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PH507 Astrophysics Dr Dirk Froebrich 1 Lecture 7: Extrasolar Planets 01/08/2013 update: 725 exoplanets (exoplanet.eu) Resources. For observations, a good starting point is Berkeley extrasolar planets search homepage http://exoplanets.org/ http://exoplanet.eu/catalog-RV.php Candidates detected by radial velocity 424 planets Candidates detected by transits 277 planets Candidates detected by microlensing or imaging 20 planets from microlensing 14 planets from imaging Candidate pulsar planets 4 planets 1candidate planet Kepler Candidate planets 3161 planets There are 104 planets in systems with more or equal to two planets. Although few of the planets have been directly imaged, the effects of the gravity tugging at the stars, as well as the way that gravitation affects can affect material close to the stars, has been clearly seen. PH507 Astrophysics Dr Dirk Froebrich 2 Disc of material around the star Beta Pictoris – the image of the bright central star has been artificially blocked out by astronomers using a ‘Coronograph’ • How can we discover extrasolar planets? • Characteristics of the exoplanet population • Planet formation • Explaining the properties of exoplanets Rapidly developing subject - first extrasolar planet around an ordinary star only discovered in 1995 by Mayor & Queloz. Observations thought to be secure, but theory still preliminary... Theory: Annual Reviews article by Lissauer (1993) is a good summary of the state of theory prior to the discovery of extrasolar planets Definition of a planet Simplest definition is based solely on mass • Stars: burn hydrogen (M > 0.075 Msun) • Brown dwarfs: burn deuterium • Planets: do not burn deuterium (M < 0.013 Msun) Deuterium burning limit occurs at around 13 Jupiter masses (1 MJ = 1.9 x 1027 kg ~ 0.001 Msun It is important to realise that for young objects, there is no large change in properties at the deuterium burning limit. ALL young stars / brown dwarfs / planets liberate gravitational potential energy as they contract PH507 Astrophysics Dr Dirk Froebrich 3 Types of planet Giant planets (gas giants, `massive’ planets) • Solar System prototypes: Jupiter, Saturn, Uranus... • Substantial gaseous envelopes • Masses of the order of Jupiter mass • In the Solar System, NOT same composition as Sun • Presence of gas implies formation while gas was still prevalent Terrestrial planets • Prototypes: Earth, Venus, Mars • Primarily composed of rocks • In the Solar System (ONLY) orbital radii less than giant planets Much more massive terrestrial planets could exist (>10 Earth masses), though none are present in the Solar System. The Solar system also has asteroids, comets, planetary satellites and rings - we won’t discuss those in this course. Detecting extrasolar planets (1) Direct imaging - difficult due to enormous star / planet flux ratio (2) Radial velocity • Observable: line of sight velocity of star orbiting centre of mass of star - planet binary system • Most successful method so far (3) Astrometry • Observable: stellar motion in plane of sky • Very promising future method: Keck interferometer, GAIA PH507 Astrophysics Dr Dirk Froebrich 4 (4) Transits • Observable: tiny drop in stellar flux as planet transits stellar disc • Requires favourable orbital inclination • Jupiter mass exoplanet observed from ground (HD209458b) • Earth mass planets detectable from space (Kepler, TESS - 2017) (5) Gravitational lensing • Observable: light curve of a background star lensed by the gravitational influence of a foreground star. The light curve shape is sensitive to whether the lensing star is a single star or a binary (star + planet is a special case of the binary) • Rare - requires monitoring millions of background stars, and also unrepeatable • Some sensitivity to Earth mass planets Each method has different sensitivity to planets at various orbital radii - complete census of planets requires use of several different techniques Planet detection method : Radial velocity technique This is also known as the "Doppler method". Variations in the speed with which the star moves towards or away from Earth — that is, variations in the radial velocity of the star with respect to Earth — can be deduced from the displacement in the parent star's spectral lines due to the Doppler effect. This has been by far the most productive technique used by planet hunters. A planet in a circular orbit around star with semi-major axis a Assume that the star and planet both rotate around the centre of mass with an angular velocity: Using a1 M* = a2 mp and a = a1 + a2, then the stellar speed (v* = aΩ) in an inertial frame is: PH507 Astrophysics Dr Dirk Froebrich 5 (assuming mp << M*). i.e. the stellar orbital speed is small….just meters per second! For a circular orbit, observe a sin-wave variation of the stellar radial velocity, with an amplitude that depends upon the inclination of the orbit to the line of sight: Hence, measurement of the radial velocity amplitude produces a constraint on: mp * sin(i) (assuming stellar mass is well-known, as it will be since to measure radial velocity we need exceptionally high S/N spectra of the star). Observable is a measure of mp sin(i). -> given vobs, we can obtain a lower limit to the planetary mass In the absence of other constraints on the inclination, radial velocity searches provide lower limits on planetary masses Magnitude of radial velocity: Sun due to Jupiter: 12.5 m/s Sun due to Earth: 0.1 m/s i.e. extremely small - 10 m/s is Olympic 100m running pace Spectrograph with a resolving power of 105 will have a pixel scale ~ 10-5 c ~ few km/s Therefore, specialized techniques that can measure radial velocity shifts of ~10-3 of a pixel stably over many years are required PH507 Astrophysics Dr Dirk Froebrich 6 High sensitivity to small radial velocity shifts is achieved by: • comparing high S/N = 200-500 spectra with template stellar spectra • using a large number of lines in the spectrum to allow shifts of much less than one pixel to be determined. • correcting for Earth’s rotation and motion in orbit, accurate timing and position required Absolute wavelength calibration and stability over long timescales is achieved by: • passing stellar light through a cell containing iodine, imprinting large number of additional lines of known wavelength into the spectrum • with the calibrating data suffering identical instrumental distortions as the data Error sources: (1) Theoretical: photon noise limit • flux in a pixel that receives N photons uncertain by ~ N1/2 • implies absolute limit to measurement of radial velocity • depends upon spectral type - more lines improve signal • around 1 m/s for a G-type main sequence star with spectrum recorded at S/N=200 • practically, S/N=200 can be achieved for V=8 stars on a 3m class telescope in survey mode (2) Practical: • stellar activity - young or otherwise active stars are not stable at the m/s level and cannot be monitored with this technique • remaining systematic errors in the observations PH507 Astrophysics Dr Dirk Froebrich 7 Currently, the best observations achieve: σ ~ 3 m/s ...in a single measurement. Thought this error can be reduced to around 1…0.6m/s with further refinements, but not substantially further. The very highest Doppler precisions of 1m/s are capable of detecting planets down to about 5 earth masses. Radial velocity monitoring detects massive planets, especially those at small a, but is not sensitive enough to detect Earth-like planets at ~ 1AU. Examples of radial velocity data 51 Peg b was the first known exoplanet with a 4 day, circular orbit: a hot Jupiter, lying close to the central star. PH507 Astrophysics Dr Dirk Froebrich 8 Example of a planet with an eccentric orbit: e=0.67 Summary of observables (1) Planet mass, up to an uncertainty from the normally unknown inclination of the orbit. Measure mp * sin(i) (2) Orbital period -> radius of the orbit given the stellar mass (3) Eccentricity of the orbit Summary: selection function Need to observe full orbit of the planet: zero sensitivity to planets with P>Psurvey For P<Psurvey, minimum mass planet detectable is one that produces a radial velocity signature of a few times the sensitivity of the experiment (this is a practical detection threshold) PH507 Astrophysics Dr Dirk Froebrich 9 Which planets are detectable? For a given radial velocity amplitude: m p sin i ∝ a 1 2 Hence, inner massive planets are selected. Current limits: • Maximum a ~ 3.5AU (i.e. orbital period ~ 7 years) • Minimum mass ~ 0.5 Jupiter masses at 1AU, scaling with square root of semi-major axis • No strong selection bias in favour/against detecting planets with different eccentricities Of the first 100 stars found to harbor planets, more than 30 stars host a Jupiter-sized world in an orbit smaller than Mercury's, whizzing around its star in a matter of days. This implies: Planet formation is a contest, where a growing planet must fight for survival lest it be swallowed by the star that initially nurtured it. Planet detection method : Astrometry The gravitational perturbations of a star's position by an unseen companion provides a signature which can be detected through precision astrometry. While very accurate wide-angle astrometry is only possible from space with a mission like the Space Interferometry Mission (SIM), narrow-angle astrometry with an accuracy of tens of micro arcseconds is possible from the ground with an optimised instrument. Conceptually identical to radial velocity searches. Light from a planet-star binary is dominated by the star. Measure stellar motion in the plane of the sky due to presence of orbiting planet. Must account for parallax and proper motion of star. PH507 Astrophysics Dr Dirk Froebrich 10 Magnitude of effect: amplitude of stellar wobble (half peak displacement) for an orbit in the plane of the sky is mp × a a1 = M * In terms of the angle: m p a ∆θ = M * d for a star at distance d. Note we have again used mp << M* Writing the mass ratio q = mp / M*, this gives: A Jupiter around a Sun at 10pc would produce a wobble with an amplitude of 0.5 milliarcseconds. Note: • Units here are milliarcseconds - very small effect • Different dependence on a than radial velocity method - astrometric planet searches are more sensitive at large a • Explicit dependence on d (radial velocity measurements also less sensitive for distant stars due to lower S/N spectra) • Detection of planets at large orbital radii still requires a search time comparable to the orbital period Detection threshold as function of semi-major axis PH507 Astrophysics Dr Dirk Froebrich 11 • Lack of units deliberate! Astrometric detection not yet achieved • As with radial velocity, dependence on orbital inclination, eccentricity • Very promising future: Keck interferometer, Space Interferometry Mission (SIM), ESA mission GAIA, and others • Planned astrometric errors at the ~10mas level – good enough to detect planets of a few Earth masses at 1AU around nearby stars Lecture 8 Planet detection method : Transits - Photometry 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 PH507 Astrophysics Dr Dirk Froebrich 12 What can we measure from the light curve? (1) Depth of transit = fraction of stellar light blocked This is a measure of planetary radius, NOT the mass! The method suffers from a high rate of false detections. A transit detection requires additional confirmation, typically from the radial-velocity method. 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). -> 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) Duration of transit plus duration of ingress, gives measure of the orbital radius and inclination (3) Bottom of light curve is not actually flat, providing a measure of stellar limb-darkening (4) 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: PH507 Astrophysics Dr Dirk Froebrich 13 Photometric precision of ~ 10-5 seems achievable from space May provide first detection of habitable Earth-like planets NASA’s Kepler mission, and planned successor TESS 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 Microlensing operates by a completely different principle, based on Einstein's General Theory of Relativity. According to Einstein, when the light emanating from a star passes very close to another star on its way to an observer on Earth, the gravity of the intermediary star will slightly bend the light rays from the source star, causing the two stars to appear farther apart than they normally would. This effect was used by Sir Arthur Eddington in 1919 to provide the first empirical evidence for General Relativity. In reality, even the most powerful Earth-bound telescope cannot resolve the separate images of the source star and the lensing star between them, seeing instead a single giant disk of light, known as the "Einstein disk," where a star had previously been. The resulting effect is a sudden dramatic increase in the brightness of the lensing star, by as much as 1,000 times. This typically lasts for a few weeks or months before the source star moves out of alignment with the lensing star and the brightness subsides. 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 PH507 Astrophysics Dr Dirk Froebrich 14 Define: • 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... PH507 Astrophysics Dr Dirk Froebrich 15 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: 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 PH507 Astrophysics Dr Dirk Froebrich 16 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 Lensing by a star and a planet PH507 Astrophysics Dr Dirk Froebrich 17 Planet detection through microlensing The microlensing process in stages, from right to left. The lensing star (white) moves in front of the source star (yellow) doubling its image and creating a microlensing event. In the fourth image from the right the planet adds its own microlensing effect, creating the two characteristic spikes in the light curve. Credit: OGLE Planet search strategy: • Monitor known lensing events in realtime with dense, high precision photometry from several sites • Look for deviations from single star light curve 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: PH507 Astrophysics Dr Dirk Froebrich 18 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: The microlensing event that led to the discovery of the new planet was first observed by the Poland-based international group OGLE, the Optical Gravitational Lensing Experiment. The microlensing light curve of planet OGLE–2005-BLG-390Lb The general curve shows the microlensing event peaking on July 31, 2005, and then diminishing. The disturbance around August 10 indicates the presence of a planet. OGLE –2005-BLG-390Lb will never be seen again. PH507 Astrophysics Dr Dirk Froebrich 19 At around five times the mass of Earth, the new planet, designated OGLE– 2005-BLG-390Lb, is the lowest-mass planet ever detected outside the solar system. And when one considers that the vast majority of the approximately 270 extrasolar planets detected so far have been Jupiter-like gas giants, dozens or hundreds of times the mass of Earth, the discovery of a planet of only five Earth masses is indeed good news. PH507 Astrophysics Dr Dirk Froebrich 20 Planet detection method: Direct detection! 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 Infrared image of 2M1207 (blue) and its planet 2M1207b, as viewed by the Very Large Telescope. As of September 2006 this was the first confirmed extrasolar planet to have been directly imaged. 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. PH507 Astrophysics Dr Dirk Froebrich 21 Located just 500 light-years away toward the constellation Scorpius, this star is only slightly less massive and a little cooler than the Sun. But it is much younger, a few million years old compared to the middle-aged Sun's 5 billion years. This sharp infrared image shows the young star has a likely companion positioned above and left - a hot planet with about 8 times the mass of Jupiter, orbiting a whopping 330 times the EarthSun distance from its parent star. The young planetary companion is still hot and relatively bright in infrared light due to the heat generated during its formation by gravitational contraction. In fact, such newborn planets are easier to detect before they age and cool, becoming much fainter. Though over 300 extrasolar planets have been found using other techniques, this picture likely represents the first direct image of a planet belonging to a star similar to the Sun. PH507 Astrophysics Dr Dirk Froebrich 22 Fomalhaut (sounds like "foam-a-lot") is a bright, young, star, a short 25 light-years from planet Earth in the direction of the constellation Piscis Austrinus. In this sharp composite from the Hubble Space Telescope, Fomalhaut's surrounding ring of dusty debris is imaged in detail, with overwhelming glare from the star masked by an occulting disk in the camera's coronagraph. Astronomers now identify, the tiny point of light in the small box at the right as a planet about 3 times the mass of Jupiter orbiting 10.7 billion miles from the star (almost 23 times the Sun-Jupiter distance). Designated Fomalhaut b, the massive planet probably shapes and maintains the ring's relatively sharp inner edge, while the ring itself is likely a larger, younger analog of our own Kuiper Belt - the solar system's outer reservoir of icy bodies. The Hubble data represent the first visiblelight image of a planet circling another star. PH507 Astrophysics Dr Dirk Froebrich 23 In the twelve years previous to 2008, over 300 candidate planetary systems have been found orbiting nearby stars. None, however, were directly imaged, few showed evidence for multiple planets, and many had a Jupitersized planet orbiting inside the orbit of Mercury. Last week, however, together with recent images of Fomalhaut b, the above picture was released showing one of first confirmed images of planets orbiting a distant Sun-like star. HR 8799 has a mass about 1.5 times that of our own Sun, and lies about 130 light years from the Sun -- a distance similar to many stars easily visible in the night sky. Pictured above, a 10-meter Keck telescope in Hawaii captured in infrared light three planets orbiting an artificially obscured central star. The 8-meter Gemini North telescope captured a similar image. Each planet likely contains several times the mass of Jupiter, but even the innermost planet, labelled d, has an orbital radius near the equivalent of the Sun- Neptune distance. Although the HR 8799 planetary system has significant differences with our Solar System, it is a clear demonstration that complex planetary systems exist, systems that could conceivable contain an Earth-like planet. PH507 Astrophysics Dr Dirk Froebrich 24 A mere 50 light-years away, young star Beta Pictoris became one of the most important stars in the sky in the early 1980s. Satellite and groundbased telescopic observations revealed the presence of a surrounding outer, dusty, debris disk and an inner clear zone about the size of our solar system -- strong evidence for the formation of planets. Now, infrared observations from European Southern Observatory telescopes incorporated in this composite offer a detection of a source in the clear zone that is most likely a giant planet orbiting Beta Pic. Designated Beta Pictoris b, the new source is more than 1,000 times fainter than the direct starlight that has been carefully subtracted from the image data. It is aligned with the disk at a projected distance that would place it near the orbit of Saturn if found in our solar system. Confirmation that the new source is a planet will come if future observations can demonstrate that the source moves in an orbit around the star. When confirmed, it will be the closest planet to its parent star directly imaged ... so far. PH507 Astrophysics Dr Dirk Froebrich 25 Pulsar Planets In early 1992, the Polish astronomer Aleksander Wolszczan (with Dale Frail) announced the discovery of planets around a pulsar, PSR 1257+12. This discovery was quickly confirmed, and is generally considered to be the first definitive detection of exoplanets. These pulsar planets are believed to have formed from the unusual remnants of the supernova that produced the pulsar, in a second round of planet formation, or else to be the remaining rocky cores of gas giants that survived the supernova and then spiralled in to their current orbits. • Pulsar timing Pulsars (the small, ultradense remnant of a star that has exploded as a supernova) emit radio waves extremely regularly as they rotate. Slight anomalies in the timing of its observed radio pulses can be used to track changes in the pulsar's motion caused by the presence of planets. PH507 Astrophysics Dr Dirk Froebrich 4 Detecting extrasolar planets: summary RV, Doppler technique (v = 3 m/s) Astrometry: angular oscillation Photometry: transits - close-in planets Microlensing: 26 PH507 Astrophysics Dr Dirk Froebrich 27 Lecture 9: The extrasolar planet population http://exoplanet.eu/ The planets are listed with indications of their approximate masses as multiples of Jupiter 's mass (MJ = 1.898 × 1027 kg) or multiples of Earth's mass (ME = 5.9737 × 1024 kg), and have approximate distances in astronomical units (1AU = 1.496 × 108 km, distance between Earth and Sun) from their parent stars. According to astronomical naming conventions, the official designation for a body orbiting a star is the star's catalogue number followed by a letter. The star itself is designated with the letter 'a', and orbiting bodies by 'b', 'c', etc. DISTRIBUTIONS: PH507 Astrophysics Dr Dirk Froebrich 28 Metallicity: Observed Properties of Exoplanets: Masses, Orbits, and Metallicities Geoffrey Marcy et al…….2005 Summary: 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. PH507 Astrophysics Dr Dirk Froebrich 29 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 M Sat) has a massive rocky core, M Core ≈ 70 M Earth. 4) A super-Earth of about 7 M Earth has been discovered. 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 20AU. 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%. Among stars with one planet, 14% have at least one additional planet, occasionally locked in resonances. Kepler and COROT will measure the occurrence of earth-sized planets. The Space Interferometry Mission (SIM) will detect planets with masses as low as 3 M Earth orbiting within 2 AU of stars within 10 pc, and it will measure masses, orbits, and multiplicity. The candidate rocky planets will be amenable to follow-up spectroscopy by the “Terrestrial Planet Finder” and Darwin. PH507 Astrophysics Dr Dirk Froebrich 30 • Planet fraction among ~ solar-type stars exceeds 7% • Most are beyond 1 AU • Four very low mass planets have been detected ….20 earth masses. Other positive detections: Microlensing: 8 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: 55 known planets. 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: • Except at very small radii, typical planet orbit has 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. PH507 Astrophysics Dr Dirk Froebrich 31 PH507 Astrophysics Dr Dirk Froebrich 32 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. 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 zero. 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 has 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: Various theories have been proposed to explain the orbital eccentricities, but none is definitive at the current time. Most proposed mechanisms invoke gravitationally scattering or perturbations of planets by other planets, perhaps in resonances, or by interactions with the protoplanetary disk. Orbital eccentricity as a function of semi major axis for the 168 known nearby exoplanets: Planets within 0.1 AU are presumably tidally circularized. Beyond 0.1 AU, the distribution of eccentricities appears essentially uniform between 0.0 and 0.8. For most Doppler surveys, sensitivity is not a strong function of eccentricity for 0<e<0.8 and a<3AU. This plot represents results from many surveys, and so is drawn from an inhomogeneous sample. PH507 Astrophysics Distribution of Eccentricity: Eccentricity vs. planet mass Dr Dirk Froebrich 33 PH507 Astrophysics Dr Dirk Froebrich 34 Distribution of orbital eccentricities as a function of minimum mass for 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. This distribution represents results from many surveys, and so is drawn from an inhomogeneous sample. Ignoring the hot Jupiters, there is no obvious correlation between planet mass and eccentricity. (1) 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. (2) 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 Dr Dirk Froebrich Minimum mass as a function of semi major axis: 35 PH507 Astrophysics Dr Dirk Froebrich 36 Nothing very striking in these plots: • Accessible region of mp - a space is fully occupied by detected planets Get rid of the log (Mj) : PH507 Astrophysics Dr Dirk Froebrich 37 Minimum mass as a function of semi major 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 (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. 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. PH507 Astrophysics Dr Dirk Froebrich 38 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. PH507 Astrophysics Dr Dirk Froebrich 39 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 This 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 PH507 Astrophysics Dr Dirk Froebrich 40 Orbital distance distribution of the 167 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 PH507 Astrophysics Dr Dirk Froebrich 41 Distribution of periods among the known nearby “hot Jupiters”. There is a clear “pile-up” of planets with orbital periods near 3 days. Doppler surveys generally have uniform sensitivity to hot Jupiters, so for massive planets, there is no important selection effect contributing to the 3-day pileup. This distribution represents results from many surveys, and so is drawn from an inhomogeneous sample. PH507 Astrophysics Dr Dirk Froebrich 42 Observed mass function increases to smaller Mp: Note: the brown dwarf desert! Minimum mass distribution of the 167 known nearby exoplanets with M sin i < 15 MJup. 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-1.16. Lower mass planets have smaller Doppler amplitudes, so the relevant selection effects enhance this effect. This distribution represents results from many surveys, and so is drawn from an inhomogeneous sample. PH507 Astrophysics Dr Dirk Froebrich 43 Metallicity distribution of stars with and without planets 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) PH507 Astrophysics Dr Dirk Froebrich 44 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 ([M/H]=-0.7 --- high for a GlCl) 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: • 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. PH507 Astrophysics Dr Dirk Froebrich 45 Microlensing Statistics: 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. This is currently consistent with the numbers seen in radial velocity searches. PH507 Astrophysics Dr Dirk Froebrich 46 HST Transit light curve from Brown et al. (2001) Consistent with expectations - the probability of a transiting system is ~10%. Measured planetary radius rp = 1.35 RJ: • Proves we are dealing with a gas giant. • Somewhat larger than models for isolated (non-irradiated) planets effect of environment on structure. Precision of photometry with HST / STIS impressive. Summary of Current/Future Missions CoRoT is a space project in Astrophysics - Convection, Rotation and Transits Its objective is double: - study the stellar interiors - detect planets analogous to the Earth orbiting around other stars than the Sun. The satellite will orbit at an altitude of 896 km. It will carry a telescope able to observe continuously many stars during very long periods and to PH507 Astrophysics Dr Dirk Froebrich 47 measure very accurately the variations of their brightness. ALREADY 25 PLANETS DISCOVERED! http://corot.oamp.fr/ Figure 1. Transit of a planet (decrease of the luminosity of the hosting star when the planet passes in front of it) as observed by Corot. The parent star is a Sun-like star. The planet is a very hot giant planet, similar to Jupiter but orbiting its star in 1.5 day, and with an estimate of the radius between 1.5 time and 1.8 time Jupiter's radius (given Corot's excellent photometric data, most of the uncertainty is in fact due to the uncertainty on the radius of the parent star, which is still preliminary). Thanks to combined spectroscopic observations from the ground, the mass of the planet has also been measured around 1.3 time that of Jupiter. PH507 Astrophysics ….down to earth-like planets. Kepler: 2008 - Transit method SIM and Gaia: astrometry Dr Dirk Froebrich 48 PH507 Astrophysics Dr Dirk Froebrich 49 Lectures: Star Formation & Theory of Exoplanets 1. Intro: Star formation is on-going. • What is the origin of our solar system? Descartes, Kant, Laplace: vortices, nebular hypothesis: importance of angular momentum. Major facts for nebula hypothesis: • Coplanar orbits of the planets • All planets have prograde revolution (orbits) • The revolution of rings and natural moons are all prograde (some moons of the outer planets are not prograde, but these are believed to be captured satellites) • All planets except Venus and Uranus have prograde rotation • The Sun contains all the mass • The planets (especially Jupiter and Saturn) contain most of the angular momentum in the solar system • Small, dense, iron and silicate rich planets in the inner 2 AU. Slow rotors, few or no moons, no rings, differentiated (molten interiors) PH507 Astrophysics Dr Dirk Froebrich 50 • Large, low density, gaseous planets rich in H, He and volatile elements at >= 5 AU • Rapid rotors, many moons, all have ring systems • Abundance gradient. Inner solar system is poor in light volatile gases such as H, He, but rich in Fe & Ni. Outer solar system is rich in volatiles H, He, etc. Abundances similar to that of the sun. • In general: Gravity is fast-acting. Galaxy is old. But young stars are still being born. • Stars don't live forever, they must continue to be "born". Where? • Born in obscurity….needed infrared/millimeter/radio wavelengths. Gas Disks around Young Stars During star formation, gas accretion occurs through a geometrically thin disk that is optically thick. The disks are cooler than the young star, and we thus see an infrared excess superimposed on the black body stellar spectrum: PH507 Astrophysics Dr Dirk Froebrich 51 PH507 Astrophysics Dr Dirk Froebrich 52 PH507 Astrophysics Dr Dirk Froebrich 53 Debris Disks Debris disks are remnant accretion disks with little or no gas left (just dust & rocks), outflow has stopped, the star is visible. Theory: Gas disperses, “planetesimals” form (100 km diameter rocks), collide & stick together due to gravity forming protoplanets). Protoplanets interact with dust disks: tidal torques cause planets to migrate inward toward their host stars. Estimated migration time ~ 2 x 105 yrs for Earth-size planet at 5 AU. Perturbations caused by gas giants may spawn smaller planets: Start with a stable disk around central star. Jupiter-sized planet forms & clears gap in gas disk. Planet accretes along spiral Disk fragments into more arms, arms become unstable. planetary mass objects. Spiral density waves continuously produced by the gravity of embedded or external perturber. Debris Disks – Outer Disk AB Aurigae outer debris disk nearly face on – see structure & condensations (possible protoplanet formation sites? Very far from star) . (Grady et al. 1999) PH507 Astrophysics Dr Dirk Froebrich 54 Debris: not from original nebula but from recent collisions. After a few hundred million years, a planetary system is expected to have assumed its final configuration and has either set the stage for life, or will probably remain barren forever. It is difficult to probe this era. Most of its traces have been obliterated in the solar system. Only a minority of the nearby stars are so young. Even for them, planets—and particularly those in the terrestrial planet/asteroidal region—are faint and are lost in the glare of their central stars. However, when bodies in this zone collide, they initiate cascades of further collisions among the debris and between it and other members of the system, eventually grinding a significant amount of material into dust grains distributed in a so-called debris disk. Because the grains have larger surface area per unit mass compared to larger bodies, they (re)radiate more energy and therefore are more easily detected in the IR compared to their parent bodies. By studying this signal, we can probe the evolution of other planetary systems through this early, critical stage. Debris disks are found around stars generally older than 10 Myr, with no signs of gas accretion (as judged from the absence of emission lines or UV excess) (Lagrange et al. 2000; Hillenbrand 2005). In the absence of gas drag, a 10 µm sized dust grain from the primordial, proto–planetary nebula cannot survive longer than ~1 Myr within 10 AU of a star due to a number of clearing processes, such as sublimation, radiation pressure, PoyntingRobertson, and stellar wind drag (Backman & Paresce 1993; Chen et al. 2005a). Therefore, any main-sequence star older than 10 Myr with an IR excess is a candidate to have circumstellar material supplied through debris disk processes. The Birth of the Solar System The properties of the Solar System hold important clues to its origin • • • Orbits of the planets and asteroids. Rotation of the planets and the Sun. Composition of the planets, especially the strong distinction between Terrestrial, Jovian, and Icy planets. Clues from planetary motions: • • • • • • Planets orbit in nearly the same plane. Planet orbits are nearly circular. Planets & Asteroids orbit in the same direction. Rotation axes of the planets tend to align with the sense of their orbits, with exceptions. Sun rotates in the same direction in the same sense. Jovian moon systems mimic the Solar System. PH507 Astrophysics Dr Dirk Froebrich 55 Clues from planet composition: Inner Planets & Asteroids: • • Small rocky bodies Few ices or volatiles Jovian Planets: • • Deep Hydrogen & Helium atmospheres rich in volatiles. Large ice & rock cores Outer solar system moons & icy bodies: • Small ice & rock mixtures with frozen volatiles. Formation of the Sun: back to the Primordial Solar Nebula Stars form out of interstellar gas clouds: • Large cold cloud of H2 molecules and dust gravitationally collapses and fragments. Rotating fragments collapse further: • • • Rapid collapse along the poles, but centrifugal forces slow the collapse along the equator. Result is collapse into a spinning disk Central core collapses into a rotating proto-Sun surrounded by a rotating "Solar Nebula" Primordial Solar Nebula The rotating solar nebula is composed of • • ~75% Hydrogen & 25% Helium Traces of metals and dust grains Starts out at ~2000 K, then cools: • • As it cools, various elements condense out of the gas into solid form as grains or ices. Which materials condense out when depends on their "condensation temperature" Condensation Temperatures PH507 Astrophysics Temp (K) Elements Dr Dirk Froebrich 56 Condensate >2000 K All elements are gaseous 1600 K Al, Ti, Ca Mineral Oxides 1400 K Iron & Nickel Metallic Grains – Refractory, Rocky 1300 K Silicon Silicate Grains - Rocky 300 K Carbon, Oxygen Carbonaceous grains -Volatiles 300-100 K Hydrogen, Nitrogen Ices (H2O, CO2, NH3, CH4) The "Frost Line" Rock & Metals can form anywhere it is cooler than about 1300 K. Carbon grains & ices can only form where the gas is cooler than 300 K. Inner Solar System: • Too hot for ices & carbon grains. Outer Solar System: • Carbon grains & ices form beyond the "frost line". The location of the "frost line" is also a matter of some debate but current thinking holds that it is probably about 4 AU. A great deal depends on how much solar radiation can penetrate deep into the outer parts of the primordial Solar Nebula. From Grains to Planetesimals to Planets Grains that have low-velocity collisions can stick together, forming bigger grains. • • Beyond the "frost line", get additional growth by condensing ices onto the grains. Grow to where their mutual gravitation assists in the aggregation process, accelerating the growth rate. Can form km-sized planetesimals after a few 1000 years of initial growth. • Aggregation of planetesimals into planets Terrestrial vs. Jovian planet formation. PH507 Astrophysics Dr Dirk Froebrich 57 Terrestrial Planets Only rocky planetesimals inside the frost line: • • • Collisions between planetesimals form small rocky bodies. It is hotter closer to the Sun, so the proto-planets cannot capture H and He gas. Solar wind is also dispersing the solar nebula from the inside out, removing H & He. Result: • Form rocky terrestrial planets with few ices. Jovian Planets The addition of ices to the mix greatly augments the masses of the planetesimals These collide to form large rock and ice cores:. • • Jupiter & Saturn: 10-15 MEarth rock/ice cores. Uranus & Neptune: 1-2 MEarth rock/ice cores. As a consequence of their larger masses & colder temperatures: • • Can accrete H & He gas from the solar nebula. Planets with the biggest cores grow rapidly in size, increasing the amount of gas accretion. Result: • Form large Jovian planets with massive rock & ice cores and heavy H and He atmospheres Moons & Asteroids Some of the gas attracted to the proto-Jovians forms a rotating disk of material: • • • Get mini solar nebula around the Jovians Rocky/icy moons form in these disks. Later moons added by asteroid/comet capture. Asteroids: • Gravity of the proto-Jupiter keeps the planetesimals in the main belt stirred up. PH507 • Astrophysics Dr Dirk Froebrich 58 Never get to aggregate into a larger bodies. Icy Bodies & Comets Outer reaches are the coldest, but also the thinnest parts of the Solar Nebula: • • Ices condense very quickly onto rocky cores. Stay small because of a lack of material. Gravity of the proto-Neptune also plays a role: • • Assisted the formation of Pluto-sized bodies in 3:2 resonance orbits (Pluto and Plutinos) Disperses the rest into the Kuiper Belt to become Kuiper Belt Objects. Comets and other Trans-Neptunian objects are the leftover icy planetesimals from the formation of the Solar System. Mopping up... The entire planetary assembly process probably took about 100 Million years. Followed by a 1 Billion year period during which the planets were subjected to heavy bombardment by the remaining rocky & icy pieces leftover from planet formation. Light from the Sun dispersed the remaining gas in the Solar Nebula gas into the interstellar medium. Planetary motions reflect the history of their formation. Planets share the same sense of rotation, but have been perturbed from perfect alignment by strong collisions during formation. The Sun "remembers" this original rotation. Rotates in the same direction with its axis aligned with the plane of the Solar System. Planetary compositions reflect the formation conditions. Terrestrial planets are rock & metal: • • They formed in the hot inner regions of the Solar Nebula. Too hot to capture Hydrogen/Helium gas from the Solar Nebula. Jovian planets contain ice, H & He: • • They formed in the cool outer regions of the Solar Nebula. Grew large enough to accrete lots of H & He. PH507 Astrophysics Dr Dirk Froebrich 59 Two obvious differences between the exoplanets and the giant planets in the Solar System: • Existence of planets at small orbital radii, where our previous theory suggested formation was very difficult. • Substantial eccentricity of many of the orbits. No clear answers to either of these surprises, but lots of ideas... It is very difficult to form planets close to the stars in a standard theory of planet formation using minimum mass solar nebula, because • • • • it's too hot there for grain condensation and there's too little solid material in the vicinity to built protoplanet's core of 10 ME (applies to r~1 AU as well). problematic to build it quickly enough (< 3 Myr) there's too little gas to build a massive envelope Most conservative (accepted) possibility: • Planet formation in these extrasolar systems was via the core accretion model – i.e. same as dominant theory for the Solar System • Subsequent orbital evolution modified the planet orbits to make them closer to the star and / or more eccentric PH507 Astrophysics Dr Dirk Froebrich 60 We will focus on this option. However, more radical options in which exoplanets form directly from gravitational instability are also possible. Gas+dust discs: Stage 1: Settling and growth of dust grains: quite well-coupled to gas, rapid only if turbulent? Gas orbits slightly slower than Keplerian, because the gas pressure is higher nearer the centre, providing an outward force additional to the centrifugal force From pebbles to planetesimals (km size): inward drift due to gas drag. So the pebble must grow quickly to avoid spiraling in. Stage 2: Planetesimal to rocky planet/gas-giant core: independent of gas. It is a slow process – gravitational dynamics (gravity increase the collision crosssection). Stage 3: Gas accretion onto core, Stage 4: Orbital evolution – migration Giant planets can form at large orbital radii. Need a migration mechanism that can move giant planets from formation at ~5 AU to a range of radii from 0.04 AU upwards. Three theories have been proposed: • Gas disc migration: planet forms within a protoplanetary disc and is swept inwards with the gas as the disc evolves and material accretes onto the star. The most popular theory, as by definition gas must have been present when gas giants form. • Planetesimal disc migration: as above, but planet interacts with a disc of rocks rather than gas. Planet ejects the rocks, loses energy, and moves inwards. PH507 Astrophysics Dr Dirk Froebrich 61 • Planet scattering: several massive planets form – subsequent chaotic orbital interactions lead to some (most) being ejected with the survivors moving inwards as above. Gas disc migration Planet interacts with gas in the disc via gravitational force. Strong interactions at resonances, e.g. where Ωdisc = nΩplanet, with n an integer. For example the 2:1 resonance, where n = 2, which lies at 2-2/3 rp = 0.63 rp Resonances at r < rp: Disc gas has greater angular velocity than planet. Loses angular momentum to planet -> moves inwards Resonances at r > rp: Disc gas has smaller angular velocity than planet. Gains angular momentum from planet -> moves outwards. Migration type I - no gap If the object has too small a mass to open a gap, it will drift inwards. The analysis of Type I migration relies on the (near) exact cancelling of the various torques. The planet, unless more massive than the surrounding disk, follows the disk's viscous flow. It is thought that the intrinsic imbalance of torques from the inner and outer disk determines this. It is very rapid, and may shift the protoplanetary core to arbitrarily small distance from the star in the allotted ~3 Myr time frame. Migration type II - inside an open gap Interaction tends to clear gas away from location of planet. Result: planet orbits in a gap largely cleared of gas and dust. Tidal locking of the planet in the gap. PH507 Astrophysics Dr Dirk Froebrich 62 This process occurs for massive planets (~ Jupiter mass) only. Earth mass planets remain embedded in the gas though gravitational torques can be very important source of orbital evolution for them too. How does this lead to migration? 1. Angular momentum transport in the gas (viscosity) tries to close the gap (diffusive evolution of an accretion disc). 2. Gravitational torques from planet try to open gap wider. 3. Gap edge set by a balance: -> Internal viscous torque = planetary torque 4. Planet acts as an angular momentum ‘bridge’: • Inside gap, outward angular momentum flux transported by viscosity within disc • At gap edge, flux transferred to planet via gravitational torques, then outward again to outer disc PH507 Astrophysics Dr Dirk Froebrich 63 • Outside gap, viscosity again operative Typically, gap extends to around the 2:1 resonances interior and exterior to the planet’s orbit. As disc evolves, planet moves within gap like a fluid element in the disc – i.e. usually inwards. Inward migration time ~ few x 105 yr from 5 AU. Mechanism can bring planets in to the hot Jupiter regime. This mechanism is quantitatively consistent with the distribution of exoplanets at different orbital radii – though the error bars are still very large! Eccentricity generation mechanisms Substantial eccentricities of many exoplanets orbits do not have completely satisfactory explanation. The theories can be divided into groups corresponding to different formation mechanisms: (A) Direct molecular cloud fragmentation (B) Protostellar disk fragmentation theories (C) Companion star-planet interaction (in double star like 16 Cyg) (D) Classical giant planet formation with planet-planet interaction (E) Resonant disk-planet interaction (D) Scattering among several massive planets Assumption: planet formation often produces a multiple system which is unstable over long timescales: • Chaotic evolution of a, e (especially e) • Orbit crossing • Eventual close encounters -> ejections • High eccentricity for survivors Advantages: • Given enough planets, close together, definitely works • Can produce very eccentric planets cf e=0.92 example discovered • Some (stable) multiple systems are already known Disadvantages: • Requires planets to form very close together. Is it plausible that unstable systems formed in a large fraction of extrasolar planetary systems? • Collisions may produce too many low e systems PH507 Astrophysics Dr Dirk Froebrich 64 (E) Disc interactions Assumption: gravitational interaction with disc generates eccentricity Advantages: • Same mechanism as invoked for migration • Works for just one planet in the system • Theoretically, interaction is expected to increase eccentricity if dominated by 3:1 resonance Disadvantages: • Gap is only expected to reach the 3:1 resonance for brown dwarf type masses, not massive planets. Smaller gaps definitely tend to circularize the orbit instead. • Seems unlikely to give very large eccentricities (B) Protoplanetary disc itself is eccentric Assumption: why should discs have circular orbits anyway? Eccentric disc -> eccentric planet? Not yet explored in much depth. A possibility, though again seems unlikely to lead to extreme eccentricities. Scattering theory is currently most popular, possibly augmented by interactions with other planets in resonant orbits.