On the contribution of microlensing to X-ray variability of high-redshifted QSOs

Abstract

We consider a contribution of microlensing in X-ray variability of high-redshifted QSOs. Such an effect could be caused by stellar mass objects (SMO) located in a bulge or/and in a halo of this quasar as well as at cosmological distances between an observer and a quasar. Here, we not considerability of microlensing caused by deflectors in our Galaxy since it is well-known from recent MACHO, EROS and OGLE observations that the corresponding optical depth for the Galactic halo and the Galactic bulge is lower than $10^{-6}$. Cosmologically distributed gravitational microlenses could be localized in galaxies (or even in bulge or halo of gravitational macrolenses) or could be distributed in a uniform way. We have analyzed both cases of such distributions. As a result of our analysis, we obtained that an optical depth for microlensing caused by stellar mass objects is usually small for quasar bulge and quasar halo gravitational microlens distributions ($τ\sim 10^{-4}$). On the other hand, the optical depth for gravitational microlensing caused by cosmologically distributed deflectors could be significant and could reach $10^{-2} - 0.1$ at $z\sim 2$. It means that cosmologically distributed deflectors may significantlly contribute to the X-ray variability of high-redshifted QSOs ($z>2$). Considering that upper limit of the optical depth ($τ\sim 0.1$) corresponds to the case when dark matter forms cosmologically distributed deflectors, therefore observations of X-ray variations of unlensend QSOs can be used for the estimation of the dark matter fraction of microlenses.