Superposition of blackbodies and the dipole anisotropy: A possibility to calibrate CMB experiments

Abstract

The CMB angular temperature fluctuations observed by COBE and WMAP enable us to place a lower limit on the spectral distortions of the CMB at any angular scale. These distortions are connected with the simple fact that the superposition of blackbodies with different temperatures in general is not a blackbody. We show that in the limit of small temperature fluctuations the superposition of blackbodies leads to a y-type spectral distortion. It is known that the CMB dipole induces a y-type spectral distortion with quadrupole and monopole angular distribution leading to a corresponding whole sky y-parameter of yd = 2.6 × 10-7. We show here that taking the difference of the CMB signal in the direction of the maximum and minimum of the CMB dipole due to the superposition of two blackbodies leads to a spectral distortion with yopt = 12yd = 3.1 × 10 -6. The amplitude of this distortion can be calculated to the same precision as the CMB dipole, i.e. 0.3% today. Therefore it may be used as a source with brightness of several or tens of μK to cross calibrate and calibrate different frequency channels of CMB surveys with a precision of a few tens or hundreds of nK. We also discuss clusters of galaxies as possible sources for calibration purposes. Furthermore, we show in this work that primordial anisotropies for multipoles 2 ≤ l ≤ 1000 also lead to spectral distortions but with a much smaller y-parameter, i.e. y ∼ 10 -11-10-9.