Small Scale Structure in Voids

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Small Scale Structure in Voids

• Danny Pan
• Advisor Michael Vogeley

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Motivation/Goal

• L-CDM models show small scale structure in voids
• Goal is to verify the small scale structure of
  voids
• Possible results?
• Structure exists, agree with models
• Structure does not exist, models may not tell the
  whole story

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Millenium Run Simulation
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Simulated Universe

• Gottlober (2003)

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Outline

• Introduction
• Research in Voids
• VoidFinder (finds voids!)
• Methods of Analysis
• Void Statistics
• Correlation Function
• ShapeFinder
• Conclusion/Results
• Future Work

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Introduction

• The Universe contains objects, but it is mostly
  empty
• Modern cosmology tells us that evolution of the
  Universe causes clumpiness
• Dense regions stay dense and grow asymmetrically
• Underdense regions stay underdense and grow
  symmetrically
• Result is spherical voids with dense walls in the
  Universe

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Research in Voids

• Gregory and Tifft (1976) first looked at
  structure in Coma Supercluster
• Found regions that seemed very empty
• Kirshner et al (1982) found a 1,000,000 cu Mpc
  region in Bootes that was empty
• Interest in voids grew
• Rojas et al. (2004) observed differences in void
  and wall galaxies

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VoidFinder

• Used to determine sample of Void regions and Void
  galaxies
• Volume limited sample from SDSS
• 4783 square degrees of the sky
• magnitude cut of 17.5
• approximately L at furthest distance
• radial cut of 100 and 300 h-1 Mpc
• 61,000 galaxies

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Galaxies
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3 Nearest Neighbors
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Potential Void Galaxies
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Walls Only
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Maximal Spheres
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Void Galaxies
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VoidFinder

• Results
• 527 void regions
• 3369 void galaxies
• 40 of the volume are voids

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Picture of VoidFinder
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Methods of Analysis

• Void Statistics
• Correlation Function
• ShapeFinder

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Void Statistics
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Void Statistics
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Void Statistics
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Void Statistics
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Void Statistics
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Correlation Function

• Probability of two points separated by a distance
  r is

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Correlation Function

• Landy-Szalay (1993) equation
• Correlation depends on data points as well as
  random points

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Correlation Function
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ShapeFinder

• Defined by Sahni et al. (1998) to assess shapes
  of objects
• Uses Minkowski Functionals to help determine
  shapes
• Volume (V)
• Surface Area (S)
• Integrated Mean Curvature (C)
• Gaussian Curvature (G)

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ShapeFinder

• Can determine 3 phase space lengths
• L1 V/S
• L2 S/C
• L3 C
• L1L2ltL3 Filament
• L1ltL2L3 Pancake
• 2 ShapeFinder statistics
• K1 (L2-L1)/(L2L1)
• K2 (L3-L2)/(L3L2)
• K10, K20 Sphere
• K11, K20 Pancake
• K10, K21 Filament

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ShapeFinder Images
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ShapeFinder Results

• TABLE OF SHAPEFINDER RESULTS ON LARGEST VOIDS

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Conclusions

• Void Statistics match other observational results
  as well as theoretical models
• Radial density profiles match very well with
  expected results, validates VoidFinder
• 2 Point Correlation Function matches various
  other samples
• Implies correlation of underdense regions mimic
  that of the entire sample

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Future Work

• ShapeFinder needs to be expanded to accommodate
  for multiple objects within each void region
• Analysis needs to be done on the Millenium Run
  sample or another Lambda CDM model to compare
  results

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Acknowledgements

• Thank you
• Dr. Michael Vogeley
• Dr. Fiona Hoyle
• Committee
• Dr. Avijit Ghosh
• Dr. Dave Goldberg
• Dr. Bhuvnesh Jain
• Dr. Gordon Richards