High-order 2MASS galaxy correlation functions: probing the Gaussianity of the primordial density field

We use the 2 Micron All Sky Survey (2MASS) extended source catalogue to determine area-averaged angular correlation functions, , to high orders (p≤ 9). The main sample used contains 650 745 galaxies below an extinction-corrected magnitude of Ks= 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 deg2). The high-order correlation functions are used to determine the projected and real-space hierarchical amplitudes, and . 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 Ks 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 , at the 2–3σ confidence level.