Abstract
We use the 2 Micron All Sky Survey (2MASS) extended source catalogue to determine area-averaged angular correlation functions, ω p , to high orders (p ≤ 9). The main sample used contains 650745 galaxies below an extinction-corrected magnitude of K s = 13.5 and limited to |b| > 10° and represents an order of magnitude increase in solid angle over previous samples used in such analysis (≈34 000 deg 2 ). The high-order correlation functions are used to determine the projected and real-space hierarchical amplitudes, s p = ω p /ω p-1 2 and S p = ξ p /ξ 2 p-1 . For p < 6 these parameters are found to be quite constant over a wide range of scales to r ≈ 40 h -1 Mpc, consistent with a Gaussian form to the primordial distribution of density fluctuations which has evolved under the action of gravitational instability. We test the sensitivity of our results to the presence of rare fluctuations in the local galaxy distribution by cutting various regions of overdensity from the main sample; unlike previous analyses, we find that at least for p ≤ 4, the high-order clustering statistics are relatively robust to the removal of the largest superclusters. Since we probe well into the linear regime we are able to make direct comparisons with perturbation theory. We therefore examine the consistency of our constraints on the K s band Sp parameters with non-Gaussian initial conditions. We are able to rule out strong non-Gaussianity in the primordial density field, as might be seeded by topological defects such as cosmic strings or global textures, producing relations of the form ξ p ∝ ξ p/2 2 , at the 2-3σ confidence level.
Highlights
The variance of local galaxy density fluctuations has been measured to high accuracy over the last decade, both through the twopoint correlation function (e.g. Hawkins et al 2003; Zehavi et al 2004; Maller et al 2005) and its Fourier transform, the power spectrum (e.g. Cole et al 2005; Frith, Outram & Shanks 2005b)
We have measured reduced angular correlation functions, ωp, to ninth order using 650 745 galaxies selected from the 2 Micron All Sky Survey (2MASS) extended source catalogue
High-order clustering analysis allows us to probe the way in which galaxies trace the underlying mass distribution; a negative offset between cold dark matter (CDM) predictions and observations by the 2dF Galaxy Redshift Survey (2dFGRS) have recently been interpreted as evidence for a quadratic contribution to the galaxy bias, these conclusions are based on constraints in the weakly non-linear regime (Gaztanaga et al 2005)
Summary
The variance of local galaxy density fluctuations has been measured to high accuracy over the last decade, both through the twopoint correlation function (e.g. Hawkins et al 2003; Zehavi et al 2004; Maller et al 2005) and its Fourier transform, the power spectrum (e.g. Cole et al 2005; Frith, Outram & Shanks 2005b). For a perfectly Gaussian density field, the two-point statistic forms a complete description of the galaxy distribution as all higher order connected moments are zero. Assuming a Gaussian form for the primordial distribution of density fluctuations, perturbation theory predicts non-zero higher order correlation functions of the local galaxy density field; as the initial inhomogeneities grow gravitationally, the density distribution becomes asymmetric, developing non-zero skewness and kurtosis etc. Journal compilation C 2006 RAS if non-zero high-order moments of the local galaxy density field are detected, these arise either via the gravitational collapse of initially Gaussian density fluctuations or from some degree of primordial non-Gaussianity
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