# Presentation: 126590

- Sergei Shandarin

**University of Kansas**

**(****theorist’s view)**

## 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**

## Discovery

**Discovery**
**  ****of Voids**

## Rood 1988: adapted from Mayall 1960

**Rood 1988: adapted from Mayall 1960**

## Mayall, 1960, Ann. Astrophys. 23, 344

**Mayall, 1960, Ann. Astrophys. 23, 344**

## from Chincarini & Rood 1975  (term “Void of Galaxies”)

**from Chincarini & Rood 1975  (term “Void of Galaxies”)**

## Kirshner, Oemler, Schechter, Shectman 1981

**Kirshner, Oemler, Schechter, Shectman 1981**

## Slide 8

## Gregory & Thompson 1978

**Gregory & Thompson 1978**

**de Lapparent, Geller & Huchra 1987**

## Klypin & Shandarin 1983

**Klypin & Shandarin 1983**
**   ****3D  N-body Simulation**

**Shandarin 1975**
**         ****2D**
**     ****Zel’dovich**
** ****Approximation**

**Doroshkevich, Kotok, Novikov,**
**Polyudov, Shandarin, Sigov 1977**
**         ****2D  N-body Simulation**
**from Zel’dovich review talk at**
**IAU Symp. No 79, Tallin Sep. 1977**

## Postman, Huchra, Geller 1986

**Postman, Huchra, Geller 1986**

**Notes:**
Text

## 2D simulations:   Initial spectrum 

**2D simulations:   Initial spectrum **

**Zel’dovich, Einasto, Shandarin 1981**
**(Simulations: Beacom et al 1991)**

## Slide 13

##  “Measuring”  Voids

** “****Measuring”  Voids**

## White 1979:           VPF (Void Probability Function)

**White 1979:           ****VPF (Void Probability Function)**
**           ****=Probability of finding no galaxy in a sphere of radius R**
**                                                                              **

## Hierarchical clustering

**Hierarchical clustering**

## Croton et al 2004 astro-ph/0401406

**Croton et al 2004 astro-ph/0401406**

## Defining, Searching for

**Defining, Searching for**
**                  ****and **
**     ****Measuring  Voids**

## (1991)

***(******1991)***

## Kauffman & Fairall 1991

**Kauffman & Fairall 1991**

## El-Ad & Piran 1997

**El-Ad & Piran 1997**

## El-Ad & Piran 1997

**El-Ad & Piran 1997**

**El-Ad & Piran 1997**

## Slide 23

## Aikio & Mahonen 1998

**Aikio & Mahonen 1998**

## Aikio & Mahonen 1998

**Aikio & Mahonen 1998**

## Aikio & Mahonen 1998

**Aikio & Mahonen 1998**

## Slide 27

## Aikio & Mahonen 1998

**Aikio & Mahonen 1998**

## Aikio & Mahonen 1998

**Aikio & Mahonen 1998**

## Hoyle & Vogeley 2002

**Hoyle & Vogeley 2002**

## Hoyle & Vogeley 2002

**Hoyle & Vogeley 2002**

## Slide 32

## Sheth, Sahni, Shandarin, Sathyaprakash 2003

**Sheth, Sahni, Shandarin, Sathyaprakash 2003**

## SURFGEN = Surface Genertor

**SURFGEN = Surface Genertor**

**Sheth, Sahni, Shandarin, Sathyaprakash 2003**

## Supercluster

**Supercluster**

**Sheth, Sahni, Shandarin, Sathyaprakash 2003**

## Superclusters (overdense)

**Superclusters (overdense)**

**Voids (underdense)**

## Percolating = Largest supercluster

**Percolating = Largest supercluster**

**Sheth, Sahni, Shandarin, Sathyaprakash 2003**

## Supercluster – Void

**Supercluster – Void**
**          ****Network**

## Slide 39

##                              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**

## Filling Factor of overdense regions

**Filling Factor of overdense regions**

## Superclusters   vs..   Voids

_**Superclusters**__**   vs..   **__**Voids**_

**Red:   super clusters = *****overdense                    *****Blue:    voids = *****underdense**** *

**dashed:  the  largest object**
**solid:    all but  the  largest**

**Solid:     90%        **
**Dashed: 10%**
**Superclusters  by mass**
**Voids   by volume**

## SUPERCLUSTERS and VOIDS should be studied before percolation in the 

**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**

**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**_

**There are practically **_**only two very complex structures**_** in between: **
**                                                  ****infinite supercluster and void.**

## Plotting morphological characteristics of SUPERCLUSTERS 

**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**

## Superclusters   vs.   Voids

_**Superclusters**__**   vs.   **__**Voids**_

**Red:   super clusters = *****overdense                    *****Blue:    voids = *****underdense**** *

**dashed: the  largest object**
**solid:    all  but  the  largest**

**Solid:     90%        **
**Dashed: 10%**
**Superclusters  by mass**
**Voids   by volume**

## Global Minkowski Functionals

**Mecke, Buchert & Wagner 1994**

## Percolation thresholds

_**Percolation thresholds**_

**Blue:        mass  estimator**
**Red:         volume  estimator**
**Green:     area  estimator**
**Magenta: curvature  estimator**

**Superclusters**

**Voids**

- Gauss

- Gauss

## AT  PERCOLATION

**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**

## Genus  vs.  Percolation

_**Genus  vs.  Percolation**_

**Genus as a function of Filling Factor**

**  ****PERCOLATION**
**           ****Ratio**
_**Genus of the Largest**_
**Genus of Exc. Set**

**Red: Superclusters**
**Blue: Voids**
**Green: Gaussian**

**     **

**Void**** ****Properties**

** ****Volumes  **
** ****Sizes  **
** ****Shapes**
** ****Topology**
**  ****Substructure**
** ****Evolution**

## Set of Morphological Parameters 

- Set of Morphological Parameters

## Sizes       and      Shapes

**Sahni, Sathyaprakash & Shandarin 1998**

**For each supercluster or void**

**Convex boundaries !**

## Toy Example: Triaxial Torus

**Sahni, Sathyaprakash & Shandarin  1998**

## LCDM

_**Superclusters**__**    vs..   **__**Voids**_

**Mass**
**Volume**
**Density**

**log(Length)**
**Breadth**
**Thickness**

**Planarity**
**Filamentarity**

**LCDM**

## LCDM

_**Superclusters**__**    vs.   **__**Voids**_

**Mass**
**Volume**
**Density**

**Length**
**Breadth**
**Thickness**

**Planarity**
**Filamentarity**

**LCDM**

## Correlation with mass (SC)

_**Correlation with mass (SC)**_
_**or volume (V)**_

**log(Length)**
**Breadth**
**Thickness**

**Planarity**
**Filamentarity**

**Genus**

**log(Genus)**

**Green: at percolation**
**Red:     just before percolation**
**Blue:    just after percolation**

**Solid lines mark the radius**
**of  sphere having same volume**
**as the object.**

##          For both SUPERCLUSTERS and VOIDS 

**         ****For both SUPERCLUSTERS and VOIDS **
** ****Length > R****,    while    ****Breadth < R****     and    ****Thickness  <  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**

## Z=2

**Z=2**

**Z=0**
**R=10/h Mpc**

**Gottlober, Lokas, Klypin, Hoffman 2003**

## (1985)

**(1985)**

## 1

**Evolution of voids in Adhesion Approximation  ****(Kofman, Pogoshyan, Shandarin 1990)**

**Voids:   (a) ****expand  (1)****    **
**              ****(b) ****collapse  (2)**
**              ****(c) ****split (3)**
**             **** ****(d) ****develop substructure (4)**** **

**3**

**3**

**3a**

**3b**

**3b**

**1**

**3a**

**2**

**2**

**1**

**1**

**1**

**4**

**4c**

**4c**

**4b**

**4d**

**4a**

**4a**

**4b**

**4d**

## Voids in LCDM simulations

**Feldman, Habib, Heitmann, Shandarin 200?**

**Voids in LCDM simulations**
**(Real space)**

## Slide 62

## Void and ellipsoid “evolution” with density threshold

**Void and ellipsoid “evolution” with density threshold**

## Feldman, Habib, Heitmann, Shandarin 200?

**Feldman, Habib, Heitmann, Shandarin 200?**

## Slide 65

## FF=0.1

**FF=0.1**

**FF=0.2**

## Shapes

**Shapes**

## Sheth, van de Weygaert 2003

**Sheth, van de Weygaert 2003**
**A hierarchy of voids**

## Mass fraction

**Mass fraction**
**in voids of radius r**

**Number density**
**of voids of radius r**

**CPF of void **
**volume fractions**

**Evolution of CPF of **
**void  volume fractions**
**           ****z=0**
**           ****z=0.5**
**           ****z=1**

## Correlation of  void diameter with initial potential

**Sahni, Sathyaprakash,**
**Shandarin 1994**

**Correlation of  void diameter with initial potential**
**               ****(in Adhesion Model)**

## Madson, Doroshkevich,

**Madson, Doroshkevich,**
**Gottlober, Muller 1998**

**CDM simulation**

## Lee, Shandarin 1998

**Lee, Shandarin 1998**

## Hoyle, Rojas, Vogeley, Brinkmann 2003

**Hoyle, Rojas, Vogeley, Brinkmann 2003**

## Hoyle, Rojas, Vogeley, Brinkmann 2003

## 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.**