Microwave background correlations from dipole anisotropy modulation

Full-sky maps of the cosmic microwave background temperature reveal a 7% asymmetry of fluctuation power between two halves of the sky. A common phenomenological model for this asymmetry is an overall dipole modulation of statistically isotropic fluctuations, which produces particular off-diagonal correlations between multipole coefficients. We compute these correlations and construct corresponding estimators for the amplitude and direction of the dipole modulation. Applying these estimators to various cut-sky temperature maps from Planck and WMAP data shows consistency with a dipole modulation, differing from a null signal at 2.5[sigma], with an amplitude and direction consistent with previous fits based on the temperature fluctuation power. The signal is scale dependent, with a statistically significant amplitude at angular scales larger than 2[degrees]. Future measurements of microwave background polarization and gravitational lensing can increase the significance of the signal. If the signal is not a statistical fluke in an isotropic universe, it requires new physics beyond the standard model of cosmology.