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Radial Velocity Detection of Planets: II. Observations 1. 2. 3. 4. 5. Period Analysis Global Parameters Classes of Planets Dependence on Stellar Parameters Sources of Noise Lecture notes: www.tls-tautenburg.de Click on Teaching -> lectures -> Extrasolar Planets Binary star simulator: http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm#instructions Also: www.exoplanet.eu 1. Period Analysis How do you know if you have a periodic signal in your data? What is the period? Try 16.3 minutes: Lomb-Scargle Periodogram of the data: 1. Period Analysis 1. Least squares sine fitting: Fit a sine wave of the form: V(t) = A·sin(wt + f) + Constant Where w = 2p/P, f = phase shift Best fit minimizes the c2: c2 = S (di –gi)2/N di = data, gi = fit Note: Orbits are not always sine waves, a better approach would be to use Keplerian Orbits, but these have too many parameters 1. Period Analysis 2. Discrete Fourier Transform: Any function can be fit as a sum of sine and cosines N0 FT(w) = Xj (T) e–iwt Recall eiwt = cos wt + i sinwt j=1 X(t) is the time series 1 Power: Px(w) = | FTX(w)|2 N0 2 1 Px(w) = Xj cos wtj + N0 [(S N0 = number of points 2 ) (S X sin wt ) ] j j A DFT gives you as a function of frequency the amplitude (power) of each sine wave that is in the data FT P Ao Ao t 1/P A pure sine wave is a delta function in Fourier space w 1. Period Analysis 2. Lomb-Scargle Periodogram: 1 Px(w) = 2 [ S X cos w(t –t)] j j S 2 j 1 + 2 2 Xj cos w(tj–t) j tan(2wt) = [ S X sin w(t –t) ] j j j S X sin j 2 w(tj–t) (Ssin 2wtj)/(Scos 2wtj) j j Power is a measure of the statistical significance of that frequency (period): False alarm probability ≈ 1 – (1–e–P)N = probability that noise can create the signal N = number of indepedent frequencies ≈ number of data points 2 Amplitude (m/s) Least squares sine fitting: The best fit period (frequency) has the lowest c2 Discrete Fourier Transform: Gives the power of each frequency that is present in the data. Power is in (m/s)2 or (m/s) for amplitude Lomb-Scargle Periodogram: Gives the power of each frequency that is present in the data. Power is a measure of statistical signficance False alarm probability ≈ 10–14 Alias Peaks Noise level Alias periods: Undersampled periods appearing as another period Lomb-Scargle Periodogram of previous 6 data points: Lots of alias periods and false alarm probability (chance that it is due to noise) is 40%! For small number of data points sine fitting is best. Raw data False alarm probability ≈ 0.24 After removal of dominant period Campbell & Walker: The Pioneers of RV Planet Searches 1988: 1980-1992 searched for planets around 26 solar-type stars. Even though they found evidence for planets, they were not 100% convinced. If they had looked at 100 stars they certainly would have found convincing evidence for exoplanets. Global Properties of Exoplanets 2. Mass Distribution The Brown Dwarf Desert e–0.3 Planet: M < 13 MJup → no nuclear burning Brown Dwarf: 13 MJup < M < ~70 MJup → deuterium burning Star: M > ~70 MJup → Hydrogen burning There mass distribution falls off exponentially. N(20 MJupiter) ≈ 0.002 N(1 MJupiter) There should be a large population of low mass planets. Brown Dwarf Desert: Although there are ~100-200 Brown dwarfs as isolated objects, and several in long period orbits, there is a paucity of brown dwarfs (M= 13–50 MJup) in short (P < few years) as companion to stars Number Number Semi-Major Axis Distribution Semi-major Axis (AU) Semi-major Axis (AU) The lack of long period planets is a selection effect since these take a long time to detect 2. Eccentricity distribution e=0.4 e=0.6 e=0.8 w=0 w=90 w=180 e Eri 2 ´´ Mass versus Orbital Distance Eccentricities 3. Classes of planets: 51 Peg Planets Discovered by Mayor & Queloz 1995 How are we sure this is really a planet? Bisectors can measure the line shapes and tell you about the nature of the RV variations: Curvature Span What can change bisectors: • Spots • Pulsations • Convection pattern on star The David Gray Controversy Gray & Hatzes 1997 If the bisector variations were real then 51 Peg has no planet Hatzes et al. : No bisector variations The final proof that these are really planets: The first transiting planet HD 209458 3. Classes of planets: 51 Peg Planets • ~25% of known extrasolar planets are 51 Peg planets (selection effect) • 0.5–1% of solar type stars have giant planets in short period orbits • 5–10% of solar type stars have a giant planet (longer periods) 3. Classes of planets: Hot Neptunes McArthur et al. 2004 Santos et al. 2004 Butler et al. 2004 Msini = 14-20 MEarth 3. Classes: The Massive Eccentrics • Masses between 7–20 MJupiter • Eccentricities, e>0.3 • Prototype: HD 114762 m sini = 11 MJup 3. Classes: The Massive Eccentrics There are no massive planets in circular orbits 3. Classes: Planets in Binary Systems Why search for planets in binary stars? • Most stars are found in binary systems • Does binary star formation prevent planet formation? • Do planets in binaries have different characteristics? • For what range of binary periods are planets found? • What conditions make it conducive to form planets? (Nurture versus Nature?) • Are there circumbinary planets? Some Planets in known Binary Systems: Star 16 Cyg B 55 CnC HD 46375 t Boo And HD 222582 HD 195019 a (AU) 800 540 300 155 1540 4740 3300 Nurture vs. Nature? The first extra-solar Planet may have been found by Walker et al. in 1992 in a binary system: g Cephei Planet Periode Msini 2,47 Jahre 1,76 MJupiter e a K 0,2 2,13 AE 26,2 m/s Doppelstern Periode Msini 56.8 ± 5 Jahre ~ 0,4 ± 0,1 MSun e a 0,42 ± 0,04 18.5 AE K 1,98 ± 0,08 km/s g Cephei Primärstern Sekundärstern Planet The planet around g Cep is difficult to form and on the borderline of being impossible. Standard planet formation theory: Giant planets form beyond the snowline where the solid core can form. Once the core is formed the protoplanet accretes gas. It then migrates inwards. In binary systems the companion truncates the disk. In the case of g Cep this disk is truncated just at the ice line. No ice line, no solid core, no giant planet to migrate inward. g Cep can just be formed, a giant planet in a shorter period orbit would be problems for planet formation theory. 3. Planetary Systems 25 Extrasolar Planetary Systems (18 shown) Star P (d) MJsini a (AU) e HD 82943 221 0.9 0.7 0.54 444 1.6 1.2 0.41 GL 876 47 UMa 30 61 1095 2594 0.6 2.0 2.4 0.8 HD 37124 153 0.9 550 1.0 55 CnC 2.8 0.04 14.6 0.8 44.3 0.2 260 0.14 5300 4.3 Ups And 4.6 0.7 241.2 2.1 1266 4.6 HD 108874 395.4 1.36 1605.8 1.02 HD 128311 448.6 2.18 919 3.21 HD 217107 7.1 1.37 3150 2.1 0.1 0.2 2.1 3.7 0.27 0.10 0.06 0.00 0.5 2.5 0.04 0.1 0.2 0.78 6.0 0.06 0.8 2.5 1.05 2.68 1.1 1.76 0.07 4.3 0.20 0.40 0.17 0.0 0.34 0.2 0.16 0.01 0.28 0.27 0.07 0.25 0.25 0.17 0.13 0.55 Star P (d) MJsini HD 74156 51.6 1.5 2300 7.5 HD 169830 229 2.9 2102 4.0 HD 160691 9.5 0.04 637 1.7 2986 3.1 HD 12661 263 1444 HD 168443 58 1770 HD 38529 14.31 2207 HD 190360 17.1 2891 HD 202206 255.9 1383.4 HD 11964 37.8 1940 m Ara: 4 planets 2.3 1.6 7.6 17.0 0.8 12.8 0.06 1.5 17.4 2.4 0.11 0.7 a (AU) 0.3 3.5 0.8 3.6 0.09 1.5 0.09 e 0.65 0.40 0.31 0.33 0 0.31 0.80 0.8 2.6 0.3 2.9 0.1 3.7 0.13 3.92 0.83 2.55 0.23 3.17 0.35 0.20 0.53 0.20 0.28 0.33 0.01 0.36 0.44 0.27 0.15 0.3 Resonant Systems Systems Star P (d) MJsini a (AU) e HD 82943 221 0.9 0.7 0.54 444 1.6 1.2 0.41 → GL 876 → 2:1 55 CnC 30 61 0.6 2.0 0.1 0.2 14.6 0.8 44.3 0.2 0.1 0.2 0.27 0.10 0.0 0.34 2:1 → 3:1 HD 108874 395.4 1.36 1605.8 1.02 1.05 2.68 0.07 0.25 → 4:1 HD 128311 448.6 2.18 919 3.21 1.1 1.76 0.25 0.17 → 2:1 2:1 → Inner planet makes two orbits for every one of the outer planet Eccentricities • Period (days) Mass versus Orbital Distance Eccentricities 4. The Dependence of Planet Formation on Stellar Mass Setiawan et al. 2005 Poor precision Too faint (8m class tel.). Ideal for 3m class tel. RV Error (m/s) Main Sequence Stars A0 A5 F0 F5 G0 G5 Spectral Type K0 K5 M0 Exoplanets around low mass stars Ongoing programs: • ESO UVES program (Kürster et al.): 40 stars • HET Program (Endl & Cochran) : 100 stars • Keck Program (Marcy et al.): 200 stars • HARPS Program (Mayor et al.):~100 stars Results: • Giant planets (2) around GJ 876. Giant planets around low mass M dwarfs seem rare • Hot neptunes around several. Hot Neptunes around M dwarfs seem common Exoplanets around massive stars Difficult on the main sequence, easier (in principle) for evolved stars Hatzes & Cochran 1993 „…it seems improbable that all three would have companions with similar masses and periods unless planet formation around the progenitors to K giants was an ubiquitous phenomenon.“ P = 1.5 yrs Frink et al. 2002 M = 9 MJ The Planet around Pollux McDonald 2.1m CFHT McDonald 2.7m TLS The RV variations of b Gem taken with 4 telescopes over a time span of 26 years. The solid line represents an orbital solution with Period = 590 days, m sin i = 2.3 MJup. HD 13189 P = 471 d Msini = 14 MJ M* = 3.5 Msun HD 13189 Sp. Type Mass V sin i K2 II–III 3.5 Msun 2.4 km/s HD 13189 b Period 471 ± 6 d RV Amplitude e a m sin i 173 ± 10 m/s 0.27 ± 0.06 1.5 – 2.2 AU 14 MJupiter HD 13189 : Short Term Variations Discovery of Stellar Oscillations in b Gem Diploma work of Mathias Zechmeister From Michaela Döllinger‘s thesis P = 517 d Msini = 10.6 MJ e = 0.09 M* = 1.84 Mסּ P = 272 d Msini = 6.6 MJ e = 0.53 M* = 1.2 Mסּ P = 657 d Msini = 10.6 MJ e = 0.60 M* = 1.2 Mסּ P = 159 d Msini = 3 MJ e = 0.03 M* = 1.15 Mסּ P = 1011 d Msini = 9 MJ e = 0.08 M* = 1.3 Mסּ P = 477 d Msini = 3.8 MJ e = 0.37 M* = 1.0 Mסּ M sin i = 3.5 – 10 MJupiter Stellar Mass Distribution: Döllinger Sample 10 N 9 8 7 6 5 4 3 2 1 0 1.05 1.25 Mean = 1.4 Mסּ Median = 1.3 Mסּ 1.45 1.65 1.85 2.05 2.25 2.45 M (M)סּ ~10% of the intermediate mass stars have giant planets Eccentricity versus Period 50 Planet Mass Distribution for Solar-type Dwarfs P> 100 d 40 30 20 10 0 1 3 5 7 9 11 13 15 7 Planet Mass Distribution for Giant and Main Sequence stars with M > 1.1 Mסּ 6 5 N 4 3 2 1 0 1 3 5 7 9 11 13 M sin i (Mjupiter) 15 More massive stars tend to have a more massive planets and at a higher frequency 4. The Planet-Metallicity Connection? Astronomer‘s Metals More Metals ! Even more Metals !! 4. The Planet-Metallicity Connection? These are stars with metallicity [Fe/H] ~ +0.3 – +0.5 Valenti & Fischer There is believed to be a connection between metallicity and planet formation. Stars with higher metalicity tend to have a higher frequency of planets. Endl et al. 2007: HD 155358 two planets and.. Hyades stars have [Fe/H] = 0.2 and according to V&F relationship 10% of the stars should have giant planets, but none have been found in a sample of 100 stars …[Fe/H] = –0.68. This certainly muddles the metallicity-planet connection Percent Planet-Metallicity Effect in Giant stars? [Fe/H] Giant stars show no metallicity effect Maybe pollution can explain the metallicity-planet connection Giant hosting planet stars do not show a metallicity enhancement such as the planet hosting stars on the main sequence. Pasquini et al. (2007) hypothesize that the high metal content is due to pollution by planets. When the stars evolve to giants they have deeper convection zones which mixes the chemicals. Jovian Analogs Definition: A Jupiter mass planet in a 11 year orbit (5.2 AU) Period = 14.5 yrs Mass = 4.3 MJupiter e = 0.16 In other words we have yet to find one. Long term surveys (+15 years) have excluded Jupiter mass companions at 5AU in ~45 stars e Eri • Long period planet • Very young star • Has a dusty ring • Nearby (3.2 pcs) • Astrometry (1-2 mas) • Imaging (Dm =20-22 mag) • Other planets? Clumps in Ring can be modeled with a planet here (Liou & Zook 2000) Radial Velocity Measurements of e Eri Hatzes et al. 2000 Large scatter is because this is an active star Scargle Periodogram of e Eri Radial velocity measurements False alarm probability ~ 10–8 Scargle Periodogram of Ca II measurements Benedict et al: HST Astrometry on e Eri • Mass = 1.55 MJupiter • Orbital plane coincides with dusty ring plane One of our planets is missing: HD 33636 P = 2173 d Msini = 10.2 MJup i = 4 deg → m = 142 MJup Velocity (m/s) 5. Habitable Terrestrial Planets Terrestrial planets in the habitable zone of low mass stars Kasting et al. (1993) The habitable zone is loosely defined as the distance where the equilibrium temperature of the planet can support water in the liquid state Lovis et al. 2007 A Habitable Super Earth? Some are in habitable zone of M dwarf P=5.4 d P=12.9 d P=83.6 d Endl et al. can exclude 1 Mearth planet in habitable zone of Barnard‘s star 5. Sources of „Noise“ Other phenomena can produce radial velocity variations and thus „pretend“ to be a planet: • Spots, plage, other surface structure • Convection pattern on the star • Pulsations • Spots, plage, etc can cause RV Variations in active stars HD 166435 •Ca II H & K measurements are important • One can attempt to correct for the activity RV variations by looking at changes in the spectral line shapes Correlation of bisector span with radial velocity for HD 166435 Ca II H & K core emission is a measure of magnetic activity: Active star Inactive star HD 166435 shows variations in all quantities Activity Effects: Convection Hot rising cell Cool sinking lane •The integrated line profile is distorted. •The ratio of dark lane to hot cell areas changes with the solar cycle This is a Jupiter! RV changes can be as large as 10 m/s with an 11 year period One has to worry even about the nature long period RV variations Confirming Extrasolar Planet Discoveries made with Radial Velocity Measurements The commandments of planet confirmation: • Must have long-lived coherent periodic variations • RV amplitude must be constant with wavelength • Must not have photometric variations with the same period as the planet • Must not have Ca II H&K emission variations with the planet period • Most not have line shape (bisector) variations with the same period as the planet The Planet around TW Hya Setiawan et al. 2007 And my doubts… The claim is no bisector variations in this star Maximum RV variations in the velocity span is ~500 m/s Doppler image of V 410 Tau: A Weak T Tauri Star The spot distribution on V410 Tau has been present for 15 years! • TW Hya is a T Tauri star (that will become a weak T Tauri star) viewed pole-on • It most likely has a decentered polar spot (Doppler images of another TW Hya association star indeed shows a polar spot) • Polar spots on a star viewed pole on causes small changes in the bisector span, but large changes in the curvature What is needed to confirm this: 1. Contemporaneous photometry 2. RV measurements in the infrared where the spot contrast is smaller. Summary Radial Velocity Method Pros: • Most successful detection method • Gives you a dynamical mass • Distance independent • Will provide the bulk (~1000) discoveries in the next 10+ years Summary Radial Velocity Method Cons: • Only effective for late-type stars • Most effective for short (< 10 – 20 yrs) periods • Only high mass planets (no Earths!) • Projected mass (msin i) • Other phenomena (pulsations, spots) can mask as an RV signal. Must be careful in the interpretation Summary of Exoplanet Properties from RV Studies • ~6% of normal solar-type stars have giant planets • ~10% or more of stars with masses ~1.5 M סּhave giant planets that tend to be more massive • < 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 • Massive planets tend to have large orbita radii • Stars with higher metallicity tend to have a higher frequency of planets, but this needs confirmation