Gravitational microlensing: an original technique to detect exoplanets
Gravitational lens effect
Microlensing and exoplanets 4
Time variation 5
Basic equations θ E (mas) = 2.854 M 1/2 1/2 L D OL R E (AU) = 2.854 M 1/2 1/2 L D OL 1 D OL D OS 1 D OL D OS 1/2 1/2 Order of magnitude: ML=0.3 Msun, DOS=8 kpc, DOL=6 kpc: θe=0.3 mas, RE=2 AU t E = θ E µ = R E V µ = 15 µas/d = 5.5 mas/yr: te = 20 d, V = 150 km/s 6
u = θ θ E A(u) = u2 + 2 u u 2 + 4 u = 1 A = 1.34 u 1 A(u) 1 u Single lens 7
Binary lens: caustics 8
EROS 2000-BLG-5 9
Planetary caustics 3 topologies: close, intermediate, wide close: 3 caustics intermediate: a single resonant caustic wide: 2 caustics: small central, larger planetary 10
t E = 20 d, M = 0.3 M sun : Jupiter : q = 3 10-3 t p =1 j Earth : q =10 5 t p =1.5 h Exoplanet detection by caustic crossing 11
Alert telescopes 1995: MOA 1993: Macho ( 1999), Ogle, EROS ( 2003)
PLANET telescope network «Sun never rises above PLANET»
Animation (Gaudi) 14
Canopus reference image of OGLE-2008-BLG-279 Normalized subtracted images vs time 15
OGLE 2005-BLG-390
Example: OGLE 2005-BLG-390 17
Finite source size effect ρ = 0.003, 0.006, 0.013, 0.03 if M = 0.3 M sun and D OS = 9 kpc Clump giant: Turn-off M.S.: R =13 R sun θ = 6.7 µas ρ = 0.013 if D OL = 0.5 D OS R = 3 R sun θ =1.6 µas ρ = 0.006 if D OL = 0.8 D OS
What do we actually measure? Source: giant: bright, but signal dilution dwarf: faint Anomaly duration: t p = t E q Mass ratio q (planet / lens star) Instantaneous projected distance s between planet and star, in unit of RE: r = s R E = s D L θ E Planetary caustic located at s-s -1 (major image: positive deviation) 19
Accuracy of measured masses Secondary effects: source resolution, parallax (annual or terrestrial), lens detection in adaptive optics Without secondary effect: bayesian analysis using a Galactic model: low accuracy Source resolution: ρ S = θ S θ E = t S t E θs estimated from a CMD deduce θe Annual parallax: πe relative parallax: π rel = π E θ E lens mass: M L = 1 8.14 θ E π E 20
Summary of 2010-2012 observing seasons Previous years: 15: 1 in 2003 and 2008, 3 in 2005, 2006, 2007, 4 in 2009 2010: MOA only, 606 events, 176 follow-up, 41 models: 3 planets (2 pub, 1 in prep, + 2 failed) 2011: OGLE-IV and MOA: 1746 events, 242 follow-up, 115 models: 5 planets (2 pub, 3 in prep) 2012: idem: 1969 events, 215 follow-up, 200 models (3 teams): 10 planets (1 double pub, 1 free-floating) 21
Two planets: OGLE 2006-BLG-109 22
Resolved source: MOA 2007-BLG-400 23
MOA 2009-BLG-266 Long event: alerted 1/6/2009, anomaly 11/9 2 Low amplification (7.7), planetary caustic Smallest measured mass ratio: q = (5.1 ± 0.1) 10-5 Giant source: diluted signal, although very clear Mp = 14 ± 3 M F IG. 1. Light curve of the microlensing event MOA-2009-BLG-266. The upper panel shows the enlargement of the perturbation region. The two curves are from the best-fit models with and without the parallax effect. Also presented are the residuals from the best-fit parallax model. The black points in the bottom panel represent the residuals for binned (by 2 days) data. an Earth-mass planet would have easily been detected 24 scope of CTIO in Chile, 1.0 m of Mt. Lemmon Observatory in Arizona, 0.4 m of Bronberg Observatory in South Africa, 0.4 m of Campo Catino Austral Observatory (CAO) in Chile, 0.4 m of Auckland Observatory, 0.4 m of Farm Cove Observatory in New Zealand, 1.54 m Danish Telescope of La Silla Observatory in Chile, 1.0 m of Mt. Canopus Observatory in Australia, and 1.0m of SAAO in South Africa. The RoboNetII team also observed the event by using the 2.0 m Faulkes Telescope S. (FTS) in Australia and 2.0 m Faulkes Telescope N. (FTN) in Hawaii. The time gap between the issue of the alert and the first follow-up observation (Wise and Bronberg) is merely 4 hours. Timely alert of the perturbation by the survey experiment and prompt response to the alert by the follow-up teams enabled dense coverage of the perturbation. Real-time modeling conducted shortly after the perturbation indicated a planetary origin of the perturbation. In addition, the relatively long time scale of the event raised the need for extended follow-up observations to measure the microlens parallax, which enables complete determination of the physical parameters of the lens when combined with the Einstein radius that is measurable from the perturbation. As a result, observations were conducted until the second week of Planetary lensing is a case of binary lensing with a very low-mass companion. Modeling binary-lens light curves requires to include various parameters. To describe light curves of standard single-lens events, a set of three parameters are needed: the Einstein time scale, te, time of the closest lenssource approach, t0, and lens-source separation normalized by the Einstein radius at the time of maximum magnification, u0. For the description of the planetary perturbation, an additional set of binary parameters is needed: the mass ratio between the lens components, q, binary separation in units of the Einstein radius, s, and angle of the source trajectory with respect to the binary axis, α. In most planetary events, planetary signals are produced by a close caustic approach or crossing of the source trajectory during which the angular radius of the source star, θ#, affects the lensing magnification. To account for this effect, it is required to include the normalized source radius, ρ# θ# /θe, where θe is the angular Einstein radius corresponding to the total mass of the binary system. For some events, it is required to include the parallax parameters πe,n and πe,e, which are the components of the microlens-parallax vector πe projected on the sky in the north and east celestial coordinates, respectively, where the direction of the parallax
Exoplanètes (janvier 2013)
Perspectives adaptive optics: 8 events observed at Keck, VLT and Subaru to measure the lens+source flux second-order effects degeneracy shows the need of very accurate photometry, probably only obtainable from space (WFIRST, EUCLID)
Subo Dong E N HST Image 1 OGLE Field