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Characterization of Planets: Mass and Radius
(Transits Results Part I)
I.
II.
III.
IV.
Results from individual transit search programs
Interesting cases
Global Properties
Spectroscopic Transits
The first time I gave this lecture (2003) there was one transiting
extrasolar planet
There are now 59 transiting extrasolar planets
First ones were detected by doing follow-up photometry of radial
velocity planets. Now transit searches are discovering
exoplanets
Radial Velocity Curve for HD 209458
Period = 3.5 days
Msini = 0.63 MJup
Charbonneau et al. (2000): The observations that started it all:
• Mass = 0,63 MJupiter
• Radius = 1,35 RJupiter
• Density = 0,38 g cm–3
Transit detection was made with the 10 cm STARE Telescope
A light curve taken by amateur astronomers…
..and by the Profis ( Hubble Space Telescope).
HD 209458b has a radius larger than expected.
Burrows et al. 2000
Evolution of the
radius of HD
209458b and t
Boob
HD 209458b
Models I, C, and D are for isolated planets
Models A and B are for irradiated planets.
One hypothesis for the large radius is that the stellar radiation hinders the
contraction of the planet (it is hotter than it should be) so that it takes
longer to contract. Another is tidal heating of the core of the planet if you
have nonzero eccentricity
Successful Transit Search Programs
• 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
• 8 Transiting planets discovered so far
The first planet found with the transit method
Konacki et al.
Until this discovery radial velocity surveys only found planets with
periods no shorter than 3 days. About ½ of the OGLE planets have
periods less than 2 days.
M = 1.03 MJup
R = 1.36 Rjup
Period = 3.7 days
Vsini = 40 km/s
K = 510 170 m/s
One reason I do not like OGLE
transiting planets. These produce
low quality transits, they are faint,
and they take up a large amount
of 8m telescope time.
i= 79.8 0.3
a= 0.0308
Mass = 4.5 MJ
Radius = 1.6 RJ
Spectral Type = F3 V
Successful Transit Search Programs
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
• 15 transiting planets discovered so far
Coordinates
RA 00:20:40.07 Dec
+31:59:23.7
Constellation
Pegasus
Apparent Visual Magnitude
11.79
Distance from Earth
1234 Light Years
WASP-1 Spectral Type
F7V
WASP-1 Photospheric
Temperature
6200 K
WASP-1b Radius
1.39 Jupiter Radii
WASP-1b Mass
0.85 Jupiter Masses
Orbital Distance
0.0378 AU
Orbital Period
2.52 Days
Atmospheric Temperature
1800 K
Mid-point of Transit
2453151.4860 HJD
WASP 12: Hottest (at the time) Transiting 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
Mass – Radius Relationship
Stars
Planets
Successful Transit Search Programs
• TrES: Trans-atlantic Exoplanet Survey (STARE is a member of the network
http://www.hao.ucar.edu/public/research/stare/)
• Three 10cm telescopes located at Lowell Observtory, Mount Palomar
and the Canary Islands
• 6.9 square degrees
• 4 Planets discovered
TrEs 1b
TrEs 2b
P = 2.47 d
M = 1.28 MJupiter
R = 1.24 RJupiter
i = 83.9 deg
Successful Transit Search Programs
• 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
• 12 Planets discovered
HAT-P-1b
Follow-up
with larger
telescope
HAT-P-1b has an anomolously
large radius for its mass
HAT-P-12b
Star = K4 V
Planet Period = 3.2 days
Planet Radius = 0.96 RJup
Planet Mass = 0.21 MJup (~MSat)
r = 0.3 gm cm–3
Special Transits: GJ 436
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
Special Transits: 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, in between Neptune (1.58) and Uranus (2.3)
Special Transits: HD 17156
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
Special Transits: HD 149026
Sato et al. 2005
Period = 2.87 d
Rp = 0.7 RJup
Mp = 0.36 MJup
Mean density = 2.8 gm/cm3
So what do all of these transiting
planets tell us?
The density is the first indication of the internal structure of the exoplanet
Solar System Object
r (gm cm–3)
Mercury
5.43
Venus
5.24
Earth
5.52
Mars
3.94
Jupiter
1.33
Saturn
0.70
Uranus
1.30
Neptune
1.76
Pluto
2
Moon
3.34
Carbonaceous
Meteorites
2–3.5
Iron Meteorites
7–8
Comets
0.06-0.6
Mass Radius Relationship
HD 209458b and HAT-P-1b have anomalously large radii that still
cannot be explained by planetary structure and evolution models
HAT-12b
CoRoT-3
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
GJ436b (transiting
Neptune) has a
density comparable
to Uranus and
Neptune and thus
we expect similar
structure
Take your
favorite
composition
and calculate
the mass-radius
relationship
5
U
GJ 436
4
N
3
R/RE
2
1
1
10
M/ME
100
The type of planet you have (rock versus iron, etc) is driven largely by
the radius determination. E.g.: a silicate planet can have a mass that
varies by more than 20%. A 20% error in the radius determines whether
the planet is a rock or a piece of iron. This is because density ~ M, but
R–3
To get a better estimate of the composition of an
exoplanet, you need to know the radius of the
planet to within 5% or better
• You need accurate transit depths → you should
probably do this from space, or lots of
measurements from the ground
• You only determine Rplanet/Rstar. This means you
need to know the radius of the star to within a few
percent. For accurate stellar radii you must use
- Interferometry
- Asteroseismology
HAT-P-12b
The best fitting model for HAT-P-12b has a core mass ≤ 10 Mearth and
is still dominated by H/He (i.e. like Saturn and Jupiter and not like
Uranus and Neptune. It is the lowest mass H/He dominated gas giant
planet.
Global Properties
Planet Radius
Most transiting planets tend to be inflated
Mass-Radius Relationship
Radius is roughly independent of mass, until you get to small planets
(rocks)
Mass of the Host Star
Transiting Planets:
45% Stars have mass
greater that 1 Msun
However, probability of a
transit is ~ Rstar/a, so this
might be a selection effect.
All Planets (mostly from
Doppler surveys). 37%
stars have mass greater
than 1 Msun
Planet Mass Distribution
It is rare to find close-in planets that have high mass, but they do exist.
Some with masses up to 20 MJup (CoRoT-3)
The Planet-Metallicity Connection
Astronomer‘s
Metals
More Metals !
Even more Metals !!
Bracket Fe/H notation : [Fe/H]
This is the ratio of metal abundance to the solar value. Often it is
for Iron lines, but sometimes other heavy elements are included.
Sometimes [M/H] is used for metals:
[Fe/H] is calculated by taking the iron abundance, divide it by the
abundance of iron in the sun, and then taking the logarithm base 10.
[Fe/H] = 0 → solar abundance
[Fe/H] = +0.5 →3.16 × solar
[Fe/H] = –1.0 →0.1 × solar
Most metal rich stars have [Fe/H] = +0.5, most metal poor have
[Fe/H] ≈ –3
The Planet-Metallicity Connection?
These are stars with metallicity [Fe/H] ~ +0.3 – +0.5
Valenti & Fischer
There is believed to be a connection between metallicity and planet
formation. Stars with higher metalicity tend to have a higher frequency of
planets. This has been used as evidence in support of the core accretion
theory
Comparison of Metalicity
Transiting Planets
All Planets
(mostly from
Doppler surveys)
%
Metallicity of Giant Stars also show no
metallicity effect
[Fe/H]
Most planets around giant stars and
transiting planets are for 1.2-1.4 MSun host
stars. And there seems to be no metallicity
effect.
Red line: Main sequence (1
solar mass)
Blue: Giants (~1.4 solar mass)
More problems with Planet – Metallicity Connection
Endl et al. 2007: HD 155358 two planets and..
Hyades stars have
[Fe/H] = 0.2 and
according to V&F
relationship 10% of
the stars should
have giant planets,
but none have been
found in a sample
of 100 stars
…[Fe/H] = –0.68. This certainly muddles the metallicity-planet connection
• 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
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
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.
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.
The Rossiter-McClaughlin Effect
What can the RM effect tell you?
1. The inclination of „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
TrES-1
Results from the Rossiter-McClaughlin Effect
So far most transiting planets for which
an RM effect has been measured has
shown prograde orbits
What about misalignment of the spin
axis?
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
This mechanism has been invoked to explain the „massive eccentrics“
Recall that there are no massive planets in circular orbits
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.
This was first investigated by Kozai who showed that satellites in orbit
around the Earth can have their orbital eccentricity changed by the
gravitational influence of the Moon
Kozai Mechanism
The Kozai mechanism has been
used to explain the high orbital
eccentricity of 16 Cyg B, a planet
in a binary system
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!
Fabricky & Winn, 2009, ApJ, 696, 1230
XO-3-b
Hebrard et al. 2008
l = 70 degrees
Winn et al. (2009) recent R-M measurements for X0-3
l = 37 degrees
Possible inclination changes in TrEs-2
Evidence that transit duration has decreased by 3.2 minutes. This
might be caused by inclination changes induced by a third body
The biggest effect should be for grazing transits
Transit Timing Variations (TTVs)
Changes in the expected times of transits are indications of other bodies
in the system:
• Another (outer) planet that influences the center of mass
motion of the star and perturbs the transiting planets orbit
• A moon that influences the planet‘s center of mass
Transit delayed from
previous time
TTVs: you need lots of transits!
Bean et al. 2009
Currently there is no evidence for TTVs in transiting planets, probably
due to the difficulty in measuring these: these are too small.
Summary
1. 59 Transiting planets have been discovered most
from the ground.
2. Most have radii that are larger than Jupiter
(inflated)
3. Smallest has radius of Neptune (wait for CoRoT
talks)
4. Mean density gives us our first estimate of the
internal structure
5. R-M effect can tell us about spin alignment. Most
transiting planets have aligned orbits
6. Transit searches may have a less biased sample
than radial velocity searches