Transcript ppt
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]. 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)