Comparing TSC

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Comparing TSC Delaunay interpolation of
peculiar velocity fields

• Groot Onderzoek
• Liesbeth Vermaas
• Supervised by Rien van de Weijgaert

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Origin of the peculiar velocity field
Importance of the peculiar velocity field
N-body simulations
TSC interpolation Delaunay tessellation
TSC, Delaunay and the peculiar velocity field
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The Universe is not homogeneous
Fluctuations seen by WMAP (2003)
Density fluctuations
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• fluctuations structures

Foam walls, filaments empty voids
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Growth of fluctuations through Gravitational
Instability (GI)
Theory
Dimensionless density
Peculiar velocity
Velocity divergence
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Graviational Instabililty
Link density and velocity field via O

• Gaussian primordial density field
• Linear regime
• Quasi/Non-linear regime

Approximation Bernardeau (92)
(Peebles 80)
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Estimate O from peculiar velocity fields

• Velocities in voids
• Velocity statistics
• - Velocity probability distribution function
• - Deviation from Gaussianity of velocity
  divergence

bias measure ßO/b!
Analyze data for density, v and div(v)
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Peculiar velocity field
from observations
PLAATJE!!!
from N-body simulations
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N-body simulations

• Initial conditions
• Gravity

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Reconstruction of the velocity field
Volume averaged (theory)
Mass averaged (discrete field)
DTFE
TSC
Volume averaged (continuous field)
DTFE Delaunay Tessellation Field Estimator TSC
Triangular Shaped Clouds
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Voronoi Delaunay tessellations
Voronoi polyhedra
Delaunay triangles in 2-d, tetrahedra in 3-d
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How to compare DTFE and TSC
Statistics, analysis velocity field Relations Skew
ness Gaussian-non-gaussian
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Method

• N-body simulation, 10 time-steps
• Apply TSC DTFE
• Top-hat smoothing 3 different radii
• Plots contours, vector fields, histograms,
  cumulative distributions, scatterplots
• Statistics mean, median, s, skewness,
  kurtostis etc.

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Summary/Conclusions

• Program that creates lots of plots and writes
  statistics to files
• Such that peculiar velocity field can be
  analyzed for TSC and DTFE
• First sight DTFE slightly better in voids
• But not very convincing in following relations
  between delta divergence
• Statistics to be done!

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Snelheidsveld

• (per deeltje) gridinterpolatie