* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Free floating planets
Dialogue Concerning the Two Chief World Systems wikipedia , lookup
Geocentric model wikipedia , lookup
International Ultraviolet Explorer wikipedia , lookup
History of astronomy wikipedia , lookup
Spitzer Space Telescope wikipedia , lookup
Observational astronomy wikipedia , lookup
Corvus (constellation) wikipedia , lookup
Space Interferometry Mission wikipedia , lookup
Circumstellar habitable zone wikipedia , lookup
Kepler (spacecraft) wikipedia , lookup
Nebular hypothesis wikipedia , lookup
Astrobiology wikipedia , lookup
Rare Earth hypothesis wikipedia , lookup
Astronomical naming conventions wikipedia , lookup
Late Heavy Bombardment wikipedia , lookup
Formation and evolution of the Solar System wikipedia , lookup
Satellite system (astronomy) wikipedia , lookup
Aquarius (constellation) wikipedia , lookup
Planets beyond Neptune wikipedia , lookup
Planets in astrology wikipedia , lookup
Dwarf planet wikipedia , lookup
History of Solar System formation and evolution hypotheses wikipedia , lookup
Extraterrestrial life wikipedia , lookup
IAU definition of planet wikipedia , lookup
Definition of planet wikipedia , lookup
Exoplanetology wikipedia , lookup
PH709 Extrasolar Planets Prof Michael Smith 1 Review We are still in the early days of a revolution in the field of planetary sciences that was triggered by the discovery of planets around other stars. Exoplanets now number over 200, with masses as small as 5–7 ME (Rivera et al. 2005; Beaulieu et al. 2006). Comparative planetology, which once included only our solar system's planets and moons, now includes sub-Neptune to super-Jupitermass planets in other solar systems. In April 2007, a team of 11 European scientists announced the discovery of a planet outside our solar system that is potentially habitable, with Earth-like temperatures. The planet was discovered by the European Southern Observatory's telescope in La Silla, Chile, which has a special instrument that splits light to find wobbles in different wave lengths. Those wobbles can reveal the existence of other worlds. What they revealed is a planet circling the red dwarf star, Gliese 581. The discovery of the new planet, named Gliese 581 c, is sure to fuel studies of planets circling similar dim stars. About 80 percent of the stars near Earth are red dwarfs. The new planet is about five times heavier than Earth, classifying it as a super-earth. Its discoverers aren't certain if it is rocky, like Earth, or if it is a frozen ice ball with liquid water on the surface. If it is rocky like Earth, which is what the prevailing theory proposes, it has a diameter about 1 1/2 times bigger than our planet. If it is an iceball, it would be even bigger. Gliese 581: M star: 3480K, mass: 0.31 solar masses; Luminosity; 0.013 solar Hot Neptune Gl 581b 15.7 ME 0.041 AU Super-earth Gl 581c 5.06ME 0.073 AU Super-earth Gl 581d 8.3 ME 0.25 AU Gl 581c: 20C (albedo = 0.5 assumed) Greenhouse? Tidal locking? Currently the most important class of exoplanets are those that PH709 Extrasolar Planets Prof Michael Smith 2 transit the disk of their parent stars, allowing for a determination of planetary radii. The 14 confirmed transiting planets observed to date are all more massive than Saturn, have orbital periods of only a few days, and orbit stars bright enough such that radial velocities can be determined, allowing for a calculation of planetary masses and bulk densities (see Charbonneau et al. 2007a). A planetary mass and radius allows us a window into planetary composition (Guillot 2005). The 14 transiting planets are all gas giants although one planet, HD 149026b, appears to be 2/3 heavy elements by mass (Sato et al. 2005; Fortney et al. 2006; Ikoma et al. 2006). Understanding how the transiting planet mass-radius relations change as a function of orbital distance, stellar mass, stellar metallicity, or UV flux, will provide insight into the fundamentals of planetary formation, migration, and evolution. The transit method of planet detection is biased toward finding planets that orbit relatively close to their parent stars. This means that radial velocity follow-up will be possible for some planets as the stellar "wobble" signal is larger for shorter period orbits. However, for transiting planets that are low mass, or that orbit very distant stars, stellar radial velocity measurements may not be possible. For planets at larger orbital distances, radial velocity observations may take years. Therefore, for the foreseeable future a measurement of planetary radii will be our only window into the structure of these planets. Orbital distances may give some clues as to a likely composition, but our experience over the past decade with Pegasi planets (or "hot Jupiters") has shown us the danger of assuming certain types of planets cannot exist at unexpected orbital distances. UPCOMING SPACE MISSIONS The French/European COROT mission, launched in 2006 December, and the American Kepler mission, set to launch in 2008 November will revolutionize the study of exoplanets. COROT will monitor 12,000 stars in each of five different fields, each for 150 continuous days (Bordé et al. 2003). Planets as small as 2 RE should be detectable around solar-type stars (Moutou et al 2006). The mission lifetime is expected to be at least 2.5 yr. The Kepler mission will continuously monitor one patch of sky, monitoring over 100,000 main-sequence stars (Basri et al. 2005). PH709 Extrasolar Planets Prof Michael Smith 3 The expected mission lifetime is at least 4 yr. Detection of sub-Earth size planets is the mission's goal, with detection of planets with radii as small at 1 Mercury radius possible around M stars. With these missions, perhaps hundreds of planets will be discovered with masses ranging from sub-Mercury to many times that of Jupiter. Of course, while planets close to their parent stars will preferentially be found, due to their shorter orbital periods and greater likelihood to transit, planetary transits will be detected at all orbital separations. In general, the detection of three successive transits will be necessary for a confirmed detection, which will limit confirmed planetary-radius objects to about 1.5 AU. http://exoplanet.eu/ http://en.wikipedia.org/wiki/Extrasolar_planet Chapter 23 of Carroll & Ostlie, Modern Astronomy, second edition Rapidly developing subject - first extrasolar planet around an ordinary star only discovered in 1995 by Mayor & Queloz. Resources. For observations, a good starting point is Berkeley extrasolar planets search homepage http://exoplanets.org/ Number: There are 243 planets listed — 60 in multiple planet systems, 178 in single planet systems, 4 orbiting pulsars, 1 orbiting a brown dwarf, 2 free floating?, plenty of candidates, retractions, cluster planets,…… Detection method: 211 planets were found by radial velocity or doppler method, 26 were found by transit method, 1 by direct imaging, and 5 by timing method. However: See the Interactive catalogue at the exoplanets.eu webpage: 252 planets as of 19/9/07 Mass: 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). Neptune = 17.1 ME, Mercury = 0.0553 ME. PH709 Extrasolar Planets Prof Michael Smith 4 Orbit/Distance: approximate distances in astronomical units (1) AU = 1.496 × 108 km, distance between Earth and Sun) from their parent stars. Names: 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 Fusing stars There are currently 238 planets known in orbit around fusing stars. There are currently 178 known planets in single-planet systems and 60 known planets in 20 multiple-planet systems (14 with two planets, 4 with three and 2 with four). "Single" here means that only one planet has been detected to date. Detection methods are not sensitive to low-mass planets, these stars may have smaller planets that are below the limits of detectability, or are so far from the star that they have not yet been observed over an orbital period (Could ALL stars harbour planets?) Pulsars There are currently four known planets orbiting two different pulsars. The planet of PSR B1620−26 is in a circumbinary orbit around a pulsar and a white dwarf star. Brown dwarfs There is currently one known planet orbiting a brown dwarf. Free floating planets There is currently one suspected free-floating planet, i.e. it doesn't appear to orbit a star. PH709 Extrasolar Planets Prof Michael Smith 5 PH709 Extrasolar Planets Prof Michael Smith These lectures: 1. 2. 3. 4. 5. 6. 7. 8. Introduction 2-component systems Definitions, planets, disks Detection methods Summary of methods Populations Theory of formation Theory of evolution 6 PH709 Extrasolar Planets Prof Michael Smith 7 1 Two-Component Systems First Law: The orbit of each planet is an ellipse with the Sun at one focus p b F C Q r S f q a Second Law: For any planet, the radius vector sweeps out equal areas in equal time intervals Kepler’s Third Law The cubes of the semi-major axes of the planetary orbits are proportional to the squares of the planets' periods of revolution 2 P = ka3 where P is the period and a is the average distance from the Sun. Or, if P PH709 Extrasolar Planets Prof Michael Smith 8 is in years and a is in AU: P 2 = a3 Kepler’s Third Law follows from the central inverse square nature of the law of gravitation. First look at Newton's law of gravitation stated mathematically this is F Gm1 m2 r2 Newton actually found that the focus of the elliptical orbits for two bodies of masses m1 and m2 is at the centre of mass. The centripetal forces of a circular orbit are r1 F1 v2 X Centre of M ass m1 m2 v1 F2 r2 2 F1 m1 v1 4 2 m1 r1 r1 P2 and 2 F2 m2 v2 4 2 m2 r2 r2 P2 where v 2r P and since they are orbiting each other (Newton’s 2nd law) r1 m2 r2 m1 PH709 Extrasolar Planets Prof Michael Smith 9 Let's call the separation a = r1 + r2. Then a r1 m1 r1 m1 r1 1 and multiplying both sides by m2 , am2 m1 r1 m2 r1 m2 m2 r1 or, solving for r1 , am2 m1 m2 Now, since we know that the mutual gravitational force is Gm1 m2 Fgrav F1 F2 2 a then substituting for r1, 2 G m m P 1 2 a3 2 4 Solving for P: P 2 a3 G M1 M2 Summary: Measuring the mass of a planet • Kepler’s third law extends to: G(M+m) = a3/P2 Since M >> m for all planets, it isn't possible to make precise enough determinations of P and a to determine the masses m of the planets. However, if satellites of planets are observed, then Kepler's law can be used. • Let mp = mass of planet Then: ms = mass of satellite Ps = orbital period of satellite as = semi-major axis of satellite's orbit about the planet. G(mp+ms) = 42 as3/Ps2 If the mass of the satellite is small compared with the mass of the planet then mp = 42 as3/(G Ps2) PH709 Extrasolar Planets Prof Michael Smith 10 Example Europa, one of the Jovian moons, orbits at a distance of 671,000 km from the centre of Jupiter, and has an orbital period of 3.55 days. Assuming that the mass of Jupiter is very much greater than that of Europa, use Kepler's third law to estimate the mass of Jupiter. Using Kepler's third law: m jupiter meuropa 4 2 a 3 GP 2 The semi-major axis, a = 6.71 x 105 km = 6.71 x 108 m, and the period, P = 3.55 x 3600 x 24 = 3.07 x 105 seconds Since mjupiter >> meuropa, then mjupiter ~ 1.9 x 1027 kg. PH709 Extrasolar Planets Prof Michael Smith 11 So: we can determine the masses of massive objects if we can detect and follow the motion of very low mass satellites. That doesn’t lead very far. How can we determine the masses of distant stars and exoplanets? BASIC STELLAR PROPERTIES - BINARY STARS • For solar type stars, single:double:triple:quadruple system ratios are 45:46:8:1. • Binary nature of stars deduced in a number of ways: 1.1 VISUAL BINARIES: - Resolvable, generally nearby stars (parallax likely to be available) - Relative orbital motion detectable over a number of years - Not possible for exoplanets! 2. ASTROMETRIC BINARY: only one component detected 3. SPECTROSCOPIC BINARIES: - Unresolved - Periodic oscillations of spectral lines (due to Doppler shift) - In some cases only one spectrum seen 4. ECLIPSING BINARY: - Unresolved - Stars are orbiting in plane close to line of sight giving eclipses observable as a change in the combined brightness with time (‘’light curves). Some stars may be a combination of these. Visual Binaries • Requires angular separation ≥ 0.5 arcsec (close to Sun, long orbital periods years – remember: at 1 parsec, 1 arcsec corresponds to 1 AU) Example: Sirius: Also known as Alpha Canis Majoris, Sirius is the fifth closest system to the Sun at 8.6 light-years. Sirius is composed of a main-sequence star and a white dwarf stellar remnant. They form a close binary, Alpha Canis Majoris A and B, that is separated "on average" by only about 20 times the distance from the Earth to the Sun -19.8 astronomical units (AUs) of an orbital semi-major axis -- which is about the same as the distance between Uranus and our Sun ("Sol"). The companion star, is so dim that it cannot be perceived with the naked eye. After analyzing the motions of Sirius from 1833 to 1844, Friedrich Wilhelm Bessel (1784-1846) concluded that it had an unseen companion. PH709 Extrasolar Planets Prof Michael Smith 12 Hubble Space Telescope : • Observations: Relative positions: = angular separation = position Absolute positions: Harder to measure orbits of more massive star A and less massive star B about centre of mass C which has proper motion µ. PH709 Extrasolar Planets Prof Michael Smith Declination N 13 M otion of centre of mass = proper motion µ Secondary E B Primary Right Ascension C A NB parallax and aberration must also be accounted for. • RELATIVE ORBITS: - TRUE orbit: q = peri-astron distance (arcsec or km) Q = apo-astron distance (arcsec or km) a = semi-major axis (arcsec or km) a = (q + Q)/2 - APPARENT orbits are projected on the celestial sphere Inclination i to plane of sky defines relation between true orbit and apparent orbit. If i≠0° then the centre of mass (e.g. primary) is not at the focus of the elliptical orbit. Measurement of the displacement of the primary gives inclination and true semi-major axis in arcseconds a". i i Incline by 45° Apparent orbit True orbit • If the parallax p in arcseconds is observable then a can be derived from a". Earth B radius of Earth's orbit Sun For i=0° a a" p r = distance of binary star a = a"/p" AU A (In general correction for i≠0 required). PH709 Extrasolar Planets Prof Michael Smith 14 Now lets go back to Kepler’s Law … • From Kepler's Law, the Period P is given by 2 3 4 a P = G (mA + mB) 2 For the Earth-Sun system P=1 year, a=1 A.U., mA+mB~msun so 4π2/G = 1 3 2 P = a (mA + mB) provided P is in years, a in AU, mA, mB in solar masses. The total system mass is determined: a" 3 1 mA + mB = ( ) p P2 • ABSOLUTE ORBITS: d c rA * B rB B f q e A Q A Semi-major axes aA = (c+e)/2 aB = (d+f)/2 Maximum separation = Q = c + f Minimum separation = q = d + e So aA + aB = (c+d+e+f)/2 = (q + Q)/2 = a a = aA + a B (1) (and clearly r = rA + rB) From the definition of centre of mass, mA rA = mB rB ( mA aA = mB aB) mA/mB = aB/aA = rB/rA So from Kepler’s Third Law, which gives the sum of the masses, and Equation (1) above, we get the ratio of masses, ==> mA, mB. Therefore, with both, we can solve for the individual masses of the two stars. 1.2 Spectroscopic Binaries PH709 Extrasolar Planets Prof Michael Smith 15 • Orbital period relatively short (hours - months) and i≠0°. • Doppler shift of spectral lines by component of orbital velocity in line of sight (nominal position is radial velocity of system): wavelength wavelength Time Time 2 Stars observable 1 Star observable PH709 Extrasolar Planets Prof Michael Smith 16 See: http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm • Data plotted as RADIAL VELOCITY CURVE: PH507 Astrophysics Professor Glenn White 17 orientation Orientation: • If the orbit is tilted to the line of sight (i<90°), the shape is unchanged but velocities are reduced by a factor sin i. • Take a circular orbit with i=90° a = rA + rB v = v A + vB Orbital velocities: vA = 2π rA / P vB = 2π rB / P Since mA rA = mB rB mA/mB = rB/rA = vB/vA (2) rB vA r •Shape of radial velocity curves depends on : v = rA v B orbital eccentricity and • In general, measured velocities are vB sin i and vA sin i, so sin i terms cancel. • From Kepler's law mA + mB = a3/P2 (in solar units). Observed quantities: vA sin i => rA sin i vB sin i => rB sin i } a sin i So can only deduce (mA + mB) sin3 i = (a sin i)3/P2 (3) For a spectroscopic binary, only lower limits to each mass can be derived, unless the inclination i is known independently. PLANET MASS: DETAILED DERIVATION ******************************************************** 1. Assume a planet and star, both of considerable mass, are in circular orbits around their centre of mass. Given the period P, the star’s orbital speed v* and mass M*, the mass of the planet, Mp is given by Mp3/ (M* + Mp)2 = v*3 P / (2 G) Note that there are 9 unknowns: P, a*, ap, M*, Mp, v*, vp, a, M - 9 variables However, PH507 Astrophysics Dr. S.F. Green 18 a = a* + ap M = M*+ Mp Centre of mass; M* a* = mp ap Kepler’s law relates: P, a, M P = 2 a*/v* P = 2 ap/vp ….so that is 6 equations.; manipulation leaves any 3 you like. Note: we usually only know vr* = v* sin i and we assume the planet mass is small. However, we must independently constrain the mass of the star! How? Depends on theoretical stellar models or model atmospheres. In terms of a more general analysis with eccentricity e and radial speed K* V* sin i 1.3 Eclipsing Binaries PH507 Astrophysics Professor Glenn White Eclipsing Binaries • Since stars eclipse, the orientation is i ~ 90° 1, 1' 2, 2' 3, 3' 4, 4' v 19 FIRST CONTACT SECOND CONTACT THIRD CONTACT FOURTH CONTACT 4' 3' 2' 1' 1 2 3 4 Observer in plane • For a circular orbit: • Variation in brightness with time is LIGHT CURVE. • Timing of events gives information on sizes of stars and orbital elements. • Shape of events gives information on properties of stars and relative temperatures. If smaller star is hotter, then: PH507 Astrophysics 20 Case 1 Smaller star is hotter Case 2 Larger star is hotter F or magnitude Secondary minimum Primary minimum time Case 1 t'1 Case 2 t 1 t'2 t2 t'3 t' 4 t3 t4 t1 t'1 t2 t'2 t3 t'3 t4 t'4 PH507 Astrophysics 21 • If orbits are circular: minima are symmetrical ie t2-t1 = t4-t3 = t2'-t1' = t4'-t3'; minima are half a period apart; eclipses are of same duration. Asymetrical and/or unevenly spaced minima indicate eccentricity and orientation of orbit. • For a circular orbit: t1 t2 t3 t 4 Distance = velocity x time 2RS = v (t2 - t1) (4) 2RL and 2RS + 2RL = v (t4 - t1) => 2RL = v(t4 - t2) (5) 2RS RS/RL = (t2 - t1) / (t4 - t2) • Light curves are also affected by: Non-total eclises No flat minimum Limb darkening (non-uniform brightness) "rounds off" eclipses Ellipsoidal stars (due to proximity) "rounds off" maxima Reflection effect (if one star is very bright) 1.4 Eclipsing-Spectroscopic Binaries • For eclipsing binaries i ≥ 70° (sin3i > 0.9) • If stars are spectroscopic binaries then radial velocities are known. So: masses are derived, radii are derived, ratio of temperatures is derived Examine spectra and light curve to determine which radius corresponds with which mass and temperature: • Densities are then derived, and since Luminosity L = 4 R2 T4, the ratio of luminosities is derived from (35) PH507 Astrophysics LA LB Summary Type Visual = RA RB 2 TA Professor Glenn White 22 4 TB Observed p, motion on sky Apparent magnitudes Spectroscopic velocity curves Eclipsing light curves Eclipsing/ light + velocity curves Spectroscopic distance Derived a, e, i, mA, mB LA, LB MA/MB, (MA+MB)sin3i, a sin i e, i, RS/RL MA, MB, RA, RB, TA/TB, a, e, i, LA, LB, TA, TB PH709 Extrasolar Planets Professor Michael Smith 23 2 Extrasolar Planets or Exoplanets Direct imaged 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. 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. 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) 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. 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. • How can we discover extrasolar planets? • Characteristics of the exoplanet population • Planet formation: theory • Explaining the properties of exoplanets PH709 Extrasolar Planets Professor Michael Smith 24 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 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 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—but 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 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 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, as opposed to the gas giants, which possess primary atmospheres — atmospheres captured directly from the original solar nebula. PH709 Extrasolar Planets Professor Michael Smith 25 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. 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. In any case, 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. (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 • 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 s Each method has different sensitivity to planets at various orbital radii - complete census of planets requires use of several different techniques PH709 Extrasolar Planets Professor Michael Smith 26 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: MF = Mp3/ (M* + Mp)2 = v*3 P / (2 G) 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) PH709 Extrasolar Planets Professor Michael Smith 27 (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 - 12.5 m/s 0.1 m/s 10 m/s is Olympic 100m running pace 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. star's radial velocity amplitude period of radial velocity variation star's absolute star's magnitude spectral (to get the star's class luminosity and relative to the sun, use mass Lstar/Lsun 2.512(4.7 - M) (solar units) don't forget to convert SC to actual luminosity of PH709 Extrasolar Planets Professor Michael Smith 28 the sun in watts by multiplying by Lsun M ( Lstar/Lsun) 86.5 m/s = .0182 au/yr HD209458 3.52 days = .00965 yr ( M/Msun) G0 V 4.6 (1.05) Entering the observed quantities for the symbols on the right side of equation (4) results in a value of the mass function MF of MF = 2.4 x 10-10 (solar masses is the unit, assuming you used the units above) Therefore, (5) MF = Mi3 sin3i / (Mi + Mv)2 = 2.4 x 10-10 Msun Because sin i < 1, (6) Mi 3 / (Mi + Mv )2 > 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) Once an upper limit to the planet's mass is known, its orbit radius (or distance from its parent star) can be found from equation (2) above. 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 center of mass condition, equation (1)], the star's orbit size around the system center of mass is much smaller than the planet's orbit size. Therefore, the av term on the right-hand side can be ignored, and (8) Mv P2 = (ai)3 Using the values of Mv and P above, we find ai = 0.046 au. This is about 9x 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 PH709 Extrasolar Planets Professor Michael Smith 29 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 Rp2 Tp4 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)/(16dp2) 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.below. The lowest albedo is around 0.05 (Earth's moon); the highest, around 0.7 (Venus). This calculation doesn't take into account: 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 • with the calibrating data suffering identical instrumental distortions as the data PH709 Extrasolar Planets Professor Michael Smith 30 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: ~ 3 m/s ...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 31 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 Summary: observables (1) Planet mass, up to an uncertainty from the normally unknown inclination of the orbit. Measure mp sin(i) PH709 Extrasolar Planets Professor Michael Smith 32 (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 PH709 Extrasolar Planets Professor Michael Smith 33 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 semimajor 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 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 PH709 Extrasolar Planets Professor Michael Smith 34 for a star at distance d. Note we have again used mp << M* Writing the mass ratio q = mp / M*, this gives: 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 • 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 ~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 PH709 Extrasolar Planets Professor Michael Smith 35 For a planet with radius rp << R*, probability of transits is: Close-in planets are more likely to be detected. P = 0.5 % at 1AU, P = 0.1 % at the orbital radius of Jupiter What can we measure from the light curve? (1) Depth of transit = fraction of stellar light blocked This is a measure of planetary radius! In practice, isolated planets with masses between ~ 0.1 MJ and 10 MJ, where MJ is the mass of Jupiter, should have almost the same radii (i.e. a flat mass-radius relation). -> 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) Duration of transit plus duration of ingress, gives measure of the orbital radius and inclination Bottom of light curve is not actually flat, providing a measure of stellar limbdarkening PH709 (4) Extrasolar Planets Professor Michael Smith 36 Deviations from profile expected from a perfectly opaque disc could provide evidence for satellites, rings etc Photometry at better than 1% precision is possible (not easy!) from the ground. HST reached a photometric precision of 0.0001. Potential for efficient searches for close-in giant planets Transit depth for an Earth-like planet is: Photometric precision of ~ 10-5 seems achievable from space May provide first detection of habitable Earth-like planets NASA’s Kepler mission, ESA version Eddington 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 37 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 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. 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 PH709 Extrasolar Planets Professor Michael Smith 38 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 Define: • Observer-lens distance • Observer-source distance • Lens-source distance 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. Dl Ds Dls PH709 Extrasolar Planets Professor Michael Smith 39 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 40 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 • Jupiter mass planet ~ 1 day • Earth mass planet ~ 1 hour The dependence on M1/2 means that all these timescales are observationally feasible. However, lensing is a very rare event, all of the projects monitor millions of source stars to detect a handful of lensing events. Lensing by a single star PH709 Extrasolar Planets Professor Michael Smith 41 N ote: 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 noonto-noon 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 42 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: • 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 PH709 Extrasolar Planets Professor Michael Smith 43 • 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: 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. PH709 Extrasolar Planets Professor Michael Smith 44 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–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 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. Planet detection method: Direct detection! Photometric : PH709 Extrasolar Planets Professor Michael Smith 45 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. 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 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. PH709 Extrasolar Planets Professor Michael Smith 4 Detecting extrasolar planets: summary RV, Doppler technique (v = 3 m/s) Astrometry: angular oscillation Photometry: transits - close-in planets Microlensing: 46