Download The Transit Method

The Transit Method
1.  Photometric
2.  Spectroscopic
Discovery Space for Exoplanets
What are Transits and why are they important?
R*
ΔI
The drop in intensity is give by the ratio of the cross-section areas:
ΔI = (Rp /R*)2 = (0.1Rsun/1 Rsun)2 = 0.01 for Jupiter
Radial Velocity measurements => Mp (we know sin i !)
=> density of planet
→ Transits allows us to measure the physical properties of the
planets
What can we learn about Planetary Transits?
1.  The radius of the planet
2.  The orbital inclination and the mass when
combined with radial velocity measurements
3.  Density → first hints of structure
4.  The Albedo from reflected light
5.  The temperature from radiated light
6.  Atmospheric spectral features
In other words, we can begin to characterize
exoplanets
Transit Probability
i = 90o+θ
θ
R*
a
sin θ = R*/a = |cos i|
a is orbital semi-major axis, and i is the
orbital inclination1
90+θ
Porb = ∫ 2π sin i di / 4π =
90-θ
–0.5 cos (90+θ) + 0.5 cos(90–θ) = sin θ
= R*/a for small angles
1by
definition i = 90 deg is
looking in the orbital plane
Transit Duration
τ = 2(R* +Rp)/v
where v is the orbital velocity and i = 90 (transit across disk center)
Exercise left to the audience: Show that the transit
duration for a fixed period is roughly related to the
mean density of the star.
τ3 ~ (ρmean)–1
Transit Duration
Note: The transit duration gives you an estimate of the stellar radius
Rstar =
0.55 τ M1/3
P1/3
R in solar radii
M in solar masses
P in days
Most Stars have
masses of 0.1 – 4
solar masses.
τ in hours
M⅓ = 0.46 – 1.6
For more accurate times need to take into account the
orbital inclination
for i ≠ 90o need to replace R* with R:
R2 + d2cos2i = R*2
d cos i
R*
R = (R*2 –
d2 cos2i)1/2
R
Making contact:
1.  First contact with star
2.  Planet fully on star
3.  Planet starts to exit
4.  Last contact with star
Note: for grazing transits there is
no 2nd and 3rd contact
1
4
2
3
The Solar System from Afar
Planet
ΔI/I
Prob.
N
τ (hrs)
forbit
Mercury
1.2 x 10-5
0.012
83
8
0.0038
Venus
7.5 x 10-5
0.0065
154
11
0.002
Earth
8.3 x 10-5
0.0047
212
13
0.0015
Mars
2.3 x 10-5
0.0031
322
16
9.6 x 10-4
Jupiter
0.01
0.0009
1100
29
2.8 x 10-4
Saturn
0.007
0.00049
2027
40
1.5 x 10-4
Uranus
0.0012
0.000245
4080
57
7.7 x 10-5
Neptune
0.0013
0.000156
6400
71
4.9 x 10-4
51 Peg b
0.01
0.094
11
3
0.03
Moon
6.2 x10-6
Ganymede
1.3 x 10-5
N is the number of stars you would have to observe to see a transit, if all stars had
such a planet. This is for our solar system observed from a distant star.
Note the closer a planet is to the star:
1.  The more likely that you have a favorable orbit
for a transit
2.  The shorter the transit duration
3.  Higher frequency of transits
→ The transit method is best suited for short period planets.
Prior to 51 Peg it was not really considered a viable detection
method.
Shape of Transit Curves
tflat
tflat
ttotal
2
=
[R* – Rp]2 – d2 cos2i
[R* +
Rp]2 – d2 cos2i
ttotal
Note that when i = 90o tflat/ttotal = (R* – Rp)/( R* + Rp)
Shape of Transit Curves
HST light curve of HD 209458b
A real transit light curve is not flat
To probe limb
darkening in other
stars..
..you can use
transiting planets
No limb darkening
transit shape
At the limb the star has less flux than is expected, thus the planet blocks less light
At different
wavelengths in Ang.
Shape of Transit Curves
Grazing eclipses/transits
These produce a „V-shaped“
transit curve that are more
shallow
Planet hunters like to see a flat part on the bottom of the transit
Probability of detecting a transit Ptran:
Ptran = Porb x fplanets x fstars x ΔT/P
Porb = probability that orbit has correct orientation
fplanets = fraction of stars with planets
fstars = fraction of suitable stars (Spectral Type later than F5)
ΔT/P = fraction of orbital period spent in transit
Estimating the Parameters for 51 Peg systems
Porb
Period ≈ 4 days → a = 0.05 AU = 10 R‫סּ‬
Porb ≈ 0.1
fplanets
Although the fraction of giant planet hosting stars is
5-10%, the fraction of short period planets is
smaller, or about 0.5–1%
Estimating the Parameters for 51 Peg systems
fstars
This depends on where you look (galactic plane,
clusters, etc.) but typically about 30-40% of the stars
in the field will have radii (spectral type) suitable for
transit searches.
Radius as a function of Spectral Type for Main Sequence Stars
A planet has a maximum radius ~ 0.15 Rsun. This means that a star can
have a maximum radius of 1.5 Rsun to produce a transit depth consistent
with a planet → one must know the type of star you are observing!
Take 1% as the limiting depth that you can detect a transit from
the ground and assume you have a planet with 1 RJ = 0.1 Rsun
Example:
B8 Star: R=3.8 RSun
ΔI = (0.1/3.8)2 = 0.0007
Suppose you detect a transit event with a depth of 0.01. This
corresponds to a radius of 50 RJupiter = 0.5 Rsun
Additional problem: It is difficult to get radial velocity
confirmation on transits around early-type stars
Transit searches on Early type, hot stars are not effective
You also have to worry about late-type giant stars
Example:
A K III Star can have R ~ 10 RSun
ΔI = 0.01 = (Rp/10)2
→ Rp = 1 RSun!
Unfortunately, background giant stars are
everywhere. In the CoRoT fields, 25% of the stars
are giant stars
Giant stars are relatively few, but they are bright and can be seen to
large distances. In a brightness limited sample you will see many
distant giant stars.
Planet Radius (RJup)
Along the Main Sequence
1 REarth
Stellar Mass (Msun)
Assuming a 1% photometric precision this is the minimum planet radius as a
function of stellar radius (spectral type) that can be detected
Estimating the Parameters for 51 Peg systems
Fraction of the time in transit
Porbit ≈ 4 days
Transit duration ≈ 3 hours
ΔT/P ≈ 0.03
Thus the probability of detecting a transit of a planet in a single
night is 0.00004.
E.g. a field of 10.000 Stars the number of expected transits is:
Ntransits = (10.000)(0.1)(0.01)(0.3) = 3
Probability of right orbit inclination
Frequency of Hot Jupiters
Fraction of stars with suitable radii
So roughly 1 out of 3000 stars will show a transit event due to a
planet. And that is if you have full phase coverage!
CoRoT: looked at 10,000-12,000 stars per field and found on
average 3 Hot Jupiters per field. Similar results for Kepler
Note: Ground-based transit searches are finding hot Jupiters 1 out of
30,000 – 50,000 stars → less efficient than space-based searches
Catching a transiting planet is thus like playing
Lotto. To win in LOTTO you have to
1.  Buy lots of tickets → Look at lots of stars
2.  Play often → observe as often as you can
The obvious method is to use CCD photometry
(two dimensional detectors) that cover a large
field. You simultaneously record the image of
thousands of stars and measure the light
variations in each.
Confirming Transit Candidates
A transit candidate found by photometry is only a candidate
until confirmed by spectroscopic measurement (radial
velocity)
Any 10–30 cm telescope can find transits. To confirm these
requires a 2–10 m diameter telescope with a high resolution
spectrograph. This is the bottleneck.
Current programs are finding transit candidates faster than
they can be confirmed.
Light curve for HD 209458
Transit Curve from a 10 cm telescope
Radial Velocity Curve for HD 209458
Transit
phase = 0
Period = 3.5 days
M = 0.63 MJup
Radial Velocity Curve: 3m telescope
Confirming Transit Candidates
Spectroscopic measurements are important to:
1.  Remove false positives
2.  Derive the mass of the planet
3.  Determine the stellar parameters
False Positives
It looks like a planet, it smells like a planet, but it is not a planet
1. Grazing eclipse by a main sequence star:
One should be able to distinguish
these from the light curve shape and
secondary eclipses, but this is often
difficult with low signal to noise
These are easy to exclude with Radial
Velocity measurements as the
amplitudes should be tens km/s
(2–3 observations)
For grazing binary star eclipses one usually sees a
secondary eclipse (transit) and ellispoidal variations
2. Giant Star eclipsed by main sequence star:
G star
Giant stars have radii of 10-100 solar radii which
translates into photometric depths of 0.0001 – 0.01 for a
companion like the sun.
These can easily be excluded using one spectrum to
establish spectral and luminosity class. In principle no
radial velocity measurements are required.
Often a giant star can be known from the transit time.
These are typically several days long!
e.g. giant star with R = 10 Rsun and M = 1 Msun and
we find a transit by a companion with a period of 10
days:
The transit duriation τ would be 1.3 days!
Probably not detectable from ground-based observations
A transiting planet around a solar-type star with a 4 day
period should have a transit duration of ~ 3 hours. If the
transit time is significantly longer then this it is a giant or
an early type star.
Low resolution spectra can easily distinguish between a giant and main
sequence star for the host.
Green: model
Black: data
CoRoT: LRa02_E2_2249
Spectral Classification:
K0 III (Giant, spectroscopy)
Period: 27.9 d
Transit duration: 11.7 hrs → implies Giant,
but long period!
Mass ≈ 0.2 MSun
3. Eclipsing Binary as a background (foreground) star:
Eclipsing Binary
Target Star
Image quality of Telescope or
photometric aperture for calculating
light curve
3. Eclipsing Binary as a background (foreground) star:
Fainter binary
system in
background or
foreground
Total = 17% depth
Light from bright
star
Light curve of
eclipsing
system. 50%
depth
Difficult case. This results in no radial velocity variations as the fainter binary
probably has too little flux to be measured by high resolution spectrographs.
Large amounts of telescope time can be wasted with no conclusion. High
resolution imaging may help to see faint background star.
If you see a nearby companion you can do „on-transit“ and „off-transit“ with
high resolution imaging to confirm the right star is eclipsing
4. Eclipsing binary in orbit around a bright star (hierarchical
triple systems)
Another difficult case. Radial Velocity Measurements of the bright
star will show either long term linear trend no variations if the orbital
period of the eclipsing system around the primary is long. This is
essentialy the same as case 3) but with a bound system
5. Unsuitable transits for Radial Velocity measurements
Transiting planet orbits an early type star with rapid rotation
which makes it impossible to measure the RV variations or
you need lots and lots of measurements.
Depending on the rotational velocity RV measurements are
only possible for stars later than about F3
Period =
Companion may be a
planet, but RV
measurements are
impossible
Period: 4.8 d
Transit duration: 5 hrs
Depth : 0.67%
No spectral line seen in this star. This is a
hot star for which RV measurements are
difficult
6. Sometimes you do not get a final answer
Period: 9.75
Transit duration: 4.43 hrs
Depth : 0.2%
V = 13.9
Spectral Type: G0IV (1.27 Rsun)
Planet Radius: 5.6 REarth
Photometry: On Target
CoRoT: LRc02_E1_0591
The Radial Velocity
measurements are
inconclusive. So, how do we
know if this is really a planet.
Note: We have over 30 RV
measurements of this star: 10 Keck
HIRES, 18 HARPS, 3 SOPHIE. In spite of
these, even for V = 13.9 we still do not
have a firm RV detection. This
underlines the difficulty of confirmation
measurements on faint stars.
Results from the CoRoT Initial Run Field: 12000 Stars
26 Transit candidates:
Grazing Eclipsing Binaries: 9
Background Eclipsing Binaries: 8
Unsuitable Host Star: 3
Unclear (no result): 4
Planets: 2
→ for every „quality“ transiting planet found there are 10
false positive detections. These still must be followed-up
with spectral observations
Search Strategies
Look at fields where there is a high density of stars.
1.  Look in galactic bulge with a large (1 m) telescope
and a small field of view
2.  Look in the galactic plane with a small (10-20 cm)
telescope with a wide field of view (few square deg)
3.  Look at stellar clusters
4.  Look one star at a time
OGLE
•  OGLE: Optical Gravitational Lens Experiment (http://www.astrouw.edu.pl/
~ogle/)
•  1.3m telescope looking into the galactic bulge
•  Mosaic of 8 CCDs: 35‘ x 35‘ field
•  Typical magnitude: V = 15-19
•  Designed for Gravitational Microlensing
•  First planet discovered with the transit method
OGLE Strategy
Look at the galactic bulge with a large (1-2m) telescope
Pros: Potentially many stars
Cons: V-mag > 14 faint!
The first planet found with the transit method
Konacki et al.
The OGLE Planets
Planet
Mass
(MJup)
Radius
(RJup)
Period
(Days)
Year
OGLE2-TR-L9 b
4.5
1.6
2.48
2007
OGLE-TR-10 b
0.63
1.26
3.19
2004
OGLE-TR-56 b
1.29
1.3
1.21
2002
OGLE-TR-111 b
0.53
1.07
4.01
2004
OGLE-TR-113 b
1.32
1.09
1.43
2004
OGLE-TR-132 b
1.14
1.18
1.69
2004
OGLE-TR-182 b
1.01
1.13
3.98
2007
OGLE-TR-211 b
1.03
1.36
3.68
2007
Prior to OGLE all the RV planet detections had periods greater than
about 3 days.
The last OGLE planet was discovered in 2007. Most likely these will be
the last because the target stars are too faint.
WASP
WASP: Wide Angle Search For Planets (http://www.superwasp.org). Also
known as SuperWASP
•  Array of 8 Wide Field Cameras
•  Field of View: 7.8o x 7.8o
•  13.7 arcseconds/pixel
•  Typical magnitude: V = 9-13
•  86 Planets discovered
•  Most successful ground-based transit search program
Another Successful Transit Search Program
•  HATNet: Hungarian-made Automated Telescope (http://www.cfa.harvard.edu/
~gbakos/HAT/
•  Six 11cm telescopes located at two sites: Arizona and Hawaii
•  8 x 8 square degrees
•  43 Planets discovered
HAT 1b
Follow-up
with larger
telescope
The MEarth Strategy
One star at a time!
The MEarth project
(http://www.cfa.harvard.edu/~zberta/mearth/)
uses 8 identical 40 cm telescopes to search
for terrestrial planets around M dwarfs one
after the other
Clusters
A dense open cluster: M 67
Stars of interest have
magnitudes of 14 or
greater
A not so dense open cluster:
Pleiades
h and χ Persei double cluster
A dense globular cluster: M 92
Stars of interest have
magnitudes of 17 or
greater
•  8.3 days of Hubble Space Telescope Time
•  Expected 17 transits
•  None found
•  This is a statistically significant result.
[Fe/H] = –0.7
Percent
Stellar Magnitude distribution of Exoplanet
Discoveries
V- magnitude
Radial Velocity Follow-up for a Hot Jupiter
The problem is not in finding the transits, the problem
(bottleneck) is in confirming these with RVs which requires
high resolution spectrographs.
Telescope
Easy
Challenging
Impossible
2m
V<9
V=10-12
V >13
4m
V < 10–11 V=12-14
V >15
8–10m
V< 12–14
V >17
V=14–16
It takes approximately 8-10 hours of telescope time on a
large telescope to confirm one transit candidate
Two Final Comments
1.  In modeling a transit light curve one only derives
the ratio of the planet radius to the stellar radius:
k = Rp/Rstar
2. In measuring the planet mass with radial velocities
you only derive the mass function:
3(1 – e2)3/2
P
K
3
(mp sin i)
=
f(m) =
2
(mp + ms)
2πG
The planet radius, mass, and thus density depends on
the stellar mass and radius. For high precision data the
uncertainty in the stellar parameters is the largest error
Important discoveries from
Ground-based Transit Surveys
Charbonneau et al. (2000): The observations that started it all:
•  Proof that RV variations are due to planet
•  Mass = 0,63 MJupiter
•  Radius = 1,35 RJupiter
•  Density = 0,38 g cm–3
GJ 436: The First Transiting Neptune
Host Star:
Mass = 0.4 M‫( סּ‬M2.5 V)
Butler et al. 2004
Special Transits: GJ 436
Butler et al. 2004
„Photometric transits of the planet across the star are ruled out for gas giant
compositions and are also unlikely for solid compositions“
The First Transiting Hot Neptune!
Gillon et al. 2007
GJ 436
Star
Stellar mass [ M‫] סּ‬
0.44 ( ± 0.04)
Planet
Period [days]
2.64385 ± 0.00009
Eccentricity
0.16 ± 0.02
Orbital inclination
86.5
Planet mass [ ME ]
22.6 ± 1.9
Planet radius [ RE ]
3.95 +0.41-0.28
0.2
Mean density = 1.95 gm cm–3,
slightly
higher
than
Neptune
(1.64)
HD 17156: An eccentric orbit planet
M = 3.11 MJup
Probability of a transit ~ 3%
Barbieri et al. 2007
R = 0.96 RJup
Mean density = 4.88 gm/cm3
Mean for M2 star ≈ 4.3 gm/cm3
HD 80606: Long period and eccentric
R = 1.03 RJup
ρ = 4.44 (cgs)
a = 0.45 AU
dmin = 0.03 AU dmax = 0.87 AU
Probability of having a favorable
orbital orientation is only 1%!
WASP 12b: The Hottest Transiting Giant Planet
High quality light curve for accurate parameters
Discovery data
Orbital Period: 1.09 d
Transit duration: 2.6 hrs
Planet Mass: 1.41 MJupiter
Planet Radius: 1.79 RJupiter
Doppler confirmation
Planet Temperature: 2516 K
Spectral Type of Host Star: F7 V
WASP 12b: The Hottest Transiting Giant Planet
High quality light curve for accurate parameters
Discovery data
Orbital Period: 1.09 d
Transit duration: 2.6 hrs
Planet Mass: 1.41 MJupiter
Planet Radius: 1.79 RJupiter
Doppler confirmation
Planet Temperature: 2516 K
Spectral Type of Host Star: F7 V
Comparison of WASP 12 to an M8 Main Sequence Star
Planet Mass: 1.41 MJupiter
Mass: 60 MJupiter
Planet Radius: 1.79 RJupiter
Radius: ~1 RJupiter
Planet Temperature: 2516 K
Teff: ~ 2800 K
WASP 12 has a smaller mass, larger radius, and comparable
effective temperature than an M8 dwarf. Its atmosphere
should look like an M9 dwarf or L0 brown dwarf. One
difference: above temperature for the planet is only on the day
side because the planet does not generate its own energy
Although WASP-33b is closer to the
planet than WASP-12 it is not as hot
because the host star is cooler (4400 K)
and it has a smaller radius
MEarth-1b: A transiting Superearth
D Charbonneau et al. Nature 462, 891-894 (2009) doi:10.1038/nature08679
Change in radial velocity of GJ1214.
D Charbonneau et al. Nature 462, 891-894 (2009) doi:10.1038/nature08679
ρ = 1.87 (cgs)
Neptune like
So what do all of these transiting planets tell us?
5.5 gm/cm3
ρ = 1.25 gm/cm3
ρ = 1.24 gm/cm3
ρ = 0.62 gm/cm3
1.6 gm/cm3
The density is the first indication of the internal structure of the exoplanet
Solar System Object
ρ (gm cm–3)
Mercury
5.43
Venus
5.24
Earth
5.52
Mars
3.94
Jupiter
1.24
Saturn
0.62
Uranus
1.25
Neptune
1.64
Pluto
2
Moon
3.34
Carbonaceous
Meteorites
2–3.5
Iron Meteorites
7–8
Comets
0.06-0.6
Rocks
He/H
Ice
Masses and radii of transiting planets.
H/He dominated
Pure H20
67.5% Si mantle
32.5% Fe
(earth-like)
75% H20,
22% Si
GJ 1214b is shown as a red filled circle (the 1σ uncertainties correspond to the size of the symbol), and the other known transiting planets
are shown as open red circles. The eight planets of the Solar System are shown as black diamonds. GJ 1214b and CoRoT-7b are the only
extrasolar planets with both well-determined masses and radii for which the values are less than those for the ice giants of the Solar
System. Despite their indistinguishable masses, these two planets probably have very different compositions. Predicted16 radii as a
function of mass are shown for assumed compositions of H/He (solid line), pure H2O (dashed line), a hypothetical16 water-dominated
world (75% H2O, 22% Si and 3% Fe core; dotted line) and Earth-like (67.5% Si mantle and a 32.5% Fe core; dot-dashed line). The radius
of GJ 1214b liesD0.49 ± 0.13
R⊕ above
water-world
curve, indicating
that even if the planet is predominantly water in composition, it
Charbonneau
et al.the
Nature
462, 891-894
(2009) doi:10.1038/nature08679
probably has a substantial gaseous envelope
HD 149026: A planet with a large core
Sato et al. 2005
Period = 2.87 d
Rp = 0.7 RJup
Mp = 0.36 MJup
Mean density = 2.8 gm/cm3
10-13 Mearth core
~70 Mearth core mass is difficult to
form with gravitational instability.
HD 149026 b provides strong
support for the core accretion theory
Rp = 0.7 RJup
Mp = 0.36 MJup
Mean density = 2.8 gm/cm3
Lower bound
ρ = 0.15 gm cm–3
Upper bound
ρ = 3 gm cm–3
Planet Radius
Most transiting planets tend to be inflated. Approximately 68% of all
transiting planets have radii larger than 1.1 RJup.
There is a slight correlation of radius
with planet temperature (r = 0.37)
Are Close-in Jupiters inflated because they are hot?
Demory and Seager 2011
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
Models I, C, and D are for isolated planets
Models A and B are for irradiated planets.
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
be the smaller radius is just due to the larger mass.
3.  We do not know what is going on.
Comparison of Mean Densities of eccentric planets
Giant Planets with M < 2 MJup : 0.78 cgs
HD 17156, P = 21 d, e= 0.68 M = 3.2 MJup, density = 4.8
HD 80606, P = 111 d, e=0.93, M = 3.9 MJup, density = 4.4
CoRoT 10b, P=13.2, e= 0.53, M = 2.7 MJup, density = 3.7
The three eccentric transiting planets have high mass
and high densities. Formed by mergers?
Period Distribution for short period Exoplanets
p = 13%
p = probability of a
favorable orbit
Number
p = 7%
Period (Days)
Both RV and Transit Searches show a peak in the
Period at 3 days
The ≈ 3 day period may mark the inner edge of
the proto-planetary disk
Radius (RJ)
Mass-Radius Relationship
Mass (MJ)
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
Summary of Global Properties of Transiting Planets
1.  Transiting giant planets (close-in) tend to have inflated radii
(much larger than Jupiter)
2.  The period distribution of close-in planets peaks around P ≈ 3
days for both RV and transit discovered planets.
3.  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)
4.  Transiting planets have been discovered around stars fainter
than those from radial velocity surveys
Summary
1.  The Transit Method is an efficient way to find
short period planets.
2.  Combined with radial velocity measurements it
gives you the mass, radius and thus density of
planets
3.  Roughly 1 in 3000 stars will have a transiting hot
Jupiter → need to look at lots of stars (in galactic
plane or clusters)
4.  Radial Velocity measurements are essential to
confirm planetary nature
5.  Anyone with a small telescope can do transit work
(i.e even amateurs)
Spectroscopic Transits
The Rossiter-McClaughlin Effect
2
1
+v
0
4
3
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.
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
λ
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
λ = –0.1 ± 2.4 deg
The first RM
measurements of
exoplanets showed
aligned systems
HD 189733
λ = –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: λ = 9.3 ± 9.3 degrees → No misalignment!
TrES-1
λ = 30 ± 21 deg
XO-3-b
Hebrard et al. 2008
λ = 70 degrees
Winn et al. (2009) recent R-M measurements for X0-3
λ = 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
λ = 182 deg!
λ = 32-87 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
λ (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.  There are 2 ways from spectroscopy to measure the
angle between the spin axis and the orbital axis of the
star:
a)  Rossiter-McClaughlin effect (most successful)
b)  Doppler tomography
2.  No technique can give you the 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)