Searches of stellar mass dark matter from an analysis of variabilities   of high red-shifted QSOs
  We consider a contribution of microlensing to the 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. 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 the optical depth for microlensing caused by stellar mass objects is usually small for quasar bulge and quasar halo gravitational microlens distributions. On the other hand, the optical depth for gravitational microlensing caused by cosmologically distributed deflectors could be significant and could reach 0.01 - 0.1 at z ~ 2. This means that cosmologically distributed deflectors may contribute significantlly to the X-ray variability of high-redshifted QSOs (z > 2). Considering that the upper limit of the optical depth (~ 0.1) corresponds to the case where dark matter forms cosmologically distributed deflectors, observations of the X-ray variations of unlensed QSOs can be used for the estimation of the dark matter fraction of microlenses. 
A.F. Zakharov (1,2), L. C. Popovic (3,4), P. Jovanovic (3) ((1)   Institute of Theoretical and Experimental Physics, (2) Ast...