Microlensing (planet detection): theory and applications Shude Mao Jodrell Bank Centre for Astrophysics University of Manchester (& NAOC) 19/12/2009 @ KIAA
Outline What is (Galactic) microlensing? Basic theory Status and applications of microlensing planetary microlensing Future and challenges of planetary microlensing
Gravitational microlensing Image credit: NASA/ESA Light curve is symmetric, achromatic & nonrepeating (Paczynski 1986)
Basic theory r c GM r D D D s r d S ds 2 4, 1, 5 3 4 2 2 2 u r r u u u u E s Lens equation: Magnification:
r E Light curve I 0, A max, t E, t peak Degeneracy!
Optical depth: =ρ/m ~M independent of the mass function of lenses τ can be used to infer the overall mass distribution of our Galaxy Event rate and duration distribution Event rate ~10 events/million stars/year, low! The analysis of event time scale distribution offers a method to determine the lens mass function, independent of light.
Status of microlensing surveys QuickTime?and a TIFF (LZW) decompressor are needed to see this picture. Microlensing surveys (MACHO, EROS, OGLE, MOA) observe dense stellar fields such as Galactic centre, LMC, SMC, M31 Many thousands of events have been discovered; ~5500 in real-time, 800/yr (duration 1 day-> 4 years, A max : 1- >3000) It provides strong constraints (stellar population, proper motions, and optical depth maps) on the Galactic structure Stellar atmospheres and metallicities 2 arcmin
Structure of the Milky Way: schematic view Disk, bulge, dark matter halo, globular clusters, satellite galaxies Milky Way is the nearest galaxy, much remains to be understood How does it form? Total mass? Shape? Dark matter fraction within the solar circle?
Star number counts Gaussian density model: a:b:c=10:3.5:2.6 Bar angle ~25 degrees Fits are not perfect! QuickTime?and a decompressor are needed to see this picture. Optical depth density Proper motions & timescale distribution kinematics timescale mass function of lenses. Rattenbury, Mao et al. (2007)
Stellar atmospheres: metallicity QuickTime?and a decompressor are needed to see this picture. Cohen et al. (2009) [Lennon, Mao et al. (1996)] Statistical fluke or some other explanations? Microlensing can also be used to study stellar atmospheres for high magnfication events.
Planetary lensing: critical curves and caustics Caustics: point source positions with magnifications Their images form critical curves
Finding Planets via Microlensing q=0.002, d=1.1 Credit: Beaulieu & Cassan tp qt E te 20 d, M 0.3: Msun Mao & Paczynski (1991); Schneider & Weiss (1986); Gould & Loeb (1992); Bennett & Rhie (1996); Griest & Safizadeh (1996); Rattenbury et al. (2002) Deviation time scale: days for Jupiter, hours for 1 Earth mass Amplitude is not necessarily low! Subo s talk.
Microlensing Extrasolar planet example Beaulieu et al. (06) Lowest mass extrasolar planet (5.5 Earth mass) at the time of discovery around a normal star.
First microlensing multiple extrasolar planet Gaudi et al. (08) Planet-to-host mass ratio and separation well determined by modelling but host stellar mass uncertain If extra information is available, then planetary
What has microlensing told us about planets? Credit: D. Bennett Ida & Lin (2008) Microlensing can probe a different part of the parameter space Cold super-earths are common (Gould et al. 2007) 1/3 of 0.3 M stars have planets ~ 10 M, from 1.5-4 AU Small number statistics!
Future of microlensing extrasolar planet search Currently survey teams discover events, and followup teams intensely monitor selected events only limited number of events can be followed up Selected by humans In the short term, need an automated algorithm In the 5-10 year term, a network of >3 2m wide-field telescopes to search for 1 M planets (Gould et al. 2007; Beaulieu, Kerins, Mao et al. 2008) Each with a few square degrees, 15 minute cadence Can detect 6000 events per year ---> combine detection and follow-up partial nodes are (will be) in place (MOA-II, OGLE-
QuickTime?and a decompressor are needed to see this picture. Microlensing extrasolar planets from space A 1m class space satellite with ~ 1 square degree field of view Better PSF, no weather limitation Will be able to determine statistics of extrasolar planets down to 0.1 M at separaton > 0.3 AU Combined with Kepler, it will provide complete census Cost: $360 million Will combine well with Dark Energy missions Similar requirements: stable PSF, large FOV JDEM (US), or EUCLID (ESA Cosmic Vision, 2017) EUCLID
Challenges in extrasolar planet search How to best utilize the microlensing datasets for diverse applications? Efficient search of planets in future microlensing dataset in the complex parameter space Multiple planets? Effects of rotation (Penny, Mao et al.2009)? Statistical comparison with planet formation theories.
Principle of extrasolar planet discovery Timescale, t E ~ 20 d. Einstein radius ~ size of solar system Mao & Paczynski (1991) Presence of planets can perturb existing images Gould & Loeb (1992); Bennett & Rhie (1996); Griest & Safizadeh (1996); Rattenbury et al. (2002) also create an extra pair of bright images, induce more dramatic deviations
Properties of planetary microlensing Rate and deviation duration scale roughly ~ (mass ratio) 1/2 Planetary deviation lasts for days for 1M J planets, but hours for one M planet Deviation amplitude can be high even for 1 M planet Microlensing has sensitivity to low-mass planets between 0.6-1.6 Einstein radii free-floating planets (seen as single events lasting hours to day) multiple planets (OGLE-2006-BLG-109, Saturn/Jupiter analogues) Current mode of discovery: survey + followup A well-sampled light curve yields mass ratio and separation/einstein radius due to degeneracy When extra information ( E, lens light) is available, the planet mass (not only mass ratio) can be inferred directly
Third microlensing extrasolar planet OGLE-2005-BLG- 390Lb t E =11.5d, A max ~3 1 day deviation M p /M * ~8x10-5, mass ~ 5.5 M Beaulieu et al. (2006), Nature Lowest mass extrasolar planet around a normal star at the time of discovery!
Multiple-planets: Jupiter/Saturn analogues Gaudi et al. (2008) Both parallax and finite source size effects were determined M b =0.7M J, M c =0.3 M J, a b =2.3AU, a c =4.6 AU (10% error)
Planetary and binary microlensing Mao & Paczynski (1991) It is an excellent method to provide statistics for planets, but too far to allow direct imaging.