Foreground mass concentrations are used to magnify and distort more distant objects
Einstein's Prediction and the Concept of Lensing
Gravitational lensing arises from the general relativity theory – mass (or energy) warps spacetime, causing light rays passing near massive objects to bend. Instead of traveling along straight trajectories, photons curve toward the mass concentration. Albert Einstein early realized that a sufficiently large foreground mass can act as a "lens" for a distant source, similar to an optical lens bending and focusing light. Initially, he thought this phenomenon was very rare. However, modern astronomy shows that lensing is not just an interesting rarity – it is a common occurrence, providing a unique opportunity to study the mass distribution (including dark matter) and magnify distant, faint background galaxy or quasar images.
Lensing occurs on various scales:
- Strong lensing – prominent multiple images, arcs, or Einstein rings when the spatial alignment is very precise.
- Weak lensing – small distortions in the shapes of background galaxies ("shear"), used statistically to model large-scale structure.
- Microlensing – a foreground star or compact object temporarily magnifies a background star, potentially revealing exoplanets or dark stellar remnants.
Each type of lensing exploits gravity's ability to bend light and thus studies massive structures – galaxy clusters, galaxy halos, or even individual stars. Therefore, gravitational lensing is considered a "natural telescope", sometimes providing enormous magnification of distant objects (which would otherwise be unseen).
2. Theoretical Foundations of Gravitational Lensing
2.1 Light Deflection According to GR
General relativity states that photons travel along geodesics in curved spacetime. Around a spherical mass (e.g., a star or cluster), the deflection angle in the weak field approximation is:
α ≈ 4GM / (r c²),
where G is the gravitational constant, M is the lens mass, r is the impact parameter, c is the speed of light. For massive galaxy clusters or large halos, the deflection can reach seconds or tens of arcseconds, large enough to create visible multiple images of background galaxies.
2.2 Lens Equation and Angular Relations
In lensing geometry, the lens equation relates the observed image position (θ) to the true angular position of the source (β) and the deflection angle α(θ). This equation system sometimes yields multiple images, arcs, or rings depending on the alignment and lens mass distribution. The “Einstein ring radius” for a simple point lens case:
θE = √(4GM / c² × DLS / (DL DS)),
where DL, DS, DLS – respectively the angular diameter distances of the lens, source, and the segment between them. In more realistic cases (galaxy clusters, elliptical galaxies), the lensing potential is solved for the two-dimensional mass projection.
3. Strong Lensing: Arcs, Rings, and Multiple Images
3.1 Einstein Rings and Multiple Images
When the background source, lens, and observer are nearly aligned, a ring-like image called the Einstein ring can be seen. If the alignment is less precise or the mass distribution is asymmetric, multiple images of the same background galaxy or quasar are observed. Famous examples:
- Double quasar QSO 0957+561
- Einstein Cross (Q2237+030) in the foreground galaxy
- Abell 2218 arcs in cluster lens
3.2 Cluster Lenses and Giant Arcs
Massive galaxy clusters are the brightest strong lenses. Their huge gravitational potential can create giant arcs – stretched images of background galaxies. Sometimes radial arcs or multiple images of different sources are seen. The Hubble Space Telescope has captured impressive arc structures around clusters like Abell 1689, MACS J1149, and others. These arcs can be magnified 10–100 times, revealing details of high-redshift (z > 2) galaxies. Occasionally a "full" ring or its segments are visible, used to determine the cluster's dark matter distribution.
3.3 Lensing as a Cosmic Telescope
Strong lensing gives astronomers the ability to observe distant galaxies with higher resolution or brightness than would be possible without lensing. For example, a faint galaxy with z > 2 can be sufficiently magnified by a foreground cluster to obtain its spectrum or morphological analysis. This "natural telescope" effect has led to discoveries about star-forming regions, metallicity, or morphological features in very high-redshift galaxies, filling observational gaps in galaxy evolution studies.
4. Weak Lensing: Cosmic Shear and Mass Maps
4.1 Small Distortions of Background Galaxies
In weak lensing, light deflections are small, so background galaxies appear slightly stretched (shear). However, by analyzing the shapes of many galaxies over large sky areas, correlated shape changes are detected, reflecting the foreground mass structure. The "noise" in the shape of a single galaxy is large, but summing data from hundreds of thousands or millions of galaxies reveals a ~1% level shear field.
4.2 Cluster Weak Lensing
Based on the average tangential shear around the cluster center, it is possible to measure the cluster mass and mass distribution. This method does not depend on dynamical equilibrium or X-ray gas models, thus directly revealing dark matter halos. Observations confirm that clusters contain much more mass than just luminous matter, emphasizing the importance of dark matter.
4.3 Cosmic Shear Surveys
Cosmic shear, large-scale weak lensing caused by the distribution of matter along the line of sight, is an important measure of structure growth and geometry. Surveys such as CFHTLenS, DES (Dark Energy Survey), KiDS, and upcoming Euclid, Roman cover thousands of square degrees, allowing constraints on the amplitude of matter fluctuations (σ8), matter density (Ωm), and dark energy. The results obtained are checked by comparison with CMB (CMB) parameters, searching for possible signs of new physics.
5. Microlensing: On the Scale of Stars or Planets
5.1 Point Mass Lenses
When a compact object (star, black hole, or exoplanet) lenses a background star, microlensing occurs. The brightness of the background star temporarily increases during the object's passage, producing a typical light curve. Since the Einstein ring is very small here, multiple images are not spatially resolved, but the total brightness change, sometimes significant, is measured.
5.2 Exoplanet Detection
Microlensing is especially sensitive to planets of the lensing star. A small deviation in the lensing light curve indicates a planet whose mass ratio can be as low as ~1:1000 or even less. Surveys like OGLE, MOA, KMTNet have already discovered exoplanets in wide orbits or around faint / central bulge stars inaccessible to other methods. Microlensing also studies stellar remnants like black holes or “rogue” objects in the Milky Way.
6. Scientific Applications and Key Results
6.1 Mass Distribution of Galaxies and Clusters
Lensing (both strong and weak) allows constructing two-dimensional mass projections – thus directly measuring dark matter halos. For example, in the “Bullet Cluster”, lensing shows that after the collision, dark matter “separated” from baryonic gas, proving that dark matter interacts very weakly. “Galaxy–galaxy” lensing accumulates weak lensing around many galaxies, allowing determination of the average halo profile depending on brightness or galaxy type.
6.2 Dark Energy and Expansion
By combining lensing geometry (e.g., strong cluster lensing or cosmic shear tomography) with distance–redshift relations, cosmic expansion can be constrained, especially by studying multiredshift lensing effects. For example, multiple quasar time delays enable calculating H0, if the well-known mass model is accurate. The “H0LiCOW” collaboration, measuring quasar time delays, obtained H0 ~73 km/s/Mpc, contributing to the “Hubble tension” discussions.
6.3 Magnification of the Distant Universe
Strong cluster lensing provides magnification for distant galaxies, effectively lowering their detection brightness threshold. This has enabled the registration of extremely high-redshift galaxies (z > 6–10) and detailed study of them, which current telescopes without lensing would not be capable of. An example is the “Frontier Fields” program, where the Hubble telescope observed six massive clusters as gravitational telescopes, detecting hundreds of faint lensed sources.
7. Future Directions and Upcoming Projects
7.1 Ground-Based Surveys
Surveys like LSST (now Vera C. Rubin Observatory) plan cosmic shear measurements over ~18,000 deg2 to incredible depth, allowing billions of galaxy shape determinations for weak lensing. Meanwhile, specialized cluster lensing programs in multiple bands will enable detailed mass measurements of thousands of clusters, studying large-scale structure and dark matter properties.
7.2 Space Missions: Euclid and Roman
Euclid and Roman telescopes will operate over a wide near-IR range and conduct spectroscopy from space, ensuring very high-quality weak lensing over large sky areas with minimal atmospheric distortion. This will enable precise mapping of cosmic shear up to z ∼ 2, linking signals with cosmic expansion, matter clustering, and neutrino mass constraints. Their collaboration with ground-based spectroscopic surveys (DESI and others) is essential for photometric redshift calibration, providing reliable 3D lensing tomography.
7.3 Next-Generation Cluster and Strong Lensing Studies
Current Hubble and upcoming James Webb and 30 m-class ground-based telescopes will allow even more detailed studies of strongly lensed galaxies, potentially detecting individual star clusters or star-forming regions during the cosmic dawn. New digital (machine learning) algorithms are also being developed to quickly find strong lensing cases in huge image catalogs, thus expanding gravitational lens selection.
8. Remaining Challenges and Prospects
8.1 Systematics of Mass Modeling
In strong lensing, if the mass distribution model is undefined, it can be difficult to precisely determine distances or the Hubble constant. In weak lensing, challenges arise from galaxy shape measurement systems and photometric redshift errors. Careful calibration and advanced models are necessary to use lensing data for precision cosmology.
8.2 Searches for Extreme Physics
Gravitational lensing can reveal unusual phenomena: dark matter subhalos (substructures in halos), interacting dark matter, or primordial black holes. Lensing can also test modified gravity theories if lensing clusters show a different mass structure than predicted by ΛCDM. So far, the standard ΛCDM does not contradict the results, but detailed lensing studies may detect subtle deviations indicating new physics.
8.3 Hubble Tension and Time Delay Lenses
Time delay lensing measures the difference in signal arrival times of different quasar images and allows determination of H0. Some studies find a higher H0 a value closer to local measurements, thus strengthening the “Hubble tension.” To reduce systematics, lens mass models are improved, supermassive black hole activity observations are expanded, and the number of such systems is increased – perhaps this will help resolve or confirm this discrepancy.
9. Conclusion
Gravitational lensing – the deflection of light by foreground masses – acts as a natural cosmic telescope, allowing simultaneous measurement of mass distribution (including dark matter) and magnification of distant background sources. From strong lensing arcs and rings around massive clusters or galaxies to weak lensing cosmic shear over large sky areas and microlensing effects revealing exoplanets or compact objects – lensing methods have become integral to modern astrophysics and cosmology.
By observing changes in light trajectories, scientists minimally assume to map dark matter halos, measure the amplitude of large-scale structure growth, and refine cosmic expansion parameters – especially by combining with baryon acoustic oscillation methods or calculating the Hubble constant from time delays. In the future, large new surveys (Rubin Observatory, Euclid, Roman, advanced 21 cm systems) will further expand lensing data, possibly revealing finer dark matter properties, refining dark energy evolution, or even opening new gravitational phenomena. Thus, gravitational lensing remains at the center of precision cosmology, linking general relativity theory with observations to understand the invisible cosmic scaffolding and the most distant Universe.
Literature and Further Reading
- Einstein, A. (1936). “Lens-like action of a star by the deviation of light in the gravitational field.” Science, 84, 506–507.
- Zwicky, F. (1937). “On the probability of detecting nebulae which act as gravitational lenses.” Physical Review, 51, 679.
- Clowe, D., et al. (2006). "A direct empirical proof of the existence of dark matter." The Astrophysical Journal Letters, 648, L109–L113.
- Bartelmann, M., & Schneider, P. (2001). “Weak gravitational lensing.” Physics Reports, 340, 291–472.
- Treu, T. (2010). “Strong lensing by galaxies.” Annual Review of Astronomy and Astrophysics, 48, 87–125.