Gravitational Microlensing and Dark Matter in Our Galaxy: 10 Years Later

Foundations of standard theory of microlensing are described, namely we consider microlensing stars in Galactic bulge, the Magellanic Clouds or other nearby galaxies. We suppose that gravitational microlenses lie between an Earth observer and these stars. Criteria of an identification of microlensing events are discussed. We also consider such microlensing events which do not satisfy these criteria (non-symmetrical light curves, chromatic effects, polarization effects). We describe results of MACHO collaboration observations towards the Large Magellanic Cloud (LMC) and the Galactic bulge. Results of EROS observations towards the LMC and OGLE observations towards the Galactic bulge are also presented. Future microlensing searches are discussed. A standard microlens model is based on a simple approximation of a point mass for a gravitational microlens. Gravitational lensing (gravitational focusing) results from the effect of light bending by a gravitating body (the phenomenon was discussed by I. Newton, but in the framework of Newtonian gravity a formal derivation of the light bending angle was published by J. Soldner [1]). In the framework of general relativity (GR) using a weak gravitational field approximation the correct bending angle is described by the following expression derived by Einstein in 1915 just after his formulation of GR δφ = − 4GM∗ cp . (1) The derivation of the famous Einstein’s formulae for the bending angle of light rays in gravitational field of a point mass M∗ is practically in all monographs and textbooks on general relativity and gravity theory (see, for example books [2, 3]). The law was firstly confirmed by Sir A. Eddington for observations of light ray bend by the Solar gravitational field near its surface. The angle is equal to 1.75, therefore Einstein prediction was confirmed by observations very soon after its discovery. The gravitational lens effect is a formation of several images instead of one (see details in [4,5]). We have two images for a point lens model (Schwarzschild lens model). The total square of the two images is larger than a source square. The ratio of these two squares is called gravitational lens amplification A. That is a reason to call gravitational lensing as gravitational focusing. The angular distance between two images is about angular size of so-called Einstein’s cone. e-mail: [email protected] The angular size of Einstein’s cone is proportional to the lens mass divided by the distance between a lens and an observer. Therefore, if we consider a gravitational lens with typical galactic mass and a typical galactic distance between a gravitational lens and an observer then the angular distance between images will be about few angular seconds; if we suppose that a gravitational lens has a solar mass and a distance between the lens and an observer is about several kiloparsecs then an angular distance between images will be about angular millisecond. If a separation angle is∼ 1, then one may observe two images in optical band although this problem is a complex one, but one cannot observe directly two images by Earth’s observer in the optical band if a separation angle is ∼ 0.001. Therefore, the microlensing effect is observed on changing of a luminosity of a source S. If the source S lies on the boundary of the Einstein cone, then we have A = 1.34. Note, that the total time of crossing the Einstein cone is T0. Sometimes the microlensing time is defined as a half of T0 we suppose that Dd < Dds (here we assume that Dds is the distance from the source S to the lens D; Dd is the distance from the lens D to the observer O; Ds is the distance from the source S to the observer O)