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PH709 Extrasolar Planets Professor Michael Smith 1 2 Extrasolar Planets or Exoplanets Direct imaging of planets is difficult because of the enormous difference in brightness between the star and the planet, and the small angular separation between them. The effects of the gravity tugging at the stars, as well as the way that gravitational affects can influence material close to the stars, has been clearly detected. ESO ADONIS adaptive optics system at the 3.6-m telescope. It shows (in false colours) the scattered light at wavelength 1.25 micron (J band) Circumstellar dust discs. (Circumstantial evidence.) 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’ This disk around Beta Pictoris is probably connected with a planetary system. The disk does not start at the star. Rather, its inner edge begins around 25 AUs away, farther than the average orbital distance of Uranus in the Solar System. Its outer edge appears to extend as far out as 550 AUs away from the star. Analysis of earlier pictures from the Hubble Space Telescope indicated that planets were only beginning to form around Beta Pictoris, a very young star at between 20 million and 100 million years old. Most dust grains in the disk are not agglomerating to form larger bodies; instead, they are eroding and being moved away from the star by radiation pressure when their size goes below about 2-10 microns. PH709 Extrasolar Planets Professor Michael Smith 2 Theoretically, this disk should have lasted for only around 10 million years. That it has persisted for the 20 to 200 million year lifetime of Beta Pictoris may be due to the presence of large disk bodies (i.e., planets) that collide with icy Edgeworth-Kuiper Belt type objects (dormant comets) to replenish the dust. Approach: • How can we discover extrasolar planets? • Characteristics of the exoplanet population? • Planet formation: theory? • Explaining the properties of exoplanets 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 Note 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 Types of planet A. Giant planets (gas giants, `massive’ planets) • Solar System prototypes: Jupiter, Saturn, (Uranus, Neptune: icy giants)... • Substantial gaseous envelopes • Masses of the order of Jupiter mass (Jovian planets) • In the Solar System, NOT same composition as Sun • Presence of gas implies formation while gas was still prevalent Cores: Gas giants may have a rocky or metallic core—in fact, such a core is thought to be required for a gas giant to form. H and He: The majority of its mass is in the form of the gaseous hydrogen and helium, with traces of water, methane, ammonia, and other hydrogen compounds. PH709 Extrasolar Planets Professor Michael Smith 3 B. Terrestrial planets • Prototypes: Earth, Venus, Mars • Primarily composed of silicate rocks (carbon/diamond planets?) • In the Solar System (ONLY) orbital radii less than giant planets Core: A central metallic core, mostly iron, with a surrounding silicate mantle. The Moon is similar, but lacks an iron core. Terrestrial planets have canyons, craters, mountains, and volcanoes. Terrestrial planets possess secondary atmospheres — atmospheres generated through internal vulcanism or comet impacts. Gas giants possess primary atmospheres — atmospheres captured directly from the original solar nebula. Much more massive terrestrial planets could exist (>10 Earth masses), though none are present in the Solar System. 3 Detecting extrasolar planets (1) Direct imaging - difficult due to enormous star / planet flux ratio. The ultimate goal of any extrasolar planet search must surely be obtaining an image of such a planet directly. This is fraught with difficulties since planets do not emit light, so any image would have to be captured with starlight reflected by the planet's atmosphere or surface. PH709 Extrasolar Planets Professor Michael Smith 4 This will depend of course on the albedo of the planet, which is hard to determine unless another detection method, such as transits, is used as well. The light from the star will swamp that of the planet by a factor of 109 in the optical, so it seems that concentrating upon the infrared region would have the best chance of success. In the infrared, the difference in the emission strength between a star and a planet is 107 (Angel & Woolf, 1997) since planets radiate strongly in the infrared and stellar emission is weaker in this region than in the optical. DD may be possible when the planet is especially large (considerably larger than Jupiter), widely separated from its parent star, and young (so that it is hot and emits intense infrared radiation). (2) Radial velocity • Observable: line of sight velocity of star orbiting centre of mass of star - planet binary system • Most successful method so far - all early detections (3) Astrometry • Observable: stellar motion in plane of sky • Very promising future method: Keck interferometer, GAIA, SIM (4) Transits: photometry • 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 (2007 launch. NASA Discovery mission), Eddington) (5) Gravitational lensing: first success in 2004 • 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 PH709 Extrasolar Planets Professor Michael Smith 5 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* = a ) in an inertial frame is: (assuming mp << M*). i.e. the stellar orbital speed is small …. just metres per second. Compare to previous formula: f(M) = Mp3/ (M* + Mp)2 = v*3 P / (2 G) PH709 Extrasolar Planets Professor Michael Smith 6 This equation is useful because only quantities that are able to be determined from observations are present on the right-hand side of this equation. 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: Sun due to Earth: i.e. extremely small running pace 12.5 m/s 0.1 m/s 10 m/s is Olympic 100m The star HD 209458 was the first to have its planet detected both by spectroscopic and photometric methods. The radial velocity of the star varies with time over a regular period of 3.52 days. PH709 Extrasolar Planets star's radial velocity amplitude HD209458 86.5 m/s = .0182 au/yr period of radial velocity variation Professor Michael Smith star's absolute magnitude 3.52 days = .00965 yr 7 star's spectral class and mass (solar units) G0 V 4.6 1.05 M/Msun To calculate the magnitude M of a star: Lstar/Lsun 2.512(4.7 - M) Since the Sun has a magnitude of 4.7. Entering the observed quantities for the symbols on the right side of equation (4) results in a value of the mass function f(M) of f(M) = 2.4 x 10-10 (solar masses is the unit, assuming you used the units above) Therefore, PH709 Extrasolar Planets Professor Michael Smith 8 (5) f(M) = Mi3 sin3i / (Mi + Mv)2 = 2.4 x 10-10 Msun Because sin i < 1, (6) 3 2 Mi / (Mi + Mv) > 2.4 x 10 -10 Msun We now have an equation in a single unknown; although it cannot be solved analytically, it can be easily solved by trial and error (guessing values) or by using a graphing calculator. Can you find the solution to this inequality? (answer: approximately Mi > 0.00064 Msun or 0.67 MJupiter) The planet's mass is very much smaller than its parent star's mass; therefore, the Mi term on the left-hand side can be ignored. Similarly, because of the centre of mass condition, the star's orbit size around the system centre of mass is much smaller than the planet's orbit size. Therefore we return to: (8) Mv P2 = ai3 Using the values of Mv and P above, we find ai = 0.046 au. This is about 9 x smaller than Mercury's orbit about the sun. Next, let's calculate the equilibrium blackbody temperature of a planet. We assume that thermal equilibirium (i.e., constant temperature) applies, and consequently that the power ( = energy/time) emitted by the planet is the power absorbed from its parent star: (9) Pabsorbed = Pemitted The left hand side is found from geometry, corrected by a coefficient that takes into account reflected light; the right hand side is given by the Stefan-Boltzmann law: Lstar (1 - A) ( Rp/4 dp)2 = 4 p 2 Tp4 PH709 Extrasolar Planets Professor Michael Smith 9 Lstar = luminosity (power) of the parent star A = planet's albedo = (light reflected)/(light incident) Rp = planet's radius Tp = planet's temperature dp = distance of planet from parent star = Stefan-Boltzmann constant Solving for Tp gives Tp4 = Lstar(1 - A)/(16 p 2 ) Notice that the equilibrium temperature depends on the "guessed" albedo of the planet; the ratio of the temperature derived with albedo = 0.95 to the temperature derived with an albedo of 0.05 is approximately 2. Albedos of planets in our solar system. The lowest albedo is around 0.05 (Earth's moon); the highest, around 0.7 (Venus). This calculation doesn't take into account the thermal energy released from the planet's interior, tidal energy released via a star-planet interaction, the greenhouse effect in the atmosphere, etc. Radial velocity measurement: 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 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. 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 PH709 Extrasolar Planets Professor Michael Smith 10 • 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 Currently, the best observations achieve: ...in a single measurement. Thought that this error can be reduced to around 1 m/s with further refinements, but not substantially further. The very highest Doppler precisions of 1 m/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 ~ 1 AU. Examples of radial velocity data PH709 Extrasolar Planets Professor Michael Smith 11 51 Peg b was the first known exoplanet with a 4 day, circular orbit: a hot Jupiter, lying close to the central star. Example of a planet with an eccentric orbit: e=0.67 where e = 1 – b2/a2 periastron = a (1-e) apastron = a (1+e) a = semi-major axis, b = semi-minor axis PH709 Extrasolar Planets Professor Michael Smith 12 Summary: 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) Which planets are detectable? Down to a fixed radial velocity: m p sin i a 1 2 Current limits: • Maximum a ~ 3.5 AU (ie orbital period ~ 7 years) • Minimum mass ~ 0.5 Jupiter masses at 1 AU, 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.) . PH709 Extrasolar Planets Professor Michael Smith 13 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 microarcseconds is possible from the ground with an optimized instrument. Measure stellar motion in the plane of the sky due to presence of orbiting planet. Must account for parallax and proper motion of star. 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 M * d for a star at distance d. Note we have again used mp << M* Writing the mass ratio q = mp / M*, this gives (in milliarcseconds): Note: • 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 PH709 Extrasolar Planets Professor Michael Smith 14 • 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 ~10 microarcsecond level – good enough to detect planets of a few Earth masses at 1 AU around nearby stars 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 PH709 Extrasolar Planets Professor Michael Smith 15 What can we measure from the light curve? (1) Depth of transit = fraction of stellar light blocked This is a measure of planetary radius! No dependence on distance from star. 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) (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 limb-darkening 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: PH709 Extrasolar Planets Professor Michael Smith 16 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 HST Transit light curve from Brown et al. (2001) A triumph of the transit method occurred in 1999 when the light curve of the star HD 209458 was shown to indicate the presence of a large exoplanet in transit across its surface from the perspective of Earth (1.7% dimming). Subsequent spectroscopic studies with the Hubble Space Telescope have even indicated that the exoplanet's atmosphere must have sodium vapor in it. The planet of HD 209458, unofficially named Osiris, is so close to its star that its atmosphere is literally boiling away into space. HD 209458 b represents a number of milestones in extraplanetary research. It was the first transiting extrasolar planet discovered, the first extrasolar planet known to have an atmosphere, the first extrasolar planet observed to have an evaporating hydrogen atmosphere, the first extrasolar planet found to have an atmosphere containing oxygen and carbon, and one of the first two extrasolar planets to be directly observed spectroscopically. Based on the application of new, theoretical models, as of April 2007, it is alleged to be the first extrasolar planet found to have water vapor in its atmosphere. PH709 Extrasolar Planets Professor Michael Smith 17 Star Data Apparent Mag.: 7.65 Spectral Type: G0 Radius: 1.18 Rsolar Mass: 1.06 Msolar Exoplanet Data Period: 3.52474 days Semi-major Axis: 0.045 AU Radius: 1.42 RJupiter Mass: 0.69 MJupiter Measured planetary radius rp = 1.35 RJ: • Proves we are dealing with a gas giant. • Somewhat larger than models for isolated (nonirradiated) planets - effect of environment on structure. Precision of photometry with HST / STIS impressive. 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 PH709 Extrasolar Planets Professor Michael Smith 18 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 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. PH709 Extrasolar Planets Professor Michael Smith 19 The deflection: light passes by the lens at a distance DL from the observer with impact parameter ro = tan D L . A photon passing a distance ro from a mass M is bent through an angle 4GM ro c 2 radians. ro = DL Two images are formed when the light from a source at distance DS passes the gravitational lens. 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: PH709 Extrasolar Planets Professor Michael Smith 20 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: Unlike strong lensing, in microlensing u changes significantly in a short period of time. The relevant time scale is called the Einstein time and it's given by the time it takes the lens to traverse an Einstein radius. 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 (Einstein radius of order a few AU) • Jupiter mass planet ~ 1 day (0.1 AU) • Earth mass planet ~ 1 hour PH709 Extrasolar Planets Professor Michael Smith 21 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 Note: The Julian day or Julian day number (JDN) is the integer number of days that have elapsed since the initial epoch defined as noon Universal Time (UT) Monday, January 1, 4713 BC in the proleptic Julian calendar [1]. That noon-tonoon day is counted as Julian day 0. The Heliocentric Julian Day (HJD) is the same as the Julian day, but adjusted to the frame of reference of the Sun, and thus can differ from the Julian day by as much as 8.3 minutes, that being the time it takes the Sun's light to reach Earth Lensing by a star and a planet. Model results: PH709 Extrasolar Planets Professor Michael Smith 22 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 Binary systems 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: PH709 Extrasolar Planets Professor Michael Smith 23 • Monitor known lensing events in real-time 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 Complementary to other methods: 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: PH709 Extrasolar Planets Professor Michael Smith 24 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. At around five times the mass of Earth, the new planet, designated OGLE–2005BLG-390Lb, is the lowest-mass planet ever detected outside the solar system. And when one considers that the vast majority of the approximately 170 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. PH709 Extrasolar Planets Professor Michael Smith 25 Planet detection method: Direct detection! Photometric : Infrared image of the brown dwarf 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. PH709 Extrasolar Planets Professor Michael Smith 26 Direct Spectroscopic Detection? 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. Pulsar Planets In early 1992, the Polish astronomer Aleksander Wolszczan (with Dale Frail) announced the discovery of planets around another pulsar, PSR 1257+12.This discovery was quickly confirmed, and is generally considered to be the first definitive detection of exoplanets. 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. These pulsar planets are believed to have formed from the unusual remnants of the supernova that produced the pulsar, in (1) a second round of planet formation, or else to be (2) the remaining rocky cores of gas giants that survived the supernova and then spiralled in to their current orbits. 4 Detecting extrasolar planets: summary RV, Doppler technique (v = 3 m/s) PH709 Extrasolar Planets Professor Michael Smith Astrometry: angular oscillation Photometry: transits - close-in planets Microlensing: 27