•ILMT - International Liquid Mirror Telescope Workshop

•29th June - 1st July 2020, ARIES, Nainital

Some problems of monitoringgravitational microlensing processes

V.I. Zhdanov1,2, A.N. Alexandrov1, V.M. Sliusar1,3, I.O. Nimyi2

1Taras Shevchenko National University of Kyiv, Kyiv, Ukraine2National Technical University of Ukraine “Igor Sikorsky Kyiv

Polytechnic Institute”3University of Geneva, Geneva, Switzerland

2

1. GALACTIC MICROLENSING.Related issues which need similar techniques:transients + variable stars +microlensing events.

2. MICROLENSING in EXTRAGALACTIC GLS.• Quasar structure.• Projected number density.• Transversal velocities.

MICROLENSING ON THE MILKY WAY OBJECTS

SOURCE(remote star)

Source plane

Lens plane

Y X

Microlensing sсheme

2

21 ER

-

y xx

2

01e

-

R

ry r

LENS MAPPING

-- standard

-- modified

The deflector: microlensing mass

Model: POINT LENS, POINT SOURCE, SMALL ANGLES

The projections onto the celestial sphere

source

Microlens(deflector)

MOTIVATIONS FOR THE SEARCH OF THE GALACTIC GRAVITATIONAL MICROLENSING EVENTS

• Detailed investigation of the Galaxy structure in theobservational field of ILMT.

• Number of faint objects.

• Exoplanets.

Observation of the Galactic microlensing light curve allows us:

• To make an independent test of the functional form of the general relativistic formula for the light deflection for impact parameters ~1 A.U.

• To test the presence of the dark matter clumps around compact objects (see Fedorova et al. MNRAS, 2016).

5

The necessary condition to observe Galactic microlensing events is monitoring of >106 sources.

Microlensing by Milky Way objects in the context of ILMT

6

J. Surdej, et al. The 4m international liquid mirror telescope (ILMT). Proc. 6267, Ground-based and Airborne Telescopes; 626704 (2006) SPIE Astronomical Telescopes + Instrumentation, 2006.J. Surdej, et al. The 4-m International Liquid Mirror Telescope. Bulletin de la Soc. Roy. des Sciences de Liege, Vol. 87, 2018, p. 68 – 79.

Data from the ESA Gaia mission (https://www.cosmos.esa.int/gaia);Gaia Data Processing and Analysis Consortium (https://www.cosmos.esa.int/web/gaia/dpac/consortium)ESA Gaia Archive, gea.esac.esa.int (https://gea.esac.esa.int/archive/)

Microlensing optical depth towards Galactic center:Paczyński, B. ApJ, 304, 1 (1986); Paczyński, B. ApJ Letters, 371, L63 (1991); Griest, K. ApJ, 366, 412-421 (1991); Paczyński, B. et al. ApJ 435, L113 (1994) ; Alcock, C. et al. ApJ 479, 119 (1997)

7

Distribution of GAIA stars over magnitude within the field of ILMT (ESA Gaia Archive, gea.esac.esa.int)

Total N=3·106 stars

ILMT (expected) N~107 stars

8

GAIA SOURCES

N=2.5·106N=4·105

ILMT observation time of one source ~ 160 nights (ideal conditions)

18h<R.A.<22h4h<R.A.<7h

9

Distribution of GAIA sources over distance within the field of ILMT

(ESA Gaia Archive, gea.esac.esa.int)

TotalN=3·106 stars ILMT

N~107 stars

10

Paczyński, B. ApJ, 304, 1 (1986); Paczyński, B. ApJ Letters, 371, L63 (1991) Griest, K. ApJ, 366, 412-421 (1991)Paczyński, B. et al. (1994), ApJ, 435, L113Alcock, C. et al. (1997), ApJ, 479, 119

22 7

2 3

20.9 10

3 30.1

ss

DGMnD

kpcc M pc

--

rt

Microlensing optical depth t: the probability that one star, at a specific instant in time, has an amplification caused by gravitational microlensing of A ≻ 1.34 (r is the mass density of microlenses, Ds-distance to the source).

11

If it is possible to register m~0.01, we must recalculate

2~ 3 , ~ 9E E ER R P R n

26

3( 0.01) 0.85 10

30.1

sDP mkpcM pc

--

r

Number of events observed for Tobs (total observation time of N distant objects (160 nights) taking into account their motion

- effective microlensing time

2 100 /0.1

1 . .E E

micromicrolens microlens

R R km sT yr

V AU V

1( 0.01) ~ 10obsevents sources

micro

TN N P m yr

T-

12

NUMBER OF MICROLENSING EVENTS??

• Paczyński (1991) estimated number of events with Dm> 0.3 mag to be ~4 per year per 106 bulge stars (16 for masses 0.01 0.1 Msun).

• Alcock et al (1997): Microlensing optical depth has appeared higher than theoretical models.

• Now OGLE group registers about thousand microlensing events per year.OGLE estimates, t ~12·10-6 .

Estimated: ~10 event per year

All theory is gray, but the tree of experiment springs ever green.

The above rough estimate is not reliable because we do not know the real mass density of microlenses and their distribution. However, there are inspirational examples from history of observations of the Galactic microlensing:

• Fedorova E., Sliusar V.M., Zhdanov V.I., Alexandrov A.N., Del PopoloA., Surdej J. Gravitational microlensing as a probe for dark matter clumps. MNRAS, 457, 4147–4159 (2016).

• Alexandrov A.N., Zhdanov V.I., Sliusar V.M. Testing the Einstein formula for gravitational bensing of light using the microlensing light curves (in Ukrainian). Bull. Taras Shevchenko Nat. Univ. of Kyiv. Astronomy” 59, No.1, 18-22 (2019).

• Alexandrov A.N., Zhdanov V.I., Sliusar V.M. Verification of Einstein’s formula for gravitational deflection of light using observations of galactic microlensing. Kinematics and Phys. of Celest. Bodies, accepted (2020).

13

TESTING GENERAL RELATIVITY WITH GRAVITATIONAL LENSING

14

Testing the Einstein’s formula for light deflection

MICROLENSING ON THE MILKY WAY OBJECTS

The standard lens equation (lens mapping) in angular variables

2

21 ER

-

y xx

1 2

2

4 dsE

s d

GM DR

c D D

The angular radius of the Einstein ring

point lens, point source

GM

pc p

2

4

15

0

2

/ , ;

,0 1

R r r

F

-

x

STATEMENT OF THE PROBLEM

2( , ) 1F e e - 0 /R r

2 20 2

4E

L

GMR R

c D

e

e

Next we consider a concrete example

, ,F ey x

“Spoiled” lens mapping

GM

pc p

e

1

2

4

Modified formula for light deflection

Simulations: Estimated error of e (from a single microlensing light curve) against

photometric accuracy

16

From one microlensing event with m~0.01 0.02we have typically e~0.1.

Im

I

17

The data from: Early Warning System (2018) Optical Gravitational Lensing Experiment (OGLE).

Paczynski B. ApJ, 304, 1 (1986); ApJ Letters, 371, L63 (1991).Udalski A., Szymanski M., Kaluzny J., Kubiak M., Krzeminski W., Mateo M., PrestonG.W., Paczynski B. Acta Astron. 1993. 43. P. 289–294.Udalski A., Szymański M.K., Szymański G. Acta Astron. 2015. 65. P. 1-38.

http://ogle.astrouw.edu.pl/ogle4/ews/ews.html

18

• Sample of 100 lightcurves (EWS OGLE-2018): arXiv:2004.07522 [Apr 2020]

SELECTION CRITERIA

• sufficient brightness enhancement at the maximum

• sufficient accuracy and the number of points on the microlensing light curve

• the absence of obvious signs of a binary system or planetary contribution

• absence of parallax effects

• Sample of 100 lightcurves (OGLE-2018)

19

Histogams of e values obtained by different methods

(i) (ii) (iii)

2

01e

-

R

ry r

20

THE RESULTS: median, mean and standard deviation obtained by three methods

1

e eN

j jj

w

From N=100 lightcurves we have a set of ej

21

51 ~ 2 10- -

Comparison with the accuracy of the Solar system tests Bertotti et al (Cassini mission) 2003; C.M.Will, 2014:

In case of Galactic microlensing: independent data of quite other sort dealing with impact distances p~108km.

p~108km

p~106km

22

Resume:

• We tested the Einstein’s formula for the gravitational light deflection using a modified power-law dependence upon the impact distance. This involves parameter e that characterizes the deviation from the general relativistic formula (in GR e =0).

• Using one microlensing light curve we predict the error e~0.1 in case of the photometric accuracy m~0.01 0.02.

• Statistical treatment of 100 light curves from the sample of OGLE database on Galactic microlensing events yields e that does not contradict the General Relativity within error ~0.01.

• Involving more light curves makes the method more accurate and competitive.

23

Thank you for attentionThank you

for attention