VOIDS

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VOIDS
(theorists view)
Sergei Shandarin
University of Kansas
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Plan

• Discovery of Voids
• Measuring Voids
• Defining, Searching for and Measuring Voids
• Supercluster Void Network
• Void Properties
• Volumes, Sizes, Shapes, Topology,
  Substructure
• Some Final Remarks

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Discovery of Voids
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Rood 1988 adapted from Mayall 1960
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Mayall, 1960, Ann. Astrophys. 23, 344
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from Chincarini Rood 1975 (term Void of
Galaxies)
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Kirshner, Oemler, Schechter, Shectman 1981
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(No Transcript)
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Gregory Thompson 1978
de Lapparent, Geller Huchra 1987
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Shandarin 1975 2D Zeldovich
Approximation
Doroshkevich, Kotok, Novikov, Polyudov,
Shandarin, Sigov 1977 2D N-body
Simulation from Zeldovich review talk at IAU
Symp. No 79, Tallin Sep. 1977
Klypin Shandarin 1983 3D N-body Simulation
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Postman, Huchra, Geller 1986
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2D simulations Initial spectrum
Zeldovich, Einasto, Shandarin 1981 (Simulations
Beacom et al 1991)
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(No Transcript)
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Measuring Voids
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White 1979 VPF (Void Probability
Function) Probability of finding no
galaxy in a sphere of radius R


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Hierarchical clustering
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Croton et al 2004 astro-ph/0401406
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Defining, Searching for and
Measuring Voids
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(1991)
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Kauffman Fairall 1991
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El-Ad Piran 1997
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El-Ad Piran 1997
El-Ad Piran 1997
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(No Transcript)
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Aikio Mahonen 1998
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Aikio Mahonen 1998
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Aikio Mahonen 1998
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(No Transcript)
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Aikio Mahonen 1998
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Aikio Mahonen 1998
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Hoyle Vogeley 2002
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Hoyle Vogeley 2002
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(No Transcript)
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Sheth, Sahni, Shandarin, Sathyaprakash 2003
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SURFGEN Surface Genertor
Sheth, Sahni, Shandarin, Sathyaprakash 2003
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Supercluster
Sheth, Sahni, Shandarin, Sathyaprakash 2003
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Superclusters (overdense)
Voids (underdense)
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Percolating Largest supercluster
Sheth, Sahni, Shandarin, Sathyaprakash 2003
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Supercluster Void Network
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(No Transcript)
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• SUPERCLUSTERS and
  VOIDS
• are defined as the regions enclosed by
  isodensity surface
• After smoothing with a chosen window
• interface surface is build by SURFGEN
  algorithm, using linear interpolation
• The density of a supercluster is higher than the
  density of the boundary surface.
• The density of a void is lower than the density
  of the boundary surface.
• The boundary surface may consist of any number
  of disjointed pieces.
• Each piece of the boundary surface must be
  closed.
• Boundary surface of SUPERCLUSTERS and VOIDS cut
  by volume boundary
• are closed by parts of the volume boundary

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Filling Factor of overdense regions
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Superclusters vs.. Voids
Red super clusters overdense
Blue voids underdense
Solid 90 Dashed 10 Superclusters
by mass Voids by volume
dashed the largest object solid all but
the largest
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SUPERCLUSTERS and VOIDS should be studied before
percolation in the
corresponding phase
occurs. Individual SUPERCLUSTERS should be
studied at the density contrasts corresponding
to filling factors Individual VOIDS should be
studied at density contrasts corresponding to
filling factors
There are practically only two very complex
structures in between
infinite supercluster and
void.
CAUTION The above parameters depend on
smoothing with decreasing smoothing scale
i.e. better resolution critical density
contrast for SUPERCLUSTERS will increase while
critical Filling Factor will decrease the
critical density contrast for VOIDS will
decrease while the critical Filling Factor will
increase
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Plotting morphological characteristics of
SUPERCLUSTERS as a function of while
morphological characteristics of VOIDS as a
function of allows direct comparison of
SUPERCLUSTERS and VOIDS
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Superclusters vs. Voids
Red super clusters overdense
Blue voids underdense
Solid 90 Dashed 10 Superclusters
by mass Voids by volume
dashed the largest object solid all but
the largest
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Global Minkowski Functionals
Mecke, Buchert Wagner 1994
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Blue mass estimator Red volume
estimator Green area estimator Magenta
curvature estimator
Percolation thresholds
Gauss
Gauss
Superclusters
Voids
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AT PERCOLATION number of superclusters/voids,
as well as volume, mass and many other
parameters of the largest supercluster/void
rapidly change but genus curve shows no
peculiarity
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Genus vs. Percolation
Red Superclusters Blue Voids Green Gaussian
Genus as a function of Filling Factor
PERCOLATION Ratio Genus of the
Largest Genus of Exc. Set
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Void Properties

• Volumes
• Sizes
• Shapes
• Topology
• Substructure
• Evolution

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Set of Morphological Parameters
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Sizes and Shapes
For each supercluster or void
Sahni, Sathyaprakash Shandarin 1998
Convex boundaries !
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Toy Example Triaxial Torus
Sahni, Sathyaprakash Shandarin 1998
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LCDM
Superclusters vs.. Voids
Planarity Filamentarity
Mass Volume Density
log(Length) Breadth Thickness
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LCDM
Superclusters vs. Voids
Length Breadth Thickness
Planarity Filamentarity
Mass Volume Density
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Correlation with mass (SC) or volume (V)
Genus
Green at percolation Red just before
percolation Blue just after percolation
Planarity Filamentarity
log(Length) Breadth Thickness
log(Genus)
Solid lines mark the radius of sphere having
same volume as the object.
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• For both SUPERCLUSTERS and VOIDS
• Length gt R, while Breadth lt R and
  Thickness lt R.
• where R is radius of sphere having same
  volume
• as SUPERCLUSTER or VOID
• The greater the SUPERCLUSTER mass
• or VOID
  volume
• the greater the difference between R and other
  parameters

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Gottlober, Lokas, Klypin, Hoffman 2003
Z0 R10/h Mpc
Z2
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(1985)
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Evolution of voids in Adhesion Approximation
(Kofman, Pogoshyan, Shandarin 1990)
1
3a
3
3a
3
3b
2
2
3b
1
1
4a
1
4a
4b
4b
4c
4c
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4d
4d
Voids (a) expand (1) (b)
collapse (2) (c) split (3)
(d) develop substructure (4)
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Feldman, Habib, Heitmann, Shandarin 200?
Voids in LCDM simulations (Real space)
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Void and ellipsoid evolution with density
threshold
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Feldman, Habib, Heitmann, Shandarin 200?
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(No Transcript)
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FF0.1
FF0.2
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Shapes
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Sheth, van de Weygaert 2003 A hierarchy of voids
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CPF of void volume fractions
Mass fraction in voids of radius r
Evolution of CPF of void volume fractions
z0 z0.5 z1
Number density of voids of radius r
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Correlation of void diameter with initial
potential (in Adhesion Model)
Sahni, Sathyaprakash, Shandarin 1994
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Madson, Doroshkevich, Gottlober, Muller 1998
CDM simulation
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Lee, Shandarin 1998
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Hoyle, Rojas, Vogeley, Brinkmann 2003
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Hoyle, Rojas, Vogeley, Brinkmann 2003
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Some final remarks
Voids must be studied along with superclusters
because 1) They both use common data
base 2) Share common origin (Rood
1988) Superclusters are regions expanding slower
than the universe. Voids are region expanding
faster than the universe. Therefore,
gravitational instability has greater rate of
growth in SCs than in Vs resulting in larger
masses of DM halos in SCs compared to Vs.
(bias) It is likely that thermal processes
result in additional biasing. VOIDS 1) are not
empty regions but the regions of lower
galaxy/mass density 2) have complex
substructure Isolated superclusters are
possible inside voids as well as tunnels. 3)
have more complex topology than superclusters.
Voids Genus 50 Superclusters Genus a
few 4) Are neither spherical nor
elliptical There is no particular threshold
defining voids except the percolation threshold
where individual voids reach the largest volumes.