The Rossiter-McLaughlin Effect

B. Scott GaudiThe Ohio State University

(special thanks to Josh Winn)

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Gaudi &Winn (2007)

What is theRossiter-McLaughlin

Effect?

What do we measure?

V (t) =VO(t)+V

R(t)+V

0

VO (t) = KO{cos[ f (t)+!]+ ecos!}

What do we measure?

Doppler

KO=2!G

P

"

#$

%

&'

1/3msin i

(M +m)2/3(1( e2 )(1/2

KO

V (t) =VO(t)+V

R(t)+V

0

What do we measure?

“Anomalous RV”

KO

What exactly is the RM effect?

•Change in line shape

•Not a Doppler shift

•Cross-correlation measures linecentroids

•Some methods attempt to correctfor line shape variations

V (x, y) = xV*sin I

VR =V* sin IxS(x, y)dxdy!!S(x, y)dxdy!!

xy

Centroid approximation

VR=V

*sin I

! 2

1"! 2g(t; x

p, y

p,!,u

1,...) # K

Rg(t)

! =r

R

Ohta et al 2005

Gimenez 2006

No limb-darkening, complete transit

g(t) = x(t) = ! cos" # bsin"

! =t " t

tra

Twhere

b

!

VR= K

Rg(t)

~ KR t

rot! t

tra

T~ b tan"

KR=V

*sin I

! 2

1"! 2

Measuring spin-orbit alignment

Ohta, Taruya, & Suto 2005; Gaudi & Winn 2007

ParametersSpecified by the photometric transit:

•Duration•Ingress/Egress Time•Impact Parameter•Limb Darkening•Planet/Star Radius Ratio

Additional Parameters Required for RM Effect•λ (Spin-Orbit alignment)•V*sinI (can also be constrained from spectrum)

Total S/NS

N! QR

1

3(1" 4b2 )cos2 # + b2$% &'

1/2

where

QR=

N

!K

R

S

N! 50

Measurement Uncertainties

!" # QR

$1 (1$ b2)cos

2 " + 3b2 sin2 "

b2(1$ b2 )

%

&'

(

)*

1/2

!V* sin I

V*sin I

" QR

#1 (1# b2)sin

2 $ + 3b2 cos2 $

b2(1# b2 )

%

&'

(

)*

1/2

Useful for estimating expected uncertainties

Gaudi &Winn (2007)

Central Transits are bad:

!

VR= K

R(! cos" # bsin")$ [K

Rcos"]!

λ is degenerate with V*sinI

Why Measure theRossiter-McLaughlin

Effect?

Spin-orbit alignment for exoplanets

Spin-orbit alignment for exoplanets• Solar system: alignment is within ~10o

Spin-orbit alignment for exoplanets• Solar system: alignment is within ~10o

• How common or unusual is this?

Spin-orbit alignment for exoplanets• Solar system: alignment is within ~10o

• How common or unusual is this?• Theoretical reasons to expect

misalignment:

Spin-orbit alignment for exoplanets• Solar system: alignment is within ~10o

• How common or unusual is this?• Theoretical reasons to expect

misalignment:– Whatever perturbs e may also perturb I

Spin-orbit alignment for exoplanets• Solar system: alignment is within ~10o

• How common or unusual is this?• Theoretical reasons to expect

misalignment:– Whatever perturbs e may also perturb I– Migration (disk interaction v. scattering, Kozai)

Chatterjee, Ford,& Rasio (2007)

Planet-Planet Scattering

Kozai Oscillations with Tides

Wu et al (2007)

Fabrycky&Tremaine (2007)

Kozai Oscillations with Tides

Spin-orbit alignment for exoplanets• Solar system: alignment is within ~10o

• How common or unusual is this?• Theoretical reasons to expect

misalignment:– Whatever perturbs e may also perturb I– Migration (disk interaction v. scattering, Kozai)

• Fundamental measurement

Measurements of theRossiter-McLaughlin

Effect

R. A. Rossiter(1896-1977)

R. A. Rossiter(1896-1977)

β Lyrae: Rossiter 1924, ApJ, 60, 15

R. A. Rossiter(1896-1977)

β Lyrae: Rossiter 1924, ApJ, 60, 15

Algol: McLaughlin 1924,ApJ, 60, 22

Queloz et al 2000

Winn, Holman,Henry, et al.

(2007)

λ = -1.1 +/– 1.4 deg (RM effect)

sin istar = [v sin istar] / (2πR/P )ψ < 27 deg (95% conf.)

λ

Ωstar

Ωorbit

ψistar

Diagram by G. Laughlin

HD 147506 =HAT-P-2

Bakos et al. (2007)

HD 149026: λ= 12º ±14º (Wolf et al)

TrES-1: λ= 30º ±21º (Narita et al 2007)

Spin-orbit alignment for exoplanets

Spin-orbit alignment for exoplanets• Random alignments ruled out (>99.9% CL)

Spin-orbit alignment for exoplanets• Random alignments ruled out (>99.9% CL)• Tidal coplanarization takes too long

Spin-orbit alignment for exoplanets• Random alignments ruled out (>99.9% CL)• Tidal coplanarization takes too long

Hut 1981; Queloz et al. 2000; Winn et al. 2005

Spin-orbit alignment for exoplanets• Random alignments ruled out (>99.9% CL)• Tidal coplanarization takes too long

• Migration generally preserves spin-orbitalignment?

Hut 1981; Queloz et al. 2000; Winn et al. 2005

Confirming PlanetsRossiter-McLaughlin

Effect

RM Effect Amplitude

Doppler and RM amplitude of the same order for Hot Jupiters

Larger for less massive planets, or longer period planets

KR

KO

!P

2"Gm

#

$%

&

'(

1/3

V*sin I

! 0.3m

MJup

"

#$$

%

&''

(1/3

P

3 days

"

#$

%

&'

1/3

V* sin I

5 km/s

"

#$

%

&'

Earthlike Planet

Gaudi & Winn(2007)

Welsh et al(2004)

Confirming Kepler Detections

Gaudi &Winn (2007)