An Analytic Model for the Tidal Effect on Cosmic Voids Jounghun Lee & Daeseong Park Seoul National...
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Transcript of An Analytic Model for the Tidal Effect on Cosmic Voids Jounghun Lee & Daeseong Park Seoul National...
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)