Statistical methods are developed for gravitational lensing in order to obtain analytic expressions for the average surface brightness that include effects of microlensing by stellar (or other compact) masses within the lensing galaxy. The primary advance here is in utilizing a Markoff technique to obtain expressions that are valid for sources of finite size when the surface density of mass in the lensing galaxy is large. The finite size of the source probably is the key consideration for the occurrence of microlensing by individual stars. For the intensity from a particular location, we find that the parameter which governs the importance of microlensing is δ = (a_0_/a)^2tau ln [3.05(N)^1/2^], where a_0_, is the characteristic impact parameter for lensing by a single star, a is the size of the source, τ is the "optical depth" for lensing, and N is the number of stars being considered. Similar statistical methods are also formulated to assess the time variation of the surface brightness due to the random motion of the masses that cause the microlensing.
No takes yet. Share an insight, caveat, or question.
Deguchi et al. (1988) studied this question.