One star can arrive from several directions
Imagine looking through a telescope at a crowded patch of the Milky Way. Most stars barely change over a night. One of them slowly brightens, reaches a peak, then fades. A dark foreground object may have crossed close to the line of sight. Light passing on opposite sides of that object bends toward the telescope, so the background star appears in more than one direction.
Usually those images are too close together for the telescope to separate. Their light lands in the same small patch of the photograph. Measuring the total repeatedly gives a light curve: a graph of how much light arrives as time passes. This temporary gravitational brightening is called microlensing.
The star itself need not change. The lens preserves the surface brightness of each little patch of the star. What changes is the combined apparent area of its images. A wider image delivers more light in the same way that a larger patch of an evenly lit wall fills more of your view.
Reading: Bozza et al. (2018), VBBinaryLensing finite-source methods
A small companion reshapes the brightening
A single compact lens makes a particularly simple pattern: two images, on opposite sides of the lens. As the alignment improves, the images spread around an angular ring. Their combined area rises smoothly. The curve is nearly symmetric when the relative motion is straight and the observing conditions stay the same.
Put a planet beside the foreground star and the two gravitational deflections add. In some source directions an extra pair of images appears. The places separating the different image patterns form curves called caustics in the source-direction map. A star crossing one can brighten much more abruptly than it does in an ordinary single-lens event.
A caustic is a boundary drawn by the geometry of the light paths. There is no glowing fence in space. It tells you where a tiny change in the background star’s direction changes its images greatly. The planet can be faint enough to contribute no detectable light and still reshape that geometry.
Reading: Bozza et al., VBMicroLensing, arXiv:2410.13660v1; A&A 694 A219 (2025)
The star takes time to cross the boundary
A real star has a disk. Its leading edge reaches the caustic before its center does, and the trailing edge leaves later. Each part has its own images; their light must be added. The result is a finite peak with a shape that depends on the star’s angular size.
Make the star larger and the sharp feature spreads over a longer time. Its edge may also be dimmer than its center, so the first and last parts of the crossing contribute less light. This gradual darkening toward a stellar edge is called limb darkening. It helps explain why a caustic crossing can teach us about both the lens and the star behind it.
Light from another unresolved star can soften the event in a different way. That other star supplies an almost constant contribution. The lensed star brightens by the same factor, but its variation becomes a smaller fraction of everything inside the telescope’s measuring patch.
Reading: Bozza et al. (2018), VBBinaryLensing finite-source methods
A brief feature led to a cold planet
The event OGLE-2005-BLG-390 showed a short planetary feature on a much broader brightening. Beaulieu and colleagues reported the discovery in 2006. Their Figure 1 compares observations from several telescopes with lens models, and Table 1 gives the fitted mass ratio and geometric scales.
The reported planet-to-host mass ratio was , about one part in thirteen thousand. The small extra mass could therefore reveal itself through a conspicuous change in the background star’s images. The analysis used the finite size and edge brightness of the source star to model the smoothed anomaly.
The ratio is easier to learn than a mass in Earth or Jupiter units. An event’s length also depends on distances and relative motion. The discovery paper combined its light-curve measurements with a model of stars in the Galaxy to estimate physical masses. The image geometry supplies the planet’s signature; additional information supplies its absolute scale.
Reading: Beaulieu et al. (2006), OGLE-2005-BLG-390 discovery, astro-ph/0601563v1
Watch area become light
The revealing moment is the birth of extra image area. Follow the outlined source across the source-direction diagram and watch the blue-white images in the sky view stretch and merge. The brightness curve below follows their integrated light. Then enlarge the source and ask which parts of the sudden feature survive.
A useful prediction is simple: if the larger star takes longer to pass the same boundary, its brightest part should also last longer. If a second star merely adds constant light, the event should become less pronounced without changing when the lensed star meets the caustic. Those are two different routes to a less dramatic light curve.
Reading: Bozza et al. (2018), VBBinaryLensing finite-source methods