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Spectroscopic Transits
The Rossiter-McClaughlin Effect
2
1
4
3
+v
1
4
0
2
–v
3
The R-M effect occurs in eclipsing systems when the companion crosses in
front of the star. This creates a distortion in the normal radial velocity of the
star. This occurs at point 2 in the orbit.
The Rossiter-McLaughlin Effect in an
Eclipsing Binary
From Holger Lehmann
The effect was discovered in 1924 independently by Rossiter and
McClaughlin
Curves show Radial Velocity after
removing the binary orbital motion
The Rossiter-McLaughlin Effect is a
„Rotation Effect“ due to stellar rotation
Average rotational velocities
in main sequence stars
i is the inclination of the rotation axis
Spectral
Type
Vequator (km/s)
O5
190
B0
200
B5
210
A0
190
A5
160
F0
95
F5
25
G0
12
The Rossiter-McClaughlin Effect
–v
+v
0
As the companion cosses the star the
observed radial velocity goes from + to –
(as the planet moves towards you the star
is moving away). The companion covers
part of the star that is rotating towards
you. You see more possitive velocities
from the receeding portion of the star) you
thus see a displacement to + RV.
+v
–v
When the companion covers the
receeding portion of the star, you see
more negatve velocities of the star rotating
towards you. You thus see a displacement
to negative RV.
The Rossiter-McClaughlin Effect
What can the RM effect tell you?
1) The orbital inclination or impact parameter
a2
Planet
a
a2
The Rossiter-McClaughlin Effect
2) The direction of the orbit
Planet
b
The Rossiter-McClaughlin Effect
2) The alignment of the orbit
Planet
c
d
l
What can the RM effect tell you?
Are the spin axes aligned?
Orbital
plane
Summary of Rossiter-McClaughlin „Tracks“
Amplitude of the R-M effect:
ARV = 52.8 m s–1
(
Vs
5 km
s–1
)(
r 2
)
RJup
(
R
R‫סּ‬
–2
)
ARV is amplitude after removal of orbital mostion
Vs is rotational velocity of star in km s–1
r is radius of planet
R is stellar radius
Note:
1. The Magnitude of the R-M effect depends on the radius of the
planet and not its mass.
2. As with photometric transits the amplitude is proportional to the
ratio of the disk area of the planet and star.
3. The R-M effect is proportional to the rotational velocity of the star.
If the star has little rotation, it will not show a R-M effect.
HD 209458
l = –0.1 ± 2.4
deg
The first RM
measurements of
exoplanets showed
aligned systems
HD 189733
l = –1.4 ± 1.1
deg
HD 147506
Best candidate for misalignment is HD 147506 because of the high
eccentricity
On the Origin of the High Eccentricities
Two possible explanations for the high eccentricities seen in exoplanet
orbits:
• Scattering by multiple giant planets
• Kozai mechanism
If either mechanism is at work, then we should expect that planets in eccentric
orbits not have the spin axis aligned with the stellar rotation. This can be checked
with transiting planets in eccentric orbits
Winn et al. 2007: HD 147506b (alias HAT-P-2b)
Spin axes are aligned within 14 degrees (error of measurement). No
support for Kozai mechanism or scattering
What about HD 17156?
Narita et al. (2007) reported a large (62 ± 25 degree) misalignment
between planet orbit and star spin axes!
Cochran et al. 2008: l = 9.3 ± 9.3 degrees → No misalignment!
TrES-1
l = 30 ± 21 deg
XO-3-b
Hebrard et al. 2008
l = 70 degrees
Winn et al. (2009) recent R-M measurements for X0-3
l = 37 degrees
From PUBL ASTRON SOC PAC 121(884):1104-1111.
© 2009. The Astronomical Society of the Pacific. All rights reserved. Printed in
U.S.A.
For permission to reuse, contact [email protected]ess.uchicago.edu.
Fig. 3.— Relative radial velocity measurements made during transits of WASP-14. The symbols are as follows: Subaru
(circles), Keck (squares), Joshi et al. 2009 (triangles). Top panel: The Keplerian radial velocity has been subtracted, to
isolate the Rossiter-McLaughlin effect. The predicted times of ingress, midtransit, and egress are indicated by vertical
dotted lines. Middle panel: The residuals after subtracting the best-fitting model including both the Keplerian radial
velocity and the RM effect. Bottom panel: Subaru/HDS measurements of the standard star HD 127334 made on the
same night as the WASP-14 transit.
Fabricky & Winn, 2009, ApJ, 696, 1230
As of 2009 there was little strong evidence that exoplanet
orbital axes were misaligned with the stellar spin axes.
HAT-P7
l = 182 deg!
An misaligned planet in CoRoT-1b
HARPS data : F. Bouchy
Model fit: F. Pont
Lambda ~ 80 deg!
Distribution of spin-orbit axes
Red: retrograde
orbits
As of 2010
~30% of transiting planets are in misaligned
or retrograde orbits
l (deg)
35% of Short Period Exoplanets show significant misalignments
~10-20% of Short Period Exoplanets are in retrograde orbits
Basically all angles are covered
Summary
1. The Rossiter-McClaughlin effect can measure the
angle between the spin axis of the star and the orbital
axis of the planet.
2. The R-M technique cannot give you the planet mass
3. Exoplanets show all possible obliquity angles, but
most are aligned (even in eccentric orbits)
4. Implications for planet formation (problems for
migration theory)