Statistical Measures of Large-Scale Structure
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**Session 67 -- Cosmology and Distance Indicators**
*Oral presentation, Thursday, January 13, 2:15-3:45, Crystal Forum Room (Crystal City Marriott)*

## [67.02] Statistical Measures of Large-Scale Structure

*Michael Vogeley (Johns Hopkins University), Margaret Geller, John Huchra (Center for Astrophysics), Changbom Park (Seoul National University), J. Richard Gott (Princeton University)*

\def\inv{$^{-1}$}
\def\hmpc{\rm*h*
\inv~Mpc}
\def\lteq{\leq}

To quantify clustering in the large-scale distribution of galaxies and to
test theories for the formation of structure in the universe,
we apply statistical measures to the CfA Redshift Survey.
This survey is complete to $m_{B(0)}=15.5$ over
two contiguous regions which cover one-quarter of the sky and include
$\sim 11,000$ galaxies.
The salient features of these data are
voids with diameter $30-50$\hmpc~ and coherent dense structures with
a scale $\sim 100$\hmpc.

Comparison with N-body simulations rules out
the ``standard" CDM model ($\Omega=1$, $b=1.5$, $\sigma_8=1$)
at the 99\% confidence level
because this model has insufficient power on scales $\lambda>30$\hmpc.
An unbiased open universe CDM model ($\Omega h =0.2$) and a
biased CDM model with non-zero cosmological constant ($\Omega h =0.24$,
$\lambda_0=0.6$) match the observed power spectrum.
The amplitude of the power spectrum depends on the luminosity of
galaxies in the sample;
bright ($L>L^*$) galaxies are more strongly clustered than faint galaxies.
The paucity of bright galaxies in low-density regions may explain
this dependence.

To measure the topology of large-scale structure, we compute the
genus of isodensity surfaces of the smoothed density field.
On scales in the ``non-linear" regime, $\lteq 10$\hmpc,
the high- and low-density regions are multiply-connected
over a broad range of density threshold, as in a filamentary net.
On smoothing scales $>10$\hmpc, the topology is
consistent with statistics of a Gaussian random field.
Simulations of CDM models fail to produce the observed coherence
of structure on non-linear scales ($>95\%$ confidence level).

The underdensity probability (the frequency of
regions with density contrast $\delta\rho/\overline{\rho}=-0.8$)
depends strongly on the luminosity of
galaxies; underdense regions are significantly more common ($>2\sigma$)
in bright ($L>L^*$) galaxy samples than in samples which include
fainter galaxies.

**Thursday
program listing**