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| Einstein rings | |
|---|---|
| Name | Einstein rings |
| Type | Gravitational lensing phenomenon |
| Discovered by | Albert Einstein |
| Discovery date | 1936 theoretical prediction |
| Major examples | B1938+666, MG 1131+0456, SDSS J0924+0219 |
Einstein rings are circular or near-circular images of a background Quasar or Galaxy produced when light is bent by the gravity of a foreground massive object such as a Galaxy cluster or an individual Galaxy. They represent a striking prediction of General relativity and provide a geometric probe of mass distributions and cosmological parameters. Observationally, rings range from full, highly symmetric circles to arcs and partial rings depending on alignment, shear, and lens substructure.
Einstein rings arise in situations studied within General relativity where a source, lens, and observer are approximately colinear. The effect was anticipated by Albert Einstein and later elaborated by researchers working on gravitational lensing such as Sjur Refsdal and Orest Chwolson. Modern surveys by teams affiliated with Hubble Space Telescope, Sloan Digital Sky Survey, and observatories like Very Large Array and Atacama Large Millimeter/submillimeter Array have discovered many systems, enriching studies initiated by the Palomar Observatory and groups at institutions including Caltech and Max Planck Institute for Astrophysics.
Theory of the rings is rooted in the lens equation derived from General relativity and the thin-lens approximation used in works by Subrahmanyan Chandrasekhar and others. The canonical Einstein radius depends on angular diameter distances in Friedmann–Lemaître–Robertson–Walker cosmologies and on the projected mass inside the lens, parameters modeled by profiles such as the Navarro–Frenk–White profile and the singular isothermal sphere used in studies at Princeton University and Cambridge University. Lens modeling techniques employ methods developed by groups at Massachusetts Institute of Technology and University of Oxford combining analytic solutions and numerical ray-tracing codes. The phenomenon links to concepts advanced by Stephen Hawking in studies of light deflection near compact objects and to microlensing work by Paczynski.
Observed rings display morphologies cataloged by collaborations like the CASTLES survey and the COSMOS field teams. Typical observables include ring radius, surface brightness distribution, color gradients, and multiple image parity measured by instruments on Hubble Space Telescope, Keck Observatory, Subaru Telescope, and the European Southern Observatory. Spectroscopic follow-up from Keck Observatory and Very Large Telescope yields redshifts for lenses and sources, enabling determination of mass-to-light ratios for lens galaxies found in catalogs maintained by Sloan Digital Sky Survey and analyses presented at conferences by International Astronomical Union. Time delays between multiple images, first exploited for Quasars by observers at University of Arizona, provide independent constraints on the Hubble constant measured also by teams from Carnegie Institution for Science.
Formation depends on precise alignment; a perfect alignment produces a full ring at the Einstein radius, derived in early notes by Albert Einstein and formalized in papers by Yakov Zeldovich and Rainer K. Sachs. The geometry involves lens plane, source plane, and critical curves and caustics characterized in theoretical work at California Institute of Technology and University of Cambridge. Complex lenses produce partial rings and arcs mapped with techniques from Institute for Advanced Study groups and lens inversion methods developed at Max Planck Institute for Astronomy. Substructure in the lens, including satellite galaxies cataloged by Sloan Digital Sky Survey and dark subhalos predicted in simulations by teams at University of California, Santa Cruz, breaks symmetry and produces anomalous flux ratios studied by researchers at Harvard University.
Detection leverages automated searches in wide-field surveys like Sloan Digital Sky Survey, machine-learning pipelines developed at Google DeepMind-collaborating projects, and citizen-science initiatives such as Zooniverse projects. High-resolution imaging from Hubble Space Telescope and adaptive optics on Keck Observatory resolve rings and enable lens modeling codes employed at Stanford University and University of Zurich. Radio interferometry with arrays like Very Large Array and Atacama Large Millimeter/submillimeter Array detects rings in radio-loud Quasars and dusty star-forming galaxies surveyed by groups at Institut d'Astrophysique de Paris. Measurement of time delays uses monitoring campaigns coordinated by collaborations such as the COSMOGRAIL team and analysis techniques refined by researchers at École Polytechnique Fédérale de Lausanne.
Einstein rings are powerful tools for mapping dark matter distributions in lenses studied by Dark Energy Survey and Hyper Suprime-Cam teams, constraining subhalo mass functions predicted by Lambda-CDM simulations run by groups at Lawrence Berkeley National Laboratory. Rings enable measurement of stellar initial mass functions in lens galaxies analyzed by researchers at Max Planck Institute for Astrophysics and provide independent probes of the Hubble constant through time-delay cosmography pursued by collaborations including H0LiCOW. They also test alternative gravity theories discussed in contexts at Perimeter Institute and constrain baryonic feedback models investigated at Flatiron Institute.
Famous systems include lenses cataloged as B1938+666, MG 1131+0456, and discoveries from the Sloan Digital Sky Survey such as SDSS J0924+0219. Surveys and programs that have substantially increased the sample include the CASTLES survey, COSMOS field, Dark Energy Survey, and targeted searches with the Hubble Space Telescope led by teams at Space Telescope Science Institute and European Space Agency. Upcoming facilities like James Webb Space Telescope and Vera C. Rubin Observatory are expected to expand samples and enable precision studies by collaborations including Euclid Consortium and Nancy Grace Roman Space Telescope science teams.