Einstein rings

4.3 Einstein rings

If a point source lies exactly behind a point lens, a ring-like image occurs. Theorists had recognized early on [39 , 54 ] that such a symmetric lensing arrangement would result in a ring-image, a so-called “Einstein-ring”. Can we observe Einstein rings? There are two necessary requirements for their occurence: the mass distribution of the lens needs to be axially symmetric, as seen from the observer, and the source must lie exactly on top of the resulting degenerate point-like caustic. Such a geometric arrangement is highly unlikely for point-like sources. But astrophysical sources in the real universe have a finite extent, and it is enough if a part of the source covers the point caustic (or the complete astroid caustic in a case of a not quite axial-symmetric mass distribution) in order to produce such an annular image.

In 1988, the first example of an “Einstein ring” was discovered [74 ]. With high resolution radio observations, the extended radio source MG1131+0456 turned out to be a ring with a diameter of about 1.75 arcsec. The source was identified as a radio lobe at a redshift of $zS = 1.13$ , whereas the lens is a galaxy at $zL = 0.85$ . Recently, a remarkable observation of the Einstein ring 1938+666 was presented [94 ]. The infrared HST image shows an almost perfectly circular ring with two bright parts plus the bright central galaxy. The contours agree very well with the MERLIN radio map (see Figure 16 ).

Figure 16: Einstein ring 1938+666 (from [94 ]): The left panel shows the radio map as contour superimposed on the grey scale HST/NiCMOS image; the right panel is a color depiction of the infrard HST/NICMOS image. The diameter of the ring is about 0.95 arcseconds. (Credits: Neal Jackson.)

By now about a half dozen cases have been found that qualify as Einstein rings [132 ].

Their diameters vary between 0.33 and about 2 arcseconds. All of them are found in the radio regime, some have optical or infrared counterparts as well. Some of the Einstein rings are not really complete rings, but they are “broken” rings with one or two interruptions along the circle. The sources of most Einstein rings have both an extended and a compact component. The latter is always seen as a double image, separated by roughly the diameter of the Einstein ring. In some cases monitoring of the radio flux showed that the compact source is variable. This gives the opportunity to measure the time delay and the Hubble constant $H0$ in these systems.

The Einstein ring systems provide some advantages over the multiply-imaged quasar systems for the goal to determine the lens structure and/or the Hubble constant. First of all the extended image structure provides many constraints on the lens. A lens model can be much better determined than in cases of just two or three or four point-like quasar images. Einstein rings thus help us to understand the mass distribution of galaxies at moderate redshifts. For the Einstein ring MG 1654+561 it was found [100 ] that the radially averaged surface mass density of the lens was fitted well with a distribution like $α Σ(r) ∝ r$ , where $α$ lies between $− 1.1 ≤ α ≤ − 0.9$ (an isothermal sphere would have exactly $α = − 1$ !); there was also evidence found for dark matter in this lensing galaxy.

Second, since the diameters of the observed rings (or the separations of the accompanying double images) are of order one or two arcseconds, the expected time delay must be much shorter than the one in the double quasar Q0957+561 (in fact, it can be arbitrarily short, if the source happens to be very close to the point caustic). This means one does not have to wait so long to establish a time delay (but the source has to be variable intrinsically on even shorter time scales…).

The third advantage is that since the emitting region of the radio flux is presumably much larger than that of the optical continuum flux, the radio lightcurves of the different images are not affected by microlensing. Hence the radio lightcurves between the images should agree with each other very well.

Another interesting application is the (non-)detection of a central image in the Einstein rings. For singular lenses, there should be no central image (the reason is the discontinuity of the deflection angle). However, many galaxy models predict a finite core in the mass distribution of a galaxy. The non-detection of the central images puts strong constraints on the size of the core radii.