Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 53, p. 29-32 (2016)

Microlensing on extended structures having a spherically-symmetric mass distribution

V. I. Zhdanov, Dr. Sci,
A. N. Alexandrov, Ph.D.,
O. S. Stashko, student
Astronomical observatory of Taras Shevchenko National University of Kyiv

Different dark matter (DM) models predict various clustering properties, i.e. the possibility of DM to form massive objects on different scales. The lower mass limit of these objects according to [1, 2]. may be of the order of planetary masses. The gravitational microlensing can be used to confirm or to reject the existence of such structures and therefore to argue in favor or against concrete DM theories. There are observational programs (OGLE, EROS etc) yielding the light curves of a remote objects in high amplification events (HAE) due to microlensing on foreground masses of the Galaxy. In case when the foreground mass is an extended one, then the light curve in HAE must differ from the light curve due to ordinary microlensing on a point mass. 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 [3–5] by means of special model lens mappings. In this paper we study this problem starting directly from mass distribution of the extended structure. Namely, we consider microlensing on an extended DM clump with the cored spherically-symmetric mass profile (without a singularity in the center). After some rescaling the lens mapping has the form

 where R characterizes the size of the clump. For

 the mapping can have either one or three images; two critical images can merge with each other and disappear when the point source crosses the caustic and their brightness amplification is infinite. For R > γλ there is no caustics and there is the only image. We present examples of the amplification curves in both cases. Then we generate the amplification curves in case of the extended clump model for different values R,γ when the clump moves uniformly with respect to the line of sight with some impact parameter p and velocity V. These curves are then fitted with the point microlens model (with free parameters р and V) and we estimate the difference between the curves. The general outcome is that the amplification curves in case of the extended clumps are very similar to those in case of the point microlens (with appropriately chosen parameters p and V that cannot be derived from observations independently), and it would be difficult to distinguish them on the basis of observations if we deal with p ~ 1 (i.e., of the order of the Einstein radius) and larger. For R larger than ~ (5 ÷ 7) γ the amplification is too small so that the event could be observed. This confirms analogous earlier results [7] obtained within different lens models. The general outcome is that for an observational confirmation or refutation of the existence of the stellar mass extended microlenses it is necessary to continue the programs like OGLE and EROS, and a refinement of the photometric accuracy is highly desirable.

Microlensing on extended structures

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