
Microlensing events caused by free-floating planets without host stars, detected through gravitational light bending.Rogue planets are worlds that drift through interstellar space without a parent star. They are extremely faint and cold, making them nearly impossible to detect directly. However, when one passes in front of a distant background star, its gravity bends and focuses the star's light, causing a brief, characteristic brightening known as a gravitational microlensing event. This effect allows astronomers to find these otherwise invisible wanderers and even measure their masses.
The concept of gravitational microlensing was proposed by Bohdan Paczyński in 1986, and the first rogue planet discovered this way was announced in 2011 by a team using data from the MOA and OGLE surveys.
According to general relativity, any mass curves spacetime. When a rogue planet passes nearly exactly along the line of sight to a background star, its gravitational field acts like a lens, bending light rays toward the observer. This amplifies the star's apparent brightness in a smooth, symmetric peak that lasts from hours to days. The duration and shape of the brightening reveal the planet's mass and its distance from Earth, while the absence of any repeated signal confirms it has no host star.
Microlensing surveys like OGLE and MOA use this technique to census free-floating planets, helping to constrain models of planetary system formation and ejection.
A single rogue planet can briefly outshine a distant star by a factor of thousands, even though the planet itself emits almost no light.
| δθ | variable | centroid shift — angular centroid shift radian |
| u | variable | impact parameter in units of Einstein radius — impact parameter |
| θ_E | variable | Einstein radius — einstein radius radian |
| \Delta\Omega | variable | precession rate of orbital nodes — angular velocity radian per second |
| \chi | variable | dimensionless spin parameter of central body — dimensionless spin parameter |
| e | variable | orbital eccentricity — eccentricity |
| r_g | variable | gravitational radius of central body — length metre |
| a | variable | semi-major axis of orbit — length metre |
















