Gravitational Microlensing and    Free Floating Planets              Denis J Sullivan     Victoria University of Wellingto...
Gravitational lensing  s   In Einstein’s theory of gravity (general relativity) light travels in      well-defined curved p...
Gravitational lensing  s   In Einstein’s theory of gravity (general relativity) light travels in      well-defined curved p...
Gravitational lensing  s   In Einstein’s theory of gravity (general relativity) light travels in      well-defined curved p...
Gravitational lensing  s   In Einstein’s theory of gravity (general relativity) light travels in      well-defined curved p...
Gravitational lensing  s   In Einstein’s theory of gravity (general relativity) light travels in      well-defined curved p...
The MOA collaboration: free floating planetsThis presentation will describe work published by the MOA collaborationearlier ...
The MOA collaboration: free floating planetsThis presentation will describe work published by the MOA collaborationearlier ...
Light path bending in a gravitational field(a) No gravitational field:                                             4 / 39
Light path bending in a gravitational field(a) No gravitational field:(b) Deflected light paths in a gravitational field:     ...
Light path bending in a gravitational field(a) No gravitational field:(b) Deflected light paths in a gravitational field:(c) D...
Weak gravitational field approximation           2RS                    2GM      α=            where RS =            (Schwa...
Einstein ring image: perfect alignmentWhen source, lensing mass and the observer are in perfect alignment anEinstein ring ...
Einstein ring image: perfect alignment                                         7 / 39
The Einstein ring radius  s   The scale of gravitational microlensing is set by the angular radius of the      Einstein ri...
The Einstein ring radius  s   The scale of gravitational microlensing is set by the angular radius of the      Einstein ri...
The Einstein ring radius  s   The scale of gravitational microlensing is set by the angular radius of the      Einstein ri...
The Einstein ring radius  s   The scale of gravitational microlensing is set by the angular radius of the      Einstein ri...
Gravitational lensing: two images                                    9 / 39
Gravitational lensing: two images                                    10 / 39
Gravitational lensing: two distorted images                                              11 / 39
Gravitational lensing: two distorted images                                              12 / 39
Resolving images at galactic distances                                         13 / 39
Microlensing images & flux changes  s   For a given source position u, the angular positions θ of the two images      are g...
Microlensing: light intensity vs time                                                                   2                 ...
An actual microlensing light curve                                     16 / 39
Lensing by multiple lenses (an aside)  s   The lensing equation for N lensing masses in the unknown (complex)      image p...
Microlensing: light intensity vs time  s   Obtain 3 parameters from fitting a single lens microlensing      lightcurve: u0 ...
The MOA 1.8 m telescope at Mt John                                     19 / 39
The MOA 1.8 m telescope at Mt John                                     20 / 39
MOA Camera III images: ten 4k×2k CCD chips                                             21 / 39
MOA Camera III images: ten 4k×2k CCD chips                                             22 / 39
digitized sky survey - sparse field                                     23 / 39
Magellan telescope field of view                                  24 / 39
Difference image analysis (DIA)The detection of microlensing events in very dense star fields necessitates theuse of differen...
The MOA microlensing free-floating planet sample  s   1000 single lens microlensing events from 2006 – 2007 observing seaso...
Microlensing event 1                       27 / 39
Microlensing event 2                       28 / 39
Microlensing event 3                       29 / 39
Microlensing event 4                       30 / 39
Microlensing event 5                       31 / 39
Microlensing event 6                       32 / 39
Microlensing event 7                       33 / 39
Microlensing event 8                       34 / 39
Microlensing event 8                       35 / 39
Microlensing event 9                       36 / 39
Microlensing event distribution                                  37 / 39
The MOA microlensing free-floating planet sample  s   1000 single lens microlensing events from 2006 – 2007 observing seaso...
Microlensing event 5                       39 / 39
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10.30 k5 d sullivan

  1. 1. Gravitational Microlensing and Free Floating Planets Denis J Sullivan Victoria University of Wellington (and the MOA collaboration) October 18, 2011
  2. 2. Gravitational lensing s In Einstein’s theory of gravity (general relativity) light travels in well-defined curved paths in a gravitational field. 2 / 39
  3. 3. Gravitational lensing s In Einstein’s theory of gravity (general relativity) light travels in well-defined curved paths in a gravitational field. s This can lead to “lensing” (mirage) effects (gravitational lensing) when massive objects are precisely aligned. 2 / 39
  4. 4. Gravitational lensing s In Einstein’s theory of gravity (general relativity) light travels in well-defined curved paths in a gravitational field. s This can lead to “lensing” (mirage) effects (gravitational lensing) when massive objects are precisely aligned. s In the 1930s Einstein predicted the formation of images and the net increase in observed flux (from unresolved images) due to the alignment of stellar objects, but never thought such effects would be observed. 2 / 39
  5. 5. Gravitational lensing s In Einstein’s theory of gravity (general relativity) light travels in well-defined curved paths in a gravitational field. s This can lead to “lensing” (mirage) effects (gravitational lensing) when massive objects are precisely aligned. s In the 1930s Einstein predicted the formation of images and the net increase in observed flux (from unresolved images) due to the alignment of stellar objects, but never thought such effects would be observed. s Applied to events involving stars in our Galaxy the phenomenon is called gravitational microlensing. 2 / 39
  6. 6. Gravitational lensing s In Einstein’s theory of gravity (general relativity) light travels in well-defined curved paths in a gravitational field. s This can lead to “lensing” (mirage) effects (gravitational lensing) when massive objects are precisely aligned. s In the 1930s Einstein predicted the formation of images and the net increase in observed flux (from unresolved images) due to the alignment of stellar objects, but never thought such effects would be observed. s Applied to events involving stars in our Galaxy the phenomenon is called gravitational microlensing. s I think it should be called gravitational millimiraging. 2 / 39
  7. 7. The MOA collaboration: free floating planetsThis presentation will describe work published by the MOA collaborationearlier this year in Nature:“Unbound or distant planetary mass population detected by gravitationalmicrolensing”T. Sumi, . . . I.A. Bond, . . . D.J. Sullivan . . . (MOA) and . . . (OGLE) 3 / 39
  8. 8. The MOA collaboration: free floating planetsThis presentation will describe work published by the MOA collaborationearlier this year in Nature:“Unbound or distant planetary mass population detected by gravitationalmicrolensing”T. Sumi, . . . I.A. Bond, . . . D.J. Sullivan . . . (MOA) and . . . (OGLE) s MOA (Microlensing Observations in Astrophysics) collaboration NZ and Japanese astronomers and astrophysicists s OGLE (Optical Gravitational lensing Experiment) collaboration Polish and US astronomers using telescope in Chile 3 / 39
  9. 9. Light path bending in a gravitational field(a) No gravitational field: 4 / 39
  10. 10. Light path bending in a gravitational field(a) No gravitational field:(b) Deflected light paths in a gravitational field: 4 / 39
  11. 11. Light path bending in a gravitational field(a) No gravitational field:(b) Deflected light paths in a gravitational field:(c) Deflected light ray seen by observer: 4 / 39
  12. 12. Weak gravitational field approximation 2RS 2GM α= where RS = (Schwarzschild radius for M) b c2and b is the light ray impact parameter 5 / 39
  13. 13. Einstein ring image: perfect alignmentWhen source, lensing mass and the observer are in perfect alignment anEinstein ring image is formed 6 / 39
  14. 14. Einstein ring image: perfect alignment 7 / 39
  15. 15. The Einstein ring radius s The scale of gravitational microlensing is set by the angular radius of the Einstein ring θE which is given by 2RS DL θE = where D= DS D DS − DL s And D is an effective length scale for the distances involved and equal to the source distance for the symmetrical case. 8 / 39
  16. 16. The Einstein ring radius s The scale of gravitational microlensing is set by the angular radius of the Einstein ring θE which is given by 2RS DL θE = where D= DS D DS − DL s And D is an effective length scale for the distances involved and equal to the source distance for the symmetrical case. s For events in our Galaxy with source stars at the Galactic centre, D ∼ DS ∼ 8.5 kpc ∼ 3.9 × 1019 m 8 / 39
  17. 17. The Einstein ring radius s The scale of gravitational microlensing is set by the angular radius of the Einstein ring θE which is given by 2RS DL θE = where D= DS D DS − DL s And D is an effective length scale for the distances involved and equal to the source distance for the symmetrical case. s For events in our Galaxy with source stars at the Galactic centre, D ∼ DS ∼ 8.5 kpc ∼ 3.9 × 1019 m s For stellar masses θE ∼ milliarcseconds (stellar disks ∼ µarcsec) – point lens a good model (but often not so with binary lenses). 8 / 39
  18. 18. The Einstein ring radius s The scale of gravitational microlensing is set by the angular radius of the Einstein ring θE which is given by 2RS DL θE = where D= DS D DS − DL s And D is an effective length scale for the distances involved and equal to the source distance for the symmetrical case. s For events in our Galaxy with source stars at the Galactic centre, D ∼ DS ∼ 8.5 kpc ∼ 3.9 × 1019 m s For stellar masses θE ∼ milliarcseconds (stellar disks ∼ µarcsec) – point lens a good model (but often not so with binary lenses). s For a background galaxy lensed by a foreground galaxy θE ∼ arcseconds. 8 / 39
  19. 19. Gravitational lensing: two images 9 / 39
  20. 20. Gravitational lensing: two images 10 / 39
  21. 21. Gravitational lensing: two distorted images 11 / 39
  22. 22. Gravitational lensing: two distorted images 12 / 39
  23. 23. Resolving images at galactic distances 13 / 39
  24. 24. Microlensing images & flux changes s For a given source position u, the angular positions θ of the two images are given by the solution of the quadratic equation 1 θ =u+ θ where u and θ are in units of the angular Einstein radius s The light intensity increase due to viewing the unresolved distorted images is u2 (t) + 2 A(t) = u(t) u2 (t) + 4 And if the relative source lens motion can be modelled by linear motion then the time-dependence of u(t) takes the form 2 t − t0 u2 (t) = u2 + 0 tE 14 / 39
  25. 25. Microlensing: light intensity vs time 2 u2 (t) + 2 t − t0 A(t) = where u2 (t) = u2 + 0 u(t) u2 (t) + 4 tE 15 / 39
  26. 26. An actual microlensing light curve 16 / 39
  27. 27. Lensing by multiple lenses (an aside) s The lensing equation for N lensing masses in the unknown (complex) image position ¯ is: z N N k j z−ω− =0 where Dk = + (¯ − ¯k ) ω r Dk z − rj k=1 j=1 s For two lensing masses this looks like: 1 2 z−ω− 1 2 − 1 2 =0 + + (¯ − ¯1 ) ω r + + (¯ − ¯2 ) ω r z − r1 z − r2 z − r1 z − r2 And after some algebra get a 5th order polynomial in the complex variable z s Lenses with 3, 4, 5, . . . masses yield polynomials of order 10, 17, 26, . . . 17 / 39
  28. 28. Microlensing: light intensity vs time s Obtain 3 parameters from fitting a single lens microlensing lightcurve: u0 , t0 , and tE . s Only the Einstein crossing time tE = θE /vT contains interesting physical information about the lens mass M . s But note 2RS 4GM (DS − DL ) θE = = D c 2 DS DL s Hence to extract a value for M requires some estimates of the relative transverse velocities and the lens, source distances. 18 / 39
  29. 29. The MOA 1.8 m telescope at Mt John 19 / 39
  30. 30. The MOA 1.8 m telescope at Mt John 20 / 39
  31. 31. MOA Camera III images: ten 4k×2k CCD chips 21 / 39
  32. 32. MOA Camera III images: ten 4k×2k CCD chips 22 / 39
  33. 33. digitized sky survey - sparse field 23 / 39
  34. 34. Magellan telescope field of view 24 / 39
  35. 35. Difference image analysis (DIA)The detection of microlensing events in very dense star fields necessitates theuse of difference image analysis to accurately identify the brightness variations.The CCD frame on the right is the difference between the other two frames,duly allowing for seeing differences. 25 / 39
  36. 36. The MOA microlensing free-floating planet sample s 1000 single lens microlensing events from 2006 – 2007 observing season s 474 events satisfied strict selection criteria – no contamination from possible background effects 1. Cosmic-ray hits 2. Fast-moving objects 3. Cataclysmic variables 4. Background supernovae 5. Binary microlensing events 6. Microlensing by high-velocity stars and Galactic-halo stellar-remnants s 10 of these events had tE < 2 days −→ planetary-mass lenses s 7 of the 10 events with tE < 2 days confirmed by OGLE collaboration data (with an eight-year) baseline s 6 events had OGLE data that agreed with MOA predictions. 26 / 39
  37. 37. Microlensing event 1 27 / 39
  38. 38. Microlensing event 2 28 / 39
  39. 39. Microlensing event 3 29 / 39
  40. 40. Microlensing event 4 30 / 39
  41. 41. Microlensing event 5 31 / 39
  42. 42. Microlensing event 6 32 / 39
  43. 43. Microlensing event 7 33 / 39
  44. 44. Microlensing event 8 34 / 39
  45. 45. Microlensing event 8 35 / 39
  46. 46. Microlensing event 9 36 / 39
  47. 47. Microlensing event distribution 37 / 39
  48. 48. The MOA microlensing free-floating planet sample s 1000 single lens microlensing events from 2006 – 2007 observing season s 474 events satisfied strict selection criteria – no contamination from possible background effects 1. Cosmic-ray hits 2. Fast-moving objects 3. Cataclysmic variables 4. Background supernovae 5. Binary microlensing events 6. Microlensing by high-velocity stars and Galactic-halo stellar-remnants s 10 of these events had tE < 2 days −→ planetary-mass lenses s 7 of the 10 events with tE < 2 days confirmed by OGLE collaboration data (with an eight-year baseline). s 6 events had OGLE data that agreed with MOA predictions. 38 / 39
  49. 49. Microlensing event 5 39 / 39

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