Estimating orbital period of exoplanets in microlensing events

mose.giordano@le.infn.it

Estimating orbital period of exoplanets in microlensing events

Mosè Giordano, Achille A. Nucita, Francesco De Paolis, Gabriele Ingrosso

Department of Mathematics and Physics “E. De Giorgi”, University of Salento, Lecce, Italy INFN, Section of Lecce, Italy

Gravitational lensing

A gravitational lens is a distribution of matter whose gravitational field distorts space-time, bends light rays and amplifies the

brightness of a source star

Credits: Hyper-Mathematics - Uzayzaman / Spacetime

Binary Lens with Orbital Motion

In microlensing events, usually, static binary systems are taken into account, but binary systems do rotate

The parameters to be determined using a fit in microlensing events by binary lens with orbital motion are

• Paczy ński curve parameters: t ₀ u ₀ t _E Ú

• finite source e ffects: â _?

• binary lens: b q

• binary lens with orbital motion: a e i ï

In addition, with small mass ratios q there is the close-wide degeneracy b ←→ b ⁻¹

What if we knew the orbital period of the lenses P = 2á

s a ³

G(m ₁ + m ₂ ) = 2á

s a ³

G m ₁ (1 + q) independently?

Fit to Real Data

Event OGLE-2011-BLG-1127/MOA-2011-BLG-322

Conclusions

Orbital period of the lenses should be shorter than the Einstein time of the event or we must have a long observational window We fit the observed amplification curve to a simple Paczy ński curve, with four easily-guessable free parameters, and then perform a periodogram on the residue curve: the period so obtained is the period of the binary system

We need to remove a very small region around the maximum

peak from the residue curve before performing the periodogram Periodic feature with the same period far from the peak =⇒

source periodicity (binary system, intrinsic variable, etc. . . )

Detecting Exoplanets with Microlensing

Microlensing is a powerful tool to detect exoplanets: a binary lens (lensing star with a companion planet) induces non-negligible

deviations to the usual symmetric Paczy ński light curve

Credits: Didier Queloz, Nature 439, 400–401. doi: 10.1038/439400a

Simulation: Amplification Curve and Periodogram

−2

−1.5

−1

−0.5 0 0.5 1 1.5

Ù

1 2 3 4 5

Amplifica tion

−0.001 0 0.001

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

R esidue

à

−3

−2

−1 0

1 2

3 t/t _E

−1

−0.5 0 0.5 1

−1 −0.5 0 0.5 1

Lensing star orbit Companion planet orbit Source trajectory Central caustic curve

Best-fitting Paczy ´nski curve Amplification curve

Parameters used: q = 10

, a = 0.2, e = 0.5, i = 45°, ï = 0°, P = t

/4

Reference

A. A. Nucita, M. Giordano, F. De Paolis, and G. Ingrosso.

“Signatures of rotating binaries in microlensing experiments”.

In: Monthly Notices of the Royal Astronomical Society 438 (Mar.

2014), pp. 2466–2473. doi: 10.1093/mnras/stt2363 (scan here: ). arXiv: 1401.6288 (scan here: ).

Summer Course on Exoplanets La Palma, Canary Islands, 24 September–2 October 2014