Transcript Making Sense of GAIA - University of Oxford

Galaxy modelling in the era of
massive surveys of the Milky Way
James Binney
Oxford University
Outline
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Surveys of the Galaxy
Power of dynamical models
Gross structure & fine structure
Hierarchical modelling
How to tune the potential
Surveys
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Proper motion
Radial velocity
Microlensing
Parallax
Proper motion catalogues
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USNO B1 catalog
Tycho 2
(1 billion stars 0.2as and pm)
(2.5 million stars to m=11.5 <0.1as and <3mas/yr)
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2MASS (0.3 billion stars 0.1as)
USNO UCAC
(70 million stars to R=16.5, <0.07as and <5 mas/yr)
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Pan-STARRS
(4x1.8m f.l.2006; all sky m=24; 10mas)
Microlensing surveys
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MACHO
EROS
OGLE III
(monitors 2x108 stars in bulge, 3x107 stars
in clouds, 400 events/yr)
Radial velocity surveys
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Geneva (~20000 stars, complete part Hipparcos)
2dF
SDSS (0.1as, currently spectra 18000 stars)
RAVE (5x107 stars all sky to V=16 by 2010; 105 stars
by 2005; vr, Z)
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GAIA (2012 --)
Parallax surveys: GAIA
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In 2011 ESA to launch GAIA mission
First mag-limited parallax survey
Complete to V = 20
Radial v 1 to 10 km/s to V = 17
4 broad + 11 medium photometric bands
Δμ < 5μas/yr
Δπ < 10 μas (V<15)
1 billion stars in catalogue
Characteristics of data sets
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Different coordinates have radically
different errors: (α,δ,μα,μδ,vr,s)
Some coordinates poorly or unconstrained
Parts of phase space inaccessible
(obscuration, magnitude limit)
Probabilistic approach essential
What we want to know
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For each component α (range of related stellar types)
seek DF fα(x,v)
Brute force: divide 6d phase space into bins & count
stars in bins
Impracticable because:
Poisson fluctuations acceptable for Ni>10 so must
have < N/10 bins
6d cube with N/10 bins has (N/10)1/6 on a side
For N=107, gives 10 bins on a side, e.g. Δv=60 km/s
Anyway this approach cannot handle errors/missing
coordinates
Reduce dimensionality
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Solar-system analogy
Distribution of asteroids in (e,a) reveals
Kirkwood gaps
Distribution in angles usually uninteresting
(but Greeks & Trojans!)
Reveal structure by projecting out actionangle variables
Application of Jeans theorem leads to
prediction of f(x,v) at observationally
inaccessible points
Problem
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For Solar system we know Hamiltonian
Not so for MW (dark matter)
Determination of H important sub-problem
Perturbation Theory
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In solar system use H = HKepler+HJupiter+…
In MW use H = Haxisymm+Hbar+Hspiral+…
How to choose Haxisymm?
Torus Programme
(McGill & Binney 1990;
Kaasalainen & Binney 1994)
Structure
from nonintegrable H
P-theory
In real space
Perturbation theory
Direct integration
For powerful
resonances
Chaotic region bounded
by constructed tori
Build hierarchy of models
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Start with integrable axisymmetric model
Add selected resonances by p-theory or subtorus construction
Add perturbation by bar
Add perturbation by regular spirals
Find acceptable model of minimal complexity
Understand physical significance of features
in data
Diagnostic Structure
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How to assess correctness of Φ?
δH
resonant trapping & gaps
Expect features in DF along n.Ω = 0
Errors in Φ
features not coincident
with n.Ω = 0
Levitation
(Sridhar & Touma 1996)
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E.g. κ-ν = 0 likely important
κ > ν before disk forms
Eventually κ = ν on Jz = 0
Very high DF on Jz = 0
Carried to Jz > 0 as disk grows
Location of resonance sensitive to disk
mass / halo flattening
Tidal Streams
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Tidal steams
clusters in J-space
around orbit of parent satellite
In preliminary Φ find loose cluster
Tweak Φ to tighten cluster
(cf adaptive optics)
Pal 5
Odenkirchen et al 01
Conclusions
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Even with billion stars kinematic modelling
hopeless
With action-angle variables can project out
irrelevant variables
Discover structure due to resonances and infall
history
Differs from solar-system work because H to be
determined
Resonant families & tidal streams enable us to
tune H
Important to control introduction of substructure;
torus programme permits