Lecture Program - Princeton University
Lecture program1. Space Astrometry 1/3: History, rationale, and Hipparcos2. Space Astrometry 2/3: Hipparcos scientific results3. Space Astrometry 3/3: Gaia4. Exoplanets: prospects for Gaia5. Some aspects of optical photon detectionMichael PerrymanFriday, 15 November 131
Astrometry in the context of exoplanetdetection/characterisationStar accretion (?)Exoplanet DetectionNovember 20131030 exoplanets(784 systems, 170 multiple)Collidingplanetesimals (1?)MiscellaneousMethods[numbers from exoplanet.eu]Radio strometryTimingX-ray emission (1)Protoplanetary/debris disksImagingRad velocitysubdwarfsdecreasingplanet mass10MJMJoptical1free-floatingspace10M5MFriday, 15 November 13photometric15 planets(12 systems,2 multiple)ground24projected (10–20 yr)2 planets(2 systems,0 multiple)24 planets(22 systems,2 multiple)n planets knowngroundground(adaptiveoptics)boundspace535535 planets(403 systems,93 millisecexisting agraphy/interferometry)39 planets(36 systems,1 multiple)discoveries173244timingresiduals(see TTVs)417 planets(318 systems,68 multiple)follow-up detections2
PhotometryFriday, 15 November 133
Hipparcos: a posteriori transit detectionHD 209458 P 3.524739(14) days(Robichon & Arenou 2000; Söderhjelm et al 2000)89 discrete observations around 1990, with 5 at transit epochs(P 3.5d and Δt 0.1 d3% transit probability)–4Normalised residualsHipparcos magnitude rvation date (JD – 2440000)Normalised residuals–4–2024–0.5 –0.4 –0.3 –0.2 –0.10.0PhaseFriday, 15 November 130.10.20.30.40.5–20HD 189733also:P 2.218574(8) days(Bouchy et al 2005;Hébrard & Lecavelier des Etangs 2006)24–0.5 –0.4 –0.3 –0.2 –0.10.00.10.2Other studies set the scene for Gaia:Phase Castellano et al 2000, 2001 Laughlin 2000 Koen & Lombard 2002 Hoeg 2002 Jenkins et al 2002 Robichon 2002 Hebrard et al 2006 Gould & Morgan 2003 Hatzes et al 2003, 2006 Beatty & Gaudi 20080.30.40.54
Number of field of view transitsFriday, 15 November 135
Gaia: estimates for (very) hot Jupiters(Dzigan & Zucker 2012)advantages: 1 mmag photometric accuracydisadvantages: n(measures), low cadenceSimulations account for planetfrequency, detection probability,stellar density, false detections, etcassumes 2-hr transit durationConclusion: few hundred to a few thousand discoveries(with the need for high-precision RV follow-up)Friday, 15 November 136
Photometry: planetary accretion events?FH Leo (Dall et al. 2005): suggestion: a planetary accretion eventrapid magnitude rise suggests asteroid mass such as Pallas or Vestadecay over 17 daysabundances of α-elements and Libut may be a nova (Vogt 2006)8.2mag8.38.48.58.6BJD - 2440000Friday, 15 November 137
Distances and space motionsFriday, 15 November 138
Distances and motionsExamples: distances provide stellar parameters e.g. transit planet diameters stellar diameters verification of seismology models for M, R proper motions characterise population(s)e.g. HIP 13044 low-metallicity Galactic halo stream (Helmi 1999, Setiawan 2010) Galactic birthplace based on metallicity-agee.g. Wielen (1996) inferred that the Sun’s birthplace was at R 6.6 kpcFriday, 15 November 139
AsteroseismologyCan hope to discriminate: primordial or self-enriched metallicity (bulk/surface): μ Ara (Pepe 2007), ι Hor (Laymand 2007) planet radii calibrated wrt stellar radii: HAT-P-7 (Christensen-Dalsgaard 2010) mass estimates cf isochrone models: β Gem, HD13189 (Hatzes 2008) etcFor this, verification of the models by comparing parallax-based L with asteroseismologyAsteroseismology of η Boo, Z 0.04.Left: M 1.70 0.005 M Right: with overshooting(Di Mauro et al 2003)Friday, 15 November 1310
Galactic birthplace (cont.)0.4Sun0.20Ri .5–1.00246810121416Age (Gyr)Friday, 15 November 1311
Hipparcos distances to exoplanet host stars100 brightest radial velocity host stars (end 2010)(versus RA, independent of dec)(a)(b)50 pcground-based: van Altena et al (1995)(unknown assigned π 10 9 mas)Friday, 15 November 13100 pc50 pc100 pcHipparcos parallaxes(Perryman et al 1997)12
Gaia distances to exoplanet host starsTransit host stars ( 280, October 2013)Friday, 15 November 1313
New astrometric detectionsFriday, 15 November 1314
Discovery from ‘astrometric signature’and provides M directly(not simply M sin i)Declination (mas)Unseen planets perturbthe photocentre, whichmoves with respect to thebarycentre(as for Doppler measures)150Parameters (x50):d 50 pcμ 50 mas/yr,over three years;orbited by a planet withMp 15 MJ, e 0.2,a 0.6 AU1002012.82011.6502010.40050100Right ascension (mas)Friday, 15 November 1315
δ (milli-arcsec)Astrometric analysis: principles50 as the satellite traces out a series of greatcircles on the sky, each star is (effectively)instantaneously stationary0 each star has a 2d position (abscissa andordinate) projected onto that great circle in principle one should solve for bothcoordinates–50 in practice, only the projection along thegreat circle (abscissa) dominates the ‘greatcircle solution’–100 least-squares adjustment gives the alongscan position of each star at that epoch all great circles over the entire mission arethen ‘assembled’–150–200–150–100–50050 a star’s position at any time t is representedby just five parameters: position (xy), propermotion components (μx, μy), parallax (π) α cos δ (milli-arcsec)Friday, 15 November 1316
Direct access to planet massdescendingnodeorbitingbodyz rpericentreν(t)ωellipse focus centre of massϒ referencedirectioniΩ longitude ofascending nodeorbit planeapocentrereference planeascending node Keplerian orbit in 3d determined by 7 parameters:a, e: specify size and shapeP: related to a and masses (Kepler’s 3rd law)tp: the position along orbit at some reference timei, Ω,ω: represent projections wrt observerto observerRadial velocity measures: cannot determine Ω, only determine the combination a sin i only determine Mp sin i if M* can be estimated cannot determine Δi for multiple planetsAll 7 parameters are determinable by astrometry ( 180º on Ω). Conceptually: xy(t) yields max and min angular rates, and hence the line of apsides (major axis) then appeal to Kepler’s third law fixes the orbit inclinationFriday, 15 November 1317
The ‘tragic history’ ofastrometric planet detection Jacob (1855) 70 Oph: orbital anomalies made it ‘highly probable’ that there was a‘planetary body’; supported by See (1895); orbit shown as unstable (Moulton 1899) Holmberg (1938): from parallax residuals. Proxima Centauri probably has a companion’of a few Jupiter masses Reuyl & Holmberg (1943) 70 Oph: planetary companion of 10 MJ early discussions of space astrometry/Hipparcos exoplanet capabilities:Strand (1943) 61 Cyg: companion of 16 MJlengthy disputes about planets around Barnard’s star: van der Kamp (1963, 1982)similarly for Lalande 21185 (e.g. Lippincott 1960)Pravdo & Shaklan (2009) vB10 with Palomar-STEPS, later disproved (Bean 2010)Muterspaugh (2010) HD 176051, only current detection: ‘may represent either thefirst such companion detected, or the latest in the tragic history of this challenging approach.’ Friday, 15 November 13Couteau & Pecker (1964), Gliese (1982)18
Astrometric signatureHipparcos astrometryis marginal for detection(and mass determination)Friday, 15 November 1319
Gaia: number of astrometric detections Gaia was studied since 1997; accepted in 2000; launch: 20 December 2013 more recent estimates (Castertano 2008): early estimates of 10 30,000 detectable exoplanets were based on target accuraciesat time of acceptance (Lattanzi et al 2000, Perryman et al 2001, Quist 2001, Sozzettiet al 2001), and are no longer applicable single measurement error for bright stars σψ 8 μasreliable detections for P 5 years and α 3σψat 2x this limit, errors on orbits and masses are 15 20% 70% of 2-planet systems with 0.2 P 9 yr and e 0.6 are identifiedtypical uncertainties on Δi for favourable systems are 10obottom line: Friday, 15 November 13discover/measure several thousand giant planets with a 3 4 AU and d 200pccharacterise hundreds of multiple systems with meaningful tests of coplanarity20
For multiple planet systems.Drawing on extensive radial velocity work, multiple systems can be fitby (e.g.) recursive decompositionNon-linearity of the fitting for Gaia/SIM: considered by Casertano et al(2008), Wright & Howard (2009), Traub et al (2010)5-planet system 55 Cnc(Fischer et al 2008)Friday, 15 November 13Periodograms wrt:(i) 2-planet model(ii) 3-planet model(iii) 4-planet modelPeriodicity of the fifthplanet in the Keck data21
Astrometric motion for multiple planets.(assuming orbits are co-planar)4 planets, 60 yr(a) Sun20204 planets, 3(b) µ AraThe sun’s motion guides us: Newton: ‘since that centre of gravity20101990is continually at rest, the Sun,according to the various positions ofthe planets, must continuously moveevery way, but will never recede farfrom that centre’ (Cajori 1934)19702030 barycentre frequently extends19802000beyond the solar disk periods when the Sun’s motion is‘retrograde’ with respect to thebarycentre ( 1990, 1811,1632)–0.008–0.00400.004Displacement (AU)Friday, 15 November 130.008–0.0100.01Displacement (AU)22
Motion of host star around barycentrefor multiple exoplanets(assuming coplanarity)2 yrHD 69830–4e–053 planets, 2 yr0Displacement (AU)Friday, 15 November 134e–05HD 155358–0.0012 planets, 10 yr00.001Displacement (AU)23
Motion for multiple planets (cont.)HIP 14810–0.0013 planets, 2 yr00.001Displacement (AU)Friday, 15 November 130.002HD 40307–4e–063 planets, 2 yr04e–06HD 69–4eDisplacement (AU)24
Astronomia Nova (1609) includes Kepler’s handdrawing of the orbit of Mars viewed from Earth.designated as ‘mandala’(Sanskrit for circle)by Wolfram (2010)Friday, 15 November 1325
Exoplanets and the solar dynamoFriday, 15 November 1326
Now for something contentious. solar axial rotation is invoked in models of the solar cycle (e.g. turbulentdynamo operating in or below the convection envelope) precise nature of the dynamo, and details of associated solar activity (sunspot cycles, and the prolonged Maunder-type solar minima) are unexplained empirical investigations have long pointed to a link between the Sun’sbarycentric motion and various solar variability indices (e.g. Wolf, 1859;Brown, 1900; Schuster, 1911; Jose, 1965; Ferris, 1969), specifically: Friday, 15 November 13the Wolf sun spot number counts (Wood & Wood, 1965)climatic changes (Mörth & Schlamminger, 1979; Scafetta, 2010)the 80-90-yr secular Gleissberg cycles (Landscheidt, 1981, 1999)prolonged Maunder-type minima (Fairbridge & Shirley, 1987; Charvátová, 1990, 2000)short-term variations in solar luminosity (Sperber et al., 1990)sun spot extrema (Landscheidt, 1999)the 2400-yr cycle seen in 14C tree-ring proxies (Charvátová, 2000)hemispheric sun spot asymmetry (Juckett, 2000)torsional oscillations in long-term sun spot clustering (Juckett, 2003)violations of the Gnevishev–Ohl sun spot rule (Javaraiah, 2005)27
Just one example.Abreu et al (2012), A&A 548, 88 (ETH Zürich)GleissbergAmplitude12088de Vries104150solar modulation potential over9400 yr from 10Be and .0150.010.005050100150200250300350Period (years)400450500550600Proposed coupling mechanisms between the solar axial rotation and orbital revolution: Zaqarashvili (1997), Juckett (2000), contested by Shirley (2006) Abreu (2012): time-dependent torque exerted by the planets on a non-spherical tachocline Callebaut & de Jager (2012): effect considered as negligibleFriday, 15 November 1328
Exoplanets can arbitrate(Perryman & Schulze-Hartung 2011) behaviour cited as correlated with the Sun’s activity includes changes in orbital angular momentum, dL/dtintervals of negative orbital angular momentum these are common (but more extreme) in exoplanet systems activity monitoring should therefore offer an independenttest of the hypothetical link between:HD 168443 and HD 74156 have dL/dt exceeding that of theSun by more than 105 Friday, 15 November 13the Sun’s barycentric motionand the many manifestations of solar activity29
HD 168433Lz(Msun AU2 d-1)dLz/dt(Msun AU2 d-2) Friday, 15 November 13two massive planets (8 18MJ) at 0.3 3 AU, e1 0.5most extreme negative Lz and largest dL/dtperiodicity of 58 days30
Coplanarity of orbitsandtransit geometryFriday, 15 November 1331
Exoplanet detection with HST FGSquite a long history, starting with Benedict et al (1993)[HST FGS yields relative parallaxes based on assumed luminosities of reference stars]4ν And d1.0ν And c0.5ν And b0.0081624Inclination ( )3240(b)220(c)20041–2y (mas)1.5X residuals (mas)(a)Y residuals (mas)Astrometric signature, α (mas)2.04202002200520032006–10ν And–2–240080012001600JD – 2 452 000 (d) radial velocity observations determine only Mp sin i astrometric measurements determine Mp directly and hence relative inclinations (van der Kamp 1981):–2–1012x (mas)For ν And, McArthur et al (2010) found: Mp (ν And c) 14.0 MJ Mp (ν And d) 10.2 MJ Δi 29.9 1 the first direct determination of relative orbit inclinationsFriday, 15 November 1332
Importance of Δi Δi 0 in the solar system various evidence that this is not necessarily the rule in exoplanets:(2) Rossiter-McLaughlin effectused to measure the (skyprojection) of the orbital andstellar rotation axes indicatesthat many orbits aremisaligned wrt stellar equator(some retrograde)Rad velocity (m s 1)(1) long-term dynamical stability (via numerical integrations)b – 0.5, λ 0 some cannot be coplanarb – 0.5, λ 30 b – 0.5, λ 60 600– 60–2–10Time (h)12–2–10Time (h)12–2–1012Time (h)(3) models of formation and evolution admit the possibilities of: (a) asymmetric protoplanetaryinfall; (b) gravitational scattering during the giant impact stage of protoplanetary collisions; (c)Kozai resonance/migration in which Lz is conserved, and hence i and e can be ‘traded’ (explainshigh e in triple systems, and hot Jupiters when combined with tidal friction)Friday, 15 November 1333
Baluev 2008optimal strategies of radial velocity observations in search surveys20J1215(inefficient)preceding observationsobservation particularly efficientHD 208487observationsnot possible10502005200620072008Yearexample: how to decide between two orbit solutions from 35 measurements (Butler 2006) Wright (2007) identified a second planet at P 28.6d or 900d J12 estimates the maximum information from the two predictions maxima give the most promising times for new observations here: predictions differed by 20m/s actual observations during 2005 were all at epochs of low information content one observation in 2005 would have resolved the degeneracy, those in 2006 could notFriday, 15 November 1334
Transit geometryHD 189733 R* 370normally, there is no informationon the position angle of atransiting planet’s orbit plane18195120 valuable for higher-order lightcurve effects?provided by Gaia if theastrometric signature of thetransiting planet is highE1S1Visibility provided (in principle) by 2dinterferometry: due to asymmetryin the source brightnessintroduced by the planetClosure phase ( ) Rp .040.08Time (d)0.120.040.080.12Time (d)(CHARA)V 7.7, K1, d 19pcFriday, 15 November 1335
Summary accurate distances:calibration of host star parameters, including R for transitingcalibration of asteroseismology modelsaccurate proper motions: Galactic dynamics and populationmulti-epoch high-accuracy photometry:new transiting systems (several hundred?)calibration of photometric jitter vs spectral typemulti-epoch astrometry:discovery of new (massive, long-period) planets (3000?)co-planarity of systems: evolutionary modelsposition angle of planet transits (some multiple?) Friday, 15 November 1336
EndFriday, 15 November 1337
Asteroseismology Asteroseismology of η Boo, Z 0.04. Left: M 1.70 0.005 M Right: with overshooting (Di Mauro et al 2003) Can hope to discriminate: primordial or self-enriched metallicity (bulk/surface): μ Ara (Pepe 2007), ι Hor (Laymand 2007) planet radii calibrated wrt stellar radii: HAT-P-7 (Christensen-D
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