Probing the dark matter distribution in the Milky Way with tidal streams

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Probing the dark matter distribution in the Milky
Way with tidal streams

• Monica Valluri
• Kavli Institute for Cosmological Physics
• University of Chicago
• University of Michigan

This work forms part of the PhD. Thesis of
graduate student Jennifer Siegal-Gaskins
(University of Chicago, KICP) Siegal-Gaskins et
al. 2007 (in preparation) Thanks to Andrey
Kravtsov, Brant Robertson Stelios Kazantzidis
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Outline

• Goals
• Simulate the effects of dynamic subhalos on the
  properties of tidal streams to derive generic
  features that can be uniquely attributed to
  subhalos independent of shape of the DM halo
• Importance of resonant orbits in halos
• GADGET 2 Simulations of tidal disruption
• of NFW satellites (with stars in a Hernquist
  profile)
• DiskbulgeNFW halo (oblate/prolate/spherical)
• two different subhalo distributions drawn from
  cosmological simulations (Kravtsov et al. 2004)
• Results

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2002 Dark subhalos will be detectable from
future observations
Mayer et al. 2002

• Tidal streams will generally be dispersed due
  to small scale tidal heating from dark and
  luminous subhalos (Also Johnston et al 2002)
• In non- spherical halos precession of streams
  will dominate over the effect of subhalos (Mayer
  et al 2002) and only very cold (e.g. globular
  cluster streams) will be useful for identifying
  dark subhalos (Ibata et al. 2002)

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Why revisit the issue?

• Missing Satellites problem not entirely solved
  currently popular solutions to this problem imply
  a population of dark subhalos they should have
  gravitational influence on streams
• New SDSS dwarfs How important are tidal effects
  from 107msun dwarf spheroidals in modeling tidal
  streams (and infering halo shape)?
• It seems unlikely that DM halos are spherical.
  Are there unique signatures of the tidal effects
  of dark subhalos that are independent of halo
  shape?

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N-body Simulations
(Similar to the preferred model of Klypin, Zhao
Somerville 2002 (KZS))

• NFW halo (1012 Msun)
• Spherical
• Oblate (replace r2 by m2R2z2/q2 q0.6)
• Prolate (q1.3)
• Miyamoto-Nagai disk (4?1010 Msun)
• Hernquist bulge (8?109 Msun)
• 250 dynamic dark matter subhalos drawn from 2
  separate cosmological realizations of a MW size
  halo (Kravtsov et al 2004), set up with same
  total KE and angular momentum but in equilibrium
  with galaxy potential. Softened point masses.
• Spherical NFW satellite represent DM dominated
  dE and dSph with 8 of particles in a Hernquist
  density distribution painted as stars
• total mass 3x109 Msun- dynamical friction can be
  ignored)

Background potential
Rotation curve deviates slightly from KZS
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Halo shape and orbital type

• Spherical DM halo
• all satellite orbits rosettes confined to a plane
• tidal streams appear as great circles on the sky
  (Johnston 1998)
• presence of substructure should be easily
  detecable (Johnston et al. 2002, Ibata et al.
  2002, Mayer et al. 2002)
• Out of plane scattering
• Small scale heating (increased velocity
  dispersion)

• In an Oblate, Prolate or Triaxial halo
• Most orbits fill 3-dimensional volumes (e.g
  regular orbits)
• Tidal streams on regular orbits are broad and not
  coherent
• Resonant orbits are not generally very numerous
• Confined to a sheet if orbital frequencies
  satisfy one resonant condition l?x m?y n?z
  0 (i.e. only two frequencies are linearly
  independent)
• Confined to a closed loop if orbital frequencies
  satisfy two resonant conditions (only one
  frequency is linearly independent)

(4,-2,-1)
(Merritt Valluri 1999)
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Surface-of-section of halo orbits map out range
of orbits
Resonant (sheet or loop) orbits appear as points
on SOS
Regular volume filling orbits appear as
continuous invarient curves on SOS
Chaotic volume filling orbits appear as broken
scattered points

• On the timescales of the formation of tidal
  streams (distinction between chaotic and regular is
  irrelevant so we just call both volume filling
  or non resonant

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Example of orbits used
Regular orbit
Resonant orbit
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Streams in a Prolate Halo

• Whether the stream is coherent or dispersed
  depends more on nature of orbit than on presence
  or absence of subhalos
• P2 is volume filling therefore more dispersed
• P4 is sheet filling - resonant.
• P2 more dispersed with subhalos
• P4 similarly dispersed with and without subhalos
• Whether or not subhalos increase dispersion of
  streams depends on type of orbit !

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Oblate Halo
Resonant
Volume filling but close O2 resonance

• Suhalos cause
• increased stream clumpiness/ transient
  projected density enhancements
• Features that appear like bifurcations
  (Fellhauer et al 2006)

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What causes increased clumping?

• Increased clumpiness is only in projection
• No difference seen in phase space density of
  debris - i.e. clumping is transient
• Results from formation of a wake of tidal
  stream particles behind a subhalo when the halo
  passes through the stream.
• Stream-subhalo encounter is impulsive wake does
  not persist
• Responsible for slightly increased velocity
  disepersion

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Spherical Halo

• Stream with and without subhalos are similarly
  dispersed
• Streams do not trace orbital path - subhalos
  cause significant deviations from orbit in smooth
  halo
• Increases difficulty of tracing a satellite
  orbit from observed streams may make it
  impossible to infer halo shape from stream orbits
  even with multiple streams.

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• Velocity dispersion of streams expected to
  increase.
• Need velocity information for large numbers of
  stars so use Vlos which will be the most easy ti
  measure for large samples.
• Clumping also is seen in (Vlos,l) plots
• Increased velocity dispersion not a robust
  prediction - in some cases streams appear thinner
  (and have lower dispersion)

Line of sight Velocity

Galactic Longitude
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Phase Space plots
Harding et al. 2001 (also Bullock Johnston
2005)

• Tidal streams are may be hard to detect in
  projection but are identifiable in phase space
  plots (Vlos vs R) thin contours even in the
  presence of substructure.

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Phase space plots - prolate halo
Heliocentric LOS velocity
Galactocentric distance

• Only use easily observable quantities - radial
  velocity, distance
• Subhalos produce streams of high velocity stars
  at large radii

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Oblate halo
Heliocentric LOS velocity
Galactocentric distance
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Spherical halo
High velocity large radius (HVLR)
streams smoking gun of dark subhalos?
Heliocentric LOS velocity
Galactocentric distance

• The formation of HVLR streams is
• Independent of halo shape
• Independent of orbit type (resonant or
  non-resonant/ coherent or not coherent)
• Not sensitive to choice of softening parameter of
  subhalos
• Seen in two independent realizations of the
  subhalo distribution

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Possible mechanisms for generating HVLR streams?
Distance from galactic center
Galactic Longitude (l)
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Possible mechanisms for generating HVLR streams
(Tentative)

• Resonant pumping - orbital frequencies of one or
  more subhalos are resonant with orbital frequency
  of the stream particles at so that the same
  subhalos interact with the stream particles
  multiple times with favorable encounter
  parameters kicking out particles (Sideris
  Kandrup 2004). (currently no evidence for
  multiple encounters with the same subhalo).
• Interaction/heating by the largest subhalos
  (significant evidence for wake - need to
  quantify mechanism for such a large kick)
• Interaction of stream particles with two bound
  subhalos (see Sales, Navarro, Abadi, Steinmetz
  2007 1/3 of DM subhalos of a MW sized galaxy
  have been part of a bound pair). (This type of
  interaction is seen in almost all the simulations
  but we need to quantify the effect.)

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Open issues and future directions

• What is the effect of the known satellite
  population on the observable properties of
  streams?
• With/ without additional dark subhalos
• Can the clumpy wakes in streams seen in the
  simulations be observed and can it be used to
  identify faint or dark subhalos?
• How likely is it that HVLR streams will be
  observationally detected (i.e. put observational
  errors on all parameters).

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Summary

• Shape of halo and nature of the orbit (resonant
  or volume filling) has a more significant
  effect on tidal debris than presence of absence
  of subhalos
• Streams in simulations with substructure can
  deviate significantly from those in simulations
  without subhalos. Using tidal debris to trace
  orbit of progenitor could be very tricky with
  dark subhalos.
• Subhalos cause significant transient clumping
  in projected distributions due to formation of
  wakes behind subhalos more massive than
  107msun
• A smoking gun of subhalos in all halo shapes
  are high velocity large radius (HVLR) streams
  seen in phase space (Vlos, R) plots.
• Further investigations are needed to determine
  the origin of HVLR streams - interactions of
  streams with binary subhalos currently appears to
  be a promising mechanism.

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Thank You!
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SOS with static subhalos
RESONANCES

• Stronger resonances resonant zones are
  enlarged (more orbits associated)
• Orbits remain trapped near resonance