10.30 k5 d sullivan

Gravitational Microlensing and

Free Floating Planets

Denis J SullivanVictoria University of Wellington(and the MOA collaboration)

October 18, 2011

Gravitational lensing

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■ In Einstein’s theory of gravity (general relativity) light travels inwell-defined curved paths in a gravitational field.


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■ This can lead to “lensing” (mirage) effects (gravitational lensing)when massive objects are precisely aligned.


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■ 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.


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■ Applied to events involving stars in our Galaxy the phenomenon iscalled gravitational microlensing.


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■ 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

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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

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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

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(a) No gravitational field:


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(b) Deflected light paths in a gravitational field:


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(b) Deflected light paths in a gravitational field:

(c) Deflected light ray seen by observer:

Weak gravitational field approximation

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α =2RS

bwhere RS =

2GM

c2(Schwarzschild radius for M)

and b is the light ray impact parameter

Einstein ring image: perfect alignment

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When source, lensing mass and the observer are in perfect alignment anEinstein ring image is formed

Einstein ring image: perfect alignment

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The Einstein ring radius

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■ 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.


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θE =

√

2RS

Dwhere D =

(

DL

DS −DL

)

DS


■ For events in our Galaxy with source stars at the Galactic centre,D ∼ DS ∼ 8.5 kpc ∼ 3.9× 1019m


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θE =

√

2RS

Dwhere D =

(

DL

DS −DL

)

DS



■ For stellar masses θE ∼ milliarcseconds (stellar disks ∼ µarcsec) – pointlens a good model (but often not so with binary lenses).


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θE =

√

2RS

Dwhere D =

(

DL

DS −DL

)

DS



■ 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

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Gravitational lensing: two images

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Gravitational lensing: two distorted images

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Gravitational lensing: two distorted images

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Resolving images at galactic distances

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Microlensing images & flux changes

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■ 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

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A(t) =u2(t) + 2

u(t)√

u2(t) + 4where u2(t) = u20 +

(

t− t0

tE

)2

An actual microlensing light curve

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Lensing by multiple lenses (an aside)

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■ 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

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■ 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

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The MOA 1.8m telescope at Mt John

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MOA Camera III images: ten 4k×2k CCD chips

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MOA Camera III images: ten 4k×2k CCD chips

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digitized sky survey - sparse field

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Magellan telescope field of view

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Difference image analysis (DIA)

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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

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■ 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

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Microlensing event distribution

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The MOA microlensing free-floating planet sample

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■ 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.


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Technology

10.30 k5 d sullivan