Dynamics of substructures: On survivors and debris

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Dynamics of substructures On survivors and
debris

• Amina Helmi
• Kapteyn Astronomical Institute

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Outline

• Substructure in the form of bound objects
• Dynamical modeling of one satellite Sculptor
• Substructure in the form of streams
• Dynamical behaviour
• Disgression Miller's instability
• Streams and the Galactic thick disk

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MW satellites

• dSph galaxies
• smallest systems containing dark-matter
• very large M/L
• internal dynamics dictated by DM -gt probe DM
  distribution
• Recent years huge data growth MOS on 4m
  8m-class telescopes
• WHT Kleyna et al (Draco, Umi) VLT
  Battaglia et al (Scl, Fnx) - Koch et al. (Leo I,
  Leo II) Magellan MMT Walker et al (7 dSph)
  Munoz et al (Carina)
• Latest results
• flat velocity dispersion profile

Walker et al (2007)
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MW satellites

• Latest results
• mass scale within 0.6 kpc similar (nearly model
  independent)
• cannot distinguish between core cusp

Strigari et al (2007)
ISO (? cst rc 0.01 kpc)
ISO (? OM rc 0.5 kpc)
NFW (? cst)
Battaglia et al. 2007
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Sculptor

• DART (PI Tolstoy) large photometric coverage
  and 1000 spectra for red giant stars in
  Sculptor
• Photometry and spectroscopy show it has two
  components
• spatially extended, metal-poor, hotter
• centrally concentrated, metal-rich, colder

RHB
BHB
RGB
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Spectroscopy of Scl two components
Battaglia et al. 2007

• Metallicity variation correlates with kinematics
  
• Velocity dispersion of populations varies with
  distance
• Two components are clearly identified
• Orbit within the same gravitational potential
  "independent" probes of the mass distribution
• This can break some degeneracies of dynamical
  models

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Dynamical Modeling of Scl

• For stationary and spherically symmetric systems

• Density of tracer population ? (R) velocity
  anisotropy ?
• Underlying potential Vc2(r) or ?(r)
• Observations give projection of the velocity
  ellipsoid along the l.o.s

• Spatial distribution of tracer population ? (R)

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Ingredients in the modeling

• Spatial distribution from WFI photometry
• Plummer profile, b 12.7 arcmin if only 1
  component
• Extended Plummer for BHB and Centrally
  concentrated Sersic for RHB
• Velocity anisotropy, ?
• constant
• varying with radius as in Osipkov-Merritt
  (isotropic in the centre, radial in the
  outskirts)
• Mass model
• CORED Pseudo-Isothermal sphere ?(r) ?0
  rc2/(r2 rc2)
• CUSPY NFW ?(r) ?0/r/rs (1 r/rs)2
• Best fit model obtained by minimizing ?2
• Beware of degeneracies, e.g. mass-anisotropy

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Global velocity dispersion profile

• Nearly flat velocity dispersion
• In the outskirts
• potentially relevant to distinguish amongst
  different mass models
• fewer tracers
• more contamination from the MW
• Maximum likelihood approach to predict number of
  foreground stars using Besancon model

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Velocity dispersion profile components
Metal-rich
Metal-poor
Battaglia et al. 2007
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Isothermal model
Metal-rich
Metal-poor

• Joint fit is more powerful because simultaneously
  fit the MR and MP
• Isothermal model with ? constant not satisfactory
  (MP is not well fit)
• Osipkov-Merritt model for ? allows excellent fit
  to both components for isothermal model with
  large core
• Favoured core radius 0.5 kpc Mlast
  3.4 x 108 Msun

constant ?
Osipkov-Merritt ?
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NFW model
Metal-rich
Metal-poor

• Constant ? overpredicts velocity dispersion in
  the centre
• Osipkov-Merritt model for ? allows very good fit
  to both components
• Low concentrations are favoured c20
• Mlast 2.41.10.9 x 108 Msun

constant ?
Osipkov-Merritt ?
Battaglia et al. 2007
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NFW model
Metal-rich
Metal-poor

• High-resolution data (vel. errors 0.1 km/s)
  suggests lower dispersion in 1st bin
• Profiles with constant ? can be ruled out
• Osipkov-Merritt model fit becomes poorer

constant ?

Osipkov-Merritt ?

Battaglia et al. 2007
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2 component models

• ? constant not favoured
• Steep decline of the velocity dispersion of MR
  requires ? radial
• If ? radial and constant anisotropy too fastly
  rising dispersion near the centre, which is not
  allowed by the data (especially the HR)
• No good fits are obtained ?2 gt 1.7
• Worse for cuspy profiles (? is larger near the
  centre)
• larger core radii are favoured from MR
• But MP requires small core radii or larger
  concentrations
• ? as in OM favours core
• Good fit for NFW (?2 1), requires c 15 - 20
  
• Excellent fit (?2 lt 1), for isothermal with core
  radius 0.5 kpc

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Outline

• Substructure in the form of bound objects
• Dynamical modeling of one satellite Sculptor
• Substructure in the form of streams
• Dynamical behaviour
• Disgression Miller's instability
• Streams and the Galactic thick disk

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Streams

• Satellite orbits around galaxy, it leaves behind
  streams
• groups of stars on similar orbits
• constrain Galactic potential, e.g. Sgr
• Dynamical evolution can be understood by
  toy-model

Johnston 1998
Helmi White (1999)
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Dynamical evolution of streams
velocity dispersion
spatial properties
direction of motion
normal to plane of motion
Orbit in Plummer sphere

• Stream becomes elongated along direction of
  motion, and thicker in plane of motion
• Width of the stream normal to plane of motion is
  roughly constant
• Conservation of phase-space density implies
  velocity dispersion should decrease

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Dynamical evolution of streams
velocity dispersion
spatial properties

• Two phases
• Long timescales
• separation between nearby particles increases as
  t
• density decreases as 1/t2 (2D problem)
• Short timescales
• transient, very fast decrease of the density

Helmi Gomez, 2007
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Miller's instability

• N-body simulations often used to represent
  galaxies
• Limited number of particles (compared to 1011
  stars in galaxies)
• Graininess in potential introduces "errors" (e.g
  2-body encounters)
• Lead to chaotic behaviour
• exponential divergence of nearby orbits
• evidence extreme sensitivity to initial
  conditions
• Since first simulations, noticeable
  behaviour on very short timescales
  Miller's instability

Valluri Merritt 1999
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Miller's instability

• initial exponential divergence of nearby orbits
  (micro-chaos)
• present in N-body realizations of both regular
  and chaotic potentials
• e-folding timescale 1/20 tcross (too short to
  be due to encounters!)

triaxial ellipsoid
Plummer sphere
Valluri Merritt 1999
Kandrup Sideris 2003
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The initial divergence of orbits

• Very similar behaviour to that found for spatial
  evolution of streams nearby particles lt-gt
  initially nearby orbits
• separation measured as ? 1/3 (?1 ?2 ?3)
• short-term divergence on t 1/20 tcross
• Near exponential divergence does not imply
  chaos (nor encounters!)
• Shape of an orbit in phase-space
• ?4

Helmi Gomez, 2007
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Outline

• Substructure in the form of bound objects
• Dynamical modeling of one satellite Sculptor
• Substructure in the form of streams
• Dynamical behaviour
• Disgression Miller's instability
• Streams and the Galactic thick disk

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Thick disks

• Significant fraction of edge-on disk galaxies
  with thick disk
• excess light above the plane different
  kinematics

Milky Way
Ibata et al (2005)
Yoachim Dalcanton (2005)
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Thick disks

• Possible formation scenario is heating by minor
  merger of pre-existent disk (e.g. Quinn et al
  1986)

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Revisiting thick disk formation

• What happens to disk and satellite?
• Is it possible to distinguish heated disk from
  satellite?
• Is this formation scenario correct?
• Simulations initial conditions
• satellites on prograde and retrograde orbits, i
  0, 15, 30, 60 deg
• 10 - 20 of mass of the host stars dark matter
  (all live disky and E-like)
• orbits consistent with subhalos in LCDM sims
  (Benson 2005)

Villalobos Helmi 2007
DISK
SAT / face on
SAT / edge on
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Thick disks

• Prograde (red) and retrograde (blue) induce
  significant tilting and heating
• Disk is flared
• Asymmetric drift
• consistent with observations
• Higher inclination
• larger scale-height ?z
• Lower inclination
• larger scale-length (always increases) ?R

Villalobos Helmi 2007
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Thick disks

• ?R/?z strong function of inclination
• could determine orbital IC
• Fraction of accreted stars as function of Z/hz
• independent of inclination
• depends only on mass-ratio
• e.g. at Z 4 hz, 20 of the stars are accreted
  for a 20 M,sat/Mdisk

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Thick disk can we find the debris?

• No spatial correlations (after few Gyr)
• Volume around the Sun
• Velocity distribution distinct from disk
• Characteristic banana shape
• Well-mixed z-velocities
• Streams in V? - VR

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Substructure in phase-space
Gomez, Villalobos Helmi, 2007

• Energy and orbits computed for approximate
  potential
• Results not sensitive to parameters substructure
  is robust
• Easy to disentangle heated disk from accreted
  satellite
• for a given energy, accreted stars are on more
  eccentric orbits
• for a given Lz, higher energy

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Substructure in phase-space

• Substructure accreted stars with similar
  eccentricity
• Streams in velocity space groups of stars with
  the same eccentricity
• at Solar nbhd now (with apocentres at varying
  radii)
• Variation in eccentricity reflects orbital
  evolution
• but not enough to confuse disk and satellite

Gomez, Villalobos Helmi, 2007
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Summary

• Thick disk heated thin disk accreted satellite
  
• Global properties in agreement with observations
• "Easy" to distinguish accreted stars from
  pre-existing disk
• kinematics (v? or z-angular momentum)
• eccentricity
• Significant amount of substructure if full
  phase-space information is available
• Future is bright RAVE dataset proper motions
  and distances could tell if model is correct

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Puzzles

• Satellites around the MW
• strongly centrally concentrated
• anisotropically distributed
• Great circle streams by Lynden-Bell?
• INCLUDE HERE PLOTS FROM KROUPA/METZ AND POSSIBLE
  SOLUTIONS BY KANG AND LIBESKIND
• MENTION ALSO LB2 RESULTS

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CDM subhalos

• Group infall
• Signal survives since z1
• Show orbits of satellites in groups, and group
  sizes
• NOTE THIS WAS KNOWN FOR CLUSTERS, BUT IT ALSO
  HAPPENS ON THE SCALE OF GALAXIES
• CAN THIS EXPLAIN ALIGNMENT?
• ONLY IF MANY SATELLITES FROM THE SAME GROUP (gt 8)
  --- CUTE TO MENTION LAURA'S RESULT
• OR IF SATELLITES FELL IN FROM SIMILAR DIRECTIONS,
  OTHERWISE PLANES WOULD BE COMPLETELY RANDOM
• MUST MEAN THAT ENVIRONMENT MUST HAVE BEEN SIMILAR
  FOR THESE OBJECTS, AND CAN EXPLAIN THE GC OF LB2.

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Kinematical status of Scl

• Velocity field is asymetric with respect to minor
  axis
• Velocity gradient along major axis 7.63-2.2
  km/s /deg
• Flattened shape would be consistent with being
  due to rotation

Battaglia et al. 2007
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Rotation signature in Scl

• Not due to tidal disruption
• Orbit models predict the opposite trend in radial
  velocity
• Rotation amplitude 5 km/s at 700 pc (4.5 Rc)
  from the centre

Vr lt Vsys
Vr gt Vsys
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One component/constant ? cuspy profiles are
favoured

• Isothermal model
• small core radii are strongly favoured
• only if ? allowed to vary with radius, good fits
  for large core
• NFW model
• mass within last measured point very similar for
  all c 1.4 x 108 Msun
• high c give better fits
• strong virial mass - concentration degeneracy
• ? tangential

NFW
ISO
rc 0.05 kpc
c 20
rc 0.5 kpc
c 35
Battaglia et al. 2007
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One component/constant ? cuspy profiles are
favoured

• Flat velocity dispersion implies that
• the profile does not fall steeply with radius, or
• the anisotropy has to be tangential
• This is why NFW profiles require ? lt 0
• Isothermal model with small core radius is
  equivalent to NFW, which is why the masses are
  similar, and the quality of the fits too.
• Wilkinson (2006) favour large cores for dSph,
  why? Impose ? 0 in their models
• Mass within last measured point is very well
  constrained all models give 1.4 x 108 Msun, 20
  uncertainty.
• This value disagrees with claim that dSph have
  common size halo 107 Msun

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Summary

• dSph complex
• Many show two stellar components with different
  spatial distribution, metallicity and kinematics
• Case for Car less clear, yet same ?0 as Scl
• Ability to retain the structure is strongly
  correlated with orbital properties
• Global kinematics of Scl
• no signs of tidal disruption
• rotation amplitude consistent with flattened
  shape

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Summary

• Dynamical models of Scl
• One component models
• Both NFW and isothermal model fit well the data
• The best-fitting isothermal model has a small
  core radius (r0.05 kpc)
• Mass within last measured point (lt tidal radius)
  is 1.3-1.4x108 Msun
• Two component models
• MR component and MP simultaneously fit disfavours
  ? constant
• MR require larger cores (ISO), or very low
  concentrations (NFW)
• Mass within last measured point (lt tidal radius)
  is 3.3x108 Msun
• Scl not a very light dwarf galaxy
• Picture of "one mass fits all" not confirmed

Scl (Mvir)
Scl (Mlast)
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Photometry of Scl

• Evidence of varying spatial distribution
  depending on stellar type
• BHB more extended
• RHB centrally
• concentrated
• Ellipticity seems to
• vary with radius

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LR data

• Members within 3 ? clear separation from
  foreground
• S/N gt 10 allows ?Fe/H 0.1 dex ?vr 2 km/s
• Fe/H derived from CaT EW calibration

513
933
364
202
Helmi et al. 2006
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LR around Ca II Triplet
Tolstoy et al. 2001
3 CaT lines at 8500Å give accurate velocities
?vr 2 km/s (S/N 20) Calibration between EW
and Fe/H allows metallicity determination with
errors ?Fe/H 0.1 dex for S/N gt 20
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Abundance check
LR(CaT) versus HR (direct) Fe/H abundances
Sculptor
Battaglia et al. 2007
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One component/constant ?

• ISO rc 0.05, rc 0.5
• NFW c 20, beta cst
• NFW c 35, beta cst
• NFW strong degeneracy between total mass and
  concentration (beta is the same in all cases)
• However, mass within the last measured point is
  1.4 x 108 Msun in all cases

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MOND

• Very good fit
• Similar quality as the best fits obtained with
  NFW and isothermal model
• Mass-to-light ratio is on the high-side