1. Detection of Extrasolar Planets through Gravitational Microlensing and Timing Method Technique & Results Timing Method

2. A Brief History of Light Deflection In 1911 Einstein derived: Einstein in 1911 was only half right !  = 2 GM סּ c2Rסּc2Rסּ = 0.87 arcsec In 1916 using General Relativity Einstein derived:  = 4 GM c2rc2r = 1.74 arcsec Light passing a distance r from object Factor of 2 due to spatial curvature which is missed if light is treated like particles

3. Eddington‘s 1919 Eclipse expedition confirmed Einstein‘s result

4. A Brief History of Light Deflection In 1924 Chwolson mentioned the idea of a „factious double star.“ In the symmetric case of a star exactly behind a star a circular image would result In 1936 Einstein reported about the appearance of a „luminous“ circle of perfect alignment between the source and the lens: „Einstein Ring“ In 1937 Zwicky pointed out that galaxies are more likely to be gravitationally lensed than a star and one can use the gravitational lens as a telescope

5. Einstein Cross Einstein Ring Evidence for gravitational lensing first appeared in extragalactic work

6. Source Lens Observer S S2S2 S1S1 Basics of Lensing:

7. Basics of Lensing: The Einstein Radius ss EE S1S1 S2S2 Lens Source off-centered EE Source centered ≈ 1 milli-arcsecond => Microlensing

8.  = 0  =  –  (  )

9. Magnification due to Microlensing: Typical microlensing events last from a few weeks to a few months

10. Time sequence: single star Top panel shows stellar images at ~1 mas resolution centered on lens star Einstein ring in green Magnified stellar images shown in blue Unmagnified image is red outline The observable total magnification is shown in the bottom panel Animation by Scott Gaudi: http://www.astronomy.ohio-state.edu/~gaudi/movies.html

13. Time sequence: star + planet A planet in the shaded (purple) region gives a detectable deviation A planet lensing event lasts 10-30 hours

15. Mao & Paczynski (1992) propose that star-planet systems will also act as lenses

16. OGLE: Optical Gravitational Lens Experiment (http://www.astrouw.edu.pl/~ogle/)http://www.astrouw.edu.pl/~ogle/ 1.3m telescope looking into the galactic bulge Mosaic of 8 CCDs: 35‘ x 35‘ field Typical magnitude: V = 15-19 Designed for Gravitational Microlensing First planet discovered with the microlensing method Successful Microlensing Programs

18. Problem: Only 4 points!

19. Solution: Multi-site Campaigns

20. Microlensing Results: 12 Planets so far Rumor has it that there are another ~20 planet candidates

21. The First Planet Candidate: OGLE-235-MOA53 OGLE alert

22. Lightcurve close-up & fit (from Bennet) Cyan curve is the best fit single lens model –  2 = 651 Magenta curve is the best fit model w/ mass fraction   0.03 –  2 = 323 7 days inside caustic = 0.12 t E –Long for a planet, –but  mag = only 20-25% –as expected for a planet near the Einstein Ring

23. 1 st definitive  lensing planetary discovery - complete coverage not required for characterization Real-time data monitoring was critical! S. Gaudi video The First Planet Candidate: OGLE-235-MOA53

24. OGLE 2005-BLG-071 Udalski et al. 2005 The Star: BASED ON GALACTIC MODEL M = 0.46 M סּ d = 3300 pc I-mag = 19.5 The Planet: M = 3.5 M Jup a = 3.6 AU

25. OGLE-06-109L The Star: M = 0.5 M סּ d = 1490 pc I-mag = 17.17 The Planets: M 1 = 0.71 M Jup a 1 = 2.3 AU M 2 = 0.27 M Jup a 2 =4.6 AU Gaudi et al. 2008, Science, 319, 927 Features 1,2,3,5 are caused by Saturn mass planet near Einstein radius. Feature 4 by another Jovian planet

26. Fig. 1.—Top: Data and best-fit model for OGLE-2005-BLG-169. Bottom: Difference between this model and a single-lens model with the same (t0, u0, tE, ρ). It displays the classical form of a caustic entrance/exit that is often seen in binary microlensing events, where the amplitudes and timescales are several orders of magnitude larger than seen here. MDM data trace the characteristic slope change at the caustic exit (Δt = 0.092) extremely well, while the entrance is tracked by a single point (Δt = −0.1427). The dashed line indicates the time t0. Inset: Source path through the caustic geometry. The source size ρ is indicated. From The Astrophysical Journal Letters 644(1):L37–L40. © 2006 by The American Astronomical Society. For permission to reuse, contact journalpermissions@press.uchicago.edu. OGLE-2005-BLG-169 The Star: M = 0.49 M סּ d = 2700 pc I-mag = 20.4 The Planet: M = 0.04 M J a = 2.8 AU

27. Microlensing planet detection of a Super Earth? OGLE-2005-BLG-390 Mass = 2.80 – 10 M earth a = 2.0 – 4.1 AU Best binary source q = 7.6 x 10 –5 Ratio between planet and star

28. MOA-2007-BLG-192-L The Star (brown dwarf): M = 0.06 M סּ d = 1000 pc J-mag = 19.6 The Planet: M = 3.3 M earth a = 0.62 AU Is it or isn‘t it a Super Earth? Best fit stellar binary

29. OGLE-2007-BLG-368

30. Mass star ~ 0.2 M sun Mass planet ~ 2.6 M Jupiter

31. To get the mass of the host star one must once again rely on statistics including a galactic model of the distribution of stars in the galaxy Red line: constraints from galactic model Black: constraints from observations with the Very Large Telescope Stellar mass ranges from 0.05 M sun (brown dwarf) to 0.2 M sun (star) M planet = 0.07 – 0.49 M Jupiter Semi-major axis = 1.1 – 2.7 AU Both at only the 90% confidence level.

32. PlanetMass (M J ) Period (yrs) a (AU) eM * (M sun ) D star (pcs) OGLE235-MOA53 b~2.6~15~5?0.635200 OGLE-05-071L b ~3.5~10~3.6?0.643300 OGLE-05-169L b0.04~9 ~2.8?0.492700 OGLE-05-390L b0.017~9.6~2.1?0.226500 MOA-2007-BLG-192-L b 0.01~20.62?0.061000 OGLE-06-109L b0.71~52.3?0.51490 OGLE-06-109L c0.27~144.60.110.51490 MOA-2007-BLG-400-L b0.9-0.50.356000 OGLE-2007-BLG-368L b0.07-3.3 MOA-2008-BLG-310-L b0.23-1.250.67>6000 MOA-2008-BLG-387-L b2.6-1.83.60.19~5700 Microlensing Planets

33. Microlensing has discovered 4-5 cold Neptunes/Superearths Neptune-mass planets beyond the snowline are at least 3 times more common than for Jupiter- mass planets But….this is based on small number statistics

34. No bias for nearby stars, planets around solar-type stars Sensitive to Earth-mass planets using ground-based observations: one of few methods that can do this Most sensitive for planets in the „lensing zone“, 0.6 < a < 2 AU for stars in the bulge. This is the habitable zone! Can get good statistics on Earth mass planets in the habitable zone of stars Multiple systems can be detected at the same time Detection of free floating planets possible The Advantages of Microlensing Searches Microlensing is complementary to other techniques

35. Fig. 3.— Exoplanet discovery potential and detections as functions of planet mass and semimajor axis. Potential is shown for current ground-based RV (yellow) and, very approximately, microlensing (red) experiments, as well as future space-based transit (cyan), astrometric (green), and microlensing (peach) missions. Planets discovered using the transit (blue), RV (black), and microlensing (magenta) techniques are shown as individual points, with OGLE-2005-BLG-169Lb displayed as an open symbol. Solar system planets are indicated by their initials for comparison. From The Astrophysical Journal Letters 644(1):L37–L40. © 2006 by The American Astronomical Society. For permission to reuse, contact journalpermissions@press.uchicago.edu.

36. Probability of lensing events small but overcome by looking at lots of stars One time event, no possibility to confirm, or improve measurements Duration of events is hours to days. Need coordinated observations from many observatories Planet hosting star is distant: Detailed studies of the host star very dfficult Precise orbital parameters of the planet not possible Light curves are complex: only one crossing of the caustic. No unique solution and often a non-planet can also model the light curves Final masses of planet and host stars rely on galactic models and statistics and are poorly known Future characterization studies of the planet are impossible The Disadvantages of Microlensing Searches

37. 2. The Timing Method

38. If you have a very stable “clock” that sends a signal with a constant pulse rate and the capability to measure the time of arrival (TOA) of the signal with very high precision  Search for systematic deviations in the TOAs that indicate different light travel times due to orbital motion The Technique:

39. time Due to the orbital motion the distance the Earth changes. This causes differences in the light travel time Timing Variations: Change in arrival time = a p m p sini M*cM*c a p, m p = semimajor axis, mass of planet time Don’t forget to take into account your own motion!!!

40. A Pulsar: a very stable astronomical clock! Rotation periods of pulsars < 10 second The fastest rotators are millisecond pulsars: PSR1257+12: P = 0.00621853193177 +/- 0.00000000000001 s radiation Strong magnetic field Acts like a cosmic lighthouse

41. The (Really) First Exoplanets: in 1992 Arecibo Radio-telescope

42. 98 d orbit removed, 66 d orbit remains 66 d orbit removed, 98 d orbit remains

44. PSR 1257+12 system: Planet A: M = 0.02 M_Earth P = 25.3 d ; a = 0.19 AU Planet B: M = 4.3 M_Earth P = 66.5 d ; a = 0.36 AU Planet C: M = 3.9 M_Earth P = 98.2 d ; a = 0.46 AU fourth companion with very low mass and P~3.5 yrs Interaction between B & C Confirms the planets and Establishes true masses!

45. Other applications of the timing method: Stably pulsating white dwarfs (P~200s) Pulsating sdB stars (P~500s) Eclipse timing Transit time variations NN Ser eclipses Kepler-9 transits

46. Timing Method Summary: First successful detection technique! Requires a suitable target (clock) Lack of large sample => not efficient In best case (very short periods) is sensitive to Earth-mass planets