Lightcurve 0 Choose your lightcurve a GLPlanet Assumptions a Gould amp Loeb planetary GLPlanet caustic crossing perturbation No parallax No blending Goal Estimate 7 Parameters of a 2L1S Model ID: 640286
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Slide1
Estimating Planet Parameters from the LightcurveSlide2
0. Choose your
lightcurve
(a
GLPlanet)
Assumptions:
a Gould & Loeb planetary (
GLPlanet
) caustic crossing
perturbation
No parallax
No blendingSlide3
Goal: Estimate 7 Parameters of a 2L1S Model
t
0
= time of closest approach b/w source and lensu0 = impact parametert
E
= Einstein timescale
s = planet-star separationq = planet-star mass ratioρ = source radiusα = angle of source trajectory
relative to Einstein ring sizeSlide4
Goal: Estimate 7 Parameters of a 2L1S Model
t
0
= time of closest approach b/w source and lensu0 = impact parametert
E
= Einstein timescale
s = planet-star separationq = planet-star mass ratioρ = source radiusα = angle of source trajectory
Parameters of the Stellar Event
Parameters of the Planet
Other ParametersSlide5
Lens
Einstein Ring
Source
Point Lens Parameters: t
0
, u
0
,
t
E
u
0
= impact parameter
t
0
time
@ u(t) = u
0
t
E
= Einstein timescale/Einstein crossing timeSlide6
Position of the Source: u(t)
u(t)
u
0Slide7
Planet Parameters: s, q, α
planet
s = separation (projected, as a fraction of the Einstein ring)
Binary axis
α = angle b/w binary axis and source trajectorySlide8
7th Parameter:
ρ
Source radius (scaled to the Einstein ring)Slide9
2 Observables: Time & MagnitudeSlide10
Relating Magnitude to Magnification
f
blend
= 0Slide11
Relating Magnification to TimeSlide12
1. Parameters of the Stellar Event: t
0
t
0
~
957Slide13
2. Parameters of the Stellar Event: u
0
0Slide14
2. Parameters of the Stellar Event: u
0
Δm
= 18.1-17.05 =
1.05
magnitudesSlide15
2. Parameters of the Stellar Event: u
0
How many magnitudes (
Δm) brighter does the event get? 1.05 magnitudes
What
magnification
(A) does that imply? 2.63
What is u0?
0.38Slide16
3. Parameters of the Stellar Event:
t
E
Use the same equations to find
t
E
.
1.
u1 = 1
A
1
= 1.34
2.
Δ
m = 0.3177Slide17
3. Parameters of the Stellar Event:
t
ESlide18
4. Parameters of the Planet: s
Where is the planet?
When is the planet?Slide19
4. Parameters of the Planet: s
Possible Planet Locations
The planet perturbs one of the images.
XSlide20
4. Parameters of the Planet: s
Where is the source at
t
planet
=
930.15
?Slide21
4. Parameters of the Planet: s
u
0Slide22
4. Parameters of the Planet: s
τ
u
=
0.605
y
+
=
1.35
y
-
=
0.742Slide23
4. Parameters of the Planet: s
Is this a major or a minor image perturbation?Slide24Slide25
Not a dip!Slide26
4. Parameters of the Planet: s
minor
s =
y
-
=
0.742
Dip!Slide27
5. Other Parameters:
α
Binary Axis
Source Trajectory
αSlide28
5
. Other Parameters:
α
u
0
α = -51.1
deg
=
-0.892 radSlide29
5
. Other Parameters:
α
α
Due to different geometric conventions, the correct value of α may be π/2 or π from the value you calculateSlide30
What’s left?
ρ
and q Slide31
3 regimes:
minor image
ρ
< caustic
major image
ρ
< caustic
major image
ρ
> caustic
distinct peaks
merged peaksSlide32
6. Major Image, ρ
>
caustic: ρ
Δ
t
= 2
t*
ρ = t* / t
E
Gould &
Gaucherel
1994Slide33
7. Major Image,
ρ
> caustic: q
Δ
m
p
ApA
p
= 2(
q
/
ρ
2
)
Gould &
Gaucherel
1994Slide34
6. Major Image, ρ
<
caustic:
ρ
Δ
t
=
2
t
*Slide35
7. Major Image, ρ
<
caustic: q
2 caustic crossings
α = 165
degSlide36
Han 2006
ApJ
638, 1080
Han 2006: Major Image CausticSlide37
7. Major Image, ρ
<
caustic: qSlide38
Minor Image,
ρ
< caustic
2 caustic crossings
TroughSlide39
6.
Minor
Image,
ρ < caustic:
ρ
2
t
*
~ 0.2 days
ρ
=
0.00175Slide40
7
.
Minor Image,
ρ < caustic: qSlide41
Han 2006
ApJ
638, 1080
Han 2006: Minor Image CausticSlide42
7
.
Minor Image,
ρ
< caustic:
q
q
~
0.00022
Δ
t
= 3.3 days
~ 0.0579