The 2MASS galaxy angular power spectrum: Probing the galaxy distribution to Gigaparsec scales

We present an angular power spectrum analysis of the 2MASS full release extended source catalogue. The main sample used includes 518,576 galaxies below an extinction-corrected magnitude of K=13.5 and limited to |b|>20. The power spectrum results provide an estimate of the galaxy density fluctuations at extremely large scales, r<1000 Mpc. We compare this with mock predictions constructed from the LCDM Hubble Volume mock catalogue. We find that over the range 1<l<100 the 2MASS C_l is steeper than that for the Hubble Volume model. However, in the linear regime (l<30) there is good agreement between the two. We investigate in detail the effects of possible sources of systematic error. Converting linear power spectrum predictions for the form of the three-dimensional matter power spectrum, P(k), and assuming a flat CDM cosmology, a primordial n_s=1 spectrum and negligible neutrino mass, we perform fits to the galaxy angular power spectrum at large linear scales (l<30, corresponding to r>50 Mpc). We obtain constraints on the galaxy power spectrum shape of Gamma=0.14+/-0.02, in good agreement with previous estimates inferred at smaller scales. We also constrain the galaxy power spectrum normalisation to (sigma_8 b_K)^2=1.36+/-0.10; in combination with previous constraints on sigma_8 we infer a K-band bias of b_K=1.39+/-0.12. We are also able to provide weak constraints on Omega_m h and Omega_b/Omega_m. These results are based on the usual assumption that the errors derived from the Hubble Volume mocks are applicable to all other models. If we instead assume that the error is proportional to the C_l amplitude then the constraints weaken; for example it becomes more difficult to reject cosmologies with lower Gamma.