1. Spectroscopic Transits

2. The Rossiter-McClaughlin Effect2 4 1 3 +v 1 4 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.

3. The Rossiter-McLaughlin Effect in an Eclipsing Binary
From Holger Lehmann

4. The effect was discovered in 1924 independently by Rossiter and McClaughlin
Curves show Radial Velocity after removing the binary orbital motion

5. The Rossiter-McLaughlin Effect is a „Rotation Effect“ due to stellar rotation

6. Spectral Type Vequator (km/s) O5 190 B0 200 B5 210 A0 A5 160 F0 95 F5
Average rotational velocities in main sequence stars
Spectral Type
Vequator (km/s) O5
190 B0
200 B5
210 A0 A5
160 F0 95 F5 25 G0 12
i is the inclination of the rotation axis

7. The Rossiter-McClaughlin Effect–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. –v +v
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.

8. The Rossiter-McClaughlin Effect
What can the RM effect tell you?
1) The orbital inclination or impact parameter a a2
Planet

9. The Rossiter-McClaughlin Effect
2) The direction of the orbit
Planet b

10. The Rossiter-McClaughlin Effect
2) The alignment of the orbit c d
Planet

11. l What can the RM effect tell you? Are the spin axes aligned?
Orbital plane l
What can the RM effect tell you?
Are the spin axes aligned?

12. Summary of Rossiter-McClaughlin „Tracks“

13. ( ) ( ) ( ) Vs r RJup R Rסּ ARV = 52.8 m s–1
Amplitude of the R-M effect: Vs
5 km s–1 ( ) r
RJup ( ) 2 R Rסּ ( ) –2
ARV =
52.8 m s–1
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:
The Magnitude of the R-M effect depends on the radius of the planet and not its mass.
As with photometric transits the amplitude is proportional to the ratio of the disk area of the planet and star.
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.

14. HD
l = –0.1 ± 2.4 deg
The first RM measurements of exoplanets showed aligned systems

15. HD
l = –1.4 ± 1.1 deg

16. HD
Best candidate for misalignment is HD because of the high eccentricity

17. 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

18. 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 b (alias HAT-P-2b)
Spin axes are aligned within 14 degrees (error of measurement). No support for Kozai mechanism or scattering

19. What about HD 17156?
Narita et al. (2007) reported a large (62 ± 25 degree) misalignment between planet orbit and star spin axes!

20. Cochran et al. 2008: l = 9.3 ± 9.3 degrees → No misalignment!

21. TrES-1
l = 30 ± 21 deg

22. XO-3-b

23. Hebrard et al. 2008
l = 70 degrees

24. Winn et al. (2009) recent R-M measurements for X0-3
l = 37 degrees

25. From PUBL ASTRON SOC PAC 121(884):1104-1111. © 2009
From PUBL ASTRON SOC PAC  121(884): © The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. For permission to reuse, contact
Fig. 3.— Relative radial velocity measurements made during transits of WASP-14. The symbols are as follows: Subaru (circles), Keck (squares), Joshi et al (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 made on the same night as the WASP-14 transit.

26. 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.

27. HAT-P7
l = 182 deg!

28. An misaligned planet in CoRoT-1b
Lambda ~ 80 deg!
HARPS data : F. Bouchy Model fit: F. Pont

30. Distribution of spin-orbit axes
Red: retrograde orbits
~30% of transiting planets are in misaligned or retrograde orbits
As of 2010

31. 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

32. Summary
The Rossiter-McClaughlin effect can measure the angle between the spin axis of the star and the orbital axis of the planet.
The R-M technique cannot give you the planet mass
Exoplanets show all possible obliquity angles, but most are aligned (even in eccentric orbits)
Implications for planet formation (problems for migration theory)