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PH507
Astrophysics
Professor Glenn White
1
Lecture 7:
Planet detection method : Transits
Simplest method: look for drop in stellar flux due to a planet
transiting across the stellar disc
Needs luck or wide-area surveys - transits only occur if the orbit is almost edge-on
For a planet with radius rp << R*, probability of transits is:
Close-in planets are more likely to be detected. P = 0.5 % at 1AU, P = 0.1 % at the
orbital radius of Jupiter
What can we measure from the light curve?
(1)
Depth of transit = fraction of stellar light blocked
This is a measure of planetary radius!
In practice, isolated planets with masses between ~ 0.1 MJ and 10 MJ, where MJ
is the mass of Jupiter, should have almost the same radii (i.e. a flat mass-radius
relation).
PH507
Astrophysics
Professor Glenn White
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-> Giant extrasolar planets transiting solar-type stars produce transits
with a depth of around 1%.
Close-in planets are strongly irradiated, so their radii can be (detectably) larger.
But this heating-expansion effect is not generally observed for short-period
planets.
(2)
(3)
(4)
Duration of transit plus duration of ingress, gives measure of the orbital radius
and inclination
Bottom of light curve is not actually flat, providing a measure of stellar limbdarkening
Deviations from profile expected from a perfectly opaque disc could provide
evidence for satellites, rings etc
Photometry at better than 1% precision is possible (not easy!) from the ground.
HST reached a photometric precision of 0.0001.
Potential for efficient searches for close-in giant planets
Transit depth for an Earth-like planet is:
Photometric precision of ~ 10-5 seems achievable from space
May provide first detection of habitable Earth-like planets
NASA’s Kepler mission, ESA version Eddington
A reflected light signature must also exist, modulated on the orbital period,
even for non-transiting planets. No detections yet.
Planet detection method : Gravitational microlensing
Light is deflected by gravitational field of stars, compact objects, clusters of galaxies,
large-scale structure etc
Simplest case to consider: a point mass M (the lens) lies along the line of sight to a
more distant source
Define:
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Astrophysics
Professor Glenn White
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• Observer-lens distance
• Observer-source distance
• Lens-source distance
Dl
Ds
Dls
Azimuthal symmetry -> light from the source appears as a ring
...with radius R0 - the Einstein ring radius - in the lens plane
Gravitational lensing conserves surface brightness, so the distortion of the image of
the source across a larger area of sky implies magnification.
The Einstein ring radius is given by:
Suppose now that the lens is moving with a velocity v. At time t, the apparent distance
(in the absence of lensing) in the lens plane between the source and lens is r0.
Defining u = r0 / R0, the amplification is:
Note: for u > 0, there is no symmetry, so the pattern of images is not a ring and is
generally complicated. In microlensing we normally only observe the magnification A,
so we ignore this complication...
Notes:
(1) The peak amplification depends upon the impact parameter, small impact
parameter implies a large amplification of the flux from the source star
(2) For u = 0, apparently infinite magnification! In reality, finite size of source
limits the peak amplification
(3) Geometric effect: affects all wavelengths equally
(4) Rule of thumb: significant magnification requires an impact parameter
smaller than the Einstein ring radius
(5) Characteristic timescale is the time required to cross the Einstein ring radius:
PH507
Astrophysics
Professor Glenn White
4
Optical depth to microlensing
Define the optical depth to microlensing as:
This is just the integral of the area of the Einstein ring along the line of sight to the
source. For a uniform density of lenses, can easily show that the maximum contribution
comes from lenses halfway to the source.
Several groups have monitored stars in the Galactic bulge and the Magellanic clouds to
detect lensing of these stars by foreground objects (MACHO, Eros, OGLE projects).
Original motivation for these projects was to search for dark matter in the form of
compact objects in the halo.
Timescales for sources in the Galactic bulge, lenses ~ halfway along the line of sight:
• Solar mass star ~ 1 month
• Jupiter mass planet ~ 1 day
• Earth mass planet ~ 1 hour
The dependence on M1/2 means that all these timescales are observationally feasible.
However, lensing is a very rare event, all of the projects monitor millions of source
stars to detect a handful of lensing events.
Lensing by a single star
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Astrophysics
Lensing by a star and a planet
Professor Glenn White
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Astrophysics
Professor Glenn White
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What has this to do with planets?
Binaries can also act as lenses
Light curve for a binary lens is more complicated, but a characteristic is the presence of
sharp spikes or caustics. With good enough monitoring, the parameters of the binary
doing the lensing can be recovered.
Orbiting planet is just a binary with mass ratio q << 1
Planet search strategy:
• Monitor known lensing events in realtime with dense, high precision
photometry from several sites
• Look for deviations from single star lightcurve due to planets
• Timescales ~ a day for Jupiter mass planets, ~ hour for Earths
• Most sensitive to planets at a ~ R0, the Einstein ring radius
• Around 3-5 AU for typical parameters
Sensitivity to planets
Complementary to other methods:
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Astrophysics
Professor Glenn White
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Actual sensitivity is hard to evaluate: depends upon frequency of photometric
monitoring (high frequency needed for lower masses), accuracy of photometry (planets
produce weak deviations more often than strong ones)
Very roughly: observations with percent level accuracy, several times per night, detect
Jupiter, if present, with 10% efficiency
Many complicated light curves observed:
...but no strong evidence for planets seen yet
RV, Doppler technique (v = 3m/s)
PH507
Astrophysics
Professor Glenn White
Astrometry: angular oscillation
Photometry: transits - close-in planets
Microlensing:
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Astrophysics
Professor Glenn White
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Photometric :
2005 image of 2M1207 (blue) and its planetary companion, 2M1207b, one of the
first exoplanets to be directly imaged, in this case from the Very Large
Telescope array in Chile
Direct detection!
Spectroscopic? The starlight scattered from the planet can be distinguished
from the direct starlight because the scattered light is Doppler shifted by virtue
of the close-in planet's relatively fast orbital velocity (~ 150 km/sec).
Superimposed on the pattern given by the planet's albedo changing slowly with
wavelength, the spectrum of the planet's light will retain the same pattern of
photospheric absorption lines as in the direct starlight.
Lecture 8 The extrasolar planet population
Current status of exoplanet searches:
Radial Velocity Method (Doppler technique, gravitational wobble)
• 156 exoplanets hosted by134 stars discovered, with masses M.sin(i) as low as 6
Earth masses. Generally:~ 0.06 MJ and 10MJ…
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Astrophysics
Professor Glenn White
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PH507
Astrophysics
Professor Glenn White
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and orbital radii from 0.02 AU to 6 AU.
• Planet fraction among ~ solar-type stars exceeds 7%
• Most are beyond 1 AU
• Around 1% of stars have hot Jupiters - massive planets at orbital radii a < 0.1
AU
• Four very low mass planets have been detected ….20 earth masses.
• Planet occurrence rises rapidly with stellar metallicity
• Multiple planets are common, often in resonant orbits
Microlensing: two strong 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: 7 known planets (5 found with OGLE photometrically – dimming).
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.
Direct Imaging: reports of detections with HST and VLT.
Eccentricity: • Except at very small radii, typical planet orbit has significant
eccentricity
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Astrophysics
Professor Glenn White
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PH507
Astrophysics
Professor Glenn White
Eccentricity:
Eccentricity vs planet mass
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Astrophysics
Professor Glenn White
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Nothing very striking in these plots:
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Astrophysics
Professor Glenn White
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• Accessible region of mp - a space is fully occupied by detected planets
• Ignoring the hot Jupiters, no obvious correlation between planet mass and
eccentricity...
Results from radial velocity searches
(1) 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.
(2) 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.
(3) 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.
PH507
Astrophysics
Professor Glenn White
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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.
Models suggest 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
Observed mass function increases to smaller Mp:
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Astrophysics
Note: the brown dwarf desert!
Professor Glenn White
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PH507
Astrophysics
Professor Glenn White
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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 - not yet
known whether there is a difference in the planet fraction between 0.3 - 1 Solar
mass stars.
Transit lightcurve from Brown et al. (2001)
Consistent with expectations - the probability of a transiting system is ~10%.
Measured planetary radius rp = 1.35 J:
• Proves we are dealing with a gas giant.
• Somewhat larger than models for isolated (non-irradiated) planets effect of environment on structure.
• In detail, suggests planet reached its current orbit within a few x 10 Myr
after its formation.
Precision of photometry with HST / STIS impressive...
Metallicity distribution of stars with and without planets
PH507
Astrophysics
Professor Glenn White
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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)
Host star metallicity
Planets are preferentially found around stars with enhanced metal abundance.
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.
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 10 -3 x 34,000 ~ few tens of planets
None were detected. Possible explanations:
PH507
Astrophysics
Professor Glenn White
• 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.
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