The document describes research by the MOA collaboration that detected evidence of free-floating planetary mass objects using gravitational microlensing. They analyzed 1000 microlensing events, identifying 10 with extremely short durations (tE < 2 days) indicating planetary masses. Follow-up analysis by the OGLE collaboration confirmed 7 of these 10 events, providing strong evidence for an unbound or distant population of planetary mass objects.

1. Gravitational Microlensing and
Free Floating Planets
Denis J Sullivan
Victoria University of Wellington
(and the MOA collaboration)
October 18, 2011

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. 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. 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. 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. 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. The MOA collaboration: free floating planets
This presentation will describe work published by the MOA collaboration
earlier this year in Nature:
“Unbound or distant planetary mass population detected by gravitational
microlensing”
T. Sumi, . . . I.A. Bond, . . . D.J. Sullivan . . . (MOA) and . . . (OGLE)
3 / 39

8. The MOA collaboration: free floating planets
This presentation will describe work published by the MOA collaboration
earlier this year in Nature:
“Unbound or distant planetary mass population detected by gravitational
microlensing”
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. Light path bending in a gravitational field
(a) No gravitational field:
4 / 39

10. Light path bending in a gravitational field
(a) No gravitational field:
(b) Deflected light paths in a gravitational field:
4 / 39

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. Weak gravitational field approximation
2RS 2GM
α= where RS = (Schwarzschild radius for M)
b c2
and b is the light ray impact parameter
5 / 39

13. Einstein ring image: perfect alignment
When source, lensing mass and the observer are in perfect alignment an
Einstein ring image is formed
6 / 39

14. Einstein ring image: perfect alignment
7 / 39

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. 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. 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. 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. Gravitational lensing: two images
9 / 39

20. Gravitational lensing: two images
10 / 39

21. Gravitational lensing: two distorted images
11 / 39

22. Gravitational lensing: two distorted images
12 / 39

23. Resolving images at galactic distances
13 / 39

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. 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. An actual microlensing light curve
16 / 39

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. 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. The MOA 1.8 m telescope at Mt John
19 / 39

30. The MOA 1.8 m telescope at Mt John
20 / 39

31. MOA Camera III images: ten 4k×2k CCD chips
21 / 39

32. MOA Camera III images: ten 4k×2k CCD chips
22 / 39

33. digitized sky survey - sparse field
23 / 39

34. Magellan telescope field of view
24 / 39

35. Difference image analysis (DIA)
The detection of microlensing events in very dense star fields necessitates the
use 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. 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. Microlensing event 1
27 / 39

38. Microlensing event 2
28 / 39

39. Microlensing event 3
29 / 39

40. Microlensing event 4
30 / 39

41. Microlensing event 5
31 / 39

42. Microlensing event 6
32 / 39

43. Microlensing event 7
33 / 39

44. Microlensing event 8
34 / 39

45. Microlensing event 8
35 / 39

46. Microlensing event 9
36 / 39

47. Microlensing event distribution
37 / 39

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. Microlensing event 5
39 / 39