Gravitational Lensing

Gravitational lensing is the alteration of light’s apparent direction and of a source’s observed appearance by the gravity of intervening matter. A foreground object acts as a lens, potentially displacing, distorting, magnifying, or producing multiple images of a background source. Explained by general relativity, the phenomenon occurs around objects ranging from individual stars to galaxy clusters. It allows astronomers to investigate both distant sources and the matter bending their light, including otherwise invisible dark matter. (science.nasa.gov)

Physical basis and geometry

In general relativity, matter and energy curve spacetime. In the geometrical-optics approximation, light follows null geodesics through this curved geometry. Lensing therefore does not require light to pass through transparent material, unlike ordinary optical refraction. Its basic geometry involves a source, an intervening lens, and an observer; the observed effect depends on their relative positions and the lens’s mass distribution. (arxiv.org)

For an isolated point-like lens of mass $M$, the weak-field deflection angle is approximately

where $G$ is the gravitational constant, $c$ is the speed of light, and $b$ is the ray’s impact parameter. This approximation applies when the ray passes sufficiently far outside the object’s strongly curved region. (arxiv.org)

A common thin-lens approximation concentrates the deflection into one plane. The lens equation is

where $\boldsymbol{\beta}$ is the unlensed source position, $\boldsymbol{\theta}$ is an image position, and the $D$ terms are angular-diameter distances. Multiple solutions correspond to multiple images. For a point mass, the characteristic Einstein radius is

Here $D_l$, $D_s$, and $D_{ls}$ denote observer–lens, observer–source, and lens–source distances. (cosmos.lbl.gov)

Strong, weak, and microlensing regimes

Strong lensing produces readily identifiable distortions, such as elongated arcs or multiple images. A background galaxy may appear stretched around a foreground galaxy or cluster, while a compact quasar may appear as several distinct points. Near-perfect alignment behind a sufficiently symmetric lens can produce an Einstein ring. These images represent different light paths from the same source, not separate objects. (esa.int)

Weak lensing causes smaller changes in apparent shape, size, and position. Because a galaxy’s original shape is generally unknown, the effect is measured statistically across many galaxies. Coherent stretching is called shear; the focusing component is called convergence. Lensing by the Universe’s large-scale matter distribution, often termed cosmic shear, provides information about the distribution and evolution of matter. (esa.int)

Microlensing typically involves image separations too small for conventional telescopes to resolve. As a foreground star or another compact object moves relative to a background source, the combined brightness of the unresolved images changes. A microlensing event can also shift the source’s apparent position. Planetary companions can introduce distinctive deviations into the brightness pattern, while a dark lens such as a black hole can be detected without observing its own light. (esa.int)

These categories describe observational regimes rather than different physical mechanisms. The same galaxy can strongly lens a background source while stars within it produce additional microlensing effects. (esa.int)

Historical development

Albert Einstein’s general relativity supplied the quantitative framework for gravitational light bending. Expeditions observing the total solar eclipse of May 29, 1919, photographed stars near the Sun and compared their apparent positions with observations made when the Sun was elsewhere. The measured deflection supplied an early observational test supporting the theory. This was a measurement of solar light bending, rather than the discovery of a multiply imaged extragalactic source. (science.nasa.gov)

In 1979, Dennis Walsh, Robert Carswell, and Ray Weymann identified the two components of quasar Q0957+561 as images of one background object. This became the first recognized multiply imaged gravitational lens system. Subsequent observations established galaxy-scale lenses, cluster arcs, rings, and stellar microlensing as practical tools in astronomy. (einstein-online.info)

Scientific applications

Lensing measures gravitational effects rather than emitted luminosity, making it valuable for reconstructing the total mass distribution of galaxies and clusters. Weak-lensing measurements across large samples map matter beyond individual luminous objects. Combined with source redshifts, these measurements probe structure at different cosmic epochs and constrain cosmological models, including the influence of dark energy on expansion and structure growth. (esa.int)

Magnification also makes otherwise faint background sources easier to observe. Foreground clusters can function as natural telescopes, revealing distant galaxies, individual stars, and supernovae. Lensing changes angular area and total received flux but, in ideal transparent geometrical optics, preserves surface brightness: it does not intrinsically brighten each unit of an extended image. (science.nasa.gov)

Multiple images of a variable source arrive at different times because their paths have different lengths and gravitational delays. Measuring these delays and modelling the lens enables time-delay cosmography, which constrains absolute distances and the Hubble constant. (arxiv.org)

Interpretation and limitations

Reconstructing a lens is an inverse problem: different mass distributions can reproduce similar observations. The mass-sheet degeneracy is an important example, involving changes to the lens mass distribution accompanied by a rescaling of the inferred source. Additional observational constraints and modelling assumptions are therefore consequential. (arxiv.org)

Weak-lensing analyses must account for instrumental image distortion, uncertain source distances, and intrinsic galaxy alignments that can imitate or contaminate gravitational shear. Strong-lens distance measurements additionally depend on the lens model and matter along the line of sight. These uncertainties limit the precision of mass maps and cosmological measurements. (arxiv.org)