Galaxy modelling in the era of massive surveys of the Milky Way

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Galaxy modelling in the era of massive surveys
of the Milky Way

• James Binney
• Oxford University

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Outline

• Surveys of the Galaxy
• Power of dynamical models
• Gross structure fine structure
• Hierarchical modelling
• How to tune the potential

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Surveys

• Proper motion
• Radial velocity
• Microlensing
• Parallax

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Proper motion catalogues

• USNO B1 catalog (1 billion stars 0.2as and pm)
• Tycho 2
  (2.5 million stars to m11.5 lt0.1as and
  lt3mas/yr)
• 2MASS (0.3 billion stars 0.1as)
• USNO UCAC
  (70 million stars to R16.5, lt0.07as and lt5
  mas/yr)
• Pan-STARRS
  (4x1.8m f.l.2006 all sky m24 10mas)

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Microlensing surveys

• MACHO
• EROS
• OGLE III (monitors 2x108 stars in bulge, 3x107
  stars in clouds, 400 events/yr)

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Radial velocity surveys

• Geneva (20000 stars, complete part Hipparcos)
• 2dF
• SDSS (0.1as, currently spectra 18000 stars)
• RAVE (5x107 stars all sky to V16 by 2010 105
  stars by 2005 vr, Z)
• GAIA (2012 --)

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Parallax surveys GAIA

• 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
• ?µ lt 5µas/yr
• ?p lt 10 µas (Vlt15)
• 1 billion stars in catalogue

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Characteristics of data sets

• Different coordinates have radically different
  errors (a,d,µa,µd,vr,s)
• Some coordinates poorly or unconstrained
• Parts of phase space inaccessible (obscuration,
  magnitude limit)
• Probabilistic approach essential

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What we want to know

• For each component a (range of related stellar
  types) seek DF fa(x,v)
• Brute force divide 6d phase space into bins
  count stars in bins
• Impracticable because
• Poisson fluctuations acceptable for Nigt10 so must
  have lt N/10 bins
• 6d cube with N/10 bins has (N/10)1/6 on a side
• For N107, gives 10 bins on a side, e.g. ?v60
  km/s
• Anyway this approach cannot handle errors/missing
  coordinates

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Reduce dimensionality

• 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 action- angle
  variables
• Application of Jeans theorem leads to prediction
  of f(x,v) at observationally inaccessible points

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Problem

• For Solar system we know Hamiltonian
• Not so for MW (dark matter)
• Determination of H important sub-problem

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Perturbation Theory

• In solar system use H HKeplerHJupiter
• In MW use H HaxisymmHbarHspiral
• How to choose Haxisymm?

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Torus Programme(McGill Binney 1990
Kaasalainen Binney 1994)
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Structure from non-integrable H
P-theory
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In real space
Perturbation theory
Direct integration
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For powerful resonances
Chaotic region bounded by constructed tori
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Build hierarchy of models

• Start with integrable axisymmetric model
• Add selected resonances by p-theory or sub-torus
  construction
• Add perturbation by bar
• Add perturbation by regular spirals
• Find acceptable model of minimal complexity
• Understand physical significance of features in
  data

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Diagnostic Structure

• How to assess correctness of F?
• dH resonant trapping gaps
• Expect features in DF along n.O 0
• Errors in F features not coincident
• with n.O 0

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Levitation(Sridhar Touma 1996)

• E.g. ?-? 0 likely important
• ? gt ? before disk forms
• Eventually ? ? on Jz 0
• Very high DF on Jz 0
• Carried to Jz gt 0 as disk grows
• Location of resonance sensitive to disk mass /
  halo flattening

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Tidal Streams

• Tidal steams clusters in J-space around
  orbit of parent satellite
• In preliminary F find loose cluster
• Tweak F to tighten cluster
• (cf adaptive optics)

Pal 5 Odenkirchen et al 01
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Conclusions

• 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