Exoplanet Detection with Radial Velocities

Astronomical Data Analysis 2011: Lecture 6

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. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 42 Problems with Transits

• Low probability, but simple observation • Many false positives: • Grazing eclipse from main-sequence star • Eclipsing binary (giant and main-sequence) • Eclipsing binary close by (foreground or background)

kepler.nasa.gov/ﬁles/mws/ aas2010-5nbFalsePositives.jpg Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 43 Kepler Object of Interest 106 • Eclipsing binary in background • Odd and even transits are different

Batalha et al. 2010 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 44 Kepler Exoplanet Candidates

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Problems with Transits

PLANETS

TARGET EB

BAKCGROUND EB NUMBER

0.001 0.01 0.1 DEPTH OF SIGNAL

www.oca.eu/cassiopee/COROTWeek10/Communications/F_Pont.pdf • Only few percent of candidates are real exoplanets • Need radial velocity conﬁrmation with large telescopes (≥4m) Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 46 First Rocky Exoplanet

CoRoT (Leger et al. 2009) HARPS (Queloz et al. 2009)

• 4.8 Earth masses • density 5.6 g/cm3

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 47 CoRoT-7b

www.eso.org/public/outreach/press-rel/pr-2009/pr-33-09.html Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 48 Second Rocky Exoplanet: Kepler-10b

Batalha et al. (2011)

• 4.6±1.2 Earth masses • Density 8.8±3 g/cm3 • 0.84 days orbital period • 0.017 AU orbital radius

49 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Kepler 10b: Vulcan

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Exoplanet Densities

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Exoplanets as Black Bodies

Seager & Deming 2010

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 52 Habitable Zone

• Radiative equilibrium temperature: Incoming stellar radiation = planet radiation into space • Corot 7b: 1300 °C • Kepler 10b: 1600 °C • Earth: -20 °C • Venus: -43 °C • Habitable zone: surface temperature between 0 and 100 Celsius: liquid water possible

• Transits: planet size • Thermal emission: emitting atmosphere, temperature and its gradient, thermal phase curve • Transmission Spectra: upper atmosphere, exosphere • Reﬂection: albedo, reﬂected light phase curve, (polarization), scattering atmosphere

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 55 Exoplanet Atmospheres

Seager & Deming 2010

• Light curve provides information on star + planet • Secondary eclipse: no planet light -> albedo • Difference at different wavelengths -> exoplanet spectrum -> atmosphere composition

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 56 Secondary Eclipse

photojournal.jpl.nasa.gov/catalog/PIA11390 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 57 Secondary Eclipse from Corot

Snellen et al. 2009 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 58 λ-Dependence of Secondary Eclipse

Charbonneau et al. 2008 Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 59 Exoplanet Atmospheres (Swain et al. 2009)

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 60 Measured Exoplanet Atmospheres

Seager & Deming 2010

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 61 The Future: Direct Imaging

• Central star much brighter than disks and planets • Disks: at least 104 times fainter than central star • Jupiter: 109 times fainter than Sun • Telescope optics, Earth atmosphere make halo • halo: 102 to 106 times fainter than central star • Space telescopes show signiﬁcant halos

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 62 1000 Million times Larger

Christoph U. Keller, [email protected] Astronomical Data Analysisen.wikipedia.org 2011: Exoplanet/wiki/ DetectionFile:Everest_kalapatthar_crop.jpg Fomalhaut b (Kalas et al. 2008)

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 64 Very Young, Very Big Exoplanets

Marois et al. 2008

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 65 Beta Pic

www.eso.org/public/images/eso1024c/

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 66 Scattering Polarization

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 67 Scattering Polarization

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection 68 ExPo at William Herschel Telescope

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Utrecht Extreme Polarimeter (ExPo)

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection SU Aurigae, a T-Tauri Star with Jet

ExPo VS HST

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Saturn with ExPo

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Exoplanet in the Lab in Utrecht

Intensity Polarization Reconstructed Polarization

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection ZIMPOL for SPHERE at VLT

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection EPICS for 42-m E-ELT

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection EPICS for the E-ELT

Top view Nasmyth implementation

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection Rocky Planet in HZ (Gliese 581 d)

Christoph U. Keller, [email protected] Astronomical Data Analysis 2011: Exoplanet Detection