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PH709
Extrasolar Planets
Professor Michael Smith
1
5 The extrasolar planet population
Observed Properties of Exoplanets: Masses, Orbits, and
Metallicities
Marcy, Butler et al…….1987-2007
Stellar Sample 1330 Nearby FGKM Stars
Star Selection Criteria:
• Vmag < 10 mag
• No Close Binaries
(~2000 stars total with Mayor et al. )
PH709
Extrasolar Planets
Professor Michael Smith
2
Age > 2 Gyr
Ongoing 18-year survey of 1330 FGKM type stars at Lick,
Keck, and the Anglo-Australian Telescopes that offers both
uniform Doppler precision (3 m s-1) and long duration.
The 104 planets detected in this survey have minimum masses (M
sin i) as low as 6 M Earth, orbiting between 0.02 and 6 AU
EXAMPLE. We report precise Doppler measurements of GJ 849
(M3.5 V) that reveal the presence of a planet with a minimum mass
of 0.82 MJup in a 5.16 yr orbit.
At a = 2.35 AU, GJ 849b is
1. the first Doppler-detected planet discovered around an M
dwarf orbiting beyond 0.21 AU, and
2. is only the second Jupiter-mass planet discovered around a
star less massive than 0.5 Msolar.
This detection brings to 4 the number of M stars known to harbour
planets. We find: Giant planets within 2.5 AU are ~3 times more
common around GK stars than around M stars.
Due to GJ 849's proximity of 8.8 pc, the planet's angular
separation is 0.27", making this system a prime target for high-
PH709
Extrasolar Planets
Professor Michael Smith
3
resolution imaging using adaptive optics and future space-borne
missions such as the Space Interferometry Mission PlanetQuest.
Different Classes of Object found:
1. Planets or Brown Dwarfs in Unclosed, Long-Period Orbits:
2. Examples of Jupiter-mass/Saturn mass Planets Detected by RV:
PH709
Extrasolar Planets
Professor Michael Smith
4
3. Sub-Saturn mass:
The core-accretion model of planet formation is supported by
four observations:
1) The mass distribution rises toward the lowest detectable
masses, dN/dM ~ M -1.0.
2) Stellar metallicity correlates strongly with the presence of
planets.
PH709
Extrasolar Planets
Professor Michael Smith
5
3) One planet (1.3 M Sat) has a massive rocky core, M Core ≈ 70 M
Earth.
4) A super-Earth of about 7 M Earth has been discovered. Four
very low mass planets have been detected (20 earth masses).
The distribution of semi-major axes rises from 0.3 – 3.0 AU (dN/d
log a) and extrapolation suggests that about 12% of the FGK stars
harbour gas-giant exoplanets within 20 AU.
The median orbital eccentricity is <e >= 0.25, and even planets
beyond 3 AU reside in eccentric orbits, suggesting that the circular
orbits in our Solar System are unusual.
The occurrence of “hot Jupiters” within 0.1 AU of FGK stars is 1.2 ±
0.2%.
Planet fraction among ~ solar-type stars exceeds 7%. Most are
beyond 1 AU
Among stars with one planet, 14% have at least one additional
planet, occasionally locked in resonances.
Other positive detections:
PH709
Extrasolar Planets
Professor Michael Smith
6
Microlensing: eight detections, low detection rate imply upper limit
of ~1/3 on the fraction of lensing stars (~ 0.3 Msun) with Jupiter
mass planets at radii to which lensing is most sensitive (1.5 - 4 AU)
Transits: over 50 known planets (5 found with OGLE
photometrically). Interesting upper limit from non-detection of
transits in globular cluster 47 Tuc.
Transits + Doppler yields mass and size, hence the density of the
planet: 0.2 – 1.4 gm/cm3 : mainly gaseous. In addition, sodium and
nitrogen found in their atmospheres.
Eccentricity:
Planet orbits have significant eccentricity.
The eccentricity of an orbit is how much it varies from a perfect
circle. A stable orbit can have an eccentricity anywhere from a
perfect circle with an eccentricity of 0, up to a highly elliptical orbit
with an eccentricity up to (but not including) 1. If an orbit had an
eccentricity of 1, it would be parabolic and escape from the system.
If it were larger than 1, it would be hyperbolic and also escape from
the system.
With k=1 for an ellipse:
e = (da – dp)/(da + dp)
PH709
Extrasolar Planets
Professor Michael Smith
7
PH709
Extrasolar Planets
Professor Michael Smith
8
Most extrasolar planets reside in non-circular orbits. Of the 90
extrasolar planets that reside beyond 0.15 AU, their average orbital
eccentricity is 0.32.
PH709
Extrasolar Planets
Professor Michael Smith
9
In contrast, planets orbiting within 0.1 AU of their host star all reside
in nearly circular orbits, no doubt enforced by tidal circularization.
Earth's eccentricity is 0.017, while Jupiter's is 0.094.
In our solar system, the planet with the largest eccentricity is Pluto
at 0.244, and Mercury with 0.205.
The planet with the lowest eccentricity is Venus with 0.007.
Unless there is some gravitational tugging (such as with the
Galilean Satellites) that keeps an orbit eccentric, orbits will usually
circularize with time.
About 10% of the planets found so far have an eccentricity of nearly
0. About 15% have an eccentricity smaller than Earth's, and over
25% have an eccentricity smaller than Jupiter's. 45% are smaller
than Mercury's eccentricity, and 50% are lower than Pluto's.
The other half have very eccentric orbits; this means that,
throughout their years, they come very close to and very far from
their parent star. This will create wide temperature swings, and for
any life like Earth's, this would make survival quite difficult, if
not impossible.
Theories: explanations uncertain
Most proposed mechanisms invoke gravitationally scattering or
perturbations of planets by other planets, perhaps in resonances, or
by interactions with the protoplanetary disk.
Planets within 0.1 AU are presumably tidally circularized.
Beyond 0.1 AU, the distribution of eccentricities appears essentially
uniform between 0 and 0.8. For most Doppler surveys, sensitivity is
not a strong function of eccentricity for 0 < e < 0.8 and a < 3 AU.
This plot represents results from many surveys, and so is drawn
from an inhomogeneous sample.
Distribution of Eccentricity:
PH709
Extrasolar Planets
Professor Michael Smith
10
Eccentricity v. planet mass
Figure: the 130 known nearby exoplanets with M sin i < 13 MJup, excluding
those for which a < 0.1 AU, i.e., those planets which may have been tidally
circularized. High-mass exoplanets (M sin i > 5MJup) have a slightly higher
median eccentricity than lower-mass exoplanets. The completeness of Doppler
surveys increases with M sin i and is generally insensitive to eccentricity.
Ignoring the hot Jupiters, no obvious correlation between planet
mass and eccentricity.
PH709
Extrasolar Planets
Professor Michael Smith
11
Hot Jupiters have close to circular orbits. All detected planets with
semi-major axis < 0.07 AU have low e. This is similar to binary stars,
and is likely due to tidal circularization.
Remaining planets have a wide scatter in e, including some planets
with large e.
Note that the distance of closest approach is a(1-e), and that the
effect of tidal torques scales as separation d-6. The very eccentric
planet around HD80606 (a = 0.438 AU, e = 0.93, a(1-e) = 0.03 AU)
may pose some problems for tidal circularization theory.
Minimum mass as a function of semi-major axis:
PH709
Extrasolar Planets
Professor Michael Smith
12
Nothing very striking in these plots: Accessible region of mp
- a space is fully occupied by detected planets
Get rid of the log (Mj) :
PH709
Extrasolar Planets
Professor Michael Smith
13
Minimum mass as a function of semimajor axis for the 164
known nearby exoplanets with 0.03 < a < 6.5 AU. Doppler surveys
are generally incomplete for exoplanets with a > 3 AU, low-mass
planets (M sin i < 1MJup) beyond 1 AU, and very low-mass planets
(M sin i < 0.1MJup) everywhere. This plot represents results from
many surveys, and so is drawn from an inhomogeneous sample.
Results from radial velocity searches
Massive planets exist at small orbital radii.
Closest-in planet is at a = 0.035 AU (cf Mercury at ~ 0.4 AU). Less
than 10 solar radii!
EXAMPLES:
Best-fit orbit to the radial velocities measured at Keck Observatory
for HD 11964,
with P = 5.8yr, e ~ 0, and M sin i = 0.6MJup.
PH709
Extrasolar Planets
Professor Michael Smith
14
Best-fit orbit to the radial velocities measured at Keck Observatory
for HD 66428, with P = 5.4yr, e = 0.5, and M sin i = 3MJup.
PH709
Extrasolar Planets
Professor Michael Smith
15
Account for this by considering only planets with masses large enough to be detectable
at any a < 2.7 AU.
-> dN / dlog(a) rises steeply with orbital radius
Implies that the currently detected planet fraction ~7% is likely to
be a substantial underestimate of the actual fraction of stars with
massive planets.
15-25% of solar-type stars may have planets with masses
0.2 MJ < mp < 10 MJ.
Strong selection effect in favour of detecting planets at small orbital
radii, arising from:
- lower mass planets can be detected there
- mass function rises to smaller masses
PH709
Extrasolar Planets
Professor Michael Smith
16
Orbital distance distribution of the 197 known nearby exoplanets with
0.03 <a < 10 in logarithmic distance bins. Planets with a > 3AU have
periods comparable to or longer than the length of most Doppler
surveys, so the distribution is incomplete beyond that distance. This
distribution represents results from many surveys, and so is drawn from
an inhomogeneous sample
PH709
Extrasolar Planets
Professor Michael Smith
17
Distribution of periods among the known nearby “hot
Jupiters”. There is a clear “pile-up” of planets with orbital
periods near 3 days.
MJ sin i Observed mass function increases to smaller Mp:
PH709
Extrasolar Planets
Professor Michael Smith
18
Note: the brown dwarf desert!
The mass distribution shows a dramatic decrease in the number of
planets at high masses, a decrease that is roughly characterized by
a power law, dN/dM ~ M-1.25.
Lower mass planets have smaller Doppler amplitudes: the selection
effects enhance this effect. This distribution represents results from many
surveys, and so is drawn from an inhomogeneous sample.
Metallicity distribution of stars with and without planets
Here NFe and NH is the number of iron and hydrogen atoms per unit of volume
respectively
PH709
Extrasolar Planets
Professor Michael Smith
19
Left plot: metallicity of stars with planets (shaded histogram)
compared to a sample of stars with no evidence for planets (open
histogram) (data from Santos, Israelian & Mayor, 2001)
Host star metallicity: Planets are preferentially found around stars
with enhanced metal abundance.
PH709
Extrasolar Planets
Professor Michael Smith
20
Cause or effect? High metal abundance could:
(a) Reflect a higher abundance in the material which formed
the star + protoplanetary disc, making planet formation more
likely.
(b) Result from the star swallowing planets or planetesimals
subsequent to planets forming. If the convection zone is fairly
shallow, this can apparently enrich the star with metals even if
the primordial material had Solar abundance.
Detailed pattern of abundances can distinguish these possibilities,
but results currently still controversial.
Clusters: Lack of transits in 47 Tuc
A long HST observation monitored ~34,000 stars in the globular
cluster 47 Tuc looking for planetary transits.
Locally: 1% of stars have hot Jupiters
~ 10% of those show transits
 Expect 0.001 x 34,000 ~ few tens of planets
None were detected. Possible explanations:
• Low metallicity in cluster prevented planet formation
• Cluster environment destroyed discs before planets formed
• Stellar fly-bys ejected planets from bound orbits
All of these seem plausible - make different predictions for other
clusters.
The lack of detections in the uncrowded outer regions of both
clusters indicates that stellar metallicity is the dominant factor
inhibiting Hot Jupiter formation in the cluster environment.
Microlensing Statistics:
PH709
Extrasolar Planets
Professor Michael Smith
21
Constraint from monitoring of 43 microlensing events.
Typically, the lenses are low mass stars.
At most 1/3 of 0.3 Solar mass stars have Jupiter mass planets between 1.5
AU and 4 AU.
Currently consistent with the numbers seen in radial velocity
searches.
SUMMARY
The core-accretion model of planet formation is supported by four
observations: 1) The mass distribution rises toward the lowest
detectable masses, dN/dM = M-1.0. 2) Stellar metallicity correlates
strongly with the presence of planets. 3) One planet (1.3 MSat) has a
massive rocky core, MCore ≈ 70 MEarth. 4) A super-Earth of ˜ 7 MEarth
has been discovered.
BUT HOW …. do massive planets end up so close to their stars?