Estimating Planet Parameters from the - PowerPoint Presentation

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?Slide24
Slide25

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