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PH709
Extrasolar Planets
Professor Michael Smith
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3 The extrasolar planet population
review: http://arxiv.org/pdf/1501.05685v1.pdf
http://adsabs.harvard.edu/abs/2014arXiv1410.4199W
Early detections by Radial Velocity method: ALL HOT JUPITERS.
What appears in the observed distribution to be a “pile-up” of hot
Jupiters (a few hundred Earth masses at a few hundredths of an
AU) has NOW vanished in volume-limited samples.
3.1 OCCURRENCE RATES
DO DWARF STARS (M STARS) HARBOUR PLANETS? Is
the disc massive enough?
In particular, a much lower incidence of Jupiter mass planets is
expected around M dwarfs in the core accretion scenario for planet
formation.
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Extrasolar Planets
Professor Michael Smith
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Small planets are more abundant around smaller stars
M dwarfs have few Jovian planets, but a wealth of Neptune-mass
planets
Ongoin 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.
We find: Giant planets within 2.5 AU are ~3 times more common
around GK stars than around M stars.
dN / ( d ln M d ln P )
p
∝
Mpα Pβ,
with α = −0.31 ± 0.20, β = 0.26 ± 0.10.
3.2 DO GIANT STARS HARBOUR PLANETS?
Yes, a few, but there are no planets orbiting closer than 0.6 AU.
(Close-in, Jovian planets are relatively easy to detect using radial
velocities because of the larger amplitude they induce and the
increased number of orbit cycles per observing time baseline.)
It appears that stellar mass has a dramatic effect on the semimajor
axis distribution of planets. However, it is not clear whether this
effect is a reflection of the process of planet formation and
migration, or instead related to the effects of the evolution of the
host stars.
Different Classes of Object found by Doppler
(RV) technique:
1. Giant Planets or Brown Dwarfs, Unclosed, LongPeriod Orbits:
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Extrasolar Planets
Professor Michael Smith
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2. Jupiter-mass/Saturn mass Planets Detected by RV:
What appears in the observed distribution to be a “pile-up” of hot Jupiters (a few hundred Earth masses at a few
hundredths of an AU) has vanished in the volume-limited sample.
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Extrasolar Planets
Professor Michael Smith
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3. Sub-Saturn mass:
Detectable mass increases with semi-major axis: a selection
effect
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Extrasolar Planets
Professor Michael Smith
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STATISTICS: Eccentricity:
Planet orbits have significant eccentricity. The median orbital
eccentricity is <e >= 0.25.
Even planets beyond 3 AU reside in eccentric orbits, suggesting
that the circular orbits in our Solar System are unusual.
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.
Ellipse with semi-major and semi-minor axes:
e2 = 1 – b2 /a2
or, for periastron and apastron:
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PH709
Extrasolar Planets
e = (da – dp)/(da + dp)
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Professor Michael Smith
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Extrasolar Planets
Professor Michael Smith
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Most extrasolar planets reside in non-circular orbits. Beyond 0.1
AU, the distribution of eccentricities appears essentially uniform
between 0 and 0.8. Highest e = 0.93 belongs to HD 80606b .
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.
Earth's eccentricity is 0.017, while Jupiter's is 0.094.
Unless there is some gravitational tugging (such as with the
Galilean Satellites) that keeps an orbit eccentric, orbits will usually
circularize with time.
In contrast, planets orbiting within 0.1 AU of their host star tend to
reside in close to circular orbits. Many detected planets with semi7
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Extrasolar Planets
Professor Michael Smith
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major axis < 0.07 AU have low e. This is similar to binary stars, and
is likely due to tidal circularization.
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.
Planets within 0.1 AU are presumably tidally circularized.
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.
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.
.
Distribution of Eccentricity:
Eccentricity v. planet mass
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Extrasolar Planets
Professor Michael Smith
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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.
STATISTICS: Minimum mass as a function of semimajor axis:
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Extrasolar Planets
Professor Michael Smith
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Extrasolar Planets
Professor Michael Smith
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Nothing very striking in these plots: Accessible region of mp
- a space is fully occupied by detected planets
Minimum mass as a function of semimajor axis for the known
nearby exoplanets. 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.
Account for this by considering only planets with masses large
enough to be detectable at any a < 2.7 AU
Get rid of the log (Mj) :
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Extrasolar Planets
Professor Michael Smith
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STATISTICS: THE HISTOGRAMS
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.
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Extrasolar Planets
Professor Michael Smith
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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.
.
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Extrasolar Planets
Professor Michael Smith
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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.
STATISTICS: Location
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
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 occurrence of “hot Jupiters” within 0.1 AU of FGK stars is 1.2 ±
0.2%.
Among stars with one planet, 14% have at least one additional
planet, occasionally locked in resonances.
Planet fraction among ~ solar-type stars exceeds 7%. Most are
beyond 1 AU:
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Extrasolar Planets
Professor Michael Smith
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dN / dlog(a) rises steeply with orbital radius ?
STATISTICS. IS THERE A PERIOD VALLEY?
A Pile-up – linear :
Distribution of periods among the known nearby “hot
Jupiters”. There is a clear “pile-up” of planets with orbital
periods near 3 days.
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Extrasolar Planets
Professor Michael Smith
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The "period valley" observed around Sun-like stars, marked by a
deficit of planets with periods ranging from roughly 10 to 100
days, a sharp increase in the number of detected planets beyond
1 AU and a pile-up near P = 3 day.
Implies that the currently detected planet fraction ~7% is likely to
be a substantial underestimate of the actual fraction of stars with
massive planets.
STATISTICS: THE MASS DISTRIBUTION
15-25% of solar-type stars may have planets with masses
0.2 MJ < mp < 10 MJ.
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Extrasolar Planets
Professor Michael Smith
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MJ sin i Observed mass function increases to smaller Mp:
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.
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Extrasolar Planets
Professor Michael Smith
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STATISTICS: Metallicity distribution of stars with and
without planets
• Metallicity is a measure of the proportion of elements
with masses greater than those of hydrogen and
helium in a star.
• Often given in terms of [Fe/H], the logarithm of the
ratio of the star’s iron abundance to its hydrogen
abundance, with respect to that of the Sun.
•
• [Fe/H] = log[n(Fe)/n(H)]star – log[n(Fe)/n(H)]sun
•
• n(Fe) and n(H) are the number of Fe and H atoms in a
given volume respectively.
• Iron chosen as it is relatively easy to measure iron
abundance through spectroscopic analysis, but other
m < 56 u elements could be used.
• Would you expect a star rich in heavier elements to be
more or less likely to host a planetary system?
Here NFe and NH is the number of iron and hydrogen atoms per unit
of volume respectively
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PH709
Extrasolar Planets
Professor Michael Smith
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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)
THIS HOLDS FOR MASSIVE PLANETS ONLY:
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Extrasolar Planets
Professor Michael Smith
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Host star metallicity: Planets are preferentially found around stars
with enhanced metal abundance.
Cause or effect? High metal abundance could:
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Extrasolar Planets
Professor Michael Smith
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(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.
DO THESE PLANETS FORM FROM DISCS?
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 associted with jupiter-sized planets
correlates strongly with the presence of planets. Sample exhibits a
planet-metallicity correlation at all stellar masses; this argues that
the high metallicities of stars with planets is not likely due to
convective envelope "pollution." BUT: Neptune-mass planets
form preferentially around metal-poor stars, in contrast to stars
with giant planets
3) Some planet have a massive rocky core, e.g. M Core ≈ 70 M
Earth.
4) Many super-Earths and Earth-twins of about 1 - 7 M Earth have
been discovered.
SUMMARY
Smaller planets (1-4 R⊕) with P ∼< 1 yr are found around about
half of Sun-like stars, often in closely-spaced multiplanet systems.
The probability density is nearly constant in log P between ≈10–300
days. For P ∼< 10 days the occurrence rate declines more sharply
with decreasing period.
The core-accretion model of planet formation is supported by four
observations: 1) The mass distribution rises toward the lowest
-1.0
detectable masses, dN/dM =∝
. 2) Stellar metallicity
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Professor Michael Smith
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correlates strongly with the presence of massive planets. 3) Some
planets have massive rocky core.
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