Analytical Methods in Gravitational Microlensing

Abstract

We discuss analytical results dealing with photometric and astrometric gravitational microlensing. The first two sections concern approximation methods that allow us to get solutions of the general lens equation near fold caustics and cusp points up to any prescribed accuracy. Two methods of finding approximate solutions near the fold are worked out. The results are applied to derive new corrections to total amplifications of critical source images. Analytic expressions are obtained in case of the Gaussian, power-law, and limb-darkening extended source models; here we present the first nonzero corrections to the well-known linear caustic approximation. Possibilities to distinguish different source models in observations are discussed on the basis of statistical simulations of microlensed light curves. In the next section, we discuss astrometric microlensing effects in various cases of extended sources and extended lenses, including a simple model of weak statistical microlensing by extended dark matter clumps. Random walks of a distant source image microlensed by stochastic masses are estimated. We note that the bulk motion of foreground stars induces a small apparent rotation of the extragalactic reference frame. Compact analytical relations describing the statistics of such motions are presented.

Microlensing on extended structures having a spherically-symmetric mass distribution

“…However the question is: what is the value of this difference and is it possible to register this difference with modern observational facilities. This question has been studied elsewhere [3][4][5] by means of special model lens mappings. In this paper we study this problem starting directly from mass distribution of the extended structure.…”

“…Питання полягає в тому, наскільки значні ці відмінності і чи можна їх зареєструвати сучасними засобами. По-дібні питання розглядалися в роботах [5][6][7] шляхом прямого розгляду модельних лінзових відображень. Разом із тим представляє інтерес моделювання виходячи безпосередньо з розподілу маси протяжної структури.…”

Cosmological and astrophysical challenges of General Relativity

“…В найпростiшому наближеннi лiнiйної каустики, яке використовують для розрахунку коефiцiєнта пiдсилення, окрiм параметрiв, що визначають положення каустики, у формули входить лише один параметр -сила каустики [3,57,5]. Наступне -пост-лiнiйне -наближення, що мiстить ще три додаткових параметри, дозволяє досить точно описати хiд кривої блиску протяжного джерела [1,12,63].…”

Gravitational microlensing as a probe for dark matter clumps

“…(3) with a = 2 (cf. Zhdanov et al (2012)). An external shear owing to the average field of the lensing galaxy will also be taken into account.…”