Methods for detection of extra-solar planets (exo-planets):

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1 Methods for detection of extra-solar planets (exo-planets): 2? 10? 3 ~100 ~500

2 51 Peg

3 Folgende Folien basieren auf der Vorlesung Physics of Planetary Systems von Prof. Artie Hatzes (TLS Tautenburg)

4 Sprache Language

5 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

6 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

7 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

8 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

9 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)

10 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

11 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

12 Jupiter only 1 milliarc-seconds for a Star at 10 parsecs

13 Microlensing

14 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)

15 A Brief History of Light Deflection In 1801 Soldner used Newtonian Physics to calculate the deflection of light by gravity:

16 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

17 Eddington s 1919 Eclipse expedition confirmed Einstein s result

18 Einstein Cross Einstein Ring

19

20 Basics of Lensing: The Einstein Radius Lens S 1 q E q E q s S 2 Source off-centered Source centered

21

22 b = 0 b = q a(q)

23 Point lens: magnification of two images m = q b dq db

24 Typical microlensing events last from a few weeks to a few months

25

26 Basics of Lensing: Caustics source: wikipedia Caustic: the envelope of light rays reflected or refracted by a curved surface or object

27 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

28 OGLE alert The First: OGLE-235-MOA53

29 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 = 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)

30 Caustic Structure Blue and red dots indicate times of observations Parameters: t E = days t 0 = MJD u min = a p = AU e = q = e/(1+ e) f = t * = days or q * /q E =

31 Alternative Models: a p < 1 D 2 = t E = 75.3 days t 0 = MJD u min = a p = e = f = -6.1 t * = days Also planetary!

32

33 Microlensing planet detection of a Super Earth? Best binary source OGLE-2005-BLG-390 Mass = M earth a = AU q = 7.6 x 10 5 Ratio between planet and star

34 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

35 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!

36 Astrometric Detection of Exoplanets

37 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

38 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 Pritchard used photography for astrometric measurements

39 Astrometry: Parallax Distant stars 1 AU projects to 1 arcsecond at a distance of 1 pc = 3.26 light years

40 Astrometry: Parallax So why did Galileo fail? q= 1 arcsecond d = 1/q, d in parsecs, q in arcseconds d = 1 parsec 1 parsec = cm F D f = F/D

41 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

42 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 = 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

43 The Space motion of Sirius A and B

44 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 Proper motion (/yr)

45 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 ( mm)

46

47 Real Astrometric Detections with the Hubble Telescope Fine Guidance Sensors

48 HST uses Narrow Angle Interferometry!

49 One of our planets is missing: sometimes you need the true mass! HD b B P = 2173 d Msini = 10.2 M Jup Bean et al. 2007AJ B i = 4 deg m = 142 M Jup = M sun

50 Gl 876

51

52

53 Vb 10 Control star

54 Space: The Final Frontier 1. Hipparcos 3.5 year mission ending in 1993 ~ Stars to an accuracy of 7 mas 2. Gaia stars V-mag 15: 24 mas V-mag 20: 200 mas Launch December 2013

55 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

56 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

57

58

59 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 )

60 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

61 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

62 V = 2p V = 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/ 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

63 Radial Velocity Amplitude of Sun due to Planets in the Solar System Planet Mass (M J ) V(m s 1 ) Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune

64 Radial Velocity (m/s) Radial Velocity Amplitude of Planets at Different a G2 V star

65 Radial Velocity (m/s) A0 V star

66 M2 V star

67 Radial velocity shape as a function of eccentricity:

68 Radial velocity shape as a function of w, e = 0.7 :

69 Eccentric orbit can sometimes escape detection: With poor sampling this star would be considered constant

70 The Grandfather of Radial Velocity Planet Detections Christian Doppler, Discoverer of the Doppler effect Born: , in Salzburg Died: in Venice Bild: Wikipedia First radial velocity measurement for a star made on Sirius by Sir William Higgins in 1868 radialvelocitydemo.htm

71 Measurement of Doppler Shifts In the non-relativistic case: l l 0 l 0 = Dv c We measure Dv by measuring Dl

72 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?

73 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 = K, 2 solar masses) f(t eff ) 0.5 for M-type star (T = 3500, 0.1 solar masses)

74 Traditional method: Observe your star Then your calibration source

75 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

76 Rate of Radial Velocity Planet Discoveries 51 Peg

77 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.

78 Classes of planets: Hot Neptunes McArthur et al Santos et al Butler et al Note that the scale on the y- axes is a factor of 100 smaller than the previous orbit showing a hot Jupiter Msini = M Earth

79 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

80 Earth-mass Planet: Kepler 78b Pepe et al. 2013, Howard et al Mass = 1.31± 0.25 M Earth (Amplitude = 1.34 m/s) Period = 8.5 hours

81 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 ± AU 1.98 ± 0,08 km/s

82 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

83 Discovery Space for Exoplanets

84 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) cos(90 q) = sin q = R * /a for small angles 1 by definition i = 90 deg is looking in the orbital plane

85 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

86 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

87 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

88 Shape of Transit Curves HST light curve of HD b A real transit light curve is not flat

89 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

90 At different wavelengths in Ang.

91 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

92 E.g. a field of 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

93 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.

94 Light curve for HD Transit Curve from a 10 cm telescope

95 Radial Velocity Curve for HD Transit phase = 0 Period = 3.5 days M = 0.63 M Jup Radial Velocity Curve: 3m telescope

96 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)

97 2. Giant Star eclipsed by main sequence star: G star Giant stars have radii of solar radii which translates into photometric depths of 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!

98 3. Eclipsing Binary as a background (foreground) star: Eclipsing Binary Target Star Image quality of Telescope or photometric aperture for calculating light curve

99 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

100 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

101 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.

102 OGLE OGLE: Optical Gravitational Lens Experiment ( 1.3m telescope looking into the galactic bulge Mosaic of 8 CCDs: 35 x 35 field Typical magnitude: V = Designed for Gravitational Microlensing First planet discovered with the transit method

103 WASP WASP: Wide Angle Search For Planets ( 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 = Planets discovered Most successful ground-based transit search program

104

105 Another Successful Transit Search Program HATNet: Hungarian-made Automated Telescope ( Six 11cm telescopes located at two sites: Arizona and Hawaii 8 x 8 square degrees 43 Planets discovered

106 The MEarth Strategy One star at a time! The MEarth project ( uses 8 identical 40 cm telescopes to search for terrestrial planets around M dwarfs one after the other

107 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

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