Galaxy Clustering Topology in the Sloan Digital Sky Survey. Yun-Young Choi Kyunghee University. Collaborators. Changbom Park (KIAS) Juhan Kim (KIAS) Rich Gott (Princeton U.) Michael Vogeley (Drexel U.) David Weinberg (Ohio State U.). Topology of Large scale structure.
Galaxy Clustering Topology in the Sloan Digital Sky Survey
Changbom Park (KIAS)
Juhan Kim (KIAS)
Rich Gott (Princeton U.)
Michael Vogeley (Drexel U.)
David Weinberg (Ohio State U.)
Standard cosmological model:
1. LSS arises from primordial zero-point energy-density fluctuations (Bardeen, Steinhardt & Turner 1983)
2. The density fluctuations have random phases or a Gaussian density distribution; which has a known topology.
The gaussian random field has analytically calculable genus curve.
Departures of the genus curve from the random phase shape:
variation in the PS slope, skewness in the initial density field, biasing in the distribution of galaxies relative to mass, redshift space distortion, gravitational evolution, and so on.
Probe of the non-Gaussianity !
Topological Genus (Gott, Melott & Dickinson 1986)
Isodensity contour surfaces at a given density threshold level
G = (number of holes in the surface of constant density)-
(number of isolated regions surrounded by the surfaces)
Advantage for the detection of the non-gaussianity
Gaussian random field has analytically calculable genus curve; g = G/V
: threshold density in units of standard deviation
What do we expect the genus curve to look like?
(Weinberg, Gott & Melott 1987)
Amplitude drop RA
RA = Aobs / ARP-PS
Shift parameter of the peak, Δν:
By fitting Gobs(ν) over –1<ν<1
AV & AC
A = ∫ Gobs(ν) d ν/∫ Gfit(ν) d ν
where intervals are
-1.2~-2.2 (AV), 1.2~2.2 (AC)
To Measure the departures of the observed
genus curve from the random phase
Final SDSS DR7 Main Galaxy Sample
(Choi et al. 2010)
The Cosmic Runner (Park et al. 2005)
The Sloan Great Wall (Gott et al. 2005)
The CfA Great Wall & the man
(de Lapparent et al. 1986)
Error estimates from 27
20483p1024s LCDM sim.)
Choi et al. 2010
Fewer voids and fewer superclusters when compared
with the Gaussian genus curve: voids and superclusters
are more connected.
Morphology and color dependence of
Galaxy Properties-environment(LSS) relation
Data: same number density & Mr-range
Distribution of early-type/red galaxies has smaller genus density, is more
meat-ball shifted, has
more isolated clusters, and fewer voids.
Test of Galaxy Formation Models
1. HGC, a Halo-Galaxy one-to-one Correspondence model [Kim, Park & Choi 2008]
2. HOD, Halo Occupation Distribution [Yang et al. 2007]
Galaxies populating in the dark halos with a halo occupation distribution model
3. SAM, Semi-Analytic Models of galaxy formation
Merger-tree + physical processes put in
Croton et al. (2006) & Bower et al. (2006)'s of SAM (which differ mainly by AGN feedback and cooling); Bertone et al. (2007)'s SAM (galactic wind)
Deviations due to combined effects of initial condition,
gravitational evolution and biasing depend on models.
Bertone et al. 2007
Yang et al. 2007
Croton et al. 2006
Bower et al. 2006
Kim et al. 2008
SDSS DR7 Main
1. Amplitude agrees - PS (but Bower et al. !)
2. too positive : all models show sponge topology (too positive thresholds).
3. Strongly disagree with observed void and cluster abundances.
Overall, no model reproduces all features of the observed topology!
To estimate the statistical significance of the failure of each model
i: the four genus-related statistics
j: the two volume-limited samples
Curve: Vobs is replaced by the average
value over the 64 mock samples.
No existing galaxy formation models
reproduce the topology of the SDSS main galaxy sample near the smoothing scales, 6.1 and 7.1 h-1Mpc.
The probability for the HGC model to be consistent with the observation is only 0.4%. The HOD and three SAM models are absolutely ruled out by this test.
Color subsets: red vsblue
: 9.1 h-1Mpc scale
: 7.0 h-1Mpc scale
Color subsets of SAM mock galaxies completely fail to explain the observed topology.
[ Observations ]
1. Topology of LSS measured from SDSS DR7
2. Dependence of LSS topology on scale, luminosity, morphology & color is measured.
Early-type/red galaxies has smaller genus, is more meat-ball shifted, has more clusters,
3. Topology bias of galaxy distribution with respect to matter is measured.
Topology bias is significantly large and scale-dependent.
[ Comparison with galaxy formation models ]
4. Topology at quasi- and non-linear scales can be used to constrain galaxy formation mechanism.
All models fail to explain the observed meat-ball shift of large-scale galaxy distribution.
SAM and HOD models fail to explain cluster and void abundances.
Color subsets of SAM models completely fail to explain the observed topology.
Galaxy formation models should be tuned to explain not only
the amplitude but also the topology of galaxy clustering!
LRGs (red dots) provide six times more
cosmological information than typical ones.
Analytic formula for the genus in weakly nonlinear regime due to gravitational evolution
The redshift space distortion effects on the
genus curve are small in the weakly-linear scales.
DR 7 Main Galaxies
DR 7 Luminous Red Galaxies
For the most massive galaxies, the HGC model (Kim et al. 2008) does seem to work well.
Initially Gaussian ΛCDM model successfully reproduce the observed topology of LRGs at 21h-1Mpc scales.
LRG distribution has meat ball topology.
Voids are more connected and clusters are more isolated when compared
with the Gaussian genus curve.
The deviation from the random phase expectation can be explained by perturbation theory: Gravitational evolution effects on genus.
Still, void abundance in very low density regions ( < -2) are not explained.