Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies

Abstract

Starting from a covariant formalism of the Sunyaev-Zeldovich effect for the thermal and non-thermal distributions, we derive the frequency redistribution function identical to Wright's method assuming the smallness of the photon energy (in the Thomson limit). We also derive the redistribution function in the covariant formalism in the Thomson limit. We show that two redistribution functions are mathematically equivalent in the Thomson limit which is fully valid for the cosmic microwave background photon energies. We will also extend the formalism to the kinematical Sunyaev-Zeldovich effect. With the present formalism we will clarify the situation for the discrepancy existed in the higher order terms of the kinematical Sunyaev-Zeldovich effect.

published in Physical Review D79, 083005 (2009)

References in corpus (17)

• Cosmology with the Sunyaev-Zel'dovich Effect
• The Sunyaev-Zel'dovich Effect
• Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies
• Relativistic corrections to the Sunyaev-Zel'dovich effect
• 1E0657-56: A Contender for the Hottest Known Cluster of Galaxies
• Chandra observations of RXJ1347.5-1145: the distribution of mass in the most X-ray luminous galaxy cluster known
• Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. II. Inclusion of Peculiar Velocities
• The Non-Thermal Sunyaev-Zel'dovich Effect in Clusters of Galaxies
• Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. IV. Analytic fitting formula for the Numerical Results
• Spectral distortion of cosmic background radiation by scattering on hot electrons. Exact calculations
• Comptonization of an isotropic distribution in moving media: higher-order effects
• Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. III. Polarization Effect
• Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. V. Multiple Scattering
• Relativistic corrections to the multiple scattering effect on the Sunyaev-Zel'dovich effect in the isotropic approximation
• Quantitative Description of the Sunyaev-Zeldovich Effect: Analytic Approximations
• Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies. V. Effect of the Motion of the Observer
• Extraction of cluster parameters from Sunyaev-Zeldovich effect observations with simulated annealing optimization

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