4. Exoplanets: Prospects for Gaia 5

Home , Gliese 784, HD 208487, Lalande 21185, Pallas (Giant), Pallas (Greek myth)

Lecture program

1. Space Astrometry 1/3: History, rationale, and Hipparcos 2. Space Astrometry 2/3: Hipparcos scientiﬁc results 3. Space Astrometry 3/3: Gaia 4. Exoplanets: prospects for Gaia 5. Some aspects of optical photon detection

Michael Perryman

Friday, 15 November 13 1 Astrometry in the context of exoplanet detection/characterisation

Star accretion (?) November 2013 Exoplanet Detection Colliding 1030 exoplanets Miscellaneous planetesimals (1?) (784 systems, 170 multiple) Methods [numbers from exoplanet.eu] Radio emission

Dynamical Microlensing Photometry X-ray emission (1)

Protoplanetary/ debris disks Timing AstrometryAstrometry Imaging Rad velocity sub TTVs decreasing dwarfs Transits planet mass optical radio white eclipsing Doppler re!ected dwarfs binaries variability light pulsars astrometric photometric 10MJ space ground 39 slow 1 2 MJ ground 8 (adaptive 1 free-!oating bound optics) millisec space ground space 173 10M space timing 24 (coronagraphy/ residuals 5 535 interferometry) (see TTVs) M 244

15 planets 535 planets 2 planets 24 planets 39 planets 417 planets Discovered: (12 systems, (403 systems, (2 systems, (22 systems, (36 systems, (318 systems, 2 multiple) 93 multiple) 0 multiple) 2 multiple) 1 multiple) 68 multiple)

existing capability projected (10–20 yr) n = planets known discoveries follow-up detections Friday, 15 November 13 2 Photometry

Friday, 15 November 13 3 Hipparcos: a posteriori transit detection

HD 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 d ⇒ 3% transit probability) also: 7.70 –4 HD 189733 ⇒ P = 2.218574(8) days

–2 7.74 (Bouchy et al 2005; 0 Hébrard & Lecavelier des Etangs 2006) 7.78 2

7.82 Normalised residuals Hipparcos magnitude Hp 4 7800 8000 8200 8400 8600 8800 9000 –0.5 –0.4 –0.3 –0.2 –0.1 0.0 0.1 0.2 0.3 0.4 0.5 Other studies set the scene for Gaia: Observation date (JD – 2440000) Phase • Castellano et al 2000, 2001 7.70 –4 • Laughlin 2000 • Koen & Lombard 2002 –2 7.74 • Hoeg 2002 0 • Jenkins et al 2002 7.78 • Robichon 2002 2 • Hebrard et al 2006 7.82 Normalised residuals • Gould & Morgan 2003 Hipparcos magnitude Hp 4 7800 8000 8200 8400 8600 8800 9000 –0.5 –0.4 –0.3 –0.2 –0.1 0.0 0.1 0.2 0.3 0.4 0.5 • Hatzes et al 2003, 2006 • Beatty & Gaudi 2008 Observation date (JD – 2440000) Phase Friday, 15 November 13 4 Number of ﬁeld of view transits

Friday, 15 November 13 5 Gaia: estimates for (very) hot Jupiters (Dzigan & Zucker 2012)

advantages: 1 mmag photometric accuracy Simulations account for planet disadvantages: n(measures), low cadence frequency, detection probability, stellar density, false detections, etc assumes 2-hr transit duration

Conclusion: few hundred to a few thousand discoveries (with the need for high-precision RV follow-up) Friday, 15 November 13 6 Photometry: planetary accretion events?

FH Leo (Dall et al. 2005): • suggestion: a planetary accretion event • rapid magnitude rise suggests asteroid mass such as Pallas or Vesta • decay over ~ 17 days • abundances of α-elements and Li • but may be a nova (Vogt 2006)

8.2

8.3

8.4 mag 8.5

8.6

BJD - 2440000

Friday, 15 November 13 7 Distances and space motions

Friday, 15 November 13 8 Distances and motions

Examples: • 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-age e.g. Wielen (1996) inferred that the Sun’s birthplace was at R=6.6 kpc

Friday, 15 November 13 9 Asteroseismology

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-Dalsgaard+ 2010) • mass estimates cf isochrone models: β Gem, HD13189 (Hatzes+ 2008) • etc

For this, veriﬁcation of the models by comparing parallax-based L with asteroseismology

Asteroseismology of η Boo, Z=0.04. Left: M=1.70±0.005 M⊙ Right: with overshooting (Di Mauro et al 2003) Friday, 15 November 13 10 Galactic birthplace (cont.)

0.4

Sun 0.2

Ri (kpc) –0.2 4.5

[Fe/H] –0.4 6.5

–0.6 8.5

10.5 –0.8

12.5 –1.0

0 2 4 6 8 10 12 14 16 Age (Gyr)

Friday, 15 November 13 11 Hipparcos distances to exoplanet host stars 100 brightest radial velocity host stars (end 2010) (versus RA, independent of dec)

(a) (b)

50 pc 100 pc 50 pc 100 pc

ground-based: van Altena et al (1995) Hipparcos parallaxes (unknown assigned π = 10±9 mas) (Perryman et al 1997)

Friday, 15 November 13 12 Gaia distances to exoplanet host stars Transit host stars (~280, October 2013)

Friday, 15 November 13 13 New astrometric detections

Friday, 15 November 13 14 Discovery from ‘astrometric signature’

Parameters (x50): 150 d = 50 pc Unseen planets perturb μ = 50 mas/yr, the photocentre, which over three years; orbited by a planet with 2012.8 moves with respect to the Mp = 15 MJ, e = 0.2, barycentre a = 0.6 AU (as for Doppler measures) 100 2011.6 and provides M directly

(not simply M sin i) Declination (mas) Declination

2010.4 0

0 50 100 Right ascension (mas)

Friday, 15 November 13 15 Astrometric analysis: principles

50 • as the satellite traces out a series of great circles on the sky, each star is (effectively) instantaneously stationary 0 • each star has a 2d position (abscissa and ordinate) projected onto that great circle • in principle one should solve for both –50 coordinates (milli-arcsec)

• in practice, only the projection along the

∆δ great circle (abscissa) dominates the ‘great- –100 circle solution’ • least-squares adjustment gives the along- scan position of each star at that epoch –150 • all great circles over the entire mission are then ‘assembled’ • a star’s position at any time t is represented –200 by just ﬁve parameters: position (xy), proper –150 –100 –50 0 50 motion components (μx, μy), parallax (π) ∆α cos δ (milli-arcsec)

Friday, 15 November 13 16 Direct access to planet mass

orbiting body pericentre descending node r z ν(t) reference plane

ω ellipse focus ≡ ϒ = Keplerian orbit in 3d determined by 7 parameters: centre of mass reference i direction a, e: specify size and shape Ω = longitude of P: related to a and masses (Kepler’s 3rd law) ascending node ascending node tp: the position along orbit at some reference time i, Ω,ω: represent projections wrt observer orbit plane ⇓ to observer apocentre Radial 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 planets

All 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 inclination

Friday, 15 November 13 17 The ‘tragic history’ of astrometric 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

• Strand (1943) 61 Cyg: companion of ~16 MJ • lengthy 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 the ﬁrst such companion detected, or the latest in the tragic history of this challenging approach.’ • early discussions of space astrometry/Hipparcos exoplanet capabilities: • Couteau & Pecker (1964), Gliese (1982)

Friday, 15 November 13 18 Astrometric signature

Hipparcos astrometry is marginal for detection (and mass determination)

Friday, 15 November 13 19 Gaia: number of astrometric detections

• Gaia was studied since 1997; accepted in 2000; launch: 20 December 2013 • early estimates of 10−30,000 detectable exoplanets were based on target accuracies at time of acceptance (Lattanzi et al 2000, Perryman et al 2001, Quist 2001, Sozzetti et al 2001), and are no longer applicable • more recent estimates (Castertano+ 2008): • single measurement error for bright stars σψ ~ 8 μas • reliable detections for P<5 years and α > 3σψ • at 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 identiﬁed • typical uncertainties on Δi for favourable systems are <10o • bottom line: • discover/measure several thousand giant planets with a =3−4 AU and d < 200pc • characterise hundreds of multiple systems with meaningful tests of coplanarity

Friday, 15 November 13 20 For multiple planet systems...

Drawing on extensive radial velocity work, multiple systems can be ﬁt by (e.g.) recursive decomposition Non-linearity of the ﬁtting for Gaia/SIM: considered by Casertano et al (2008), Wright & Howard (2009), Traub et al (2010)

Periodograms wrt: 5-planet system 55 Cnc (i) 2-planet model Periodicity of the ﬁfth (Fischer et al 2008) (ii) 3-planet model planet in the Keck data (iii) 4-planet model

Friday, 15 November 13 21 Astrometric motion for multiple planets... (assuming orbits are co-planar)

(a) Sun 4 planets, 60 yr (b) µ Ara 4 planets, 30 yr (c) HD 37124 3 planets, 30 yr The sun’s motion guides us:

2020 • Newton: ‘since that centre of gravity is continually at rest, the Sun, according to the various positions of the planets, must continuously move every way, but will never recede far 2010 1970 from that centre’ (Cajori 1934) 1990 2030 • barycentre frequently extends 1980 beyond the solar disk 2000 • periods when the Sun’s motion is ‘retrograde’ with respect to the barycentre (~1990, 1811,1632)

–0.008 –0.004 0 0.004 0.008 –0.01 0 0.01 –0.002 0 0.002 0.004 Displacement (AU) Displacement (AU) Displacement (AU)

Friday, 15 November 13 22 Motion of host star around barycentre for multiple exoplanets (assuming coplanarity)

HIP 14810 3 planets, 2 yr HD 40307 3 planets, 2 yr HD 69830 3 planets, 2 yr HD 155358 2 planets, 10 yr

–0.001 0 0.001 0.002 –4e–06 0 4e–06 –4e–05 0 4e–05 –0.001 0 0.001 Displacement (AU) Displacement (AU) Displacement (AU) Displacement (AU)

Friday, 15 November 13 23 Motion for multiple planets (cont.)

HIP 14810 3 planets, 2 yr HD 40307 3 planets, 2 yr HD 69830 3 planets, 2 yr HD 155358 2 planets, 10 yr

–0.001 0 0.001 0.002 –4e–06 0 4e–06 –4e–05 0 4e–05 –0.001 0 0.001 Displacement (AU) Displacement (AU) Displacement (AU) Displacement (AU)

Friday, 15 November 13 24 Astronomia Nova (1609) includes Kepler’s hand drawing of the orbit of Mars viewed from Earth

...designated as ‘mandala’ (Sanskrit for circle) by Wolfram (2010)

Friday, 15 November 13 25 Exoplanets and the solar dynamo

Friday, 15 November 13 26 Now for something contentious...

• solar axial rotation is invoked in models of the solar cycle (e.g. turbulent dynamo operating in or below the convection envelope) • precise nature of the dynamo, and details of associated solar activity (sun spot cycles, and the prolonged Maunder-type solar minima) are unexplained • empirical investigations have long pointed to a link between the Sun’s barycentric motion and various solar variability indices (e.g. Wolf, 1859; Brown, 1900; Schuster, 1911; Jose, 1965; Ferris, 1969), speciﬁcally: • the 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)

Friday, 15 November 13 27 Just one example... Abreu et al (2012), A&A 548, 88 (ETH Zürich) solar modulation potential over 9400 yr from 10Be and 14C Gleissberg de Vries 120 88 104 150 208 506 solar 80 activity

Amplitude 40

0 torque 0.015 modulus 0.01

Amplitude 0.005

0 50 100 150 200 250 300 350 400 450 500 550 600 Period (years)

Proposed 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 negligible

Friday, 15 November 13 28 Exoplanets can arbitrate (Perryman & Schulze-Hartung 2011)

• behaviour cited as correlated with the Sun’s activity includes • changes in orbital angular momentum, dL/dt • intervals of negative orbital angular momentum • these are common (but more extreme) in exoplanet systems • HD 168443 and HD 74156 have dL/dt exceeding that of the Sun by more than 105 • activity monitoring should therefore offer an independent test of the hypothetical link between: • the Sun’s barycentric motion • and the many manifestations of solar activity

Friday, 15 November 13 29 HD 168433

Lz 2 -1 (Msun AU d )

dLz/dt 2 -2 (Msun AU d )

• two massive planets (8−18MJ) at 0.3−3 AU, e1~0.5 • most extreme negative Lz and largest dL/dt • periodicity of ~58 days

Friday, 15 November 13 30 Coplanarity of orbits and transit geometry

Friday, 15 November 13 31 Exoplanet detection with HST−FGS quite a long history, starting with Benedict et al (1993) [HST−FGS yields relative parallaxes based on assumed luminosities of reference stars]

2.0 4 (a) (b) (c) 2 2004 2

1.5 ν And d (mas) 0 α 1

X residuals (mas) X residuals –2

1.0 4 0 2005 2002

(mas) 2003 y 2006 ν And c 2 –1 0.5 0

Astrometric signature, signature, Astrometric ν And ν And b –2 Y residuals (mas) Y residuals –2 0.0 0 8 16 24 32 40 400 800 1200 1600 –2 –1 0 1 2 Inclination (˚) JD – 2 452 000 (d) x (mas)

• radial velocity observations determine only Mp sin i For ν And, McArthur et al (2010) found: • astrometric measurements determine Mp directly • Mp (ν And c) = 14.0 MJ • and hence relative inclinations (van der Kamp 1981): • Mp (ν And d) = 10.2 MJ • Δi = 29.9°±1° the ﬁrst direct determination of relative orbit inclinations

Friday, 15 November 13 32 Importance of Δi

• Δi ~ 0 in the solar system • various evidence that this is not necessarily the rule in exoplanets: (1) long-term dynamical stability (via numerical integrations) ⇒ some cannot be coplanar

(2) Rossiter-McLaughlin effect used to measure the (sky projection) of the orbital and b = – 0.5, λ = 0" b = – 0.5, λ = 30" b = – 0.5, λ = 60" ) 1 stellar rotation axes indicates − + 60 that many orbits are misaligned wrt stellar equator 0 (some retrograde) – 60

Rad (m s velocity –2 –1 0 1 2 –2 –1 0 1 2 –2 –1 0 1 2 Time (h) Time (h) Time (h)

(3) models of formation and evolution admit the possibilities of: (a) asymmetric protoplanetary infall; (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’ (explains high e in triple systems, and hot Jupiters when combined with tidal friction)

Friday, 15 November 13 33 Baluev 2008 optimal strategies of radial velocity observations in search surveys

20 (ine!cient) observation particularly e!cient preceding observations HD 208487 15 J12 observations

not possible 10

0 2005 2006 2007 2008 Year

example: • 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 not

Friday, 15 November 13 34 Transit geometry

HD 189733 • normally, there is no information R* = 370 on the position angle of a 181

transiting planet’s orbit plane Rp = 120 95 64 • provided (in principle) by 2d interferometry: due to asymmetry in the source brightness E1S1 W1E1 S1W1 0.008 introduced by the planet 0.000 valuable for higher-order light Visibility • –0.008 curve effects? 0.2 0.1 • provided by Gaia if the 0.0 astrometric signature of the –0.1

transiting planet is high phase (˚) Closure –0.2 0.04 0.08 0.12 0.04 0.08 0.12 Time (d) Time (d)

(CHARA) V = 7.7, K1, d = 19pc

Friday, 15 November 13 35 Summary

• accurate distances: • calibration of host star parameters, including R for transiting • calibration of asteroseismology models • accurate proper motions: Galactic dynamics and population • multi-epoch high-accuracy photometry: • new transiting systems (several hundred?) • calibration of photometric jitter vs spectral type • multi-epoch astrometry: • discovery of new (massive, long-period) planets (3000?) • co-planarity of systems: evolutionary models • position angle of planet transits (some multiple?)

Friday, 15 November 13 36 End

Friday, 15 November 13 37