method

microlensing

Microlensing is a gravitational lensing method that magnifies light from distant objects using intervening masses.
59 related articles · 4 formulas · 2 who worked here

Description

Gravitational microlensing is a phenomenon where an unresolved massive object (with mass ranging from a planet to a star) temporarily magnifies a distant source. Light rays are deflected by the lens's gravity, forming two images that merge into one spot. Amplification depends on the alignment and mass of the lens, reaching a maximum at the smallest angular distance. The light curve has a characteristic symmetry, and when a planetary companion is present, it produces sharp spikes—caustics (sharp brightness peaks). The method does not require the lens itself to shine, making it ideal for searching for substellar bodies and dark clumps.

History

Einstein in 1936 calculated the magnification for a star lens, but considered the event incredibly rare. In the 1960s, Refsdal and others pointed out its observational potential. The first detection came in 1993 by the MACHO project: monitoring millions of stars confirmed dark compact bodies in the Milky Way's halo. Surveys like OGLE and MOA now record thousands of events per year, discovering exoplanets and placing constraints on dark matter.

How it works

The lens equation relates the true and observed positions of the source. For a point mass, magnification is maximum at minimum u. The lens's motion relative to the line of sight gives a time-dependent u(t), producing a symmetric light curve of duration t_E. With a second mass (a planet), critical curves and caustics appear in the source plane; when the source crosses a caustic, the brightness changes sharply. Analysis of such anomalies yields the mass ratio and projected separation. Chromatic microlensing uses the absorption difference between the center and edge of the source disk, enabling reconstruction of the brightness profile of a distant star.

In practice

Microlensing reveals 'invisibles': lone rogue planets, black holes, dark dwarfs. This is how dark matter is mapped and distant icy worlds are discovered.

Fun fact

In 2017, microlensing revealed a lone planet the size of Jupiter wandering without a parent star through interstellar darkness.

Concept graph →

Formulas

$$\delta\theta(u) = \frac{u}{u^2+2}\theta_E$$
Angular centroid shift depends on impact parameter in microlensing.
What is in the formula
δθvariablecentroid shift — angular centroid shift radian
uvariableimpact parameter in units of Einstein radius — impact parameter
θ_EvariableEinstein radius — einstein radius radian
δθ(u)=\frac{u}{u^2+2}θ_e · 2607.12144
$$M_{\min} \propto \frac{\sigma_{\text{th}}^2 D_L D_S}{G D_{LS}}$$
Minimum lens mass for detectable astrometric shift scales with astrometric precision squared.
What is in the formula
M_minvariableMinimum lens mass — mass kilogram
sigma_thvariableAstrometric precision threshold — angular resolution radian
D_LvariableDistance to lens — distance metre
D_SvariableDistance to source — distance metre
D_LSvariableDistance between lens and source — distance metre
GconstantUniversal gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\proptooperatorIndicates proportionality — proportionality
m_{\min}\simeq\frac{2c^2σ_{{th}}^2d_ld_s}{gd_{ls}} · 2607.12144
$$\mu \propto \ell^{-1/2}$$
Magnification scales inversely with square root of distance to caustic.
What is in the formula
μvariablemagnification — magnification
ℓvariabledistance to caustic — distance to caustic metre
∝operatorindicates the left side scales as a constant times the right side — proportionality
μ\propto(\frac{\ell}{r})^{-1/2} · 2607.14034
$$h_L(f) = \mu(f) h_{unL}(f)$$
Lensed wave equals unlensed wave multiplied by magnification factor.
What is in the formula
h_LvariableLensed gravitational wave strain — gravitational wave strain
h_unLvariableUnlensed gravitational wave strain — gravitational wave strain
μvariableMagnification factor — magnification
h_l(f)=f(f)h_{unl}(f) · 2607.21834v1

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