method

gravitational lensing analysis

Using light bending by gravity to measure cosmic structures and infer properties like dark matter distribution.
24 related articles · 3 formulas

Description

Gravitational lensing analysis uses the bending of light by massive objects to map the distribution of matter in the universe, including dark matter. When light from distant galaxies passes near a massive foreground object, its path is curved, creating distorted, magnified, or multiple images. By analyzing these distortions, astronomers can infer the mass distribution of the lensing object, even if that mass is invisible, such as dark matter.

History

The theory of gravitational lensing was first derived by Einstein in 1936, but the first complete gravitational lens was discovered in 1979. Weak lensing became a major cosmological tool in the 1990s and 2000s.

How it works

The gravitational field of a massive object acts like a lens, deflecting light rays according to general relativity. In strong lensing, this produces dramatic effects like Einstein rings and multiple images. In weak lensing, the distortion is subtle, but by statistically analyzing the shapes of many background galaxies, astronomers can map the dark matter distribution. The degree of distortion depends on the mass and distance of the lens, allowing precise measurements of cosmic structure.

In practice

Gravitational lensing is used to map dark matter in galaxy clusters, measure the expansion rate of the universe, and detect exoplanets via microlensing. It also helps test modified gravity theories.

Fun fact

A single galaxy cluster can act as a gravitational lens, producing multiple images of the same background galaxy, sometimes arranged in a near-perfect Einstein ring.

Concept graph →

Formulas

$$\beta = \frac{D_{ds} D_s'}{D_{ds}' D_s}$$
Ratio of angular diameter distances in lensing cosmology.
What is in the formula
βvariableratio of angular diameter distances — distance ratio
D_dsvariableangular diameter distance from lens to source — angular diameter distance metre
D_s'variableangular diameter distance from observer to source in a reference cosmology — angular diameter distance metre
D_ds'variableangular diameter distance from lens to source in a reference cosmology — angular diameter distance metre
D_svariableangular diameter distance from observer to source — angular diameter distance metre
β_{e,{pl}}=(β-(1-λ)(1-β))^{\frac{1}{γ_{{pl}}-1}} · 2607.01005v1
β=\frac{d_{ds1}d_{s2}}{d_{ds2}d_{s1}} · 2607.01005v1
$$\theta_E = \sqrt{\frac{4GM}{c^2} \frac{D_{\rm LS}}{D_{\rm L} D_{\rm S}}}}$$
Angular size of gravitational lensing depends on mass and distances.
What is in the formula
\theta_EvariableEinstein ring angular radius — angle radian
MvariableMass of the lensing object — mass kilogram
D_{\rm LS}variableAngular diameter distance from lens to source — distance metre
D_{\rm L}variableAngular diameter distance from observer to lens — distance metre
D_{\rm S}variableAngular diameter distance from observer to source — distance metre
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
\sqrt{}operatorTakes the square root of the argument — square root
θ_e=\sqrt{\frac{4gm_l}{c^2}\frac{d_s-d_l}{d_sd_l}} · 2607.01853v1
θ_e=\sqrt{\frac{4gmd_{ls}}{c^2d_ld_s}} · 2607.02663
$$\frac{dN}{dL} \propto L^{-\alpha}$$
Power-law distribution of objects by luminosity.
What is in the formula
Nvariablenumber of objects — number of objects
Lvariableluminosity of objects — luminosity watt
αvariablepower-law index (slope) — power law index
d/dLoperatordifferentiation with respect to luminosity — derivative with respect to luminosity
ndm\propto10^{βm}dm\quad{или}\quadndl\proptol^{-α}dl · 2607.26330v1

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