Abstract

We measure the variance in the distribution of off-plane (|b| > 20 ◦ ) galaxies with mK < 13.5 from the 2MASS K-band survey in circles of diameter between 0.344 ◦ and 57.2 ◦ . The use of a near-infrared survey makes the contribution of Galactic extinction to these fluctuations negligible. We calculate these variances within the standard ΛCDM model assuming that the sources are distributed like halos of the corresponding mass, and it reproduces qualitatively the galaxy count variance. Therefore, we conclude that the counts can be explained in terms only of the large scale structure. A second result of this paper is a new method to determine the two point correlation function obtained by forcing agreement between model and data. This method does not need the knowledge of the two-point angular correlation function, allows an estimation of the errors (which are low with this method), and can be used even with incomplete surveys. Using this method we get ξ(z = 0,r < 10 h −1 Mpc) = (29.8 ± 0.5)(r/h −1 Mpc) −1.79±0.03 , which is the first measure of the amplitude of ξ in the local Universe for the K-band. It is more or less in agreement with those obtained through red optical filter selected samples, but it is larger than the amplitude obtained for blue optical filter selected samples. The distribution of the number of galaxies or clusters of galax- ies in a certain volume V can be used to test the large-scale structure of the universe. The calculation of probabilities of finding different structures in a clustering model are some- times amenable to analytical techniques: for instance, for voids (Betancort-Rijo 1990), density of Abel clusters (Betancort-Rijo 1995), number of galaxies in a randomly placed sphere and cluster density profiles (Betancort-Rijo & Lopez-Corredoira 1996), etc. The calculation of variance of the number of galax- ies within the cones corresponding to the circles in the sky, or another 2D figure, (i.e., galaxy counts) is another possibility, and even easier to compare with the observations since we do not need any information about the redshifts of the individual galaxies. This is precisely the purpose of this paper: the calcu- lation from a model of the variance of the number of galaxies in the different regions of the sky, and to see how well they fit real data obtained directly from a sky survey. This will allow us to determine some parameters of the two-point correlation function independent of any other method. One disadvantage of galaxy counts is that they are af- fected by Galactic extinction, and it is difficult to separate the fluctuations due to this extinction from the real fluctuation in the galaxy distribution. However, the arrival of near-infrared

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