Space Astrometry: 2/2 Gaia - and Global Data Analysis - Michael Perryman (KIS Freiburg, 2 November 2016) - Index of
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Space Astrometry: 2/2
Gaia - and Global Data Analysis
Michael Perryman
(KIS Freiburg, 2 November 2016)
Hyades Cluster:
over 60,000 years
2
3
4
Pleiades Cluster:
age = 120 Myr, d=120 pc,
animation=150,000 yr
5
6
7
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)
8
Local Solar Vega
Neighbourhood
(100,000 years)
61 Cygni
Groombridge 1830
Sun
Sirius
9
Our Galaxy has been
built from mergers...
Galactic
centre
Captured galaxy:
30 kpc - satellite mass: 4 × 108 Mo
- pericentre: 7 kpc
- simulation over 3 Gyr
10Halo Accretion
(Paul Harding)
Halo accretion (Harding image)
11
Stellar motions and chemical compositions are a fossil record of the Galaxy’s formation• small irregular movements of the Earth’s geographic poles relative to crust
Earth’s Polar Motion • originates from misalignment between rotation and symmetry axes
• dominant term: seasonal redistribution of mass ~0.3 arcsec (Chandler 1891)
(since ~1895) • originally measured by visual and photographic zenith tubes, now VLBI and GPS
• ILS (1900), IPMS (1962), IERS (1988), BIH (1955), IAU MERIT (1978)
• all historical measurements reanalysed within Hipparcos reference frame
Introduction
of TAI
Participating observatories (Vondrák & Ron 2000)
189 191 193 195 197 199
Number of instruments (Vondrák et al 1997)
Polar motion versus time
(Vondrák & Ron 2000)
... illustrating 6-year beating
between the Chandler period
(435 d) and annual term
12Some limitations of Hipparcos
• a modest telescope aperture (30cm)
• modulating grid leading to ~30% light loss
• a low-efficiency photocathode detector (~10%)
• sequential (non-multiplexed) star observations
These shortcomings are addressed by Gaia,
which uses the same principles as Hipparcos
to improve accuracies by x50
13Gaia: 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 Science Programme Committee, target launch 2012 • 2013: launch in December (Hip+24yr) by Soyuz-Fregat from Kourou • 2014−2019 (beyond?): operated from the Sun-Earth L2 Lagrange point • first data release: September 2016
☜ schematic of a distorted reference frame
200
Difference in declination (milli-arcsec)
Hipparcos − FK5
100
0
...it has proven impossible to −100
eliminate these local distortions
from small field observations
−200
(photographic plate or CCD), even −50 0 50
using the method of ‘block Declination (degrees)
adjustment’ (Eichhorn 1988)
Hipparcos − ground-based (FK5)
systematic errors (Schwan 2002)
15Measurement principle
`background’ star
2π0
small angle star large angle star
measurements: measurements:
⇒ relative parallax: ⇒ absolute parallax:
π1 − π0 = (Α−Β)/2 2π1 π1 = (Α−Β)/2 2π1
Α Β
Earth’s reference Α Β
orbit star
ground, or HST−FGS etc Hipparcos, GaiaTechnical limitations of Hipparcos
beam
combining
mirror spherical primary
mirror
29º field 2
baffle modulating
aperture grid
• a modest telescope aperture (30 cm) field 1
• modulating grid with ~30% light loss flat-folding
mirror
• 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)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
Hipparcos (58º) Gaia (106º) 1
—
2
1.5
log V (n, m, γ)
1
—
3
1
—
4
2
1 —
— 5
1.0 5
1 2
— —
6 7
1
— 2
1 7 —
— 9
1 8 2
1 — —
— 9
1 10 2
11
1 — 2 —
— 11 — 13
12 15
0.5
5 4 3 5 5 3 7 4 5 6
—— — — — — ————
14 11 8 13 12 7 16 9 11 13
0
0 30 60 90 120 150 180
Basic angle, γ (degrees)Gaia: payload/telescope
Rotation axis
SiC primary mirrors
1.45 × 0.5 m2 at 106°
Superposition of
fields of view
Combined SiC toroidal
focal plane (CCDs) structure
Basic angle
monitoring systemGaia: specifications
• astrometry:
• 10 stars to 20 mag (complete: on-board detection)
9
• 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 starsGaia compared with Hipparcos
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 10 6 - 10 7
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 unbiasedAccuracy over time
eye photomultiplier
plates
CCD
arcsec
Hipparchus - 1000 stars
1000 Landgrave of Hessen - 1000
100 Tycho Brahe - 1000
Flamsteed - 4000
10
CPD/CD
1 Argelander - 26000 PPM - 400 000
0.1 FK5 - 1500
Bessel - 1
UCAC2 - 58 million
0.01 Jenkins - 6000 Tycho2 - 2.5 million
errors of best:
0.001 USNO - 100
positions Hipparcos - 120 000
0.0001 parallaxes
surveys
0.00001 all
Gaia - 1000 million
150 BC 1600 1800 2000 YearWhy a Survey to 20 mag?
Focal Plane Star transit
Single star-mapper function
for all instruments
ASM1
ASM2
RVS1
RVS2
RVS3
AF1
AF2
AF3
AF4
AF5
AF6
AF7
AF8
AF9
RP
BP
row 7
row 6
row 5
0.420 m
WFS2
row 4
BAM-N BAM-R WFS1
row 3
row 2
row 1
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 focusingChromatic 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 star1000
Radial Velocity 100
1 pc
ϖ (µas yr –1)
10
10 pc
• a limitation of Hipparcos was the
1
absence of stellar radial velocities
.
• RV is crucial for any kinematic or 0.1
100 pc
dynamical analysis of the data 0.01
0 100 200 300 400 500
• their absence would be a major vr (km s–1)
limitation for Gaia
• therefore efforts to measure bright 1000
1 pc
stars on-board at the same epoch as
100
the astrometry and photometry
µ (µas yr –2)
10
10 pc
• uses a narrow band around Ca II 1
.
0.1 100 pc
• provides: 0.01
0 2000 4000 6000 8000 10000
–full 3-dimensional space motion
vr × vt (km s–1) 2
–time-dependent characterisation
of binary stars Effects of source motion:
–input for the correction of rate of parallax change as a function of vr (top):
perspective acceleration rate of proper motion change vs vr × vt (bottom)Perspective Acceleration
a radial velocity
epoch 1 epoch 2 component changes the
proper motion rate of angular
displacement with time
d∗ θ
A’ A
B
Earth orbitRadial 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
Hipparcos: measurements at the focal plane
• star images pass behind grid
• detector with piloted field of view sampled
the modulated signal by switching rapidly
between star images several times per sec
0.1 mm • both fields of view are sampled
• modulation intensity → star magnitude
• relative signal phase → along-scan
separation (modulo grid period and γ)
• star positions established to ~1 arcsec
a priori, to allow detector piloting, and to
resolve the grid period ambiguity in the
• a high fidelity modulating grid relative separation
• 2688 grid lines
• signal digitised at 1200 Hz, sent to ground
• about 2.5 cm x 2.5 cm
• grid period = 1.208 arcsec on sky
30The complete package of CCDs, bolted to the SiC support
structure, providing thermo-mechanical stability
Astrium, January 2012CCD 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 starSky-Scanning Principle
45o
Sun
Spin axis 45o to Sun
Scan rate: 60 arcsec s-1
Spin period: 6 hours
34Sky scanning
• scanning of celestial great circles by the two • precession of the spin axis at 45° around the Sun
fields of view due to the six hour spin period with a period of 63 days
• the slow precession of the spin axis changes the • this period gives the depicted overlap which
orientation of the scanned great circles allowing ensures that each position on the sky is observed
coverage of different areas on the sky in at least three distinct epochs each half yearSky coverage for the adopted scanning law
Number of field of view transits
Star Observing Principles: Hipparcos & Gaia
Scan width = 0.7°
1. Object matching in successive scans
Sky scans 2. Attitude and calibrations are updated
(highest accuracy 3. Objects positions etc. are solved
4. Higher-order terms are solved
along scan)
5. More scans are added
6. System is iteratedThe 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 solutionsThe 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 • S: the star update
• A=S+G+C • A: the attitude update
• G = S +A + C • C: the calibration update
• C = S +A + G • 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 (around 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 Auxiliary data
Global parameters
reference system (quasars)
Astrometric model
Auxiliary data Frame
(Gaia orbit, solar Astrometric rotator
system ephemerides) proper direction u parameters
( , )
Attitude
Attitude model
parameters
instrument angles ( , ) Least-squares
adjustment
of parameters
Geometric Geometric calibra-
instrument model tion parameters
CCD observation time tobs
pixel coordinates ( , ) AC pixel coordinate
Optics/detector Instrument response Image parameter
model parameters estimation
model estimated CCD sample data Nk observed CCD sample data Nk
Lindegren et al (2011)Data 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
∆δ (milli-arcsec)
• in principle one should solve for both
–50 coordinates
• in practice, only the projection along the
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 (12 hr duration) over the
entire 3-year 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)
43Gaia Data-Processing Concept (simplified)
Object
Processing
CU4
Intermediate Iteration in 6-month cycles
Photometric
Data Update Processing
CU3/CU5
CU5
Raw Initial Data Astrometric Main Spectroscopic
Database Treatment Solution Database Processing
CU3/CU5 CU3 CU6
Variability
First-Look Processing
Processing CU7
CU3
Users Gaia Astrophysical
(Scientific Archive Parameters
Community) CU9 CU8
(Activated in 2013)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 solutionGaia 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+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): everythingThe 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 typesOne 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, etcAccuracy example: stars at 15 mag with σπ/π ≤ 0.02
Galactic coordinatesRelativistic Light Deflection (1/2)
80
1.4
60
1.2 weight = 1
40 weight < 1
1.0
Deflection (arcsec)
20
0.8
y (mm)
0
0.6
–20
0.4
–40 0.2
–60 0.0
–80 –0.2
100 80 60 40 20 0 –20 –40 –60 –80 –100 0 1 2 3 4 5 6 7 8 9
x (mm) R (solar radii)
State-of-the-art (ground):
Texas 1973 solar eclipse
(Jones 1976)
From Hipparcos residuals:
(1+ϒ)/2 = 0.9985±0.0015
(Froeschlé et al 1997)
Constraints
on γ
Expected from Gaia: (Will 2006)
ϒ to 1 part in 107
52General Relativistic Light Bending
Near Earth Asteroids
Potentially hazardous objects
Oct 2001 – Oct 2002M83
(David Malin)
Hipparcos
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Our Sun
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