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II. Results from Transiting
Planets
1. Global Properties
2. The Rossiter-McClaughlin Effect
Planet Radius
Most transiting planets tend to be inflated. Approximately 68% of all
transiting planets have radii larger than 1.1 RJup.
Viewgraph from
Borucki et al.
Possible Explanations for the Large Radii
1. Irradiation from the star heats the planet and slows
its contraction it thus will appear „younger“ than it is
and have a larger radius
Possible Explanations for the Large Radii
2. Slight orbital eccentricity (difficult to measure)
causes tidal heating of core → larger radius
Slight Problem:
HD 17156b: e=0.68
R = 1.02 RJup
HD 80606b: e=0.93
R = 0.92 RJup
CoRoT 10b: e=0.53
R = 0.97RJup
Caveat: These planets all have masses 3-4 MJup, so it may
not be the smaller radius is just due to the larger mass.
3. We do not know what is going on.
Density Distribution
S
J/U
N
14
12
Number
10
8
N
6
4
2
0
0.2
0.6
1.0
1.4
1.8
Density (cgs)
2.2
2.6
3.0
Comparison of Mean Densities
Giant Planets with M < 2 MJup : 0.78 cgs
HD 17156, P = 21 d, e= 0.68 M = 3.2 MJup, density = 3.8
HD 80606, P = 111 d, e=0.93, M = 3.9 MJup, density = 6.4
CoRoT 10b, P=13.2, e= 0.53, M = 2.7 MJup, density = 3.7
CoRoT 9b, P = 95 d, e=0.12, M = 1 MJup, density = 0.93
The three eccentric transiting planets have high mass
and high densities. Formed by mergers?
According to formation models of Guenther Wuchterl CoRoT-10
cannot be a planet. It is 2x the highest mass objects that can
form in the proto-nebula
MNep
MJup
One interpretation: it is the merger of two 1.3 MJup planets. This
may also explain the high eccentricity
Period Distribution for short period Exoplanets
p = 13%
16
14
12
Number
10
p = 7%
Transits
RV
8
6
4
2
0
0.25 1.75 3.25 4.75 6.25 7.75 9.25
Period (Days)
The ≈ 3 day period may mark the inner edge of
the proto-planetary disk
Mass-Radius Relationship
Radius is roughly independent of mass, until you get to small planets
(rocks)
Planet Mass Distribution
RV Planets
Close in planets
tend to have
lower mass, as
we have seen
before.
Transiting
Planets
70
60
50
40
RV
30
20
Number
10
Metallicity Distribution
0
-0.45
-0.25
-0.05
0.15
0.35
[Fe/H]
18
16
14
12
10
8
6
Transits
4
2
0
-0.45
-0.25
-0.05
0.15
[Fe/H]
0.35
30
Host Star Mass Distribution
25
Transiting
Planets
20
15
10
Nmber
5
0
0.5
0.7
0.9
1.1
1.3
1.5
80
70
60
RV Planets
50
40
30
20
10
0
0.5
0.7
0.9
1.1
Stellar Mass (solar units)
1.3
1.5
Magnitude distribution of Exoplanet Discoveries
35,00%
Percent
30,00%
25,00%
20,00%
Transits
RV
15,00%
10,00%
5,00%
0,00%
0.5
4,50
8,50
12,50
V- magnitude
16,50
• 8.3 days of Hubble Space Telescope Time
• Expected 17 transits
• None found
• This is a statistically significant result.
[Fe/H] = –0.7
[Fe/H] = +0.4
Expected number of transiting planets = 1.5
Number found = 0
This is not a statistically significant result.
Summary of Global Properties of Transiting Planets
1. Transiting giant planets (close-in) tend to have inflated radii
(much larger than Jupiter)
2. A significant fraction of transiting giant planets are found around
early-type stars with masses ≈ 1.3 Msun.
3. There appears to be no metallicity-planet connection among
transiting planets
4. The period distribution of close-in planets peaks around P ≈ 3
days.
5. Most transiting giant planets have densities near that of Saturn.
It is not known if this is due to their close proximity to the star
(i.e. inflated radius)
6. Transiting planets have been discovered around stars fainter
than those from radial velocity surveys
• Early indications are that the host stars of transiting
planets have different properties than non-transiting
planets.
• Most likely explanation: Transit searches are not as
biased as radial velocity searches. One looks for
transits around all stars in a field, these are not preselected. The only bias comes with which ones are
followed up with Doppler measurements
• Caveat: Transit searches are biased against smaller
stars. i.e. the larger the star the higher probability that
it transits
Spectroscopic Transits:
The Rossiter-McClaughlin Effect
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 or
„Rotation Effect“
For rapidly rotating stars you can „see“ the planet in the spectral line
For stars whose spectral line profiles are dominated by rotational
broadening there is a one to one mapping between location on the star and
location in the line profile:
V = –Vrot
V = +Vrot
V=0
Formation of the Pseudo-emission bumps
A „Doppler Image“ of a Planet
For slowly rotationg stars you do not see the distortion, but you
measure a radial velocity displacement due to the distortion.
The Rossiter-McClaughlin Effect
–v
+v
0
As the companion crosses 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 inclination or„impact parameter“
–v
–v
+v
+v
Shorter duration
and smaller
amplitude
The Rossiter-McClaughlin Effect
What can the RM effect tell you?
2. Is the companion orbit in the same direction as the rotation of the star?
–v
+v
+v
–v
l
What can the RM effect tell you?
3. Are the spin axes aligned?
Orbital
plane
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 in Jupiter radii
R is stellar radius in solar radii
Note:
1. The Magnitude of the R-M effect depends on the
radius of the planet and not its mass.
2. 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
HD 189733
l = –1.4 ± 1.1 deg
CoRoT-2b
l = –7.2 ± 4.5 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
Planet-Planet Interactions
Initially you have two giant
planets in circular orbits
These interact gravitationally.
One is ejected and the
remaining planet is in an
eccentric orbit
Kozai Mechanism
Two stars are in long period orbits around each other.
A planet is in a shorter period orbit around one star.
If the orbit of the planet is inclined, the outer planet can „pump up“ the
eccentricity of the planet. Planets can go from circular to eccentric orbits.
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.
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. 4.— Spin-orbit configuration of the WASP-14 planetary system. The star has a unit radius and the relative size of the
planet and impact parameter are taken from the best-fitting transit model. The sky-projected angle between the stellar
spin axis (diagonal dashed line) and the planet’s orbit normal (vertical dashed line) is denoted by λ, which in this diagram
is measured counterclockwise from the orbit normal. Our best-fitting λ is negative. The 68.3% confidence interval for λ is
traced on either side of the stellar spin axis and denoted by σλσλ.
Fabricky & Winn, 2009, ApJ, 696, 1230
HAT-P7
l = 182 deg!
HAT-P7
Evidence for an
additional
companion
HD 80606
l = 32-87 deg
HD 15082 = WASP-33
No RV variations are seen, but we
can apply the „Sherlock Holmes“
Proof. A companion of radius 1.5 RJup
is either a planet, brown dwarf, or low
mass star. The RV variations exclude
BD and stellar companion.
The Line Profile Variations of HD 15082 = WASP-33
Pulsations
Concern: The planet is not seen in the
wings of the line!
RM anomaly
HARPS data : F. Bouchy
Model fit: F. Pont
HARPS data : F. Bouchy
Model fit: F. Pont
Lambda ~ 80 deg!
Distribution of spin-orbit axes
Red: retrograde
orbits
14
12
10
8
Number
6
4
2
0
-160
-80
0
80
160
l (deg)
40% of Short Period Exoplanets show significant misalignments
20% of Short Period Exoplanets are in retrograde orbits
What are the implications?
The Hill Criteria is a simple way to
assess the stability of planetary
systems.
Suppose that Nature fills the parameter space with ultra-compact planets: if it
can form a planet it can. If many Giant planets are formed, these will interact
and scatter some towards the inner regions. The close-in planets may not be
formed by migration at all, but by scattering of planets from the outer to the inner
regions of the star. Ultracompact systems can also explain the eccentric close in
planets as „mergers“.