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The Twin Quasar QSO 0957+561. Credits - ESA/Hubble & NASA
In the 1970s, the MkIA telescope at Jordell Bank was conducting radio surveys of the sky, when it observed two blue stellar objects, 0957+561 A and B almost overlapping each other, separated by a mere 6 arcseconds. The radio telescope had a resolution of 5-10 arcseconds and 80% reliability. The spectrum and redshift of both these images was analyzed by Walsh D., Carswell R.F., & Weymann R.J. (1979). They found the redshifts to be close to each other, and that the object B was redder than A. They also found that the velocity difference between the images, calculated from the redshifts, was approximately of the order of 100km/s, which is almost negligible in such large scales. This led them to conclude that the observed images were indeed of a single object.
The question that remained was what could cause this lensing? Observations were made and within a year, a lens galaxy was found near the images (Soifer B., Neugebauer G., Matthews K. et al., (1980)). It was later realized that this galaxy lies in a cluster of galaxies, and it was the brightest one among them (Young P. et. al. (1981)). Yet, it did not lie between the line connecting A and B, implying the lens models were not going to be circularly symmetric. From our derivations in the previous section, we know that neither of the models will be fit for this system as they are all spherically or circularly symmetric. The first proposed model for this lens was known as a spherically-symmetric King model (King I.R. (1966))
SDSS J1004+4112 - The four lensed images are labeled A, B, C and D, with a bright galaxy in between labeled G. This galaxy is part of a cluster of galaxies. Credits - Inada N., Oguri M., Pindor B. et al., (2003)
In 2003, the Sloan Digital Sky Survey observed the quasar SDSS J1004+4112, which was seen as four strongly lensed images with separation of about 14 arcseconds. The system is considered to be lensed because all the four images have a redshift of $z = 1.734 \pm 0.002$, the relative velocities of the images are of the order of $100km/s$, and there is a Carbon IV absorption line in all four images.
A spherically symmetric lens can only produce 1 or 3 images, if it is completely transparent. this system was first modelled using the Singular Isothermal Ellipsoid(SIE) model for the galaxy cluster with external shear.
From the SIE model of len galaxy cluster, this is the best fit model for the lensing system, produced by Inada et. al. (2003)
In the best fit plot, the blue curve represents a rough boundary of the gravitational lens, whereas the green curve represents a caustic, which is the curve traced by the points at which light is focused after deflecting from the lens. The number of images/arcs observed due to lensing depends on the relative position of the source with respect to the caustic, as viewed by the observer.
Dependence of number of lensed images on the position of source with respect to the caustic. The red curve is the critical curve, and the blue curve is the caustic. Credits - PBworks
It was mentioned in the Methods that a transparent lens should produce an odd number of images. This result was known well before this quasar was detected. Hence the same group of authors were able to detect a fifth image a year later, very close to the brightest galaxy of the lens cluster near the center(Inada et. al (2005)).