Methods for detection of extra-solar planets (exo-planets): 2? 10? 3 ~100 ~500
51 Peg
Folgende Folien basieren auf der Vorlesung Physics of Planetary Systems von Prof. Artie Hatzes (TLS Tautenburg)
Sprache Language
Literature By Carole Haswell Contents: Our Solar System from Afar (overview of detection methods) Exoplanet discoveries by the transit method What the transit light curve tells us The Exoplanet population Transmission spectroscopy and the Rossiter-McLaughlin effect Host Stars Secondary Eclipses and phase variations Transit timing variations and orbital dynamics Brave new worlds
Literature Contents: Radial Velocities Astrometry Microlensing Transits Imaging Host Stars Brown Dwarfs and Free floating Planets Formation and Evolution Interiors and Atmospheres The Solar System
Contributions: Radial Velocities Exoplanet Transits and Occultations Microlensing Direct Imaging Astrometric Detections Planets Around Pulsars Statistical Distribution of Exoplanets Non-Keplerian Dynamics of Exoplanets Tidal Evolution of Exoplanets Protoplanetary and Debris Disks Terrestrial Planet Formation Planet Migration Terrestrial Planet Interiors Giant Planet Interior Structure and Thermal Evolution Giant Planet Atmospheres Terrestrial Planet Atmospheres and Biosignatures Atmospheric Circulation of Exoplanets
How to search for Exoplanets: There are many Ways Indirect Techniques 1. Radial Velocity 2. Astrometry 3. Transits 4. Microlensing Direct Techniques 4. Spectroscopy/Photometry: Reflected or Radiated light 5. Imaging All of these techniques have successfully discovered a planet, or detected a known planet
Radial velocity measurements using the Doppler Wobble The closer the planet, the higher the velocity amplitude. The RV method is more sensitive for planets close to the star (short orbital periods)
Radial Velocity measurements Requirements: Accuracy of better than 10 m/s Stability for at least 10 Years V obs = 28.4 m p sin i P 1/3 m 2/3 s Jupiter: 12 m/s, 11 years Saturn: 3 m/s, 30 years
Astrometric Measurements of Spatial Wobble Center of mass q = m M a D 2q 2q = 8 mas at a Cen 2q = 1 mas at 10 pcs Current limits: 1-2 mas (ground) 0.1 mas (HST) Since D ~ 1/D can only look at nearby stars
Jupiter only 1 milliarc-seconds for a Star at 10 parsecs
Microlensing
Methods of Detecting Exoplanets 1. Doppler wobble - Velocity reflex motion of the star due to the planet: 601 planets (107 systems) 2. Transit Method - photometric eclipse due to planet: 1206 planets (357 systems) 3. Astrometry - spatial reflex motion of star due to planet: 0 discoveries, 6 detections of known planets 4. Direct Imaging: 51 planets (1 system) 5. Microlensing gravitational perturbation by light: 35 planets (2 Systems) 6. Timing variations changes in the arrival of pulses (pulsars), oscillation frequencies, or time of eclipses (no transit timing variations): 19 planets (4 systems)
A Brief History of Light Deflection In 1801 Soldner used Newtonian Physics to calculate the deflection of light by gravity:
A Brief History of Light Deflection In 1911 Einstein derived: a = 2 GM סּ c 2 R סּ = 0.87 arcsec Einstein in 1911 was only half right! In 1916 using General Relativity Einstein derived: a = 4 GM c 2 r Light passing a distance r from object = 1.74 arcsec Factor of 2 due to spatial curvature which is missed if light is treated like particles
Eddington s 1919 Eclipse expedition confirmed Einstein s result
Einstein Cross Einstein Ring
Basics of Lensing: The Einstein Radius Lens S 1 q E q E q s S 2 Source off-centered Source centered
b = 0 b = q a(q)
Point lens: magnification of two images m = q b dq db
Typical microlensing events last from a few weeks to a few months
Basics of Lensing: Caustics source: wikipedia Caustic: the envelope of light rays reflected or refracted by a curved surface or object
For planets q << 1 x c h c s + s 1 + 2(cos 3 f -2 cos f) s + s 1 2(cos2f -2 cos f) 2 q 2 sin 3 f s + s 1 2(cos2f -2 cos f) 2 q q= mass ratio s = planet star separation Analytic solution for planetary caustics
OGLE alert The First: OGLE-235-MOA53
Cyan curve is the best fit single lens model D 2 = 651 Magenta curve is the best fit model w/ mass fraction e 0.03 D 2 = 323 7 days inside caustic = 0.12 t E Long for a planet, but Dmag = only 20-25% as expected for a planet near the Einstein Ring Lightcurve close-up & fit (from Bennet)
Caustic Structure Blue and red dots indicate times of observations Parameters: t E = 61.6 1.8 days t 0 = 2848.06 0.13 MJD u min = 0.133 0.003 a p = 1.120 0.007 AU e = 0.0039 0.007 q = e/(1+ e) f = 223.8 1.4 t * = 0.059 0.007 days or q * /q E = 0.00096 0.00011
Alternative Models: a p < 1 D 2 = 110.4 t E = 75.3 days t 0 = 2850.64 MJD u min = 0.098 a p = 0.926 e = 0.0117 f = -6.1 t * = 0.036 days Also planetary!
Microlensing planet detection of a Super Earth? Best binary source OGLE-2005-BLG-390 Mass = 2.80 10 M earth a = 2.0 4.1 AU q = 7.6 x 10 5 Ratio between planet and star
Let s play Devil s advocate Not all possible models have been exhausted. Only 9 data points define planet Source binary model conveniently has a peak in the data gap Source is a G4 III giant star. Giant stars are known to have spots and pulsations. Host star parameters relies on statistics and galactic models
All derived parameters depend on Bayesian Statistics: Robert Kraft: If you have to integrate, you don t understand it. If you have to use statistics, it doesn t exist!
Astrometric Detection of Exoplanets
Brief History Astrometry - the branch of astronomy that deals with the measurement of the position and motion of celestial bodies It is one of the oldest subfields of the astronomy dating back at least to Hipparchus (130 B.C.), who combined the arithmetical astronomy of the Babylonians with the geometrical approach of the Greeks to develop a model for solar and lunar motions. He also invented the brightness scale used to this day. Galileo was the first to try measure distance to stars using a 2.5 cm telescope. He of course failed. Hooke, Flamsteed, Picard, Cassini, Horrebrow, Halley also tried and failed
1838 first stellar parallax (distance) was measured independently by Bessel (heliometer), Struve (filar micrometer), and Henderson (meridian circle). Modern astrometry was founded by Friedrich Bessel with his Fundamenta astronomiae, which gave the mean position of 3222 stars. 1887-1889 Pritchard used photography for astrometric measurements
Astrometry: Parallax Distant stars 1 AU projects to 1 arcsecond at a distance of 1 pc = 3.26 light years
Astrometry: Parallax So why did Galileo fail? q= 1 arcsecond d = 1/q, d in parsecs, q in arcseconds d = 1 parsec 1 parsec = 3.08 10 18 cm F D f = F/D
Astrometry: Proper motion Barnard is the star with the highest proper motion (~10 arcseconds per year) Barnard s star in 1950 Barnard s star in 1997
Astrometry: Orbital Motion The astrometric signal is given by: q = m M a D This is in radians. More useful units are arcseconds (1 radian = 206369 arcseconds) or milliarcseconds (0.001 arcseconds) = mas m = mass of planet M = mass of star a = orbital radius D = distance of star q = m P 2/3 M 2/3 D Note: astrometry is sensitive to companions of nearby stars with large orbital distances Radial velocity measurements are distance independent, but sensitive to companions with small orbital distances
The Space motion of Sirius A and B
Astrometric Detections of Exoplanets The Challenge: for a star at a distance of 10 parsecs (=32.6 light years): Source Displacment (mas) Jupiter at 1 AU 100 Jupiter at 5 AU 500 Jupiter at 0.05 AU 5 Neptune at 1 AU 6 Earth at 1 AU 0.33 Parallax 100000 Proper motion (/yr) 500000
The Importance of Reference stars Example Focal plane Detector Perfect instrument Perfect instrument at a later time Reference stars: 1. Define the plate scale 2. Monitor changes in the plate scale (instrumental effects) 3. Give additional measures of your target Typical plate scale on a 4m telescope (Focal ratio = 13) = 3.82 arcsecs/mm = 0.05 arcsec/pixel (15 mm) = 57 mas/pixel. The displacement of a star at 10 parsecs with a Jupiter-like planet would make a displacement of 1/100 of a pixel (0.00015 mm)
Real Astrometric Detections with the Hubble Telescope Fine Guidance Sensors
HST uses Narrow Angle Interferometry!
One of our planets is missing: sometimes you need the true mass! HD 33636 b B P = 2173 d Msini = 10.2 M Jup Bean et al. 2007AJ...134..749B i = 4 deg m = 142 M Jup = 0.142 M sun
Gl 876
Vb 10 Control star
Space: The Final Frontier 1. Hipparcos 3.5 year mission ending in 1993 ~100.000 Stars to an accuracy of 7 mas 2. Gaia 1.000.000.000 stars V-mag 15: 24 mas V-mag 20: 200 mas Launch 2011 2012 19 December 2013
Number of Expected Planets from GAIA 8000 Giant planet detections 4000 Giant planets with orbital parameters determined 1000 Multiple planet detections 500 Multiple planets with orbital parameters determined
Summary 1. Astrometry is the oldest branch of Astronomy 2. It is sensitive to planets at large orbital distances complimentary to radial velocity 3. Gives you the true mass 4. Least successful of all search techniques because the precision is about a factor of 1000 to large. 5. Will have to await space based missions to have a real impact
Newton s form of Kepler s Law V m p m s a p a s P 2 = 4p 2 (a s + a p ) 3 G(m s + m p )
P 2 = 4p 2 (a s + a p ) 3 G(m s + m p ) Approximations: a p» a s m s» m p P 2 4p 2 a p 3 Gm s
Circular orbits: V = 2pa s P Lever arm : m s a s = m p a p a s = m p a p m s Solve Kepler s law for a p : a p = ( P 2 Gm s ) 1/3 4p 2 and insert in expression for a s and then V for circular orbits
V = 2p V = 0.0075 m p P 1/3 m 2/3 = s m p P 2/3 G 1/3 m 1/3 s P(4p 2 ) 1/3 28.4 m p P 1/3 m 2/3 s m p in Jupiter masses m s in solar masses P in years V in m/s V obs = 28.4 m p sin i P 1/3 m 2/3 s
Radial Velocity Amplitude of Sun due to Planets in the Solar System Planet Mass (M J ) V(m s 1 ) Mercury 1.74 10 4 0.008 Venus 2.56 10 3 0.086 Earth 3.15 10 3 0.089 Mars 3.38 10 4 0.008 Jupiter 1.0 12.4 Saturn 0.299 2.75 Uranus 0.046 0.297 Neptune 0.054 0.281
Radial Velocity (m/s) Radial Velocity Amplitude of Planets at Different a G2 V star
Radial Velocity (m/s) A0 V star
M2 V star
Radial velocity shape as a function of eccentricity:
Radial velocity shape as a function of w, e = 0.7 :
Eccentric orbit can sometimes escape detection: With poor sampling this star would be considered constant
The Grandfather of Radial Velocity Planet Detections Christian Doppler, Discoverer of the Doppler effect Born: 29.11.1803, in Salzburg Died: 17.03.1853 in Venice Bild: Wikipedia First radial velocity measurement for a star made on Sirius by Sir William Higgins in 1868 radialvelocitydemo.htm
Measurement of Doppler Shifts In the non-relativistic case: l l 0 l 0 = Dv c We measure Dv by measuring Dl
The Radial Velocity Measurement Error with Time Fastest Military Aircraft (SR-71 Blackbird) Average Jogger High Speed Train Casual Walk World Class Sprinter How did we accomplish this?
Including dependence on stellar parameters s (m/s) Constant (S/N) 1 R 3/2 v sin i (Dl) 1/2 ( 2 ) f(t eff ) v sin i : projected rotational velocity of star in km/s f(t eff ) = factor taking into account line density f(t eff ) 1 for solar type star f(t eff ) 3 for A-type star (T = 10000 K, 2 solar masses) f(t eff ) 0.5 for M-type star (T = 3500, 0.1 solar masses)
Traditional method: Observe your star Then your calibration source
51 Pegasi b: The Discovery that Shook up the Field Period = 4,3 Days Semi-major axis = 0,05 AU (10 Stellar Radii!) Mass ~ 0,45 M Jupiter Discovered by Michel Mayor & Didier Queloz, 1995
Rate of Radial Velocity Planet Discoveries 51 Peg
Eccentricity versus Orbital Distance Note that there are few highly eccentric orbits close into the star. This is due to tidal forces which circularizes the orbits quickly.
Classes of planets: Hot Neptunes McArthur et al. 2004 Santos et al. 2004 Butler et al. 2004 Note that the scale on the y- axes is a factor of 100 smaller than the previous orbit showing a hot Jupiter Msini = 14-20 M Earth
If there are hot Jupiters and hot Neptunes it makes sense that there are hot Superearths CoRoT-7b Mass = 7.4 M E P = 0.85 d Hot Superearths were discovered by space-based transit searches
Earth-mass Planet: Kepler 78b Pepe et al. 2013, Howard et al. 2013 Mass = 1.31± 0.25 M Earth (Amplitude = 1.34 m/s) Period = 8.5 hours
g Cephei Planet Period 2.47 Years Msini 1.76 M Jupiter e 0.2 a 2.13 AU K 26.2 m/s Period Msini e a K Binary 56.8 ± 5 Years ~ 0.4 ± 0.1 M Sun 0.42 ± 0.04 18.5 AU 1.98 ± 0,08 km/s
Summary of Exoplanet Properties from RV Studies ~10 % of normal solar-type stars have giant planets < 1% of the M dwarfs stars (low mass) have giant planets, but may have a large population of neptune-mass planets low mass stars have low mass planets, high mass stars have more planets of higher mass planet formation may be a steep function of stellar mass 0.5 1% of solar type stars have short period giant plants Exoplanets have a wide range of orbital eccentricities (most are not in circular orbits) Massive planets tend to be in eccentric orbits and have large orbital radii
Discovery Space for Exoplanets
Transit Probability i = 90 o +q q a R * sin q = R * /a = cos i a is orbital semi-major axis, and i is the orbital inclination 1 90+q P orb = 2p sin i di / 4p = 90-q 0.5 cos (90+q) + 0.5 cos(90 q) = sin q = R * /a for small angles 1 by definition i = 90 deg is looking in the orbital plane
Transit Duration t = 2(R * +R p )/v where v is the orbital velocity and i = 90 (transit across disk center) Exercise left to the audience: Show that the transit duration for a fixed period is roughly related to the mean density of the star. t 3 ~ (r mean ) 1
For more accurate times need to take into account the orbital inclination for i 90 o need to replace R * with R: R 2 + d 2 cos 2 i = R * 2 d cos i R * R = (R * 2 d 2 cos 2 i) 1/2 R
Making contact: 1. First contact with star 2. Planet fully on star 3. Planet starts to exit 4. Last contact with star Note: for grazing transits there is no 2nd and 3rd contact 1 2 3 4
Shape of Transit Curves HST light curve of HD 209458b A real transit light curve is not flat
To probe limb darkening in other stars....you can use transiting planets No limb darkening transit shape At the limb the star has less flux than is expected, thus the planet blocks less light
At different wavelengths in Ang.
Shape of Transit Curves Grazing eclipses/transits These produce a V-shaped transit curve that are more shallow Planet hunters like to see a flat part on the bottom of the transit
E.g. a field of 10.000 Stars the number of expected transits is: N transits = (10.000)(0.1)(0.01)(0.3) = 3 Probability of right orbit inclination Frequency of Hot Jupiters Fraction of stars with suitable radii So roughly 1 out of 3000 stars will show a transit event due to a planet. And that is if you have full phase coverage! CoRoT: looked at 10,000-12,000 stars per field and found on average 3 Hot Jupiters per field. Similar results for Kepler Note: Ground-based transit searches are finding hot Jupiters 1 out of 30,000 50,000 stars less efficient than space-based searches
Catching a transiting planet is thus like playing Lotto. To win in LOTTO you have to 1. Buy lots of tickets Look at lots of stars 2. Play often observe as often as you can The obvious method is to use CCD photometry (two dimensional detectors) that cover a large field. You simultaneously record the image of thousands of stars and measure the light variations in each.
Light curve for HD 209458 Transit Curve from a 10 cm telescope
Radial Velocity Curve for HD 209458 Transit phase = 0 Period = 3.5 days M = 0.63 M Jup Radial Velocity Curve: 3m telescope
False Positives It looks like a planet, it smells like a planet, but it is not a planet 1. Grazing eclipse by a main sequence star: One should be able to distinguish these from the light curve shape and secondary eclipses, but this is often difficult with low signal to noise These are easy to exclude with Radial Velocity measurements as the amplitudes should be tens km/s (2 3 observations)
2. Giant Star eclipsed by main sequence star: G star Giant stars have radii of 10-100 solar radii which translates into photometric depths of 0.0001 0.01 for a companion like the sun. These can easily be excluded using one spectrum to establish spectral and luminosity class. In principle no radial velocity measurements are required. Often a giant star can be known from the transit time. These are typically several days long!
3. Eclipsing Binary as a background (foreground) star: Eclipsing Binary Target Star Image quality of Telescope or photometric aperture for calculating light curve
4. Eclipsing binary in orbit around a bright star (hierarchical triple systems) Another difficult case. Radial Velocity Measurements of the bright star will show either long term linear trend no variations if the orbital period of the eclipsing system around the primary is long. This is essentialy the same as case 3) but with a bound system
5. Unsuitable transits for Radial Velocity measurements Transiting planet orbits an early type star with rapid rotation which makes it impossible to measure the RV variations or you need lots and lots of measurements. Depending on the rotational velocity RV measurements are only possible for stars later than about F3
6. Sometimes you do not get a final answer Period: 9.75 Transit duration: 4.43 hrs Depth : 0.2% V = 13.9 Spectral Type: G0IV (1.27 R sun ) Planet Radius: 5.6 R Earth Photometry: On Target CoRoT: LRc02_E1_0591 The Radial Velocity measurements are inconclusive. So, how do we know if this is really a planet. Note: We have over 30 RV measurements of this star: 10 Keck HIRES, 18 HARPS, 3 SOPHIE. In spite of these, even for V = 13.9 we still do not have a firm RV detection. This underlines the difficulty of confirmation measurements on faint stars.
OGLE OGLE: Optical Gravitational Lens Experiment (http://www.astrouw.edu.pl/~ogle/) 1.3m telescope looking into the galactic bulge Mosaic of 8 CCDs: 35 x 35 field Typical magnitude: V = 15-19 Designed for Gravitational Microlensing First planet discovered with the transit method
WASP WASP: Wide Angle Search For Planets (http://www.superwasp.org). Also known as SuperWASP Array of 8 Wide Field Cameras Field of View: 7.8 o x 7.8 o 13.7 arcseconds/pixel Typical magnitude: V = 9-13 86 Planets discovered Most successful ground-based transit search program
Another Successful Transit Search Program HATNet: Hungarian-made Automated Telescope (http://www.cfa.harvard.edu/~gbakos/hat/ Six 11cm telescopes located at two sites: Arizona and Hawaii 8 x 8 square degrees 43 Planets discovered
The MEarth Strategy One star at a time! The MEarth project (http://www.cfa.harvard.edu/~zberta/mearth/) uses 8 identical 40 cm telescopes to search for terrestrial planets around M dwarfs one after the other
Percent Stellar Magnitude distribution of Exoplanet Discoveries 35,00% 30,00% 25,00% 20,00% 15,00% 10,00% Transits RV 5,00% 0,00% 0.5 4,50 8,50 12,50 16,50 V- magnitude