Astronomical Data Analysis 2011: Lecture 6 Exoplanet Detection with Radial Velocities Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Exoplanet Detection Rate Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Outline 1. Introduction 2. Radial Velocity Detection 3. Exoplanet Properties from Radial Velocities 4. Transits 5. Exoplanet Atmospheres 6. The Future Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 3 What is a Planet? www.solarviews.org/cap/misc/solarsystem.htm • <13 Jupiter masses (no nuclear fusion), orbits star • Same for exoplanets and solar system planets • Earth-like: Earth-mass, -density, -temperature Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Planet vs. Star Jupiter Brown Dwarf Sun Solar 0.1 0.2 1 Diameters Jupiter 1 55 1000 Masses Convection partial full outer 30% Fusion none deuterium hydrogen Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 5 Detection vs. Characterization Detection: • Detect presence of exoplanet around a star • Determine mass to distinguish from brown dwarfs • Determine orbit around star Characterization: • Determine radius • Determine surface properties • Determine atmosphere properties Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 6 Main Exoplanet Detection Methods • Radial velocity (stellar wobble): • period • semi-major axis • eccentricity • lower limit to mass • Transits (stellar occultation): • period • semi-major axis • inclination • radius • planet temperature • planet atmosphere Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 8 Spectral Lines in the Solar Spectrum www.noao.edu/image_gallery/images/d5/suny.jpg Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 9 Radial Velocity • Star, planet move around common center of mass • Doppler effect moves spectral lines • Look for periodic variations in stellar velocity Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Radial Velocity Signal Semi-amplitude of radial velocity given by 1 3 2πG MP sin i 1 K = 2 P 3 √ 2 orb (M + MP ) 1 e ! " ∗ − • Porb: orbital period • M*: mass of star • MP: mass of planet • i: inclination, angle between normal to orbital plane and line of sight • e: excentricity Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 11 Radial Velocity Signal For circular orbits with MP << M* in meter/second: MP sin i vobs = 28.4 1/3 2/3 P M orb ∗ • MP in Jupiter masses • Porb in years • M* in solar masses Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 12 Radial Velocity Signal Amplitude 1 3 2πG MP sin i 1 K = 2 P 3 √ 2 orb (M + MP ) 1 e ! " ∗ − • Observe: period, velocity amplitude and shape • Stellar mass unknown, but good estimate from stellar spectrum • Jupiter: 12.4 m/s maximum velocity • Saturn: 2.8 m/s • Earth: 9 cm/s • Heavier stars reduce the signal • Lighter stars increase the signal Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 13 Spectrometer en.wikipedia.org/wiki/Extrasolar_planet • Wavelength cannot be measured directly • Spectrograph transforms wavelength into position information • Must measure spatial location of spectral lines Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 14 Positional Stability Requirement • Visible spectrum: ~ 500 nm • Typical high-resolution spectrograph: 0.005 nm per camera pixel • One pixel in velocity: 3*108m/s/105 = 3000 m/s • Typical CCD camera pixel size: 15 μm • 1 m/s is 15000/3000 nm = 5 nm • Need to keep this stability over years • 1-meter aluminum bar expands 24 μm per deg C Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 15 HARPS obswww.unige.ch/Instruments/Harps/ gallery/Integration_LSO/ • Velocity noise 0.7 - 2 m/s over many years • Thorium-Argon calibration source simultaneous with stellar spectrum Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 16 HARPS Polarimeter Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 17 Example 1: 51 Pegasi b Mayor and Queloz 1995 Figure 4 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 18 Example 2: e=0 Butler et al. 2006, ApJ, 646, 505 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 19 Example 3: e=0.5 Butler et al. 2006, ApJ, 646, 505 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 20 Multiple Planets: One-Planet Fit exoplanets.org/esp/55cnc/55cnc.shtml Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 21 Multiple Planets: Two-Planet Fit exoplanets.org/esp/55cnc/55cnc.shtml Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 22 Multiple Planets: Three-Planet Fit exoplanets.org/esp/55cnc/55cnc.shtml Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 23 Radial Velocity Observables • Period • Lower limit to mass: (MP sin i) • Eccentricity of orbit Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 24 Problems with Radial velocity • Correction of earth orbital motion (up to 30 km/s) and earth rotation (0.5 km/s) • Period analysis (see Lecture on Periodicity) • Only good for cool stars such as the Sun • Hot stars (O,B,A) do not have enough narrow, spectral lines • Stellar rotation, starspots, oscillations, convection impact Doppler signal Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 25 Radial Velocity Limits MP sin i vobs = 28.4 P 1/3M 2/3 orb ∗ rd 1/3 1/2 1/6 • Kepler’s 3 law: Porb ~ a /M* 1/2 • Limit given by MP sin i ~ a • Need to observe at least one full orbit • Detection limit proportional to a1/2 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 26 Problems with Statistics • Selection effects: • some aspects of observed distributions are inconsistent with real population of exoplanets • depend on exoplanet detection approach • Mass is mostly a lower limit to real mass Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 27 Exoplanet Orbital Distances Compared to Earth and Mercury Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Exoplanet Masses & Lower Limits Compared to Jupiter and Earth Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Mass Distribution Interpretation • Low end of mass distribution: • Heavily affected by selection • low-mass planets induce small velocity variations, difficult to detect, underrepresented • High end of mass distribution: • Massive planets easier to detect • Apparent decrease for M > 3MJ real • Apparent decrease for M >12MJ real, ‘‘brown dwarf desert’’ Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 30 Exoplanet Masses and Orbits Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Exoplanet Eccentricities Mercury Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 32 Eccentricity • Exoplanets within 0.1 AU on nearly circular orbits • Beyond 0.3 AU, distribution of eccentricities is essentially uniform between 0 and 0.8 • Radial velocity survey sensitivity not a strong function of eccentricity for 0 < e < 0.7 and a < 3 AU Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 33 Eccentricity Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 34 Distance vs. Eccentricity Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 35 Orbital Eccentricity Interpretation • Overestimation of eccentricity because of e > 0 • Probably 30-40% have e < 0.05 • For a<0.1 mostly circular orbits due to tidal circularization • Large eccentricities for more distant exoplanets may be due to • Perturbations by other planets • Resonances • Interactions with protoplanetary disk • No clear correlation between eccentricity and mass • But high-mass exoplanets (M sin i > 5MJ) have higher median eccentricity than lower mass exoplanets Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 36 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 37 Transits • Can use small telescopes (<1 m diameter) • Space missions avoid problems with Earth’s atmosphere • Transit timing variations may reveal hidden exoplanets sci.esa.int/science-e/www/object/index.cfm?fobjectid=35225 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 38 Mercury Transit 8 November 2006 sohowww.nascom.nasa.gov/hotshots/2006_11_06/ Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Transit of Kepler 10b 0.017% kepler.nasa.gov/Mission/discoveries/kepler10b/ Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 40 Transit Signals • Intensity signal ∆I R 2 R* = P I R ! ∗ " RP • R* stellar radius • Rp planet radius • About 1% for Jupiter and Sun 1/3 1/3 • Transit duration proportional to Porb R*/M* • Transit duration: also estimate of stellar radius • Intensity change then provides planetary radius Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 41 Transit Observables • Period • Orbit inclination (i≈90°) • Planet radius • Planet temperature from secondary eclipse • Stellar limb darkening • Good for large planets close to the star Christoph U.