Gravitational microlensing and its capabilities for research of the dark matter Lyudmila Berdina Institute of Radio Astronomy NAS of Ukraine
Gravitational lensing Spherically symmetric mass distribution Elliptical mass distribution Galactic cluster 2
Gravitational microlensing 3 The effect of microlensing creates objects with masses: The information from the analysis of microlensing: the masses of microlenses; the speed of their movement; the structure of radiation sources. The star light curves of LMC in blue and red ray
Microlensing in gravitationally lensed quasars 4 16.5 GLS Q2237+0305 "Einstein Cross" Maidanak 17.0 A R, magnitude 17.5 18.0 18.5 B C D+0.5 m 19.0 1986 1989 1992 1995 1998 2001 2004 2007 2010 Date, years
Substars (brown dwarfs) 5 Substars (brown dwarfs) are an intermediate class between stars and planets. Substars are surrounded: dense atmospheres hydrogen, helium dense plasma environment Brown dwarfs -- class of objects -- baryonic component of the dark matter.
Focusing features of the lens systems System of macro + micro lenses => difference of focusing scales on separate parts of the trace => GMFS ( Generalized method of the phase screen ) accounting the gravitational fields with different spatial scales 6
Generalized method of the phase screen 7 Transfer of the solving from a plane on a plane -- accounting an environment with an index of refraction between planes: Eikonal 1 1 2 1 Z2 d p z p1, p2 n z, p z 1 dz Z dz 1 p2 p1 p z p z Z Z Z 2 Field in plane (z₂, p₂ ): k U ( Z, p ) U ( Z, p )exp i k p, p dp 2 i( z z ) 2 2 2 1 1 1 1 2 1 2 1
System of macro + micro lenses 8 the path: source macrolens the path: macrolens - observer MUTUAL-COHERENCE FUNCTION: ( Z, p ) ( Z, p ) f p ( Z; p) ( Z ; p ) m 0 m m m 0 m m m m p p p BRIGHTNESS in point of observation : 2 k p, s d 2 p p p,0 exp ik p 4 MAGNIFICATION FACTOR
Model representation Model representation : 2237+0305 Einstein Cross The source model -- specified in a form of radiating surface elements with the Gaussian distribution law of intensity. The microlens -- point mass randomly placed into the galaxy. The macrolens -- galaxy is approximated in the rough by a compact spherical mass. 9
Parameters of the models Angular size of the radiation source -- 0 0.04 as Angular coordinate of the source radiation maximum -- Angular sizes of the macrolens Einstein rings -- Angular sizes of the microlens Einstein rings -- Distance to observer and distance to source --, G g g G Z 152 Mpc ; Z 1607 Mpc Distribution of the intensity in a source macro image unperturbed by microlens G p 0.9 0 0.7 as g 0.1 s s 1o
The path: source macrolens Distribution of the intensity in visible image of a source for different positions of a microlens between a source and mass center of a galaxy. ZZ ms m s 11
The path: source macrolens 12 ZZ ms m s
The path: macrolens observer Distribution of the intensity in visible image of a source for different positions of a microlens between a mass center of a galaxy and observer. ZZ mp m p 13
The path: macrolens observer 14 ZZ mp m p
Magnification factor Magnification factor of complex lens (1) and magnification factor of microlens (2), normalized to magnification factor of macro image. 15
16 Conclusions 1. A generalized method of phase screen has been proposed -- allows to analyze the microlensing effect taking into account the influence both of large-scale inhomogeneities of the gravitational field (galaxy) and small-scale one (microlenses). 2. The analytical expressions for the intensity distribution in macroimages and the amplification factor are derived. The results of numerical analysis are presented as intensity contours of macroimages and dependence of amplification factor on the microlens distance from the galaxy plane. 3. The effect of a microlens is shown to become stronger as it approaches the observer plane. The changes of magnification factor in depend on the position of the microlenses within the thickness of a typical galaxy are not great, however, in solving the inverse problem of parameters recovery of the gravitational-lens system, the role of this factor may be appreciable.
17 The time delays formation between signals from a source observed in its macroimages
18 Examples of macroimages light curves 16.5 17.0 GLS Q2237+0305 "Einstein Cross" A Maidanak R, magnitude 17.5 18.0 18.5 B C D+0.5 m 19.0 1986 1989 1992 1995 1998 2001 2004 2007 2010 Date, years
19 Constraints of the accuracy of time delays determination the systematic and random errors in the measurement of the quasar brightness; the small amplitude of variations in the intrinsic brightness of quasars; the microlensing events. The essence of the proposed method Representation of the observations data by the orthogonal polynomials allows to mitigate the microlensing effects by the simple way (Tsvetkov, Shulga & Berdina. MNRAS, 461, 2016, pp. 3714)
Participation in the international campaign TDC 20
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The estimates of the time delays and robustness test of proposed method Conclusions. The determined time delays in artificially synthesized light curves are in a good agreement with the true values. Due to the applying of the fundamental properties of the functions approximation, a simple and objective procedure for mitigating the microlensing effects on estimates of time delays are achieved. 22
Thank you for your attention! With best regards, Lyudmila!