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Astron. Astrophys. 325, 74-80

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A deprojection method to obtain the spectral index distribution
in diffuse radio halos of clusters of galaxies

Bruno M. Deiss*

Institut für Theoretische Physik, J.W. Goethe-Universität, Robert-Mayer-Straße 10, D-60054 Frankfurt am Main, Germany

Received 2 January 1997 / Accepted 20 January 1997


Diffuse radio halos of clusters of galaxies are generally classified as ''steep-spectrum radio sources'' according to the observed spectral index of the integrated flux density of FORMULA . It is shown that the spectral index of the underlying synchrotron emission coefficient can be considerably smaller than FORMULA due to a frequency-dependent effective emission volume observed in some radio halos. Deiss, Reich, Lesch & Wielebinski (1996 A&A, in press) have suggested an analytic deprojection method to derive the spatial distribution of the emissivity index from the observed spectral-index distribution of the surface brightness assuming a spherically symmetric gaussian radio halo source. The formalism also allows to check on the consistency of the observational data at different frequencies. The method is generalized to the case of any halo model that is symmetric about the center but otherwise arbitrary. It is shown that, as an example, in the central region of the extended radio halo of the Coma cluster, the spectral index of the emission coefficient may be as low as 0.43, which is smaller than the observed integrated-flux density index by about 0.8. Differences of this magnitude are significant, since FORMULA is an important discriminator of cosmic-ray acceleration models in the intracluster medium.

Key words: methods: data analysis - galaxies: clusters of - intergalactic medium - radio continuum: galaxies

*Present address: Department of Astronomy, University of Toronto, Toronto, Ontario, Canada M5S 1A7

© European Southern Observatory (ESO) 1997