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PH709 Extrasolar Planets - 6 Professor Michael Smith 1 Two obvious differences between the exoplanets and the giant planets in the Solar System: A) Existence of planets at small orbital radii, where our previous theory suggested formation was very difficult. B) Substantial eccentricity of many of the orbits. No clear answers to either of these surprises, but lots of ideas... The Problem: 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 build 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 PH709 Extrasolar Planets - 6 Professor Michael Smith 2 Disk gravitational instability theory. The more radical option in which exoplanets form directly from gravitational instability are also possible. This depends on the Jeans Mass. The Toomre parameter expresses the condition associated wit a disk: a disk needs to be sufficiently massive to be gravitationally unstable to overcome the shearing effects. http://www.astro.virginia.edu/class/whittle/astr553/Topic06/L ecture_6.html Jeans Length L : > L = cs2 / (G ) Toomre parameter Q: Q = cs / G ) < 1.5 where is the surface density of the disk (mass per unit area) and is the epicyclic frequency: 2 = 4 2 + R d2/dR and the angular rotation speed is 1. :(R) = GM/R3 2. Rigid body: (R) = constant, = 2 uniform density) 3. Keplerian:(R) = 1/R 3/2, = point mass) 4. Flat rotation; :(R) = 1/R, = 2 1/2 To form a solid core, the heavy elements must settle. Cooling is important for object to collapse – not clear this occurs sufficiently fast. PH709 Extrasolar Planets - 6 Professor Michael Smith 3 Core-accretion Theory. Most conservative (accepted) possibility: • Planet formation in these extrasolar systems was via the “core-accretion gas-capture” 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. We will focus on this option. PH709 Extrasolar Planets - 6 Professor Michael Smith 4 PH709 Extrasolar Planets - 6 Professor Michael Smith 5 Stage 1: Settling and growth of dust grains: quite well-coupled to gas. Rapid growth if turbulent motion increase collision rate? Grains settle toward the mid-plane of the gas disk. Gas orbits slightly slower than Keplerian, because the gas pressure is higher nearer the centre, providing an outward force in additional to the centrifugal force. Friction between gas and dust causes grains to decelerate and move in. 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 increases the collision cross-section). Stage 3: Gas accretion onto core When is the gas/dust bound to the planetesimal rather than the star? The Hill radius is found by equating the orbital periods of the planetesimal and the star. From Kepler’s law: P = 2p a3 G (M1 + M2 ) RHill = (Mp/M*)1/3 a PH709 Extrasolar Planets - 6 Professor Michael Smith 6 In this way, the planetesimal acquires mass, and the Hill Radius grows! Stage 4: Orbital evolution – migration Giant planets can form at large orbital radii. Need a migration mechanism that can move giant planets from formation site at ~5 AU to a range of radii from 0.04 AU upwards. Three theories have been proposed: • 1. 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. • 2. 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. • 3. 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 • migration from larger radii offers a plausible way to form giant planets at small radii, but: – – – why did the migration stop? why are the planetary semi-major axes distributed over a wide range? why did migration not occur in the solar system? PH709 Extrasolar Planets - 6 Professor Michael Smith 7 Disc ‘Clearing’ Planet interacts with gas in the disc via gravitational force. Strong interactions at resonances, e.g. where disc = nplanet, 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. 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. PH709 Extrasolar Planets - 6 Professor Michael Smith 8 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. PH709 Extrasolar Planets - 6 Professor Michael Smith 9 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 PH709 Extrasolar Planets - 6 Professor Michael Smith 10 • 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 The substantial eccentricities of many exoplanets orbits do not have a 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) • Some (stable) multiple systems are already known Disadvantages: • Requires planets to form very close together. PH709 Extrasolar Planets - 6 Professor Michael Smith 11 Is it plausible that unstable systems formed in a large fraction of extrasolar planetary systems? • Collisions may produce too many low e systems (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. THE PLANET ITSELF Luminosity evolution (theory) PH709 Extrasolar Planets - 6 50% of D burned Professor Michael Smith 12 50% of Li burned stars brown dwarfs “planets” Burrows et al. (2001) THE END FURTHER¬ READING: NOT PART OF EXOPLANET COURSE DARWIN – 2020 ? Life? PH709 Extrasolar Planets - 6 Professor Michael Smith 13 PH709 Extrasolar Planets - 6 Professor Michael Smith 14 7 Summary of (Future) Missions CoRoT is a space project: Convection, Rotation and Transits The COROT instrument makes it possible, with a method called stellar seismology, to probe the inner structure of the stars, as well as to detect many extrasolar planets, by observing the periodic micro-eclipses occurring when these bodies transit in front of their parent star. Its objective is double: - study stellar interiors - detect planets analogous to the Earth orbiting around other stars than the Sun. A Russian Soyuz 2-1B rocket lifted the satellite into a circular polar orbit with an altitude of 827 km on 27 December 2006. It will carry a telescope able to observe continuously many stars during very long periods and to measure very accurately the variations of their brightness. http://corot.oamp.fr/ PH709 Extrasolar Planets - 6 Professor Michael Smith 15 ….down to earth-like planets. Kepler: 2009 - Transit method, occurrence of earth-sized planets. http://www.kepler.arc.nasa.gov/ PH709 Extrasolar Planets - 6 Professor Michael Smith 16 Concept Study Mar 2001 to July 2001 Discovery selection Dec. 21, 2001 Phase B Feb 2002 to Oct 2004 Phase C/D Nov 2004 to Oct 2008 Launch February 2009 Commissioning Launch + 30 days Phase E Flight operations For 3.5 years from end of commissioning Data analysis For 5 years from end of commissioning The Kepler instrument 0.95-meter diameter telescope. It has a very large field of view for an astronomical telescope —105 square degrees— or about the area of both your hands held at arm's length, in order to observe the necessary large number of stars. It stares at the same star field for the entire mission and continuously and simultaneously monitors the brightnesses of more than 100,000 stars for the life of the mission—3.5 years. The diameter of the telescope needs to be large enough to reduce the noise from photon counting statistics, so that it can measure the small change in brightness of an Earth-like transit. The design of the entire system is such that the combine differential photometric precision over a 6.5 hour integration is less than 20 ppm (one-sigma) for a 12th magnitude solar-like star including an assumed stellar variability of 10 ppm. (This is a conservative, worse-case assumption of a grazing transit. A central transit of the Earth crossing the Sun lasts 13 hours. And about 75% of the stars older than 1 Gyr are less variable than the Sun on the time scale of a transit. ) The photometer must be space-based to obtain the photometric precision needed to reliably see an Earth-like transit and to avoid interruptions caused by day-night cycles, seasonal cycles and atmospheric perturbations, such as, extinction associated with ground-based observing. Space Interferometry Mission SIM and Gaia: astrometry 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. PH709 Extrasolar Planets - 6 Professor Michael Smith 17 TPF: Direct imaging detection and spectroscopic characterization of nearby Earthlike planets will be undertaken by the Terrestrial Planet Finder missions. The TPF Coronagraph (TPF-C), planned for launch in 2014, will operate at visible wavelengths. It will suppress the light of the central star to unprecedented levels, allowing it to search for terrestrial planets in ~150 nearby planetary systems. TPF-C will be followed about five years later by the TPF Interferometer (TPF-I). TPF-I will operate in the mid-IR and will survey a larger volume of our solar neighborhood, searching for terrestrial planets around as many as 500 nearby stars.