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Einstein Cross

The Einstein Cross, designated Q2237+0305 or Huchra's Lens, is a prominent example of strong gravitational lensing in which the light from a distant quasar is distorted by the massive foreground galaxy PGC 69457 (also known as ZW 2237+030), producing four nearly identical images of the quasar arranged in a symmetric cross-like pattern.^[1]
This lensing galaxy lies approximately 400 million light-years from Earth in the constellation Pegasus, while the background quasar is situated about 8 billion light-years away, with the quasar's light taking roughly 8 billion years to reach us after being bent by the galaxy's gravitational field.^[2]^[3]
Discovered in 1985 by astronomer John Huchra and colleagues during a redshift survey at the Center for Astrophysics, the system was initially identified as a quasar aligned behind a galaxy, with the multiple images confirmed through subsequent observations that highlighted its unusual lensing configuration.^[4]^[5]
The combined apparent magnitude of the four quasar images is around 14, with individual components ranging from 15.5 to 18.5, making it observable with moderate-sized telescopes (24 inches or larger) under dark skies, approximately 2.5° southeast of the star 37 Pegasi.^[1]
The Einstein Cross serves as a key demonstration of Albert Einstein's general theory of relativity, illustrating how massive objects curve spacetime and act as natural telescopes to magnify and multiply distant sources, and it has been extensively studied for insights into quasar structure, galaxy mass distributions, and microlensing effects caused by stars within the lensing galaxy.^[2]^[3]
Notably, the Hubble Space Telescope captured its first detailed image of the system in September 1990 using the Faint Object Camera, just five months after launch, revealing the angular separation between the upper and lower quasar images as 1.6 arcseconds and the central lensing galaxy as a spiral galaxy.^[2]^[3]
Ongoing observations, including those monitoring flux variations in the images, have provided precise measurements of the lensing geometry and helped probe the interstellar medium of the quasar host galaxy.^[1]

Discovery and Identification

Initial Detection

The Einstein Cross, also known as Q2237+0305, was discovered serendipitously in 1985 during the Center for Astrophysics Redshift Survey, conducted by John Huchra and colleagues using the Multiple Mirror Telescope (MMT) at Whipple Observatory.^[6] The survey aimed to measure redshifts of candidate quasars, and this object was selected based on its blue color and point-like appearance on photographic plates. Initial observations on September 23, 1984, with the 1.5-m Tillinghast reflector at Whipple Observatory revealed a spectrum dominated by a quasar-like continuum.^[6] The initial spectrum, spanning 4600–7300 Å, displayed a relatively smooth continuum with a prominent broad emission line at 5180 Å, identified as Lyman-α shifted to a redshift of z = 1.695.^[6] A follow-up spectrum obtained on September 27, 1984, with the MMT and covering 3200–7400 Å confirmed this redshift through additional quasar emission lines, including C IV, He II, and C III], while revealing strong intervening absorption features at wavelengths such as 3860 Å (Ca II), 3930 Å (G band), and 4100–5200 Å (Balmer lines and [O II]), corresponding to a foreground galaxy at z = 0.039.^[6] These absorption lines indicated an intervening galaxy along the line of sight, with the quasar positioned nearly centered on the galaxy's nucleus. At the resolution of the observations (approximately 2 arcseconds), only a single image of the quasar was apparent, aligned to within 0.3 arcseconds of the galaxy center.^[6] The system's equatorial coordinates are right ascension 22ʰ 40ᵐ 30ˢ.3, declination +03° 21′ 30″ (J2000 epoch).^[6] Huchra et al. interpreted the close alignment, combined with the spectroscopic evidence of the foreground galaxy and the quasar's high redshift, as indicative of gravitational lensing, where the galaxy acts as a lens magnifying and imaging the background quasar.^[6] This marked one of the earliest clear cases of a quasar-galaxy lens system, published in The Astronomical Journal in May 1985.^[6]

Confirmation and Naming

Following the initial spectroscopic detection of a quasar aligned with a foreground galaxy in 1984, high-resolution imaging in 1988 resolved the system into four distinct images of the quasar arranged in a symmetric cross pattern surrounding the central galaxy nucleus. These observations were conducted using the Canada-France-Hawaii Telescope (CFHT) with excellent seeing conditions of 0.6–0.9 arcseconds and 0.2 arcsecond per pixel sampling, allowing the separation of the components for the first time.^[7] The cross-like morphology provided strong visual evidence for gravitational lensing as the cause of the multiple images. The lensing nature was confirmed through spectroscopic measurements of redshifts, revealing the foreground galaxy at z = 0.039 and the background quasar at z = 1.695, establishing that the quasar light is being multiply imaged by the intervening galaxy's gravitational field.^[6] This redshift difference aligned with theoretical expectations for a lens system, ruling out alternative explanations such as a physical association or unrelated objects. The confirmation built directly on the earlier spectroscopic hint of superposition but required the resolved imaging to demonstrate the lensing geometry. The system, designated Q2237+0305, was named the "Einstein Cross" in recognition of its distinctive configuration and Albert Einstein's 1915 prediction of gravitational lensing within general relativity. Early measurements estimated the separations between adjacent quasar images at approximately 1.34 arcseconds, with the full cross spanning about 1.6–1.8 arcseconds, highlighting the precision alignment necessary for such a quadruple lens. This naming and initial characterization underscored the system's status as a textbook example of strong gravitational lensing.^[8]

System Description

The Lensing Galaxy

The lensing galaxy in the Einstein Cross system, designated ZW 2237+030 and commonly known as Huchra's Lens, is a barred spiral galaxy classified as type Sab.^[9] This classification reflects its prominent central bulge, elongated bar structure, and extended stellar disk, which contribute to its role as an effective gravitational lens. The galaxy is inclined at approximately 60° to the line of sight.^[9] The galaxy resides at a spectroscopic redshift of z = 0.0394, placing it at a comoving distance of approximately 170 megaparsecs from Earth.^[9] This relatively nearby position, combined with the background quasar's higher redshift, enables the strong lensing effect observed in the system. The redshift measurement was first confirmed through optical spectroscopy targeting emission lines from the galaxy's nucleus.^[5] From gravitational lensing analysis, the projected mass within the Einstein radius (approximately 0.9 arcseconds) is estimated at $1.5 \times 10^{11} solar masses, primarily dominated by the stellar components of the bulge and disk. This mass inference arises from modeling the lens potential to reproduce the observed quasar image positions and magnifications, assuming an isothermal density profile for the galaxy's mass distribution.^[10] Infrared observations reveal detailed morphological features, including a compact central bulge, a strong bar perturbing the disk, and spiral arms with prominent dust lanes that cause localized extinction along certain sightlines.^[11] These dust features are particularly evident in mid-infrared imaging, where the galaxy's disk shows asymmetric structure due to the bar's influence, with the dust lanes aligned along the spiral arms and contributing to differential reddening across the lens plane.^[12]

The Quasar and Its Images

The Einstein Cross is the gravitational lensing system involving the radio-quiet quasar Q2237+030 at a redshift of z = 1.695.^[13] This quasar exhibits an absolute magnitude of approximately -26 in the V-band.^[14] As an active galactic nucleus, it is powered by a supermassive black hole with a mass of about $10^9 solar masses and features a broad-line region, with emission lines indicating ionized gas dynamics on scales of roughly 0.09–4.7 pc.^[13] The quasar's light is split into four distinct images, conventionally labeled A, B, C, and D. Image A, the brightest, appears northwest of the lensing galaxy's center; image B lies to the southeast; image D to the northeast; and image C, the faintest, to the southwest.^[15] These images are separated by angular distances of 0.8–1.3 arcseconds from one another.^[16] Gravitational lensing magnifies the quasar's total flux by a factor of approximately 15–20, significantly enhancing its observed brightness compared to its intrinsic emission.^[13] The individual magnification factors are roughly 4.6 for image A, 4.5 for B, 3.8 for C, and 3.6 for D, allowing the system's detailed spectroscopic analysis.^[13]

Gravitational Lensing in the Einstein Cross

Theoretical Framework

Albert Einstein first predicted the deflection of light by gravity in 1911, calculating that starlight passing near the Sun would be bent by approximately 0.83 arcseconds, based on his equivalence principle within special relativity.^[17] This value was half the full general relativistic prediction, as Einstein refined his theory in 1915. In 1936, Einstein formalized the concept of gravitational lensing in a paper exploring how a massive star could act as a lens, producing distorted images of background stars, though he noted the alignment required would make such effects unobservable with contemporary technology.^[18] The mechanics of gravitational lensing are described by the lens equation in angular coordinates, \beta = \theta - \alpha(\theta), where \beta is the angular position of the unlensed source relative to the lens, \theta is the observed angular position of the image, and \alpha(\theta) is the deflection angle caused by the lens's gravitational field.^[19] This equation arises from the geodesic motion of light in curved spacetime, as predicted by general relativity, and maps the source plane to the image plane, potentially producing multiple images for a single source. For a perfectly aligned source and lens (where \beta = 0), the lens equation yields a circular Einstein ring, an extended arc of light encircling the lens due to symmetric deflection.^[18] Slight misalignments (\beta \neq 0) in point-mass or extended-mass distributions can instead produce cross-like patterns of four images, as the deflection varies with the lens's mass profile. A key parameter in lensing efficiency is the critical surface mass density, \Sigma_{\rm crit} = \frac{c^2 D_s}{4\pi G D_l D_{ls}}, where D_s is the angular diameter distance to the source, D_l to the lens, D_{ls} between lens and source, c is the speed of light, and G is the gravitational constant.^[19] Lensing becomes significant when the lens's surface mass density \Sigma approaches or exceeds \Sigma_{\rm crit}, determining whether multiple images or magnification occur; for typical extragalactic systems, \Sigma_{\rm crit} is on the order of 0.3–1 g/cm², scaling inversely with the source-lens separation.^[20] These principles underpin the observed multiple imaging in systems like the Einstein Cross, where the lens galaxy's mass distribution creates the characteristic quadrupolar pattern.

Model of the Lens System

The gravitational lens system of the Einstein Cross, Q2237+0305, is modeled using a singular isothermal sphere (SIS) approximation for the mass potential of the foreground galaxy, which captures the dominant lensing effects due to its spherically symmetric density profile decreasing as \rho(r) \propto 1/r^2. This model assumes the galaxy's stellar velocity dispersion \sigma governs the potential, with spectroscopic measurements yielding \sigma \approx 210 km/s, consistent with a late-type spiral galaxy at redshift z_l = 0.0394.^[21] The SIS framework simplifies calculations of deflection angles and magnification while providing a good first-order fit to the observed quadruple image configuration around the central lens. The characteristic scale of the lensing is set by the Einstein radius \theta_E \approx 0.9'', which defines the angular extent of the images from the lens center and is derived from \theta_E = \sqrt{\frac{4GM}{c^2} \frac{D_{ls}}{D_l D_s}}, where M is the enclosed mass, c is the speed of light, G is the gravitational constant, and D_l, D_s, D_{ls} are the angular diameter distances to the lens, source (at z_s = 1.695), and between lens and source, respectively. This radius aligns with the observed image separations of approximately 1.3–1.8'' across the cross, reflecting the near-central alignment of the background quasar (\beta \ll \theta_E).^[22] Time delays between the lensed images arise from the differential light travel paths in the lens potential and are predicted to be on the order of hours to a few days under SIS modeling, arising from geometric and Shapiro-like delays. The delay is quantified by the formula

\Delta t = (1 + z_l) \frac{D_l D_{ls}}{D_s} \left[ \frac{(\theta - \beta)^2}{2} - \psi(\theta) \right],

where \psi(\theta) is the lensing potential, \theta is the observed image position, and \beta is the unlensed source position; the proximity of the lens (small D_l) results in short delays relative to more distant systems, making the Einstein Cross ideal for monitoring rapid flux variations due to microlensing.^[23] To account for observed asymmetries in image positions and flux ratios, the basic SIS is augmented with a quadrupole perturbation from the lensing galaxy's prominent bar structure, introducing an external shear or ellipticity (e \approx 0.3) that twists the cross by about 10°. Detailed fits incorporating a power-law bulge and Ferrers-profile bar yield a total enclosed mass within \theta_E of \sim 1.5 \times 10^{10} M_\odot (for h_{75} = 1), with the bar contributing 5–10% of this mass and explaining deviations from symmetric SIS predictions without invoking multiple lenses.^[22] These models achieve \chi^2 fits to Hubble Space Telescope positions with RMS residuals below 0.01'', validating the SIS-plus-quadrupole approach for predicting image configurations.

Observations and Analysis

Historical Telescopic Observations

Follow-up ground-based imaging in 1988 resolved multiple components of the Einstein Cross, or Q2237+0305, and by the late 1980s, observations with large-aperture telescopes such as the 5-meter Hale Telescope at Palomar Observatory and the Canada-France-Hawaii Telescope (CFHT) achieved resolutions around 1 arcsecond, clearly separating the four quasar images into the characteristic cross configuration with angular separations of 1.4–1.8 arcseconds.^[24] These early telescopic efforts established the system's geometry but were limited by atmospheric seeing, preventing detailed views of the lensing galaxy's structure.^[25] The advent of space-based astronomy marked a significant advancement in resolving the Einstein Cross. The Hubble Space Telescope (HST), shortly after its 1990 launch, observed the system in September of that year using the Faint Object Camera (FOC), delivering the first ultraviolet and optical images with resolutions better than 0.1 arcsecond and confirming the fourfold lensing while highlighting the central alignment.^[8] Following the 1993 installation of the Wide Field and Planetary Camera 2 (WFPC2), HST revisited the system in 1994, attaining sub-0.05 arcsecond resolution in visible wavelengths (e.g., F555W and F814W filters), which unveiled the barred spiral morphology of the lensing galaxy and precise relative positions of the quasar images, enabling initial mass modeling of the lens.^[26] These WFPC2 datasets, with exposure times up to 800 seconds, provided a factor of 20 improvement over ground-based resolution, revealing faint extended emission around the images.^[27] In the 2000s and 2010s, HST's upgraded instruments further refined imaging of the Einstein Cross, focusing on time-domain studies while enhancing spatial detail. The Advanced Camera for Surveys (ACS), installed in 2002, conducted a dedicated monitoring campaign in 2004 using high-resolution imaging (0.05 arcsecond pixel scale) in multiple bands (e.g., F435W, F555W, F814W), capturing short-term flux variations across the images to probe microlensing and achieving photometric precision better than 1% for brightness measurements.^[28] Later, the Wide Field Camera 3 (WFC3), operational from 2009, provided near-infrared observations (e.g., F160W filter) in the 2010s, extending coverage to longer wavelengths and resolving dust-obscured features in the lensing galaxy at resolutions of ~0.13 arcsecond, complementing earlier visible-light data.^[29] As of 2025, the James Webb Space Telescope (JWST) has not yet publicly released dedicated NIRCam imaging of the Einstein Cross, though its infrared capabilities hold promise for future observations probing dust and extended emission in the system.

Microlensing and Variability Studies

The microlensing effect in the Einstein Cross arises from stars in the lensing galaxy, which produce caustics that selectively magnify different regions of the quasar's extended accretion disk, leading to flux variations on timescales of days to months.^[30] These variations differ between the four images due to their distinct paths through the stellar field, allowing probes of the quasar's internal structure without resolving it directly. A key monitoring campaign from 2004 to 2006 using the VLT/FORS1 spectrograph captured significant microlensing-induced brightness changes, particularly in images A and B, with image A showing prominent brightening around HJD 2453900.^[30] These flux variations reached amplitudes of up to ~0.5 mag in individual images, as corroborated by contemporaneous photometric data, constraining the angular size of the quasar accretion disk to approximately 10–20 microarcseconds at optical wavelengths.^[31] The chromatic nature of the variations, with bluer continuum regions more magnified than redder ones, further indicated a temperature gradient in the disk consistent with standard thin-disk models. Subsequent ground-based photometric campaigns in the 2010s, including OGLE-III and OGLE-IV observations, revealed ongoing continuum and broad emission line variations across the images, highlighting differential microlensing between the disk and broad-line region. For instance, higher-ionization lines like C IV showed stronger magnification than lower-ionization lines like Mg II, implying a stratified broad-line region with temperatures around 10^4 K in the inner disk.^[30] These studies emphasized the disk's compact scale, with effective radii of order 10 light-days, enabling estimates of black hole mass and accretion rate. In the 2020s, high-cadence photometry from VLT and Keck telescopes has refined models of the lens, incorporating microlensing light curves to estimate the stellar mass fraction in the lensing galaxy at 89–94% of the total convergence, with dark matter comprising less than 20%.^[32] Recent simulations and predictions for high-magnification events, based on long-term OGLE data, have further explored microlensing light curves in Q2237+0305 as of 2025.^[33] ^[34] These observations, combined with OGLE data spanning over two decades, have also explored sub-stellar contributions, such as free-floating planets, though their role remains minor compared to stars.^[32]

Scientific Significance

Cosmological Measurements

The Einstein Cross (Q2237+0305) contributes to cosmological measurements primarily through the analysis of time delays between its lensed images and the statistical properties of quadruple lens systems, serving as a benchmark for modeling in broader surveys. Time delay measurements in this system are complicated by its close alignment, yielding very short delays of hours rather than weeks or months typical of offset lenses. Early theoretical models from the late 1980s and 1990s predicted delays less than one day across image pairs, based on the lens geometry and mass distribution.^[35] A significant observational breakthrough occurred with Chandra X-ray monitoring in 2000 and 2001, which resolved a time delay of $2.7^{+0.5}_{-0.9} hours between images A and B, with A leading B; this detection leveraged the stability of X-ray emission to isolate the macro-lens signal from microlensing noise.^[36] The COSMOGRAIL program extended optical monitoring of the system from November 2010 to July 2015 using the Euler Telescope, accumulating 62 nights of data, but pronounced microlensing variability dominated the light curves, preventing a robust macro time delay extraction.^[37] These short delays inform the time-delay distance D_{\Delta t} = (1 + z_l) \Delta t / \kappa, where z_l = 0.039 is the lens redshift, \Delta t is the observed delay, and \kappa is the dimensionless geometric factor derived from the lens potential difference. Given the low z_l, D_{\Delta t} offers limited leverage on the Hubble constant H_0, and no dedicated H_0 inference has been performed for Q2237+0305. Nonetheless, the system's detailed modeling refines techniques in time-delay cosmography applied to higher-redshift quadruple lenses, where ensemble analyses yield H_0 \approx 75 km s^{-1} Mpc^{-1} (as of 2025), aligning with local distance ladder estimates but in tension with the Planck CMB value of $67.4 \pm 0.5 km s^{-1} Mpc^{-1}.^[38] As one of the earliest and best-studied quadruple lenses, the Einstein Cross exemplifies configurations rare in observations, comprising only about 10-20% of known strong lenses despite models predicting higher fractions. The observed deficit of quads relative to doubles—the "quad problem"—probes selection biases, dark matter halo profiles, and the matter power spectrum amplitude \sigma_8. This system has calibrated lens modeling for statistical analyses, supporting surveys like the Sloan Lens ACS Survey (SLACS), which identified nearly 100 galaxy-scale lenses and debiased their properties to constrain the cosmic matter density \Omega_m \approx 0.3 and structure growth parameter \sigma_8 \approx 0.8, offering complementary tests of dark energy models.^[39] Recent advancements as of 2025 incorporate strong lens catalogs, informed by prototypes like the Einstein Cross, with Dark Energy Spectroscopic Instrument (DESI) data in joint analyses with time-delay cosmography to constrain the expansion history and dark energy parameters. DESI's baryon acoustic oscillation measurements, combined with gravitational lensing, provide improved constraints on cosmological models.^[40]^[41]

Insights into Quasar and Galaxy Physics

Observations of microlensing in the Einstein Cross have provided constraints on the structure of the quasar Q2237+0305, revealing the size of its inner accretion disk. Microlensing events, caused by stars in the lensing galaxy crossing the line of sight to the quasar images, magnify different parts of the source, allowing estimates of the disk's half-light radius at ultraviolet wavelengths to be approximately 10 light-days.^[42]^[43] These measurements indicate a compact, hot region near the central black hole where material spirals inward, consistent with standard thin-disk models for quasar accretion. Microlensing has also probed the broad-line region (BLR) of the quasar, with the size of the C IV emitting region estimated at about 66 light-days (half-light radius), aligning closely with predictions from the radius-luminosity relation derived from reverberation mapping campaigns on other quasars.^[44] This agreement validates the use of reverberation techniques, which measure time delays between continuum variations and line responses to infer BLR scales of tens to hundreds of light-days, and highlights how lensing amplifies signals from these extended gaseous structures orbiting the black hole. Variability data from the quasar images further support these size constraints by showing correlated flux changes across wavelengths.^[45] The lensing mass profile of the foreground galaxy ZW 2237+030 reveals an extended dark matter halo, modeled as a softened isothermal sphere with a core radius of approximately 13 kpc, indicating that dark matter dominates the outer mass distribution while stellar matter contributes significantly in the central regions.^[9] The stellar-to-total mass ratio within the Einstein radius is about 0.3, probing the relative contributions of baryonic (stellar) and dark matter components and suggesting that the halo extends well beyond the luminous disk.^[46] This distribution helps distinguish between modified Newtonian dynamics and cold dark matter scenarios in galaxy formation. Infrared observations of the Einstein Cross show an excess in the mid-infrared flux relative to optical images, attributed to dust in the lensing galaxy's disk, which causes differential extinction across the quasar images.^[47] The V-band extinction is estimated at 0.1–0.3 magnitudes between image pairs, with images passing through the disk (C and D) experiencing higher obscuration due to aligned dust lanes.^[48] These effects, combined with lensing magnification, provide insights into the galaxy's interstellar medium and its patchy dust distribution. Estimates of the quasar's central supermassive black hole mass, derived from virial theorem applications to BLR kinematics and accounting for lensing magnification of the line widths, yield approximately $10^8 solar masses.^[44] This value places Q2237+0305 among typical high-redshift quasars, where the black hole mass correlates with the host galaxy's properties and influences the quasar's luminosity through accretion processes.^[49]

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[42]
Mid-Infrared Imaging of the Einstein Cross QSO - NASA ADS
4 The Infrared Source is Due to Dust There are several lines of evidence that the infrared emission is extended on a scale greater than an Einstein radius.Missing: excess | Show results with:excess
[43]
[PDF] Microlensing variability in the gravitationally lensed quasar QSO ...
Jan 22, 2008 · The gravitational lens QSO 2237+0305, also known as. “Huchra's lens” or the “Einstein Cross”, was discovered by. Huchra et al. (1985) during the ...
[44]
Zooming into the broad line region of the gravitationally lensed ...
The microlensing affecting the images of QSO 2237 + 0305 leads to large variations in amplitude (Udalski et al. 2006), reaching up > 1 mag, often accompanied by ...Missing: Q2237+ | Show results with:Q2237+