorial fetches them from the author project and verifies byte counts and SHA256. An explicit redistribution license was not found; they are not mirrored here.
- Dong et al., A Saturn-mass microlensing object, arXiv:2601.00057v1; Science
Fixed author version, Figure 2 and supplement S5–S11: finite-source scale, ground/Gaia parallax, alternative blending and solution weights. arXiv identifies the paper as published in Science. This guide reads the evidence; it does not rerun that event.
- Johnson et al. (2020), Roman free-floating-planet forecast, arXiv:2006.10760v2
Sections 2 and 5, Figures 3–5 and Appendix A: Cycle 7 survey assumptions, finite-source light curves, detection cuts and mass-function-conditioned yields. These are the fixed 2020 predictions.
- Mróz et al., host-star limits, arXiv:2609.12743v1, submitted to A&A
Read Figures 2–3, sections 4–5 and Appendix B for interferometric contrast, correlated noise and conversion to a conditional host limit. The fixed version remains a submitted preprint in the metadata checked on 2026-11-03.
- NASA Roman Galactic Bulge Time-Domain Survey
Official microlensing survey context checked on 2026-11-03. The cited programme observes the bulge repeatedly with the Wide Field Instrument.
- JPL Horizons vector ephemeris documentation
The exercise retains a fixed 161-node DE441 geometric ICRF Earth vector response, positions in AU, velocities in AU/day and TDB epochs. The headerless photometry keeps its separate timing qualification.