method

gravitational microlensing

Using the bending of light by massive objects to detect faint or dark celestial bodies.
37 related articles · 3 formulas

Description

Gravitational microlensing is an astronomical technique that uses the gravitational field of a massive object to bend and magnify light from a background star, acting as a natural lens. Unlike strong lensing, which produces dramatic arcs and multiple images, microlensing causes a temporary brightening of the background source as the lens passes in front of it. This effect is sensitive to dark, faint, or isolated objects that emit little or no light, making it a powerful tool for detecting exoplanets, black holes, and dark matter candidates.

History

The concept was proposed by Einstein in 1936 and by Soviet astronomer Todorov in 1937, but the first microlensing event was observed in 1993 by the MACHO and EROS collaborations.

How it works

When a foreground object (the lens) passes near the line of sight to a distant star, its gravity warps spacetime, focusing more light toward the observer. The observed brightness of the background star rises and falls smoothly over days to weeks, following a characteristic curve. The peak magnification and duration depend on the lens mass, distance, and relative motion. By analyzing these light curves, astronomers can infer the lens properties, even if it is invisible.

In practice

Microlensing surveys like OGLE and MOA have discovered thousands of exoplanets, including free-floating planets, and are used to search for primordial black holes as dark matter candidates.

Fun fact

Microlensing can detect planets as small as Earth orbiting stars thousands of light-years away, even though the planet itself never emits or reflects enough light to be seen directly.

Concept graph →

Formulas

$$\kappa(\boldsymbol{\theta}) = \frac{3H_0^2\Omega_m}{2c^2} \int_0^{\chi} d\chi' \, \frac{q(\chi')}{a(\chi')} f_K(\chi') \delta(f_K(\chi')\boldsymbol{\theta}, \chi')$$
Convergence is a weighted integral of density contrast along the line of sight.
What is in the formula
kappavariableweak lensing convergence — convergence
thetavariableangular position on the sky — angular position radian
chivariablecomoving distance to the source — comoving distance metre
chi'variablecomoving distance along the line of sight — comoving distance metre
qvariablelensing efficiency function — lensing efficiency
avariablescale factor — scale factor
f_Kvariablecomoving angular diameter distance — comoving angular diameter distance metre
deltavariablematter density contrast — density contrast
H_0constantcurrent expansion rate of the universe — hubble constant = 2.2e-18 per second
Omega_mconstantratio of matter density to critical density today — matter density parameter = 0.315
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
∫operatorsummation over infinitesimal elements — integral
\kappa(\boldsymbol{\vartheta})=\frac{3h_0^2ω_m}{2c^2}\int_0^{χ_{\lim}}dχ\frac{q(χ)}{a(χ)}f_k(χ)δ(f_k(χ)\boldsymbol{\vartheta},χ) · 2606.31988
$$M_{\min} \propto \frac{\sigma_{\text{th}}^2 D_L D_S}{G D_{LS}}$$
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

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