Gravitational lensing is an effect of the General Theory of Relativity. This is the bending of a distant source light in the gravitational field of a massive body; this bending, of course, is valid not only for light, but for the whole electromagnetic spectrum radiation. The massive body causing the light bending is called gravitational lens. Stars, galaxies and clusters of galaxies can act as gravitational lenses while the source is a high redshift galaxy or a quasar. As a result of gravitational lensing the parameters (position, brightness, shape) of the source are changed. Therefore, we have to consider rather the image of the source created by a gravitational lens than the source itself. Under certain conditions the image of the source could be split into several distinct images each with characteristics that differ from those of the source - this is the strong lensing. The weak lensing changes the source parameters, but does not split the source image. The changes of the source parameters induced by a gravitational lens help us to study the gravitational lens (light and dark) mass distribution. If the source is placed right behind the lens, then a ring of light, the so called Einstein ring, will result. The ring radius is tightly constrained by the mass projected inside the ring. If the source is variable and strong lensing takes place, there will be a time delay between the variability patterns of the distinct source images. We can estimate the Hubble parameter value measuring the time delay and building the lens mass model. This provides to us an independent Hubble parameter estimate.

Note, that our Sun also acts as a gravitational lens shifting the position of the stars projected close to the solar limb. This was observed firstly by A. Eddington during the solar eclipse in 1919 and was used as an observational confirmation of the General Theory of Relativity. The real development in the area of gravitational lensing started in 1979 when the first multiply imaged quasar (0957+561A & B) was discovered by Walsh, Carswell and Weymann.

Click here for more details about Gravitational Lensing.


Among the various astrophysical applications of gravitational lensing we are interested mainly in studying the galaxies mass distribution and Hubble parameter estimation. The main outgoing or finished research subjects are listed below:
  1. Gravitational lens mass model for 2237+0305. We proposed two mass models: two-plane and shear, for the galaxy 2237+0305 which quadruply lensed the quasar 2237+0305 and achieved the best fit to the observations at that time. We modelled the main lens as a nonsingular isothermal ellipsoid, and the secondary lens as a singular isothermal sphere in the two-plane mass model. The observed ultraviolet positions and radio flux ratios of the images were taken from the papers of Blanton et al. (1998) and Falco et al. (1996), respectively.
  2. Time delay determination for 0957+561 on the base of La Palma archival data. We estimated the time delay between the variations in the images of the double quasar 0957+561 on the base of the La Palma archive and made a Hubble parameter estimate based on the lens mass model of Grogin and Narayan (1996a, 1996b). We did a light curves cross-correlation using a method developed by V. Oknyanskij.


  1. The external shear in the gravitationally lensed system Q 2237+0305: A two-plane lens modelling, Mihov, B. M. 2001, Astronomy and Astrophysics, v.370, p.43-52
  2. CCD Photometry of QSO 0957+561 A & B for the period 1987-1992 using La Palma archive, Slavcheva-Mihova, L. S., Oknyanskij, V. L., Mihov, B. M. 2001, Astrophysics and Space Science, v. 275, Issue 4, p. 385-389
  3. Monte Carlo simulations of quasars' brightness magnification due to gravitational lensing: the highly luminous quasar HS 1946+7658, Mihov, B. M. 2001, In: Balkan Meeting of Young Astronomers, 25 - 29 September 2000, Belogradchik, Bulgaria, edited by Alexander Antov, Renada Konstantinova-Antova, Rumen Bogdanovski and Milcho Tsvetkov, Belogradchik: Belogradchik Astronomical Observatory, ISBN 954-90133-2-4, 2001, p. 80 - 83 [PDF]
  4. A Lens Model for Q2237+0305, Petrov, G., Strigatchev, A., Mihov, B., 1996, Compt. rend. l'Acad. bulg. Sci., vol. 49, No 1, p. 5
  5. PETROV G., STRIGATCHEV A., poster, International scool at NAO Rozhen, april 1994. Observations of the Double Quasar 0957+561 at NAO Rozhen following the MEGAPHOT collaboration.
  6. MIHOV B.,BACHEV R.,STRIGACHEV A., SLAVCHEVA L., PETROV G., IAU Symp. 194, p.175, 1999. Photometric monitoring of selected quasars. The highly luminous quasar HS 1946+7658.

Written by B. Mihov, 2005