Cosmic temperature fluctuations from two years of COBE differential microwave radiometers observations

The first two years of Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) observations of the cosmic microwave background (CMB) anisotropy are analyzed and compared with our previously published first year results. The results are consistent, but the addition of the second year of data increases the precision and accuracy detected CMB temperature fluctuations. The 2 yr 53 GHz data are characterized by rms temperature fluctuations of (delta-T)(sub rms) (7 deg) = 44 +/- 7 micro-K and (delta-T)(sub rms) (10 deg) = 30.5 +/- 2.7 micro-K at 7 deg and 10 deg angular resolution, respectively. The 53 x 90 GHz cross-correlation amplitude at zero lag is C(0)(sup 1/2) = 36 +/- 5 micro-K (68% CL) for the unsmoothed (7 deg resolution) DMR data. We perform a likelihood analysis of the cross-correlation function, with Monte Carlo simulations to infer biases of the method, for a power-law model of initial density fluctuations, P(k) proportional to R(exp n). The Monte Carlo simulations indicate that derived estimates of n are biased by +0.11 +/- 0.01, while the subset of simulations with a low quadrupole (as observed) indicate a bias of +0.31+/- 0.04. Derived values for 68% confidence intervals are given corrected (and not corrected) for our estimated biases. Including the quadrupole anisotropy, the most likely quadrupole-normalized amplitude is Q(sub rms-PS) = 14.3(sup + 5.2 sub -3.3) micro-K (12.8(sup + 5.2 sub -3.3) micro-K0 with a spectral index n = 1.42(sup + 0.49 sub -0.55)(n = 1.53(sup + 0.49 sub -0.55). With n fixed to 1.0 the most likely amplitude is 18.2 +/- 11.5 micro-K (17.4 +/- 1.5 micro-K). The marginal likelihood of n is 1.42 +/- 0.37 (1.53 +/- 0.37). Excluding the quadrupole anisotropy, the most likely quadrupole-normalized amplitude is Q(sub rms-PS) = 17.4(sup + 7.5 sub -5.2) micro-K (15.8(sup + 7.5 sub -5.2) micro-K) with a spectral index n = 1.11(sup + 0.60 sub -0.55) (n = 1.22(sup + 0.60 sub -0.55). With n fixed to 1.0 the most likely amplitude is 18.6 +/- 1.6 micro-K (18.2 +/- 1.6 micro-K). The marginal likelihood of n is 1.11 +/- 0.40 (1.22 +/- 0.40). Our best estimate of the dipole from the 2 yr DMR data is 3.363 +/- 0.024 mK toward Galactic coordinates (l, b) = (264.4 deg +/- 0.2 deg, 48.1 deg +/- 0.4 deg), and our best estimate of the rms quadrupole amplitude in our sky is 6 +/- 3 micro-K (68% CL).