Dark Matter Haloes in the Cosmic Web

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Dark Matter Haloes in the Cosmic Web

• Cristiano Porciani (ETH Zurich)
• with OLIVER HAHN, Marcella Carollo, Avishai Dekel
  

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A bit of background (and advertisement)
Multiwavelength imaging from X-ray to radio over
2 sq. deg. including HST ACS imaging of the
entire field

• 28,000 spectra for galaxies at 0.2ltzlt1.2 to have
  IABlt22.5 at a sampling rate of 70
• 12,000 spectra of galaxies at 1.2ltzlt3 with
  BABlt25 and chosen by different color criteria at
  a 70 sampling rate
• Understanding how galaxies evolve in different
  environments is the primary goal of the
  collaborations

PI Nick Scoville (Caltech)
PI Simon Lilly (ETH)
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HOW CAN WE OPTIMALLY DEFINE THE
ENVIROMENT?Need a template to test several
plausible and operative definitions!
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The Cosmic Web
Courtesy V. Springel
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Galaxies and DM Halos as Tracers of the Cosmic
Web
Courtesy V. Springel
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Defining the environment of a DM halo

• Although the LSS of matter is prominently
  reflected in the halo distribution, no efficient
  automated method has been proposed to associate a
  given halo to the dynamical structure it belongs
  to.
• Most of the environmental studies performed so
  far use the local mass density within a few Mpc
  as a proxy for environment.

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A new (ideal) method

• We present a novel and SIMPLE approach that
  associates DM haloes to structures with different
  dynamics
• Voids, sheets, filaments and clusters are
  distinguished based on a local-stability
  criterion for the orbit of test particles based
  on the theory of dynamical systems and which is
  inspired by the Zeldovich approximation

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Orbit stability and environment - I

• Consider a test particle in the peculiar
  gravitational potential generated by a
  cosmological distribution of matter
• The linear dynamics near local extrema of ? is
  fully governed by the eigenvalues of the
  tidal-field tensor Tij (the Hessian of the
  gravitational potential)
• The number of positive eigenvalues of Tij is
  equivalent to the dimension of the stable
  manifold at the fixed points

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Orbit stability and environment - II

• We thus define as
• Voids the region of space where Tij has no
  positive eigenvalues (unstable orbits)
• Sheets the set of points with one positive and
  two negative eigenvalues (1D stable manifold)
• Filaments the sites with two positive and one
  negative eigenvalue (2D stable manifold)
• Clusters the zones with three positive
  eigenvalues (attractive fixed points)

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Practical implementation

• Assign particle masses on a Cartesian grid and
  smooth the density field with a Gaussian kernel
  of radius R
• Solve Poissons equation on the grid via FFT to
  obtain the gravitational potential ?
• Apply the second derivative operator to the
  potential
• Compute the eigenspace of the tidal tensor at
  each desired point

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Testing the algorithm with simulations

• Three N-body simulations with 5123 particles in
  periodic boxes of size 45 h-1 Mpc, 90 h-1
  Mpc, and 180 h-1 Mpc
• One simulation with 10243 particles within a 90
  h-1 Mpc box
• All simulations performed using GADGET-2
  (Springel 2005) on the Gonzales cluster
• FOF haloes with b0.2 (plus unbinding)
• Only haloes containing more than 300 particles
  are considered since most halo properties show
  strong numerical artefacts for less well resolved
  haloes
• Our catalog spans 5 orders of magnitude in halo
  mass with well resolved objects ranging from the
  size of dwarf galaxies (1010 h-1 M?) to massive
  clusters (1015 h-1 M? )

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Optimisation

• Our classification scheme contains one free
  parameter, the smoothing radius R
• The particular choice of R affects the
  eigenstructure of the tidal tensor and changes
  the classification of environment

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S to V
F to S
S to F
What happens changing from R2.1 to R4.5 Mpc/h
(a factor of 10 in volume)? Some of the regions
where one of the eigenvalues was close to zero
change classification. Basically no halo inverts
the sign of more than one eigenvalue.
C to F
F to C
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R2.1Mpc/h
Volume fractions 13.5 V 53.6 S 31.2 F 1.7
C Each cluster contains at least one halo with
Mgt 1013 h-1 M? plus a number of smaller halos
orbiting around or infalling onto the central
one The typical cluster diameter is a few Mpc
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Orbit Stability vs Density

• Density correlates with the dimension of stable
  manifold
• The median overdensity in a volume-weighted
  sample is -0.79 for voids, -0.55 for sheets, 0.28
  for filaments and 4.44 for clusters
• Densities are typically a factor of 2 larger for
  statistics weighted by halo abundance

R2.1Mpc/h
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RedshiftEvolution
z0.5
For a fixed comoving smoothing scale of 2.1
Mpc/h 84 of the haloes which are in voids at
z0 were in voids at z1 (the remaining 16 were
is sheets) Of the halos that were in voids at
z1 61 are in voids at z0 37 are in sheets
2 are in filaments
z1.0
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RedshiftEvolution - II
z0.0
z0.5
z1.0
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Mass function and environment
M dn/dM (vcgt 50 km/s in voids) 10-3 Mpc-3 (in
voids) M dn/dM (vcgt 50 km/s in voids) 10-4
Mpc-3 (everywhere)
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Two-point correlation functions
Voids
Sheets
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Halo shapes and environment
Sphere
Prolate
Oblate
Needle
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Assembly history and environment
5 x 1010 h-1 M?ltMlt5 x 1011 h-1 M?

• 2 x 1010 h-1 M?ltMlt1011 h-1 M?

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Formation time and environment
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Halo spin and environment
5 x 1010 h-1 M?ltMlt5 x 1011 h-1 M?

• Mgt5 x 1012 h-1 M?

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Halo spin and formation time
5 x 1010 h-1 M?ltMlt5 x 1011 h-1 M?
Mgt5 x 1012 h-1 M?
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Halo spin and LSS

• Do halo spin directions retain memory of the
  cosmic web in which the haloes formed?

v
v
J
J
sheets
filaments
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Halo spin and LSS - II
M/M
M/M
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Spin-spin correlation function

• Are spins of haloes in the same environment
  preferentially aligned?
• This would likely generate a spurious signal in
  weak lensing studies

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Spin-orbit correlation function

• Are intrinsic spins and orbital angular momenta
  of haloes in the same environment preferentially
  aligned?

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Orbit Stability vs Density

• Density correlates with the dimension of stable
  manifold
• The median overdensity in a volume-weighted
  sample is -0.79 for voids, -0.55 for sheets, 0.28
  for filaments and 4.44 for clusters
• Densities are typically a factor of 2 larger for
  statistics weighted by halo abundance

R2.1Mpc/h
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Density vs environment - II
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Density and shear
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Conclusions

• We presented a classification scheme that allows
  to distinguish between haloes in clusters,
  filaments, sheets and voids
• Applying this scheme to simulations we found that
  many halo properties retain memory of the
  environment in which they formed
• This provides a first step towards understanding
  how the galaxy formation process is influenced by
  the LSS
• We also showed that density-based definitions of
  environment are nearly optimal at late times (if
  you can infer the underlying DM density)