An Analytic Model for the Tidal Effect on Cosmic Voids

Jounghun Lee & Daeseong Park Seoul National University

Lee & Park 2006, ApJ, 652, 1Park & Lee 2006, astro-ph/0610520

Table of Contents

Introduction & Motivation Analytic Model

Key concepts & basic assumptions Mathematical framework Main results & implications

Numerical Test Voids from the Millennium Run simulation Comparison: numerical vs. analytical

Summary & Future work

Collection of bubble-like voids separated by filaments and sheets

Voids occupy 40 % of

cosmic volume

Voids have very low density

Introduction – The Universe on the Largest Scale

9.0

Hoyle & Vogeley 2004

void regions

Introduction – Origin & Properties of Cosmic Voids Originated from the local minima of the

initial density field

Expansion only – spherical shape

void galaxies

void

Motivation

Come on! voids are not spherical at all …

Come on! voids are not spherical at all …

Shandarin et al. 2004

MotivationWhy? well, it should be because of the tidal force …

Why? well, it should be because of the tidal force …

Shandarin et al. 2006

Strong tidal effect – non spherical shape

rv

0vr

rv

0vr

Spherical case Nonspherical case

Key Concept

Void spin angular momentum, J :

m: the mass of a void galaxy x: the position of a void galaxy v: the velocity of a void galaxy

vrJ

N

m1

Mathematical Framework

The Tidal Torque Theory (Peebles 1969, Doroshekvich 1970, White 1984)

Tij : the local tidal shear tensor Iij : the inertia momentum tensor

lkjlijki ITJ

Basic Assumption

For the case of voids, the principal axes of the inertia momentum and the tidal shear tensors are maximally misaligned with each other:

sqlkpsjlsqpslkjl IITTITIT

preferential alignment of J with the intermediate principal axis of Tij

Mathematical Framework

Alignment of void spins with local shears

Lee & Pen (2000, 2001)

kjikijji TTJJ ˆˆ5

3

15

8ˆˆˆ T

JJJ /ˆ TTT /ˆ

2

1

3

Jˆ

J

1

2

3

r

strong spatial correlations between neighbor void spins

Intrinsic correlation

Intrinsic correlation

Spatial correlation

Spatial correlation

Main Prediction

Void spin-spin correlation function

Rrthe two-point correlations of the density field smoothed on the void scale, R

3

1)(ˆ)(ˆ)(

2 rxJxJrV

)0(

)(

50

32

2

R

R r

Numerical Test

Millennium Run Galaxy Catalog (Springel et al. 2005) CDM cosmology (m=0.25,ns=1,8=0.9,h=0.73) A cubic box of linear size 500 h-1Mpc 809848723 galaxies at z=0

Void-Finder Algorithm (Hoyle & Vogeley 2002) The number of voids identified: 24037 The mean effective radius: 10.45 Mpc/h 13507 voids with more than 30 galaxies

Numerical Test

(Lee & Park 2006)

(Lee & Park 2006)

vrJ

N

m1 (Lee & Park 2006)

(Lee & Park 2006)

Summary

A new concept of the void spin angular momentum introduced to quantify the tidal effect on voids.

The linear tidal torque theory used to derive analytically the void spin-spin correlations.

The analytic prediction agrees excellently with the Millennium Run numerical data points.

Key Concept

Void ellipticity

where

3

2

1

,,

00

00

00

I

I

I

xxI jiij

123

3211III

III

Basic Assumption

3

1

1

11

V

Void ellipticity is related to the eigenvalues of the tidal tensor as

Void forms in the local minima of the initial density field:

3

2

1

00

00

00

ijT

Mathematical Framework

)|,,( 321 Vp

);( LRp

Mathematical Framework

The distribution of {1,2,3} (Doroshkevich 1970)

))()((2

153exp

53

3375),,( 3132212

221

6321

p

3211 3132212

.)(

),,,()|,,( 321

321V

VV p

pp

Main Prediction

The void ellipticity distribution

EVL RR 3/1)1(

Park & Lee 2006Astro-ph/0610520

WMAP 3rd year

WMAP 1st year

Numerical Test

(Park & Lee 2006, astro-ph/0610520)

(Park & Lee 2006, astro-ph/0610520)

Projected Images of Voids

(Park & Lee 2006, astro-ph/0610520)

Summary

The Zel’dovich approximation used to derive analytically the void ellipticity distribution.

The void ellipticity distribution depends sensitively on the values of the key cosmological parameters.

The analytic prediction agrees excellently with the numerical result from the Millennium Run simulation.

Ongoing & Future Works

Application to observational data SDSS void catalogs

Evolution of the void ellipticity distribution as a probe of dark energy equation of state (Lee 2007, in preparation)

Void-supercluster alignment connection as a new clue to the filamentary cosmic web (Park & Lee 2007, in preparation)