Gravitational lensing is an universal natural phenomenon where the gravitational force of lensing object induce either the amplification of some background source (**microlensing**), or the appearance of its multiple images (**macrolensing**),
due to light bending in a gravitational field of the deflector. Separation angle between the images of background source depends on the mass of gravitational lens and therefore, multiple images can be observed only in the case of a massive lensing
object, such as galaxy (see below figure for an example). In the case of a small mass lens (e.g. a star), the separation angle is also small and therefore, different images of background source cannot be resolved. Instead, its intensity is amplified,
causing the changes in the observed light curve. Common name for both, macrolensing (or simply lensing) and microlensing is **strong lensing**, contrary to **weak lensing**, which causes distortions in observed images of distant objects which can
be then used for studying the mass distribution along the line of sight.

Top: Gravitational lens system SDSS J1004+4112 with 4 images observed at different wavelengths. Redshifts of the source and lens are 1.74 and 0.68, respectively. Bottom: Optical spectra of all four images of the
lens. More information about this gravitational lens system can be found in this paper. |

Some recent observational and theoretical studies suggest that gravitational microlensing can induce variability in the emission from accretion disks of AGN, especially in the case of gravitationally lensed quasars. In order to study such variability we developed the following three models of gravitational microlensing:

**Point-like microlens**- applied in the case of microlensing by an isolated compact object such as e.g. a star (see below figure)**Straight-fold caustic**- applied when the size of the microlens projected Einstein Ring Radius is larger than the size of the accretion disk (see below figure)

Top: Numerical simulations of a point-like gravitational microlens crossing over an accretion disk in Kerr metric with angular momentum a = 0.998 (left) and the corresponding undeformed (blue line) and deformed
(red line) shapes of the Fe Kα line (right). Einstein Ring of the point-like microlens is schematically presented by yellow Euclidian circle. Bottom: The same as in top figure, but for straight-fold caustic crossing in oposite
direction. More information about these two models of gravitational microlensing can be found in this and this paper. |

**Quadruple microlens (microlensing map, microlensing pattern or caustic network)**- the most complex and realistic model for gravitational microlensing applied in order to obtain a spatial distribution of magnifications in the source plane (where an accretion disk of AGN is located), produced by a random star field placed in the lens plane (see below figure)

Left: Magnification map of a "typical" lens system, i.e. for the redshit of the source equals 2 and redshift of the lens equals 0.5. The vertical white solid line represents a path of an accretion disk center
during its crossing over the magnification map. Right: Simulated light curves showing variations in the X-ray (solid), UV (dashed) and optical (dotted) spectral bands corresponding to the disk crossing along the given path in the left
magnification map. More information about this microlensing model can be found in this paper. |

Microlensig time-scales for all three spectral bands, estimated from rise times (t_{HME}) of so called "high magnification events" (sharp asymmetric peaks) in the above simulated light curves. More information about
microlensing time-scales can be found in this paper. |

As a result of our investigations in this field, we found that gravitational microlensing can produce significant variations and amplifications of the line and continuum spectra of AGN. During a microlensing event, even very small mass objects could
produce noticeable changes in the X-ray radiation from accretion disks of AGN. Such changes are significantly larger and faster than the corresponding effects in the optical and UV emission. For a more detailed review on this topic see e.g.
**this paper**.

The probability of observing a gravitational lensing effect, i.e. the chance of seeing a gravitational lens, is usually expressed in terms of the optical depth *τ*. In the case of gravitational lensing caused by cosmologically distributed
deflectors, *τ* strongly depends on cosmological model (see below figure). More precisely, it depends on dimensionless density parameters corresponding to the mass density of the Universe at the present epoch (Ω_{0}) and the
matter fraction in compact lenses (Ω_{L}).

The calculated optical depth of cosmologically distributed microlenses as a function of redshift for 3 different values of Ω_{L}. |

Our results show that the optical depth of gravitational lensing caused by cosmologically distributed deflectors could be significant and could be used as a tool for estimation of dark and visible matter fractions in the compact objects. For more
details about optical depth of gravitational lensing see **this paper** and references therein.

Last updated on October 15