Download Space astrometry 3: Gaia: scientific rationale, principles, and data analysis

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)...
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Interferometry:
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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*:
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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
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1990: ideas for a follow-up mission in Russia
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2013: launch currently 20 December (Hip+24yr) by Soyuz-Fregat
from Kourou, French Guyana
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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
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astrometry:
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represents ~1% of the Galaxy’s stellar population
accuracy at 15 mag: 25 microarcsec
applies to positions, parallaxes, annual proper motions
photometry:
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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
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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
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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
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scanning of celestial great circles by the two
fields of view due to the six hour spin period
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precession of the spin axis at 45° around the Sun
with a period of 63 days
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the slow precession of the spin axis changes the
orientation of the scanned great circles allowing
coverage of different areas on the sky
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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:
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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
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data transfer and iterations:
• in practice, the data analysis was also demarcated geographically, with the various
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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:
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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
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the solution can be visualised as a successive iteration of:
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S =A + G + C
A=S+G+C
G = S +A + C
C = S +A + G
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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:
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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’
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In Gaia, a rigorous software engineering approach has been used, including:
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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)
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do not underestimate the problem of communicating the numerical parameters
relevant to a large, complex and distributed software system
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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
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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
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Agile is a collective term to describe iterative and incremental software
development techniques (in contrast to waterfall development). Emphasises:
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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
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CONF
Newton’s universal constant of gravitation
Planck Constant
h = 6.62606896 · 10−34 J s
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CONF
Planck’s constant
VelocityOfLight Constant Vacuum
c = 299792458 m s−1
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CONF
Velocity of light in vacuum (defining constant)
Wien Constant
b = 2.8977685 · 10−3 m K
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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
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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
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CONF
Astronomical unit (AU) length (TCBcompatible value in SI units; INPOP06
value)
•
CONF
Geocentric gravitational constant (TCBcompatible value in SI units; INPOP06
value)
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CONF
Equatorial radius of the Earth (INPOP06
value)
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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:
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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
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L+28m: full astrometry, radial velocities for brighter stars
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L+65m: updates on previous, more sources, classification, variable star
solutions, epoch photometry
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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