The Galaxy Angular Correlation Functions and Power Spectrum from the Two Micron All Sky Survey

We calculate the angular correlation function of galaxies in the Two Micron All Sky Survey. We minimize the possible contamination by stars, dust, seeing, and sky brightness by studying their cross correlation with galaxy density and limiting the galaxy sample accordingly. We measure the correlation function at scales between 1^'<θ<18^deg using a half-million galaxies. We find that a best-fit power law to the correlation function has a slope of -0.79+/-0.02 and an amplitude at 1° of 0.10+/-0.01 in the range 1'-2.5d. However, there are statistically significant oscillations around this power law. The largest oscillation occurs at about 0.8d, corresponding to 700 h^-1 kpc at the median redshift of our survey, as expected in halo occupation distribution descriptions of galaxy clustering. In addition, there is a break in the power-law shape of the correlation function at θ>2.5d. Our results are in good agreement with other measurements of the angular correlation function. We invert the angular correlation function using singular value decomposition to measure the three-dimensional power spectrum and find that it too is in good agreement with previous measurements. A dip seen in the power spectrum at small wavenumber k is statistically consistent with cold dark matter (CDM) type power spectra. A fit of CDM-type power spectra in the linear regime (k<0.15 h Mpc^-1) gives constraints of Ω_mh=0.13+/-0.07 and σ₈=1.0+/-0.09 for a spectral index of 1.0. This suggests a K_s-band linear bias of 1.1+/-0.2. These measurements are in good agreement with other measurements of the power spectrum on linear scales. On small scales the power-law shape of our power spectrum is shallower than that derived for the Sloan Digital Sky Survey. This may imply a biasing for these different galaxies that could be either waveband- or luminosity-dependent. The power spectrum derived here in combination with the results from other surveys can be used to constrain models of galaxy formation.