2MASS constraints on the local large-scale structure:: a challenge to ΛCDM?

We investigate the large-scale structure of the local galaxy distribution using the recently completed 2-Micron All Sky Survey (2MASS) via three techniques. First, we determine the K-s-band number counts over the approximate to 4000 deg(2) APM survey area where optical evidence for a large-scale 'local hole' has previously been detected and compare them to a non-evolving homogeneous prediction. Considering a ACDM form for the two-point angular correlation function, the observed deficiency represents a 5 sigma fluctuation in the galaxy distribution. We check the model normalization using faint K-band data compiled from the literature; the normalization used in this paper is in excellent agreement, although the resulting best-fitting normalization is slightly lower. Nevertheless the observed counts over the APM survey area would require the best-fitting model normalization to be lowered by 3.8 sigma. However, the issue is complicated by the b >= 20 degrees and b <= -20 degrees 2MASS counts which lie below this model normalization. Secondly, since the K-s-band counts over the APM survey area continue to suggest the possible presence of excess clustering over the ACDM prediction, we next probe the power at large scales by comparing the 2MASS and ACDM mock galaxy angular power spectra. We find a 3 sigma excess in the 2MASS catalogue over the ACDM prediction at large scales (l <= 30) using a bias of b(K) = 1.1. However, this excess is not enough to account for the low counts over the APM survey area. Finally, in order to probe more directly whether the ACDM mocks can reproduce observed features in the galaxy distribution at large scales, we apply a counts-in-cells analysis to the 2MASS data and mock catalogues; on the assumption that the 2MASS catalogue at vertical bar b vertical bar >= 20 degrees is representative, we find excellent agreement between the biased ACDM mocks and the 2MASS catalogue to approximate to 30 degrees. The crux of the interpretation of these results appears to be whether the 2MASS volume is yet big enough to constitute a fair sample of the Universe. The number-count models based on fainter counts suggest that it may not be, although normalization uncertainties remain. It is also the case that the 2MASS depth remains comparable to the possible size of large-scale inhomogencities. Analyses which assume the 2MASS average density is a fair sample, such as counts in cells and to a lesser extent, power spectral analysis, may return results which see less contradiction with ACDM than the number-count analysis in the APM survey area. Further progress on assessing the significance of the local hole and thus the consistency of the local galaxy distribution with ACDM will require deeper all-sky number-counts and redshift surveys in both the optical and the infrared.