Space Astrometry: 3/3 Gaia - and Global Data Analysisstrauss/perryman/perryman3-astrometry-gaia.pdf• for the 100,000 stars of Hipparcos, correction of colour-dependent shifts used

Space Astrometry: 3/3Gaia - 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

• 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

• 2013: launch currently 20 December (Hip+24yr) by Soyuz-Fregat from Kourou, French Guyana

• 2014−2019: operated from the Sun-Earth L2 Lagrange point

2!0

2!1

" #

2!1

#"referencestar

Earth’sorbit

star

`background’ star

starsmall anglemeasurements:

$ relative parallax:!1 % !0 = ("%#)/2

large anglemeasurements:

$ absolute parallax:!1 = ("%#)/2

Measurement principle

ground, or HST−FGS etc Hipparcos, Gaia

Technical limitations of Hipparcos

• a modest telescope aperture (30 cm)

• modulating grid with ~30% light loss

• a low-efficiency photocathode (~10%)

• sequential (non-multiplexed) star observations

These shortcomings are all addressed by Gaia.It uses the same principles as Hipparcos to improve accuracies by x50

(attributable to the above factors)

modulatinggrid

!at-foldingmirror

spherical primarymirror

beamcombining

mirror

ba"eaperture

#eld 1

#eld 229º

Rigidity of the basic angle

Basic angle, ! (degrees)

log

V (n

, m, !

)

n = 780 stars per scanm = 4 stars per "eld of view

(Hoyer et al 1981 A&A 101, 228)

0 30 60 90 120 150 1800

0.5

1.0

1.5

2.0

1—3

2—5

3—73—8

5—135—12

7—164—9

5—114—11

5—146—13

2—7

2—92—112—132—15

1—4

1—5

1—61—71—81—91—101—111—12

1—2Hipparcos (58º) Gaia (106º)

SiC primary mirrors1.45 × 0.5 m2 at 106°

Superposition offields of view

SiC toroidalstructure

Basic anglemonitoring system

Combinedfocal plane (CCDs)

Rotation axis

Gaia: payload/telescope

Gaia: specifications

• astrometry:

• 109 stars to 20 mag (complete: on-board detection)

• represents ~1% of the Galaxy’s stellar population

• accuracy at 15 mag: 25 microarcsec

• applies to positions, parallaxes, annual proper motions

• photometry:

• multi-colour, in about 10 bands (cf 2 for Hip-Tycho)

• radial velocities for 5-150 million stars

Hipparcos Gaia

Magnitude limit 12 20 mag Completeness 7.3 – 9.0 ~20 mag Bright limit ~0 ~3-7 mag Number of objects 120 000 26 million to V = 15 250 million to V = 18 1000 million to V = 20 Effective distance limit 1 kpc 1 Mpc Quasars None ~5 × 105 Galaxies None 106 - 107 Accuracy ~1 milliarcsec 7 µarcsec at V = 10 25 µarcsec at V = 15 300 µarcsec at V = 20 Photometry 2-colour (B and V) Spectrum to V = 20 Radial velocity None 1-10 km/s to V = 16 -17 Observing programme Pre-selected Complete and unbiased

Gaia compared with Hipparcos

Why a Survey to 20 mag?

Star transit

0.4

20 m

0.930 m

row 1

row 2

row 3

row 4

row 5

row 6

row 7

WF

S2

AF

1

AF

2

AF

3

AF

4

AF

5

AF

6

AF

7

AF

8

AF

9

BP

AS

M1

AS

M2

RP

WF

S1

BA

M-N

BA

M- R

RV

S1

RV

S2

RV

S3

Single star-mapper function for all instruments

Focal Plane

• 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

Radial Velocity

• a limitation of Hipparcos was the absence of stellar radial velocities

• RV is crucial for any kinematic or dynamical analysis of the data

• their absence would be a major limitation for Gaia

• therefore efforts to measure bright stars on-board at the same epoch as the astrometry and photometry

• uses a narrow band around Ca II

• provides:

– full 3-dimensional space motion

– time-dependent characterisation of binary stars

– input for the correction of perspective acceleration

1 pc

10 pc

100 pc

1 pc

10 pc

100 pc

vr (km s–1)

! (

µas y

r –1 )

.µ

(µas

yr –

2 ).

0 2000 4000 6000 8000 10000

0 100 200 300 400 5000.01

0.1

1

10

100

1000

0.01

0.1

1

10

100

1000

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

proper motionepoch 1 epoch 2

Earth orbit

AA’

B

!d"

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

• 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

• clocked in TDI mode at satellite spin frequency

Sky scanning

• scanning of celestial great circles by the two fields of view due to the six hour spin period

• the slow precession of the spin axis changes the orientation of the scanned great circles allowing coverage of different areas on the sky

• precession of the spin axis at 45° around the Sun with a period of 63 days

• 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

Sky scans(highest accuracy

along scan)

Scan width = 0.7°

1. Object matching in successive scans2. Attitude and calibrations are updated3. Objects positions etc. are solved4. Higher-order terms are solved5. More scans are added6. 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)

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

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

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

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

• data transfer and iterations:• in practice, the data analysis was also demarcated geographically, with the various

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

• 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)

• S: the star update• A: the attitude update• C: the calibration update• G: the global parameters update

Schematic Representation

Auxiliary data (Gaia orbit, solar

system ephemerides)

Celestialreference system

Astrometric parameters

Astrometric model

source i observed at time t

Attitude model Attitude parameters

proper direction u

Geometric instrument model

Geometric calibra-tion parameters

instrument angles (�, � )

Optics/detectormodel

Instrument responseparameters

pixel coordinates (�, � )

estimated CCD sample data Nk

Global parameters

Least-squaresadjustment

of parameters

Image parameterestimation

CCD observation time tobsAC pixel coordinate �

observed CCD sample data Nk

Frame rotator

Auxiliary data (quasars)

(�, � )

model

Lindegren et al (2011)

First-LookProcessing

Raw Database

Initial Data Treatment

Astrometric Solution

PhotometricProcessing

ObjectProcessing

VariabilityProcessing

AstrophysicalParameters

SpectroscopicProcessing

Main Database

GaiaArchive

Users(Scientific

Community)

(Activated in 2013)

Intermediate Data Update

Iteration in 6-month cycles

CU3

CU3/CU5

CU3/CU5

CU3

CU9

CU4

CU5

CU6

CU7

CU8

Gaia Data-Processing Concept (simplified)

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 teraflopsused 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)

:Nature: 2

Newton Constant G = 6.67428 · 10!11 m3kg!1s!2 • • CONF Newton’s universal constant of gravitation P.J. Mohr, B.N. Taylor, D.B.Newell, 7 March 2007, ’The 2006CODATA Recommended Valuesof the Fundamental PhysicalConstants’, National Instituteof Standards and Technology,Gaithersburg, MD 20899-8401;http://www.codata.org/ and http:-//physics.nist.gov/constants (WebVersion 5.0)

Planck Constant h = 6.62606896 · 10!34 J s • • CONF Planck’s constant P.J. Mohr, B.N. Taylor, D.B.Newell, 7 March 2007, ’The 2006CODATA Recommended Valuesof the Fundamental PhysicalConstants’, National Instituteof Standards and Technology,Gaithersburg, MD 20899-8401;http://www.codata.org/ and http:-//physics.nist.gov/constants (WebVersion 5.0)

VelocityOfLight Constant Vacuum c = 299792458 m s!1 • • CONF Velocity of light in vacuum (defining constant) P.J. Mohr, B.N. Taylor, D.B.Newell, 7 March 2007, ’The 2006CODATA Recommended Valuesof the Fundamental PhysicalConstants’, National Instituteof Standards and Technology,Gaithersburg, MD 20899-8401;http://www.codata.org/ and http:-//physics.nist.gov/constants (WebVersion 5.0)

Wien Constant b = 2.8977685 · 10!3 m K • • CONF Wien’s displacement-law constant (for\lambda max)

P.J. Mohr, B.N. Taylor, D.B.Newell, 7 March 2007, ’The 2006CODATA Recommended Valuesof the Fundamental PhysicalConstants’, National Instituteof Standards and Technology,Gaithersburg, MD 20899-8401;http://www.codata.org/ and http:-//physics.nist.gov/constants (WebVersion 5.0)

Gaia Parameter Data Base: Example (1/2)(parameters from CODATA06)

unique parameter name

project-widenumerical value

:Nature:INPOP06: 4

AsteroidRingMass SolarMassError value = 1.5 · 10!11 • • CONF Uncertainty of the INPOP06 value of theratio of the Krasinsky asteroid ring to solarmass (1-\sigma uncertainty from the directINPOP06 fit). Following G.A. Krasinsky,E.V. Pitjeva, M.V. Vasilyev, E.I. Yagudina, 1February 2002, ’Hidden Mass in the AsteroidBelt’, Icarus, 158, 98-105, the gravitationaleffect of all but the 300 heaviest asteroidscan be modeled as an acceleration causedby a solid ring with a certain mass (param-eter :Nature:INPOP06:AsteroidRingMass-SolarMass) in the ecliptic plane at acertain barycentric distance (param-eter :Nature:INPOP06:AsteroidRing-OrbitalSemiMajorAxis)

A. Fienga, J. Laskar, H. Manche,M. Gastineau, 19 April 2007, ’So-lar System Planetary EphemerisDelivery: INPOP06’, GAIA-CA-TN-IMC-AF-001-01 (see alsohttp://www.imcce.fr/Equipes-/ASD/inpop/inpop06 preprint.pdf)

AstronomicalUnit Second !A = 4.990047838061357 · 102 s • CONF Astronomical unit (AU) light time (TCB-compatible value in SI units; INPOP06 value)


AstronomicalUnit Meter -/ :Nature:VelocityOfLight-Constant Vacuum

AstronomicalUnit Meter AU = c!A = 1.495978706910000 ·1011 m

• • CONF Astronomical unit (AU) length (TCB-compatible value in SI units; INPOP06value)


Earth GM GM" = 3.986004390773178 ·1014 m3s!2

• CONF Geocentric gravitational constant (TCB-compatible value in SI units; INPOP06value)


Sun GM / SunToEarth MassRatio

Earth EquatorialRadius a(= R) = 6378137 m • • CONF Equatorial radius of the Earth (INPOP06value)


Earth JSub2Dot dJ2"/dt = !3.0 · 10!9 cy!1 • • CONF Secular (long-term) variation of the dynami-cal form-factor J 2 of the Earth (also knownas oblateness and as Stokes’ second-degreezonal harmonic of the geopotential) due to thepost-glacial rebound of the mantle (INPOP06value)


Earth SpinRate Nominal "" = 7.2921150 · 10!5 rad s!1 • CONF Nominal mean angular velocity of the Earth(INPOP06 value)


6.30038736 / :Nature:Day Second

Gaia Parameter Data Base: Example (2/2)(parameters from INPOP06)

Gaia data releaseLogistics:

• 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+40m: orbital solutions, some red/blue photometry, radial velocities, RVS spectra, some astrophysical parameters

• L+65m: updates on previous, more sources, classification, variable star solutions, epoch photometry

• end(5yr)+36m (~2021): everything

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 AsteroidsPotentially hazardous objects

Oct 2001 – Oct 2002

Accuracy over time

arcsec

1000

100

10

1

0.1

0.01

0.001

0.0001

0.00001

150 BC 1600 1800 2000 Year

errors of best:positionsparallaxes

Hipparchus - 1000 starsLandgrave of Hessen - 1000

Tycho Brahe - 1000Flamsteed - 4000

Argelander - 26000 PPM - 400 000FK5 - 1500

UCAC2 - 58 millionTycho2 - 2.5 million

Hipparcos - 120 000

Bessel - 1Jenkins - 6000

USNO - 100

Gaia - 1000 million

surveys

CPD/CD

all

eye platesCCD

photomultiplier

M83(David Malin)

Our Sun

Text

Hipparcos

Gaia

The End