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Plenary 2: D Sullivan
Citation preview
Gravitational Microlensing and
Free Floating Planets
Denis J SullivanVictoria University of Wellington(and the MOA collaboration)
October 18, 2011
Gravitational lensing
2 / 39
■ In Einstein’s theory of gravity (general relativity) light travels inwell-defined curved paths in a gravitational field.
Gravitational lensing
2 / 39
■ In Einstein’s theory of gravity (general relativity) light travels inwell-defined curved paths in a gravitational field.
■ This can lead to “lensing” (mirage) effects (gravitational lensing)when massive objects are precisely aligned.
Gravitational lensing
2 / 39
■ In Einstein’s theory of gravity (general relativity) light travels inwell-defined curved paths in a gravitational field.
■ This can lead to “lensing” (mirage) effects (gravitational lensing)when massive objects are precisely aligned.
■ In the 1930s Einstein predicted the formation of images and the netincrease in observed flux (from unresolved images) due to thealignment of stellar objects, but never thought such effects wouldbe observed.
Gravitational lensing
2 / 39
■ In Einstein’s theory of gravity (general relativity) light travels inwell-defined curved paths in a gravitational field.
■ This can lead to “lensing” (mirage) effects (gravitational lensing)when massive objects are precisely aligned.
■ In the 1930s Einstein predicted the formation of images and the netincrease in observed flux (from unresolved images) due to thealignment of stellar objects, but never thought such effects wouldbe observed.
■ Applied to events involving stars in our Galaxy the phenomenon iscalled gravitational microlensing.
Gravitational lensing
2 / 39
■ In Einstein’s theory of gravity (general relativity) light travels inwell-defined curved paths in a gravitational field.
■ This can lead to “lensing” (mirage) effects (gravitational lensing)when massive objects are precisely aligned.
■ In the 1930s Einstein predicted the formation of images and the netincrease in observed flux (from unresolved images) due to thealignment of stellar objects, but never thought such effects wouldbe observed.
■ Applied to events involving stars in our Galaxy the phenomenon iscalled gravitational microlensing.
■ I think it should be called gravitational millimiraging.
The MOA collaboration: free floating planets
3 / 39
This presentation will describe work published by the MOA collaborationearlier 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)
The MOA collaboration: free floating planets
3 / 39
This presentation will describe work published by the MOA collaborationearlier 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)
■ MOA (Microlensing Observations in Astrophysics) collaborationNZ and Japanese astronomers and astrophysicists
■ OGLE (Optical Gravitational lensing Experiment) collaborationPolish and US astronomers using telescope in Chile
Light path bending in a gravitational field
4 / 39
(a) No gravitational field:
Light path bending in a gravitational field
4 / 39
(a) No gravitational field:
(b) Deflected light paths in a gravitational field:
Light path bending in a gravitational field
4 / 39
(a) No gravitational field:
(b) Deflected light paths in a gravitational field:
(c) Deflected light ray seen by observer:
Weak gravitational field approximation
5 / 39
α =2RS
bwhere RS =
2GM
c2(Schwarzschild radius for M)
and b is the light ray impact parameter
Einstein ring image: perfect alignment
6 / 39
When source, lensing mass and the observer are in perfect alignment anEinstein ring image is formed
Einstein ring image: perfect alignment
7 / 39
The Einstein ring radius
8 / 39
■ The scale of gravitational microlensing is set by the angular radius of theEinstein ring θE which is given by
θE =
√
2RS
Dwhere D =
(
DL
DS −DL
)
DS
■ And D is an effective length scale for the distances involved and equalto the source distance for the symmetrical case.
The Einstein ring radius
8 / 39
■ The scale of gravitational microlensing is set by the angular radius of theEinstein ring θE which is given by
θE =
√
2RS
Dwhere D =
(
DL
DS −DL
)
DS
■ And D is an effective length scale for the distances involved and equalto the source distance for the symmetrical case.
■ For events in our Galaxy with source stars at the Galactic centre,D ∼ DS ∼ 8.5 kpc ∼ 3.9× 1019m
The Einstein ring radius
8 / 39
■ The scale of gravitational microlensing is set by the angular radius of theEinstein ring θE which is given by
θE =
√
2RS
Dwhere D =
(
DL
DS −DL
)
DS
■ And D is an effective length scale for the distances involved and equalto the source distance for the symmetrical case.
■ For events in our Galaxy with source stars at the Galactic centre,D ∼ DS ∼ 8.5 kpc ∼ 3.9× 1019m
■ For stellar masses θE ∼ milliarcseconds (stellar disks ∼ µarcsec) – pointlens a good model (but often not so with binary lenses).
The Einstein ring radius
8 / 39
■ The scale of gravitational microlensing is set by the angular radius of theEinstein ring θE which is given by
θE =
√
2RS
Dwhere D =
(
DL
DS −DL
)
DS
■ And D is an effective length scale for the distances involved and equalto the source distance for the symmetrical case.
■ For events in our Galaxy with source stars at the Galactic centre,D ∼ DS ∼ 8.5 kpc ∼ 3.9× 1019m
■ For stellar masses θE ∼ milliarcseconds (stellar disks ∼ µarcsec) – pointlens a good model (but often not so with binary lenses).
■ For a background galaxy lensed by a foreground galaxy θE ∼ arcseconds.
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
14 / 39
■ For a given source position u, the angular positions θ of the two imagesare given by the solution of the quadratic equation
θ = u+1
θ
where u and θ are in units of the angular Einstein radius
■ The light intensity increase due to viewing the unresolved distortedimages is
A(t) =u2(t) + 2
u(t)√
u2(t) + 4
And if the relative source lens motion can be modelled by linear motionthen the time-dependence of u(t) takes the form
u2(t) = u20 +
(
t− t0
tE
)2
Microlensing: light intensity vs time
15 / 39
A(t) =u2(t) + 2
u(t)√
u2(t) + 4where u2(t) = u20 +
(
t− t0
tE
)2
An actual microlensing light curve
16 / 39
Lensing by multiple lenses (an aside)
17 / 39
■ The lensing equation for N lensing masses in the unknown (complex)image position z̄ is:
z− ω −
N∑
k=1
ǫk
Dk
= 0 where Dk =N∑
j=1
ǫj
z− rj+ (ω̄ − r̄k)
■ For two lensing masses this looks like:
z− ω−
ǫ1ǫ1
z− r1+
ǫ2
z− r2+ (ω̄ − r̄1)
−
ǫ2ǫ1
z− r1+
ǫ2
z− r2+ (ω̄ − r̄2)
= 0
And after some algebra get a 5th order polynomial in the complexvariable z
■ Lenses with 3, 4, 5, . . . masses yield polynomials of order 10, 17, 26, . . .
Microlensing: light intensity vs time
18 / 39
■ Obtain 3 parameters from fitting a single lens microlensinglightcurve: u0, t0, and tE .
■ Only the Einstein crossing time tE = θE/vT contains interestingphysical information about the lens mass M .
■ But note
θE =
√
2RS
D=
√
4GM(DS −DL)
c2DSDL
■ Hence to extract a value for M requires some estimates of therelative transverse velocities and the lens, source distances.
The MOA 1.8m telescope at Mt John
19 / 39
The MOA 1.8m 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)
25 / 39
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.
� �
The MOA microlensing free-floating planet sample
26 / 39
■ 1000 single lens microlensing events from 2006 – 2007 observing season
■ 474 events satisfied strict selection criteria – no contamination frompossible background effects
1. Cosmic-ray hits2. Fast-moving objects3. Cataclysmic variables4. Background supernovae5. Binary microlensing events6. Microlensing by high-velocity stars and Galactic-halo
stellar-remnants
■ 10 of these events had tE < 2 days −→ planetary-mass lenses
■ 7 of the 10 events with tE < 2 days confirmed by OGLE collaborationdata (with an eight-year) baseline
■ 6 events had OGLE data that agreed with MOA predictions.
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
38 / 39
■ 1000 single lens microlensing events from 2006 – 2007 observing season
■ 474 events satisfied strict selection criteria – no contamination frompossible background effects
1. Cosmic-ray hits2. Fast-moving objects3. Cataclysmic variables4. Background supernovae5. Binary microlensing events6. Microlensing by high-velocity stars and Galactic-halo
stellar-remnants
■ 10 of these events had tE < 2 days −→ planetary-mass lenses
■ 7 of the 10 events with tE < 2 days confirmed by OGLE collaborationdata (with an eight-year baseline).
■ 6 events had OGLE data that agreed with MOA predictions.
Microlensing event 5
39 / 39