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Space Astrometry: 3/3 Gaia - and Global Data Analysis Michael Perryman 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 Other space astrometry studies (apart from narrow-field HST-FGS)... • • • • • Interferometry: • • • SIM (10-m, Shao 1993), SIM PlanetQuest (Unwin+2008), SIM Lite (6-m, Goullioud+2008) PlanetHunter study (1 μas, Marcy 2009) POINTS (Reasenberg, 1979−89), Thousand Astronomical Unit (TAU, Etchegaray 1987) Germany: DIVA targeted 0.2 mas to 15 mag (Roser 1999) Russia: Lomonosov, Regatta-Astro, AIST (~1990); OSIRIS and LIDA (Bagrov 2006) Japan: nano-Jasmine (1 mas, Kobayashi+2008); (small-)Jasmine (10 μas, Gouda+2008) USNO sky-scanning and step-stare*: • • • • • FAME: 10 million stars to 14 mag (Johnston 2003) AMEX (Gaume+2003) OBSS* (Johnston+2006) MAPS* (Zacharias+2006) JMAPS* (Joint Milliarcsec Pathfinder Survey), 1 mas to 14 mag (Dorland+2009) Gaia: timeline • • • • • • 1990: ideas for a follow-up mission in Russia • 2013: launch currently 20 December (Hip+24yr) by Soyuz-Fregat from Kourou, French Guyana • 2014−2019: operated from the Sun-Earth L2 Lagrange point 1993: Roemer (Hoeg)... rejected by ESA as too modest 1995: Cambridge conference on microarcsec astrometry 1997: Gaia proposed to ESA (Lindegren & Perryman), interferometer 1998−2000: technical/scientific studies 2000: accepted by ESA Science Programme Committee (Hip+20yr), with a target launch in 2012 Measurement principle `background’ star 2π0 small angle measurements: ⇒ relative parallax: star 2π1 π1 − π0 = (Α−Β)/2 Α Earth’s orbit ground, or HST−FGS etc large angle measurements: ⇒ absolute parallax: star 2π1 π1 = (Α−Β)/2 Β reference star Α Hipparcos, Gaia Β Technical limitations of Hipparcos beam combining mirror spherical primary mirror 29º baffle aperture • a modest telescope aperture (30 cm) • modulating grid with ~30% light loss • a low-efficiency photocathode (~10%) • sequential (non-multiplexed) star observations field 2 modulating grid field 1 flat-folding mirror These shortcomings are all addressed by Gaia. It uses the same principles as Hipparcos to improve accuracies by x50 (attributable to the above factors) Rigidity of the basic angle n = 780 stars per scan m = 4 stars per field of view (Hoyer et al 1981 A&A 101, 228) 2.0 log V (n, m, γ) Hipparcos (58º) Gaia (106º) 1.5 1 — 2 1 — 3 1 — 4 2 — 5 1 — 5 1.0 1 — 6 1 1 — 9 1 — — 10 1 11 — 12 0.5 2 — 7 1 — 7 1 — 8 2 — 15 2 — 11 2 — 13 2 — 9 5 4 3 5 —— — — 14 11 8 13 5 3 7 4 5 6 — — ———— 12 7 16 9 11 13 0 0 30 60 90 120 Basic angle, γ (degrees) 150 180 Gaia: payload/telescope Rotation axis SiC primary mirrors 1.45 × 0.5 m2 at 106° Superposition of fields of view Combined focal plane (CCDs) SiC toroidal structure Basic angle monitoring system Gaia: specifications • astrometry: • • • • • represents ~1% of the Galaxy’s stellar population accuracy at 15 mag: 25 microarcsec applies to positions, parallaxes, annual proper motions photometry: • • 109 stars to 20 mag (complete: on-board detection) multi-colour, in about 10 bands (cf 2 for Hip-Tycho) radial velocities for 5-150 million stars Gaia compared with Hipparcos Hipparcos Gaia Magnitude limit Completeness Bright limit Number of objects 12 7.3 – 9.0 ~0 120 000 Effective distance limit Quasars Galaxies Accuracy 1 kpc None None ~1 milliarcsec Photometry Radial velocity Observing programme 2-colour (B and V) None Pre-selected 20 mag ~20 mag ~3-7 mag 26 million to V = 15 250 million to V = 18 1000 million to V = 20 1 Mpc ~5 × 105 10 6 - 10 7 7 µarcsec at V = 10 25 µarcsec at V = 15 300 µarcsec at V = 20 Spectrum to V = 20 1-10 km/s to V = 16 -17 Complete and unbiased Why a Survey to 20 mag? Focal Plane RVS3 RVS2 RVS1 RP BP AF9 AF8 AF7 AF6 AF5 AF4 AF3 AF2 AF1 ASM2 Single star-mapper function for all instruments ASM1 Star transit row 7 WFS2 row 5 row 4 row 3 row 2 row 1 BAM-N BAM-R WFS1 0.420 m row 6 0.930 m • • • • • • stars detected (ASM1) and confirmed (ASM2) as they enter the field; no input catalogue this is crucial for variable stars, high proper motions stars, asteroids, etc measured using TDI as they cross the astrometric field (AF1 to AF9), centroiding on ground photometric measurements across blue and red photometers → classification, chromaticity radial velocity spectrometer: measurements (in Ca II) for bright stars across RVS1 to RVS3 also: Basic Angle Monitoring (BAM) and Wave Front Sensors (WFS) for focusing Chromatic Aberration • star images (centroids) are displaced differently for different star colours • not generally associated with reflective systems with no dioptric elements, but it exists for Hipparcos (and others) since the telescope optics are asymmetric • for the 100,000 stars of Hipparcos, correction of colour-dependent shifts used approximate star colours, either a priori from ground-based photometry, or from the satellite (star mapper ‘Tycho’) 2-colour measurements • this is totally unrealistic for Gaia: 1 billion stars, many of which will be variable • at the 10 μas accuracy level, the effects of chromaticity are (very) significant • solution: – on-board filters measure multi-colour photometry at each epoch of observation – optimised to characterise the star (metallicity, luminosity class, reddening,...) – also used in the Global Iterative Solution to correct for chromaticity, star by star ϖ (µas yr –1) • a limitation of Hipparcos was the absence of stellar radial velocities . Radial Velocity 1000 100 10 1 0.01 • their absence would be a major limitation for Gaia 100 pc 0 100 200 µ (µas yr –2) 1000 – full 3-dimensional space motion – time-dependent characterisation of binary stars – input for the correction of perspective acceleration 400 500 8000 10000 1 pc 100 10 10 pc 1 0.1 • provides: 300 vr (km s–1) . • uses a narrow band around Ca II 10 pc 0.1 • RV is crucial for any kinematic or dynamical analysis of the data • therefore efforts to measure bright stars on-board at the same epoch as the astrometry and photometry 1 pc 0.01 100 pc 0 2000 4000 6000 vr × vt (km s–1) 2 Effects of source motion: rate of parallax change as a function of vr (top): rate of proper motion change vs vr × vt (bottom) Perspective Acceleration epoch 1 epoch 2 proper motion d∗ A’ θ A B Earth orbit a radial velocity component changes the rate of angular displacement with time Radial velocities: spectrum around Ca II Effect of temperature: A to M stars Effect of metal abundance in G stars Expected from the radial velocity instrument... • V<17: radial velocities, 1−10 km/s (~150 million objects) • V<13: multi-epoch (5 million objects) • V<13: rotational velocities, atmospheric parameters, reddening • V<12: abundances (2 million objects) The complete package of CCDs, bolted to the SiC support structure, providing thermo-mechanical stability Astrium, January 2012 CCD Measurements • each CCD: 4500 TDI stages with 10 µm pitch pixels • clocked in TDI mode at satellite spin frequency • • operating temperature: 165 K (optimises charge-transfer efficiency, due to radiation-induced charge traps) centroiding results: 0.0026 pixel rms error for a 12.9 mag star Sky scanning • scanning of celestial great circles by the two fields of view due to the six hour spin period • precession of the spin axis at 45° around the Sun with a period of 63 days • the slow precession of the spin axis changes the orientation of the scanned great circles allowing coverage of different areas on the sky • this period gives the depicted overlap which ensures that each position on the sky is observed in at least three distinct epochs each half year Sky coverage for the adopted scanning law Number of field of view transits Star Observing Principles: Hipparcos & Gaia Scan width = 0.7° Sky scans (highest accuracy along scan) 1. Object matching in successive scans 2. Attitude and calibrations are updated 3. Objects positions etc. are solved 4. Higher-order terms are solved 5. More scans are added 6. System is iterated The Three-Step Reduction for Hipparcos (1/2) 1. ~5 successive precessing great-circle scans (~12 hr data) are treated together: the 1d along-scan coordinates for each star are then established by least-squares • the data set is a compromise for projection effects • also requires solving for satellite attitude (gyros, torque models, etc), as well as instrument calibration terms (evolve only slowly with time), and slit ambiguities • also corrected for aberration and GR light-bending • the efficient solution of the large system of equations was not trivial (Cholesky sparse matrix factorisation) 2. an arbitrary origin (zero point) is defined; the entire set of great circles (e.g. over 1, 2, or 3 years) are then interconnected [just two such are shown], by solving for the zero points 3. this allows all observations for each star to be collected together; the 5 astrometric parameters for each star are then solved, again by least-squares • adjustment must account for chromatic aberration using the star’s colour index • solutions not well modeled by 5 parameters were subject to double-star treatment: solving for 7 or 9 parameters (acceleration), or even full orbital solutions The Three-Step Reduction for Hipparcos (2/2) Some practicalities: • • link to an extragalactic reference system (6 degrees of freedom) an elaborate system was needed to verify reliability of the final solution: • essentially, two data reduction teams carried out the entire processing (with subgroups • • data transfer and iterations: • in practice, the data analysis was also demarcated geographically, with the various • • charged with the double star analysis, and the photometric analysis) although they worked independently, with different detailed methods (numerical solution, attitude modeling, etc), various intermediate check points ensured that the outputs of each step were consistent with the expected statistical errors experts in different geographic locations (institutes): e.g. in the NDAC consortium, the three steps were split into Cambridge (UK), Copenhagen (DK), and Lund (S) in the early 1990s the only way to ‘pass the data on’ was using magnetic tapes sent by normal mail (!). This made iterations time consuming (and therefore costly) perspective: • rigorous mathematical formulation • numerous skilled computer scientists/statisticians for implementation • as always, the devil is in the detail! Gaia: a Global Iterative Solution The Hipparcos and Gaia data are amenable to a more ‘logical’ and more rigorous solution: • the satellite observations (star positions and motions), as well as instrument calibration parameters, the satellite attitude, and its orbit and velocity are self-consistent • therefore a block iterative solution can be adopted. As implemented, it consists of four blocks which can be calculated independently, although each block depends on every other block; evaluated cyclicly until convergence • the solution can be visualised as a successive iteration of: • • • • • • • • S =A + G + C A=S+G+C G = S +A + C C = S +A + G • • • • S: the star update A: the attitude update C: the calibration update G: the global parameters update details: mathematical formulation: Lindegren et al (2012, A&A); computational aspects : O’Mullane et al (2011, ExA) the data processing (currently 1.5 Tflops at ESAC), and data storage requirements (~10 PBytes), are very large the intention is to directly iterate some 100 million sources, and interpolate the remaining 90% the practical implementation has proven very difficult: • • • • • studies were already made (in Italy) in the context of the Hipparcos data processing ~1990 first experiments was based on a re-analysis of the Hipparcos data (100,000 stars) ~1997 groups in Madrid (GMV), Barcelona (UB) and Torino (OATo) have not been able to get a working solution it has been the subject of a major effort at ESAC (Spain) since ~2005 the Gaia s/w will be used for the analysis of the Japanese nano-Jasmine satellite data (Gouda et al) Schematic Representation source i observed at time t Celestial reference system Auxiliary data (quasars) Global parameters Astrometric model Auxiliary data (Gaia orbit, solar system ephemerides) Frame rotator Astrometric parameters proper direction u ( , Attitude parameters Attitude model instrument angles ( , ) Geometric instrument model Geometric calibration parameters Optics/detector model estimated CCD sample data Nk Least-squares adjustment of parameters CCD observation time tobs AC pixel coordinate pixel coordinates ( , ) model ) Instrument response parameters Image parameter estimation observed CCD sample data Nk Lindegren et al (2011) Gaia Data-Processing Concept (simplified) Object Processing CU4 Intermediate Data Update Iteration in 6-month cycles Photometric Processing CU3/CU5 Raw Database Initial Data Treatment CU5 Astrometric Solution Main Database CU6 CU3 CU3/CU5 Spectroscopic Processing Variability Processing First-Look Processing CU7 CU3 Users (Scientific Community) Gaia Archive Astrophysical Parameters CU9 (Activated in 2013) CU8 The Mare Nostrum Supercomputer, Barcelona the second most powerful in Spain (was 3rd or 4th in world in 2006) 2560 JS21 blade computing nodes, 10,240 CPUs in total weighs 40 tons; capable of 60 teraflops used extensively for Gaia simulations and the iterative solution A Few Software ‘Lessons’ • In Gaia, a rigorous software engineering approach has been used, including: • • • • • Java is adopted/imposed for the distributed computing (O’Mullane et al, 2011, ExA) ICDs (Interface Control Documents) for data exchange a parameter data base is used for all numerical values (Perryman et al, 2008, ExA) • do not underestimate the problem of communicating the numerical parameters relevant to a large, complex and distributed software system • realise that different people will use different numerical values for (even) fundamental quantities, e.g. the mass of the Sun, the Astronomical Unit, or even π • even when properly communicated, ensuring that correct values are implemented, or updated (either through oversight, error, or neglect) is not at all trivial • differences may critically affect the results, and are almost impossible to track work packages adhere to ECSS (European Cooperation for Space Standardization) development has adopted Agile techniques, in particular eXtreme programming • Agile is a collective term to describe iterative and incremental software development techniques (in contrast to waterfall development). Emphasises: • • • • individuals and interactions (over processes and tools) working software (over comprehensive documentation) customer collaboration (over contract negotiation) responding to change (over following a plan) Gaia Parameter Data Base: Example (1/2) (parameters from CODATA06) :Nature: unique parameter name project-wide numerical value Newton Constant G = 6.67428 · 10−11 m3 kg−1 s−2 • • CONF Newton’s universal constant of gravitation Planck Constant h = 6.62606896 · 10−34 J s • • CONF Planck’s constant VelocityOfLight Constant Vacuum c = 299792458 m s−1 • • CONF Velocity of light in vacuum (defining constant) Wien Constant b = 2.8977685 · 10−3 m K • • CONF Wien’s displacement-law \lambda max) constant (for P.J. Mohr, B.N. Taylor, D.B. Newell, 7 March 2007, ’The 2006 CODATA Recommended Values of the Fundamental Physical Constants’, National Institute of Standards and Technology, Gaithersburg, MD 20899-8401; http://www.codata.org/ and http://physics.nist.gov/constants (Web Version 5.0) P.J. Mohr, B.N. Taylor, D.B. Newell, 7 March 2007, ’The 2006 CODATA Recommended Values of the Fundamental Physical Constants’, National Institute of Standards and Technology, Gaithersburg, MD 20899-8401; http://www.codata.org/ and http://physics.nist.gov/constants (Web Version 5.0) P.J. Mohr, B.N. Taylor, D.B. Newell, 7 March 2007, ’The 2006 CODATA Recommended Values of the Fundamental Physical Constants’, National Institute of Standards and Technology, Gaithersburg, MD 20899-8401; http://www.codata.org/ and http://physics.nist.gov/constants (Web Version 5.0) P.J. Mohr, B.N. Taylor, D.B. Newell, 7 March 2007, ’The 2006 CODATA Recommended Values of the Fundamental Physical Constants’, National Institute of Standards and Technology, Gaithersburg, MD 20899-8401; http://www.codata.org/ and http://physics.nist.gov/constants (Web Version 5.0) AsteroidRingMass SolarMassError value = 1.5 · 10 • • CONF Uncertainty of the INPOP06 value of the ratio of the Krasinsky asteroid ring to solar mass (1-\sigma uncertainty from the direct INPOP06 fit). Following G.A. Krasinsky, E.V. Pitjeva, M.V. Vasilyev, E.I. Yagudina, 1 February 2002, ’Hidden Mass in the Asteroid Belt’, Icarus, 158, 98-105, the gravitational effect of all but the 300 heaviest asteroids can be modeled as an acceleration caused by a solid ring with a certain mass (parameter :Nature:INPOP06:AsteroidRingMassSolarMass) in the ecliptic plane at a certain barycentric distance (parameter :Nature:INPOP06:AsteroidRingOrbitalSemiMajorAxis) Astronomical unit (AU) light time (TCBcompatible value in SI units; INPOP06 value) A. Fienga, J. Laskar, H. Manche, M. Gastineau, 19 April 2007, ’Solar System Planetary Ephemeris Delivery: INPOP06’, GAIA-CATN-IMC-AF-001-01 (see also http://www.imcce.fr/Equipes/ASD/inpop/inpop06 preprint.pdf) Gaia Parameter Data Base: Example (2/2) (parameters from INPOP06) AstronomicalUnit Second τA = 4.990047838061357 · 102 s AstronomicalUnit Meter AU = cτA = 1.495978706910000 · 1011 m Earth GM GM⊕ = 3.986004390773178 · 1014 m3 s−2 Earth EquatorialRadius a(= R) = 6378137 m Earth JSub2Dot dJ2⊕ /dt = −3.0 · 10−9 cy−1 Earth SpinRate Nominal ω⊕ = 7.2921150 · 10−5 rad s−1 • CONF • CONF Astronomical unit (AU) length (TCBcompatible value in SI units; INPOP06 value) • CONF Geocentric gravitational constant (TCBcompatible value in SI units; INPOP06 value) • • CONF Equatorial radius of the Earth (INPOP06 value) • • CONF Secular (long-term) variation of the dynamical form-factor J 2 of the Earth (also known as oblateness and as Stokes’ second-degree zonal harmonic of the geopotential) due to the post-glacial rebound of the mantle (INPOP06 value) • CONF Nominal mean angular velocity of the Earth (INPOP06 value) • A. Fienga, J. Laskar, H. Manche, M. Gastineau, 19 April 2007, ’Solar System Planetary Ephemeris Delivery: INPOP06’, GAIA-CATN-IMC-AF-001-01 (see also http://www.imcce.fr/Equipes/ASD/inpop/inpop06 preprint.pdf) A. Fienga, J. Laskar, H. Manche, M. Gastineau, 19 April 2007, ’Solar System Planetary Ephemeris Delivery: INPOP06’, GAIA-CATN-IMC-AF-001-01 (see also http://www.imcce.fr/Equipes/ASD/inpop/inpop06 preprint.pdf) A. Fienga, J. Laskar, H. Manche, M. Gastineau, 19 April 2007, ’Solar System Planetary Ephemeris Delivery: INPOP06’, GAIA-CATN-IMC-AF-001-01 (see also http://www.imcce.fr/Equipes/ASD/inpop/inpop06 preprint.pdf) A. Fienga, J. Laskar, H. Manche, M. Gastineau, 19 April 2007, ’Solar System Planetary Ephemeris Delivery: INPOP06’, GAIA-CATN-IMC-AF-001-01 (see also http://www.imcce.fr/Equipes/ASD/inpop/inpop06 preprint.pdf) A. Fienga, J. Laskar, H. Manche, M. Gastineau, 19 April 2007, ’Solar System Planetary Ephemeris Delivery: INPOP06’, GAIA-CATN-IMC-AF-001-01 (see also http://www.imcce.fr/Equipes/ASD/inpop/inpop06 preprint.pdf) A. Fienga, J. Laskar, H. Manche, M. Gastineau, 19 April 2007, ’Solar System Planetary Ephemeris Delivery: INPOP06’, GAIA-CATN-IMC-AF-001-01 (see also http://www.imcce.fr/Equipes/ASD/inpop/inpop06 preprint.pdf) Gaia data release Logistics: • • • • L+6 months: positioning at L2, commissioning L+12m: first full sky scan completed L+24m (18 months data): parallaxes and proper motions separable internal database to public archive (validation): ~3 months Products: • L+22m: positions + G mag (all sky, single stars, alerts, NEOs) + 105 proper motions (Hipparcos + Gaia) at 50 micro-arcsec/yr • • L+28m: full astrometry, radial velocities for brighter stars • L+65m: updates on previous, more sources, classification, variable star solutions, epoch photometry • end(5yr)+36m (~2021): everything L+40m: orbital solutions, some red/blue photometry, radial velocities, RVS spectra, some astrophysical parameters The final Gaia Catalogue will be available ~2020, although many preliminary catalogues will be available before It will advance.... Stellar astrophysics • Comprehensive luminosity calibration, for example: – distances to 1% for ~10 million stars to 2.5 kpc – distances to 10% for ~100 million stars to 25 kpc – rare stellar types and rapid evolutionary phases in large numbers – parallax calibration of all distance indicators e.g., Cepheids and RR Lyrae to LMC/SMC • Physical properties, for example: – clean Hertzsprung–Russell diagrams throughout the Galaxy – Solar-neighbourhood mass and luminosity function e.g., white dwarfs (~400,000) and brown dwarfs (~50,000) – initial mass and luminosity functions in star-forming regions – luminosity function for pre-main-sequence stars – detection and dating of all spectral types and Galactic populations – detection and characterisation of variability for all spectral types One billion stars in 3-d will provide … • in our Galaxy … – – – – – – – the distance and velocity distributions of all stellar populations the spatial and dynamic structure of the disk and halo its formation history a detailed mapping of the Galactic dark-matter distribution a rigorous framework for stellar-structure and evolution theories a large-scale survey of extra-solar planets (~10,000) a large-scale survey of Solar-system bodies (~250,000) • … and beyond – – – – definitive distance standards out to the LMC/SMC rapid reaction alerts for supernovae and burst sources (~20,000) quasar detection, redshifts, microlensing structure (~500,000) fundamental quantities: γ to 2×10−6 (2×10−5 present) Distances from Ground, Hipparcos, and Gaia e.g. the Hyades: distance, membership, age, dynamics, mass segregation, evolution, main sequence, etc Accuracy example: stars at 15 mag with σπ/π ≤ 0.02 Galactic coordinates General Relativistic Light Bending Near Earth Asteroids Potentially hazardous objects Oct 2001 – Oct 2002 Accuracy over time eye photomultiplier plates CCD arcsec 1000 Hipparchus - 1000 stars Landgrave of Hessen - 1000 Tycho Brahe - 1000 Flamsteed - 4000 100 10 1 0.1 0.01 0.001 0.0001 0.00001 CPD/CD Argelander - 26000 PPM - 400 000 FK5 - 1500 Bessel - 1 UCAC2 - 58 million Jenkins - 6000 Tycho2 - 2.5 million errors of best: USNO - 100 positions Hipparcos - 120 000 parallaxes surveys all Gaia - 1000 million 150 BC 1600 1800 2000 Year M83 (David Malin) Hipparcos Text Our Sun Gaia The End