method

dark matter lensing

Using gravitational lensing effects to detect and map the distribution of dark matter in the universe.
28 related articles · 6 formulas

Description

Gravitational lensing is a phenomenon predicted by Einstein's general relativity: massive objects like galaxies or black holes bend the path of light passing near them, acting like a giant lens. When this lensing is caused by dark matter — the invisible substance that outweighs ordinary matter by a factor of five — it distorts the images of background galaxies in characteristic ways. By mapping these distortions, astronomers can trace the distribution of dark matter even though it emits no light. This technique has become a cornerstone of modern cosmology, revealing that dark matter forms a vast cosmic web of filaments and halos around galaxies.

History

The concept of gravitational lensing was first discussed by Einstein in 1936, but the first observed lens was the 'Twin Quasar' in 1979. Dark matter mapping via weak lensing was pioneered in the 1990s by groups including Anthony Tyson and Yannick Mellier.

How it works

Light from a distant galaxy travels in straight lines through empty space, but when it passes through a region with dark matter, the gravitational field curves spacetime. The light follows the curved paths, so the galaxy appears shifted, stretched, or even split into multiple images. The amount of distortion depends on the mass of the dark matter along the line of sight. By measuring the shapes of millions of background galaxies statistically, astronomers can reconstruct the dark matter map — a method called weak lensing. Strong lensing, where a single galaxy is dramatically warped into arcs or rings, provides a more direct but rarer probe.

In practice

Gravitational lensing is used to map dark matter distributions in galaxy clusters, measure the expansion rate of the universe, and even detect exoplanets via microlensing events.

Fun fact

The Hubble Space Telescope's most famous deep-field images are actually gravitational lenses — the faint smudges of distant galaxies are magnified and distorted by dark matter in the foreground.

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
$$\theta_E = \sqrt{\frac{4GM}{c^2} \frac{D_{LS}}{D_L D_S}}$$
Angular radius of gravitational lensing Einstein ring.
What is in the formula
\theta_EvariableAngular radius of the Einstein ring — einstein radius angle radian
GvariableGravitational constant — gravitational constant cubic metre per kilogram per second squared
MvariableMass of the lensing object — mass kilogram
cvariableSpeed of light in vacuum — speed of light metre per second
D_{LS}variableAngular diameter distance between lens and source — distance metre
D_LvariableAngular diameter distance from observer to lens — distance metre
D_SvariableAngular diameter distance from observer to source — distance metre
\sqrt{}operatorTakes the square root of the argument — square root
θ_{\rme}=\sqrt{\kappamπ_{\rmrel}},\quad\kappa=\frac{4g}{c^2{\rmau}}\approx8.144~{\rmmas}m_\odot^{-1} · 2607.04594v1
θ_e=\sqrt{\kappam_lπ_{{rel}}} · 2607.04955
$$\frac{dN}{dL} \propto L^{-\alpha}$$
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
$$C^{\ell} = \int dz \frac{H(z)}{c\chi^2(z)} W^2(z) P\left(k=\frac{\ell+1/2}{\chi(z)},z\right)$$
Angular power spectrum relates to 3D power spectrum via projection along line of sight.
What is in the formula
C^ellvariableAngular power spectrum at multipole ell — angular power spectrum
zvariableRedshift — redshift
H(z)variableHubble parameter at redshift z — hubble parameter kilometre per second per megaparsec
chi(z)variableComoving distance to redshift z — comoving distance metre
W(z)variableWindow function (selection function) at redshift z — window function
P(k,z)variableThree-dimensional power spectrum at wavenumber k and redshift z — power spectrum cubic metre
kvariableWavenumber — wavenumber reciprocal metre
ellvariableMultipole moment — multipole moment
cconstantFundamental constant relating distance and time in relativity — speed of light = 299792458 metre per second
∫ dzoperatorSum over all redshifts along the line of sight — integral operator
c_{\rmlss-lss}^{\ell}=\intdz\frac{h(z)}{cχ^2(z)}w_{\rmlss}^2(z)p_{\rmee}(k=\frac{\ell+1/2}{χ(z)},z) · 2607.04106v1
$$\log_{10}(M/M_\odot) = a \log_{10}(L/L_\odot) + b$$
Relates stellar mass to luminosity.
What is in the formula
Mvariablestellar mass — mass kilogram
Lvariablestellar luminosity — luminosity watt
M_sunvariablesolar mass — mass kilogram
L_sunvariablesolar luminosity — luminosity watt
aconstantempirical slope of the relation — empirical slope = 3.5
bconstantempirical intercept of the relation — empirical intercept = 0
log10operatorbase-10 logarithm — logarithm base 10
\log_{10}(m_{{he}}/m_\odot)=0.659\log_{10}(l/l_\odot)-2.630 · 2601.06577
$$\Delta t = \frac{D_{\Delta t}}{c} \Delta\phi$$
Time delay is proportional to the time delay distance and lensing potential difference.
What is in the formula
\Delta tvariabletime delay between images — time delay second
D_{\Delta t}variabletime delay distance — distance metre
\Delta\phivariabledifference in lensing potential — lensing potential difference
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
δt_{ij}=\frac{d_{δt}}{c}δφ_{ij} · 2606.03634v1

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