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

Free access article

Issue		A&A Volume 424, Number 2, September III 2004


Page(s)		389 - 408
Section		Cosmology (including clusters of galaxies)
DOI		http://dx.doi.org/10.1051/0004-6361:20041016

A&A 424, 389-408 (2004)
DOI: 10.1051/0004-6361:20041016

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

J. Chluba¹ and R. A. Sunyaev^{1, 2}

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 86740 Garching bei München, Germany
e-mail: jchluba@mpa-garching.mpg.de
² Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32 Moscow, Russia

(Received 3 April 2004/ Accepted 11 May 2004 )

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 $y_{\rm d}=2.6\times 10^{-7}$ . 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 $y_{\rm opt}=12\,y_{\rm d}=3.1\times 10^{-6}$ . 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 $\mu$ K 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 $2\leq l \leq 1000$ also lead to spectral distortions but with a much smaller y-parameter, i.e. $y\sim 10^{-11}{-}10^{-9}$ .

Key words: cosmology: cosmic microwave background -- cosmology: observations

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