Topology Topology of Large Scale of Large Scale StructuresStructures

Introduction Theory and Progress ReportIntroduction Theory and Progress Report

2004 10 28-292004 10 28-29

Changbom Park Changbom Park (Korea Institute for Advanced Study)(Korea Institute for Advanced Study)

KIAS Workshop on KIAS Workshop on Cosmology and Structure FormationCosmology and Structure Formation

11 Genus Genus ndash A Measure of Topologyndash A Measure of Topology

DefinitionDefinition G = of holes - of isolated regionsG = of holes - of isolated regions

= 14= 14ππ intintSS κ dA (Gauss-Bonnet Theorem) κ dA (Gauss-Bonnet Theorem)

[ex G(sphere)=-1 G(torus)=0 ][ex G(sphere)=-1 G(torus)=0 ]

2 holes ndash 1 body = +1

Why TopologyWhy Topology

1 Gaussianity of the 1 Gaussianity of the primordial density fieldprimordial density field a as predicted by many inflationary scenarioss predicted by many inflationary scenarios

2 Topology of galaxy distribution at non-linear scales is sensi2 Topology of galaxy distribution at non-linear scales is sensitive to initial density power spectrum cosmological parative to initial density power spectrum cosmological parameters and to meters and to galaxy formation mechanismgalaxy formation mechanism

That isThat is

A Initial density fluctuation A Initial density fluctuation random phase random phase Gaussian Gaussian (L scale)(L scale)B Gravitational Instability B Gravitational Instability G formation G formation non-Gaussian (NL scale) non-Gaussian (NL scale)C Non-gravitational effects of G formation C Non-gravitational effects of G formation non-Gaussian (NL scale) non-Gaussian (NL scale)GENUS as a PRECISION MEASUREGENUS as a PRECISION MEASURE

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Genus of iso-density contour surfaces in smootheGenus of iso-density contour surfaces in smoothed galaxy density distributiond galaxy density distribution

as a function of density threshold levelas a function of density threshold level

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Gaussian FieldGaussian Field

Genusunit volume Genusunit volume g(ν) = A (1-νg(ν) = A (1-ν22) e) e- ν22- ν22

where ν=(ρ- ρwhere ν=(ρ- ρbb) ρ) ρbbσ amp σ amp

A=1(2π)A=1(2π)22 ltk ltk223gt3gt32 32

if P(k)~kif P(k)~knn

A=[8radic2πA=[8radic2π22 R RGG33]]-1-1

[(n+3)3][(n+3)3]32 32

Non-Gaussian FieldNon-Gaussian Field (Toy models) (Toy models)

Clusters Bubbles HDM

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

Genus-Related StatisticsGenus-Related Statistics

Amplitude dropAmplitude drop RRAA

RRAA = A = Aobsobs A APSPS

Shift parameterShift parameter ΔνΔν By fitting GBy fitting Gobsobs((ν) ν) over ndash1ltover ndash1ltνlt1νlt1

Asymmetry parametersAsymmetry parameters AACC amp amp AAVV

A = A = intint G Gobsobs((ν) d νintν) d νint G Gfitfit((ν) d νν) d ν

where intervals are where intervals are

12~22 (12~22 (AACC) -12~-22 () -12~-22 (AAVV))

UZC+SSRS2

22 History History of Topology Study in Cosmologyof Topology Study in Cosmology

I Early WorksI Early Works 1986 Hamilton Gott Weinberg Gott Melott Dickinson1986 Hamilton Gott Weinberg Gott Melott Dickinson ndash ndash smooth small-scale NL clustering to recover initial topologysmooth small-scale NL clustering to recover initial topology

1987-8 GWM WGM MWG Gott et al1987-8 GWM WGM MWG Gott et al ndash ndash cosmological amp toy models Rcosmological amp toy models RGGgt3rgt3rcc to recover initial topology to recover initial topology

1989 Gott et al1989 Gott et al ndash observed galaxies dwarfs clustersndash observed galaxies dwarfs clusters

1991 Park Gott1991 Park Gott ndash gravitational amp biasing effectsndash gravitational amp biasing effects

1992 Weinberg Cole1992 Weinberg Cole ndash PS initial skewness biasing effectsndash PS initial skewness biasing effects

1994 Matsubara 1994 Matsubara ndash 2ndash 2ndnd order perturbation in weakly NL regime order perturbation in weakly NL regime

1996 Matsubara 1996 Matsubara ndash redshift space distortion in L regimendash redshift space distortion in L regime

1996 Matsubara Suto 1996 Matsubara Suto ndash gravitational amp z-space distortionndash gravitational amp z-space distortion

EtchellipEtchellip

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

11 Genus Genus ndash A Measure of Topologyndash A Measure of Topology

DefinitionDefinition G = of holes - of isolated regionsG = of holes - of isolated regions

= 14= 14ππ intintSS κ dA (Gauss-Bonnet Theorem) κ dA (Gauss-Bonnet Theorem)

[ex G(sphere)=-1 G(torus)=0 ][ex G(sphere)=-1 G(torus)=0 ]

2 holes ndash 1 body = +1

Why TopologyWhy Topology

1 Gaussianity of the 1 Gaussianity of the primordial density fieldprimordial density field a as predicted by many inflationary scenarioss predicted by many inflationary scenarios

2 Topology of galaxy distribution at non-linear scales is sensi2 Topology of galaxy distribution at non-linear scales is sensitive to initial density power spectrum cosmological parative to initial density power spectrum cosmological parameters and to meters and to galaxy formation mechanismgalaxy formation mechanism

That isThat is

A Initial density fluctuation A Initial density fluctuation random phase random phase Gaussian Gaussian (L scale)(L scale)B Gravitational Instability B Gravitational Instability G formation G formation non-Gaussian (NL scale) non-Gaussian (NL scale)C Non-gravitational effects of G formation C Non-gravitational effects of G formation non-Gaussian (NL scale) non-Gaussian (NL scale)GENUS as a PRECISION MEASUREGENUS as a PRECISION MEASURE

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Genus of iso-density contour surfaces in smootheGenus of iso-density contour surfaces in smoothed galaxy density distributiond galaxy density distribution

as a function of density threshold levelas a function of density threshold level

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Gaussian FieldGaussian Field

Genusunit volume Genusunit volume g(ν) = A (1-νg(ν) = A (1-ν22) e) e- ν22- ν22

where ν=(ρ- ρwhere ν=(ρ- ρbb) ρ) ρbbσ amp σ amp

A=1(2π)A=1(2π)22 ltk ltk223gt3gt32 32

if P(k)~kif P(k)~knn

A=[8radic2πA=[8radic2π22 R RGG33]]-1-1

[(n+3)3][(n+3)3]32 32

Non-Gaussian FieldNon-Gaussian Field (Toy models) (Toy models)

Clusters Bubbles HDM

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

Genus-Related StatisticsGenus-Related Statistics

Amplitude dropAmplitude drop RRAA

RRAA = A = Aobsobs A APSPS

Shift parameterShift parameter ΔνΔν By fitting GBy fitting Gobsobs((ν) ν) over ndash1ltover ndash1ltνlt1νlt1

Asymmetry parametersAsymmetry parameters AACC amp amp AAVV

A = A = intint G Gobsobs((ν) d νintν) d νint G Gfitfit((ν) d νν) d ν

where intervals are where intervals are

12~22 (12~22 (AACC) -12~-22 () -12~-22 (AAVV))

UZC+SSRS2

22 History History of Topology Study in Cosmologyof Topology Study in Cosmology

I Early WorksI Early Works 1986 Hamilton Gott Weinberg Gott Melott Dickinson1986 Hamilton Gott Weinberg Gott Melott Dickinson ndash ndash smooth small-scale NL clustering to recover initial topologysmooth small-scale NL clustering to recover initial topology

1987-8 GWM WGM MWG Gott et al1987-8 GWM WGM MWG Gott et al ndash ndash cosmological amp toy models Rcosmological amp toy models RGGgt3rgt3rcc to recover initial topology to recover initial topology

1989 Gott et al1989 Gott et al ndash observed galaxies dwarfs clustersndash observed galaxies dwarfs clusters

1991 Park Gott1991 Park Gott ndash gravitational amp biasing effectsndash gravitational amp biasing effects

1992 Weinberg Cole1992 Weinberg Cole ndash PS initial skewness biasing effectsndash PS initial skewness biasing effects

1994 Matsubara 1994 Matsubara ndash 2ndash 2ndnd order perturbation in weakly NL regime order perturbation in weakly NL regime

1996 Matsubara 1996 Matsubara ndash redshift space distortion in L regimendash redshift space distortion in L regime

1996 Matsubara Suto 1996 Matsubara Suto ndash gravitational amp z-space distortionndash gravitational amp z-space distortion

EtchellipEtchellip

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Why TopologyWhy Topology

1 Gaussianity of the 1 Gaussianity of the primordial density fieldprimordial density field a as predicted by many inflationary scenarioss predicted by many inflationary scenarios

2 Topology of galaxy distribution at non-linear scales is sensi2 Topology of galaxy distribution at non-linear scales is sensitive to initial density power spectrum cosmological parative to initial density power spectrum cosmological parameters and to meters and to galaxy formation mechanismgalaxy formation mechanism

That isThat is

A Initial density fluctuation A Initial density fluctuation random phase random phase Gaussian Gaussian (L scale)(L scale)B Gravitational Instability B Gravitational Instability G formation G formation non-Gaussian (NL scale) non-Gaussian (NL scale)C Non-gravitational effects of G formation C Non-gravitational effects of G formation non-Gaussian (NL scale) non-Gaussian (NL scale)GENUS as a PRECISION MEASUREGENUS as a PRECISION MEASURE

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Genus of iso-density contour surfaces in smootheGenus of iso-density contour surfaces in smoothed galaxy density distributiond galaxy density distribution

as a function of density threshold levelas a function of density threshold level

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Gaussian FieldGaussian Field

Genusunit volume Genusunit volume g(ν) = A (1-νg(ν) = A (1-ν22) e) e- ν22- ν22

where ν=(ρ- ρwhere ν=(ρ- ρbb) ρ) ρbbσ amp σ amp

A=1(2π)A=1(2π)22 ltk ltk223gt3gt32 32

if P(k)~kif P(k)~knn

A=[8radic2πA=[8radic2π22 R RGG33]]-1-1

[(n+3)3][(n+3)3]32 32

Non-Gaussian FieldNon-Gaussian Field (Toy models) (Toy models)

Clusters Bubbles HDM

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

Genus-Related StatisticsGenus-Related Statistics

Amplitude dropAmplitude drop RRAA

RRAA = A = Aobsobs A APSPS

Shift parameterShift parameter ΔνΔν By fitting GBy fitting Gobsobs((ν) ν) over ndash1ltover ndash1ltνlt1νlt1

Asymmetry parametersAsymmetry parameters AACC amp amp AAVV

A = A = intint G Gobsobs((ν) d νintν) d νint G Gfitfit((ν) d νν) d ν

where intervals are where intervals are

12~22 (12~22 (AACC) -12~-22 () -12~-22 (AAVV))

UZC+SSRS2

22 History History of Topology Study in Cosmologyof Topology Study in Cosmology

I Early WorksI Early Works 1986 Hamilton Gott Weinberg Gott Melott Dickinson1986 Hamilton Gott Weinberg Gott Melott Dickinson ndash ndash smooth small-scale NL clustering to recover initial topologysmooth small-scale NL clustering to recover initial topology

1987-8 GWM WGM MWG Gott et al1987-8 GWM WGM MWG Gott et al ndash ndash cosmological amp toy models Rcosmological amp toy models RGGgt3rgt3rcc to recover initial topology to recover initial topology

1989 Gott et al1989 Gott et al ndash observed galaxies dwarfs clustersndash observed galaxies dwarfs clusters

1991 Park Gott1991 Park Gott ndash gravitational amp biasing effectsndash gravitational amp biasing effects

1992 Weinberg Cole1992 Weinberg Cole ndash PS initial skewness biasing effectsndash PS initial skewness biasing effects

1994 Matsubara 1994 Matsubara ndash 2ndash 2ndnd order perturbation in weakly NL regime order perturbation in weakly NL regime

1996 Matsubara 1996 Matsubara ndash redshift space distortion in L regimendash redshift space distortion in L regime

1996 Matsubara Suto 1996 Matsubara Suto ndash gravitational amp z-space distortionndash gravitational amp z-space distortion

EtchellipEtchellip

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Genus of iso-density contour surfaces in smootheGenus of iso-density contour surfaces in smoothed galaxy density distributiond galaxy density distribution

as a function of density threshold levelas a function of density threshold level

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Gaussian FieldGaussian Field

Genusunit volume Genusunit volume g(ν) = A (1-νg(ν) = A (1-ν22) e) e- ν22- ν22

where ν=(ρ- ρwhere ν=(ρ- ρbb) ρ) ρbbσ amp σ amp

A=1(2π)A=1(2π)22 ltk ltk223gt3gt32 32

if P(k)~kif P(k)~knn

A=[8radic2πA=[8radic2π22 R RGG33]]-1-1

[(n+3)3][(n+3)3]32 32

Non-Gaussian FieldNon-Gaussian Field (Toy models) (Toy models)

Clusters Bubbles HDM

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

Genus-Related StatisticsGenus-Related Statistics

Amplitude dropAmplitude drop RRAA

RRAA = A = Aobsobs A APSPS

Shift parameterShift parameter ΔνΔν By fitting GBy fitting Gobsobs((ν) ν) over ndash1ltover ndash1ltνlt1νlt1

Asymmetry parametersAsymmetry parameters AACC amp amp AAVV

A = A = intint G Gobsobs((ν) d νintν) d νint G Gfitfit((ν) d νν) d ν

where intervals are where intervals are

12~22 (12~22 (AACC) -12~-22 () -12~-22 (AAVV))

UZC+SSRS2

22 History History of Topology Study in Cosmologyof Topology Study in Cosmology

I Early WorksI Early Works 1986 Hamilton Gott Weinberg Gott Melott Dickinson1986 Hamilton Gott Weinberg Gott Melott Dickinson ndash ndash smooth small-scale NL clustering to recover initial topologysmooth small-scale NL clustering to recover initial topology

1987-8 GWM WGM MWG Gott et al1987-8 GWM WGM MWG Gott et al ndash ndash cosmological amp toy models Rcosmological amp toy models RGGgt3rgt3rcc to recover initial topology to recover initial topology

1989 Gott et al1989 Gott et al ndash observed galaxies dwarfs clustersndash observed galaxies dwarfs clusters

1991 Park Gott1991 Park Gott ndash gravitational amp biasing effectsndash gravitational amp biasing effects

1992 Weinberg Cole1992 Weinberg Cole ndash PS initial skewness biasing effectsndash PS initial skewness biasing effects

1994 Matsubara 1994 Matsubara ndash 2ndash 2ndnd order perturbation in weakly NL regime order perturbation in weakly NL regime

1996 Matsubara 1996 Matsubara ndash redshift space distortion in L regimendash redshift space distortion in L regime

1996 Matsubara Suto 1996 Matsubara Suto ndash gravitational amp z-space distortionndash gravitational amp z-space distortion

EtchellipEtchellip

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

GenusGenus - LS Galaxy Distribution- LS Galaxy Distribution

Gaussian FieldGaussian Field

Genusunit volume Genusunit volume g(ν) = A (1-νg(ν) = A (1-ν22) e) e- ν22- ν22

where ν=(ρ- ρwhere ν=(ρ- ρbb) ρ) ρbbσ amp σ amp

A=1(2π)A=1(2π)22 ltk ltk223gt3gt32 32

if P(k)~kif P(k)~knn

A=[8radic2πA=[8radic2π22 R RGG33]]-1-1

[(n+3)3][(n+3)3]32 32

Non-Gaussian FieldNon-Gaussian Field (Toy models) (Toy models)

Clusters Bubbles HDM

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

Genus-Related StatisticsGenus-Related Statistics

Amplitude dropAmplitude drop RRAA

RRAA = A = Aobsobs A APSPS

Shift parameterShift parameter ΔνΔν By fitting GBy fitting Gobsobs((ν) ν) over ndash1ltover ndash1ltνlt1νlt1

Asymmetry parametersAsymmetry parameters AACC amp amp AAVV

A = A = intint G Gobsobs((ν) d νintν) d νint G Gfitfit((ν) d νν) d ν

where intervals are where intervals are

12~22 (12~22 (AACC) -12~-22 () -12~-22 (AAVV))

UZC+SSRS2

22 History History of Topology Study in Cosmologyof Topology Study in Cosmology

I Early WorksI Early Works 1986 Hamilton Gott Weinberg Gott Melott Dickinson1986 Hamilton Gott Weinberg Gott Melott Dickinson ndash ndash smooth small-scale NL clustering to recover initial topologysmooth small-scale NL clustering to recover initial topology

1987-8 GWM WGM MWG Gott et al1987-8 GWM WGM MWG Gott et al ndash ndash cosmological amp toy models Rcosmological amp toy models RGGgt3rgt3rcc to recover initial topology to recover initial topology

1989 Gott et al1989 Gott et al ndash observed galaxies dwarfs clustersndash observed galaxies dwarfs clusters

1991 Park Gott1991 Park Gott ndash gravitational amp biasing effectsndash gravitational amp biasing effects

1992 Weinberg Cole1992 Weinberg Cole ndash PS initial skewness biasing effectsndash PS initial skewness biasing effects

1994 Matsubara 1994 Matsubara ndash 2ndash 2ndnd order perturbation in weakly NL regime order perturbation in weakly NL regime

1996 Matsubara 1996 Matsubara ndash redshift space distortion in L regimendash redshift space distortion in L regime

1996 Matsubara Suto 1996 Matsubara Suto ndash gravitational amp z-space distortionndash gravitational amp z-space distortion

EtchellipEtchellip

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Non-Gaussian FieldNon-Gaussian Field (Toy models) (Toy models)

Clusters Bubbles HDM

(Weinberg Gott amp Melott 1987)(Weinberg Gott amp Melott 1987)

Genus-Related StatisticsGenus-Related Statistics

Amplitude dropAmplitude drop RRAA

RRAA = A = Aobsobs A APSPS

Shift parameterShift parameter ΔνΔν By fitting GBy fitting Gobsobs((ν) ν) over ndash1ltover ndash1ltνlt1νlt1

Asymmetry parametersAsymmetry parameters AACC amp amp AAVV

A = A = intint G Gobsobs((ν) d νintν) d νint G Gfitfit((ν) d νν) d ν

where intervals are where intervals are

12~22 (12~22 (AACC) -12~-22 () -12~-22 (AAVV))

UZC+SSRS2

22 History History of Topology Study in Cosmologyof Topology Study in Cosmology

I Early WorksI Early Works 1986 Hamilton Gott Weinberg Gott Melott Dickinson1986 Hamilton Gott Weinberg Gott Melott Dickinson ndash ndash smooth small-scale NL clustering to recover initial topologysmooth small-scale NL clustering to recover initial topology

1987-8 GWM WGM MWG Gott et al1987-8 GWM WGM MWG Gott et al ndash ndash cosmological amp toy models Rcosmological amp toy models RGGgt3rgt3rcc to recover initial topology to recover initial topology

1989 Gott et al1989 Gott et al ndash observed galaxies dwarfs clustersndash observed galaxies dwarfs clusters

1991 Park Gott1991 Park Gott ndash gravitational amp biasing effectsndash gravitational amp biasing effects

1992 Weinberg Cole1992 Weinberg Cole ndash PS initial skewness biasing effectsndash PS initial skewness biasing effects

1994 Matsubara 1994 Matsubara ndash 2ndash 2ndnd order perturbation in weakly NL regime order perturbation in weakly NL regime

1996 Matsubara 1996 Matsubara ndash redshift space distortion in L regimendash redshift space distortion in L regime

1996 Matsubara Suto 1996 Matsubara Suto ndash gravitational amp z-space distortionndash gravitational amp z-space distortion

EtchellipEtchellip

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Genus-Related StatisticsGenus-Related Statistics

Amplitude dropAmplitude drop RRAA

RRAA = A = Aobsobs A APSPS

Shift parameterShift parameter ΔνΔν By fitting GBy fitting Gobsobs((ν) ν) over ndash1ltover ndash1ltνlt1νlt1

Asymmetry parametersAsymmetry parameters AACC amp amp AAVV

A = A = intint G Gobsobs((ν) d νintν) d νint G Gfitfit((ν) d νν) d ν

where intervals are where intervals are

12~22 (12~22 (AACC) -12~-22 () -12~-22 (AAVV))

UZC+SSRS2

22 History History of Topology Study in Cosmologyof Topology Study in Cosmology

I Early WorksI Early Works 1986 Hamilton Gott Weinberg Gott Melott Dickinson1986 Hamilton Gott Weinberg Gott Melott Dickinson ndash ndash smooth small-scale NL clustering to recover initial topologysmooth small-scale NL clustering to recover initial topology

1987-8 GWM WGM MWG Gott et al1987-8 GWM WGM MWG Gott et al ndash ndash cosmological amp toy models Rcosmological amp toy models RGGgt3rgt3rcc to recover initial topology to recover initial topology

1989 Gott et al1989 Gott et al ndash observed galaxies dwarfs clustersndash observed galaxies dwarfs clusters

1991 Park Gott1991 Park Gott ndash gravitational amp biasing effectsndash gravitational amp biasing effects

1992 Weinberg Cole1992 Weinberg Cole ndash PS initial skewness biasing effectsndash PS initial skewness biasing effects

1994 Matsubara 1994 Matsubara ndash 2ndash 2ndnd order perturbation in weakly NL regime order perturbation in weakly NL regime

1996 Matsubara 1996 Matsubara ndash redshift space distortion in L regimendash redshift space distortion in L regime

1996 Matsubara Suto 1996 Matsubara Suto ndash gravitational amp z-space distortionndash gravitational amp z-space distortion

EtchellipEtchellip

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

22 History History of Topology Study in Cosmologyof Topology Study in Cosmology

I Early WorksI Early Works 1986 Hamilton Gott Weinberg Gott Melott Dickinson1986 Hamilton Gott Weinberg Gott Melott Dickinson ndash ndash smooth small-scale NL clustering to recover initial topologysmooth small-scale NL clustering to recover initial topology

1987-8 GWM WGM MWG Gott et al1987-8 GWM WGM MWG Gott et al ndash ndash cosmological amp toy models Rcosmological amp toy models RGGgt3rgt3rcc to recover initial topology to recover initial topology

1989 Gott et al1989 Gott et al ndash observed galaxies dwarfs clustersndash observed galaxies dwarfs clusters

1991 Park Gott1991 Park Gott ndash gravitational amp biasing effectsndash gravitational amp biasing effects

1992 Weinberg Cole1992 Weinberg Cole ndash PS initial skewness biasing effectsndash PS initial skewness biasing effects

1994 Matsubara 1994 Matsubara ndash 2ndash 2ndnd order perturbation in weakly NL regime order perturbation in weakly NL regime

1996 Matsubara 1996 Matsubara ndash redshift space distortion in L regimendash redshift space distortion in L regime

1996 Matsubara Suto 1996 Matsubara Suto ndash gravitational amp z-space distortionndash gravitational amp z-space distortion

EtchellipEtchellip

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

II Recent WorksII Recent Works 2000 Colley et al2000 Colley et al ndash Simulation of SDSSndash Simulation of SDSS 2001 2003 Hikage Taruya amp Suto2001 2003 Hikage Taruya amp Suto ndash dark halos (analytic amp numerical)ndash dark halos (analytic amp numerical) 2003 Matsubara2003 Matsubara ndash 2 ndash 2ndnd orber perturbation theory orber perturbation theory [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing [ Minkowski functionals (Mecke Buchert amp Wagner 1994 Schmalzing

amp Buchert 1997 etc)]amp Buchert 1997 etc)]

III 3D genus analysis of observational dataIII 3D genus analysis of observational data

1989 Gott et al - CfA 1 etc1989 Gott et al - CfA 1 etc1992 Park Gott amp da Costa - SSRS 11992 Park Gott amp da Costa - SSRS 11992 Moore et al - IRAS QDOT 1992 Moore et al - IRAS QDOT 1994 Rhoads et al - Abell Clusters1994 Rhoads et al - Abell Clusters1994 Vogeley et al - CfA 1+21994 Vogeley et al - CfA 1+21997 Protogeros amp Weinbergs - IRAS 12Jy1997 Protogeros amp Weinbergs - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Springel et al - IRAS 12Jy1998 Canavezes et al - IRAS PSCz1998 Canavezes et al - IRAS PSCz2002 Hikage et al - SDSS EDR2002 Hikage et al - SDSS EDR2003 Hikage et al - SDSS LSS Sample 122003 Hikage et al - SDSS LSS Sample 122004 Canavezes amp Efstathious - 2dFRGS2004 Canavezes amp Efstathious - 2dFRGS

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

IV 2D Genus (LSS)IV 2D Genus (LSS)

2D genus before SDSS2D genus before SDSS Suggested by Melott (1987)Suggested by Melott (1987) Coles amp Plionis (1991) Lick Galaxy CatalogueColes amp Plionis (1991) Lick Galaxy Catalogue Plionins Valdarnini amp Coles (1992) Abell and ACO cluster cataloguePlionins Valdarnini amp Coles (1992) Abell and ACO cluster catalogue Park et al (1992) CfA SlicePark et al (1992) CfA Slice Colley (2000) Simulated SDSSColley (2000) Simulated SDSS Park Gott amp Choi (2001) HDFPark Gott amp Choi (2001) HDF Hoyle Vogeley amp Gott (2002) 2dFGRSHoyle Vogeley amp Gott (2002) 2dFGRS

2D genus with SDSS2D genus with SDSS Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with Hoyle Vogeley amp Gott (2002) weak evidence for variation in the genus with

galaxy typegalaxy type

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

ΛΛCDM SimulationCDM Simulation (Kim amp Park 2004)

PMTree codePMTree code (Dubinski Kim Park 2003)

2048204833 mesh mesh (initial condition)

2048204833 (86G) (86G) CDM particles

1024 amp 5632 h1024 amp 5632 h-1-1MpcMpc size boxes

50 amp 275 h50 amp 275 h-1-1kpckpc force resolutions

3 Gravitational Evolution Biasing Redshift 3 Gravitational Evolution Biasing Redshift Space DistortionSpace Distortion Effects on TopologyEffects on Topology

(Park et al 1994)(Tegmark et al

2004)

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Park Kim amp Gott (2004)Genus of matter distr

ibutionAmplitude drop RA= A= Asimsim A APSPS

Shift Δν

of Voids and Clusters AV amp AC

(at z = 0 1 2 5 8)

8 5

2

1

0

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Biasing AV at small scales

Redshift space distortion small for AV

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

33 Analytic ModelAnalytic Model

Matsubara (19942003)

perturbation theory

Matsubara(1996) linear theory of z-effects

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Sloan Digital Sky Survey Sloan Digital Sky Survey

1 Imaging of North Galactic Cap1 Imaging of North Galactic Cap25m APO telescope with a mosaic CCD camera 25m APO telescope with a mosaic CCD camera

u g r i z photometric bandpasses u g r i z photometric bandpasses selected for spectroscopy selected for spectroscopy

2 Spectroscopy2 Spectroscopy~~ 10 1066 galaxies amp 10 galaxies amp 1055 quasars with rms z-error quasars with rms z-error ~ 30 kms~ 30 kms

3 Samples3 SamplesMain Galaxies Main Galaxies rrPetPet lt 1777 Quasars lt 1777 Quasars

Luminous Red Galaxies (LRG) zlt04 amp gt04 samplesLuminous Red Galaxies (LRG) zlt04 amp gt04 samples

Korean Scientist Group (KSG)Korean Scientist Group (KSG)KIAS Changbom Park amp SNU Myeong Lee Myungshin ImKIAS Changbom Park amp SNU Myeong Lee Myungshin ImKNU Myeong-Gu Park amp SU Hwankyung SungKNU Myeong-Gu Park amp SU Hwankyung Sung

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

As of Oct 14 2004

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

SDSS LSS Sample 14 in equatorial coordinate (314K galaxies)

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

SDSS LSS Sample 14 in survey coordinate (314K galaxies)

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

SDSS galaxies in region 1

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

SDSS galaxies in Region 1(Park et al 2004)

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Genus Analysis of SDSS LSS Sample 14Genus Analysis of SDSS LSS Sample 14

Best sample to test

Gaussianity of primordial fluctuation (randomness of quantum fluctuation) Not yet

Structure formation mechanism OK

If Gaussian G(ν) = A(1- ν2)exp(- ν22)G = of holes - of isolated regions

SDSS Large volume amp dense sampling of galaxies

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Volume-limited subsamples

For scale For scale dependencedependence

For luminosity For luminosity dependencedependence

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Best SubsetBest Subset-2021lt Mr lt-2159

160 lt r lt 314 h-1Mpc

0054 lt z lt 0107

31580 galaxies

d = 63 h-1Mpc

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Scale DependenceScale Dependence

Within a Subset

Same place(structure) amp luminosity

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

LuminosityLuminosity DependenceDependence

Each Subset

Same place(structure) luminosity smoothing

L1 -205 ~ -225 L3 -190 ~ -210

L2 -195 ~ -215 (25524 154~235 h-1Mpc)

9 subsets with the same of galaxies

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

YOU CAN SEE

Few bright galaxies in under dense regions

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Luminosity biasPark et al (1994) nearly scale-independent biasing

underdense regions lack bright galaxies

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

Internal Physical Parameters of

Galaxies

Collective Physical Properties of Galaxy

Subsets

Morphology Surface Brightness

Luminosity Velocity Dispersion

Color Spectral Type

SFR etc

Galaxy Clustering Properties (z)

Correlation Function Power Spectrum Count

in Cell Topology etc

Velocity Field

Halo Mass Distribution Luminosity Function (z)

Color-Magnitude Relation etc

Environment Local Density

Galaxy Biasing Gaussianity of Initial Density Fluctuation Ωm σ8 b etc

Ωm σ8 b etc

Galaxy Formation

Different Tracers of Structure Formation Galaxy Cluster Group Void Quasar etc

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing

ConclusionsConclusions

0 Wait for SDSS to finish for LS topology0 Wait for SDSS to finish for LS topology

1 Topology analysis does differentiate galaxy species1 Topology analysis does differentiate galaxy species

Brighter meat-ball topology smaller voidsBrighter meat-ball topology smaller voids

Fainter bubble topology bigger voidsFainter bubble topology bigger voids

2 Topology changes below the characteristic magnitude M2 Topology changes below the characteristic magnitude Mrr

=-204+5 log h=-204+5 log h

3 AV lt 1 (few amp big voids) consistently

at all scales lt 10 h-1 Mpc independantly of L

Not gravitational evolution effectsNot gravitational evolution effects

Existence of biasing Existence of biasing