A caustic crossing occurs when the apparent path of a background star crosses a boundary in the magnification pattern of a two-body gravitational lens. The star does not travel through a foreground planet or collide with a lens. The changing alignment produces a rapid, finite feature in the measured brightness.
This article separates three things that are easy to confuse: the caustic boundary, the star’s passage across that boundary, and the wider event used to identify the lens.
Where the boundary comes from
Two foreground masses—a stellar pair or a star and planet—deflect light together. Their gravitational mapping creates critical curves in the image plane and corresponding caustics in the source plane. A smooth caustic segment is a fold; a pointed junction is a cusp. Neither is a physical filament in space.
For an isolated binary point-mass lens, an ordinary fold crossing changes the number of point-source images by two. An entering source gains a highly magnified image pair; an exiting source loses one. A telescope usually measures the summed light rather than resolving these images.
Read the crossing in three stages
| Stage | What changes | Interpretation |
|---|---|---|
| Leading limb reaches a fold | Part of the stellar disk enters the high-magnification region | The signal starts before the source center crosses |
| Disk straddles the fold | Different surface regions receive different magnifications | Finite source size and limb darkening shape the profile |
| Trailing limb clears the fold | The whole disk lies on the other side | The local transition ends; the wider event continues |
The infinite peak of an ideal point source is not an observable stellar brightness. Averaging over a real star’s finite disk removes that divergence. The source’s brightness profile matters because its center and edge need not contribute equal light.
A duration you can calculate
For a locally straight fold with approximately constant relative motion, the diameter-crossing time is Δt ≈ 2θ* / μ⊥. Here θ* is the source’s angular radius and μ⊥ is the angular speed perpendicular to the fold, relative to that caustic.
Illustrative values: let θ* = 0.5 microarcsecond and μ⊥ = 5 milliarcseconds/year. Convert the latter to 5,000 microarcseconds/year. Then Δt = 1/5,000 year ≈ 1.75 hours. Halving the perpendicular speed doubles the crossing time.
This is not the time between entering and leaving the entire caustic region. A shallow crossing angle can lengthen the local transition even when the total relative speed stays unchanged. Caustic motion also matters when the lens orbit evolves.
Why two peaks are not two separate lenses
A simple track through a caustic can yield entry and exit features. They mark boundaries of one combined magnification pattern. They are not automatically one peak per foreground mass. A cusp approach can produce a strong peak without a crossing; other trajectories can cross several folds.
What would make the interpretation convincing?
- Obtain frequent measurements across the transition, with enough baseline to establish the unmagnified source.
- Model finite-source effects rather than fitting an infinitely sharp point-source spike.
- Include the light curve outside the crossing; local fold behavior does not uniquely specify the whole binary.
- Compare competing mass ratios, separations, trajectories, and any relevant parallax or orbital motion.
A sharp feature alone does not prove a planet or fix its mass. It constrains a geometry that must work with the rest of the observations.
Technical reading and the next step
Dominik’s fold-caustic analysis explains why local crossing information must be connected to the wider event. VBBinaryLensing describes numerical treatment of finite-source light curves.
Continue with the finite-source calculation or why microlensing can change the measured color.
Revised October 26, 2026. Numerical values above are a teaching example, not an observed event.