Aspects of the cosmic microwave background dipole

Cosmic microwave background (CMB) experiments generally infer a temperature fluctuation from a measured intensity fluctuation through the first term in the Taylor expansion of the Planck function, the relation between the intensity in a given frequency and the temperature. However, with the forthcoming Planck satellite, and perhaps even with the Microwave Anisotropy Probe, the CMB-dipole amplitude will be large enough to warrant inclusion of the next higher order term. To quadratic order in the dipole amplitude, there is an intensity quadrupole induced by the dipole with a frequency dependence given by the second derivative of the Planck function. The Planck satellite should be able to detect this dipole-induced intensity quadrupole and distinguish it through its frequency dependence from the intrinsic CMB temperature and foreground quadrupoles. This higher-order effect provides a robust pre-determined target that may provide tests of Planck's and MAP's large-angle-fluctuation measurements and of their techniques for multifrequency foreground subtraction.