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The 2dF Galaxy Redshift Survey: voids and hierarchical scaling models

Croton, D.J.; Colless, M.; Gaztañaga, E.; Baugh, C.M.; Norberg, P.; Baldry, I.K.; Bland-Hawthorn, J.; Bridges, T.; Cannon, R.; Cole, S.; Collins, C.; Couch, W.; Dalton, G.; de Propris, R.; Driver, S.P.; Efstathiou, G.; Ellis, R.S.; Frenk, C.S.; Glazebrook, K.; Jackson, C.; Lahav, O.; Lewis, I.; Lumsden, S.; Maddox, S.; Madgwick, D.; Peacock, J.A.; Peterson, B.A.; Sutherland, W.; Taylor, K.


D.J. Croton

M. Colless

E. Gaztañaga

I.K. Baldry

J. Bland-Hawthorn

T. Bridges

R. Cannon

C. Collins

W. Couch

G. Dalton

R. de Propris

S.P. Driver

G. Efstathiou

R.S. Ellis

K. Glazebrook

C. Jackson

O. Lahav

I. Lewis

S. Lumsden

S. Maddox

D. Madgwick

J.A. Peacock

B.A. Peterson

W. Sutherland

K. Taylor


We measure the redshift-space reduced void probability function (VPF) for 2dFGRS volume-limited galaxy samples covering the absolute magnitude range M b JGraphic−5 log10h=−18 to −22. Theoretically, the VPF connects the distribution of voids to the moments of galaxy clustering of all orders, and can be used to discriminate clustering models in the weakly non-linear regime. The reduced VPF measured from the 2dFGRS is in excellent agreement with the paradigm of hierarchical scaling of the galaxy clustering moments. The accuracy of our measurement is such that we can rule out, at a very high significance, popular models for galaxy clustering, including the lognormal distribution. We demonstrate that the negative binomial model gives a very good approximation to the 2dFGRS data over a wide range of scales, out to at least 20 h−1 Mpc. Conversely, the reduced VPF for dark matter in a Λ cold dark matter (ΛCDM) universe does appear to be lognormal on small scales but deviates significantly beyond ∼4 h−1 Mpc. We find little dependence of the 2dFGRS reduced VPF on galaxy luminosity. Our results hold independently in both the North and South Galactic Pole survey regions.


Croton, D., Colless, M., Gaztañaga, E., Baugh, C., Norberg, P., Baldry, I., …Taylor, K. (2004). The 2dF Galaxy Redshift Survey: voids and hierarchical scaling models. Monthly Notices of the Royal Astronomical Society, 352(3), 828-836.

Journal Article Type Article
Publication Date 2004-08
Deposit Date Apr 19, 2011
Journal Monthly Notices of the Royal Astronomical Society
Print ISSN 0035-8711
Electronic ISSN 1365-2966
Publisher Royal Astronomical Society
Peer Reviewed Peer Reviewed
Volume 352
Issue 3
Pages 828-836