Analytical study on the Sunyaev-Zeldovich effect for clusters of galaxies

Physical review D: Particles and fields (Impact Factor: 4.86). 04/2009; 79(8). DOI: 10.1103/PhysRevD.79.083005
Source: arXiv


Starting from a covariant formalism of the Sunyaev-Zeldovich effect for the thermal and nonthermal 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.

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    • "(2.2) Here σ T is the non-relativistic Thomson cross section that fully characterizes interactions of CMB photons with electrons of Lorentz factor γ e 10 8 . As far as τ ≪ 1, the single scattering approximation is fully justified [23]. "
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    ABSTRACT: We revisit the prospects for detecting the Sunyaev Zel'dovich (SZ) effect induced by dark matter (DM) annihilation or decay. We show that with standard (or even extreme) assumptions for DM properties, the optical depth associated with relativistic electrons injected from DM annihilation or decay is much smaller than that associated with thermal electrons, when averaged over the angular resolution of current and future experiments. For example, we find: $\tau_{\rm DM} \sim 10^{-9}-10^{-5}$ (depending on the assumptions) for $\mchi = 1$ GeV and a density profile $\rho\propto r^{-1}$ for a template cluster located at 50 Mpc and observed within an angular resolution of $10"$, compared to $\tau_{\rm th}\sim 10^{-3}-10^{-2}$. This, together with a full spectral analysis, enables us to demonstrate that, for a template cluster with generic properties, the SZ effect due to DM annihilation or decay is far below the sensitivity of the Planck satellite. This is at variance with previous claims regarding heavier annihilating DM particles. Should DM be made of lighter particles, the current constraints from 511 keV observations on the annihilation cross section or decay rate still prevent a detectable SZ effect. Finally, we show that spatial diffusion sets a core of a few kpc in the electron distribution, even for very cuspy DM profiles, such that improving the angular resolution of the instrument, e.g. with ALMA, does not necessarily improve the detection potential. We provide useful analytical formulae parameterized in terms of the DM mass, decay rate or annihilation cross section and DM halo features, that allow quick estimates of the SZ effect induced by any given candidate and any DM halo profile. Comment: 27 p, 6 figs, additional section on spatial diffusion effects. Accepted for publication in JCAP
    Journal of Cosmology and Astroparticle Physics 07/2009; 2010(2). DOI:10.1088/1475-7516/2010/02/005 · 5.81 Impact Factor
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    ABSTRACT: We derive the covariant formalism associated with the relativistic Sunyaev-Zel’dovich effect due to a nonthermal population of high energy electrons in clusters of galaxies. More precisely, we show that the formalism proposed by Wright in 1979, based on an empirical approach to compute the inverse Compton scattering of a population of relativistic electrons on CMB photons, can actually be reinterpreted as a Boltzmann-like equation, in the single scattering approximation.
    Physical review D: Particles and fields 04/2009; 79(8). DOI:10.1103/PhysRevD.79.083505 · 4.86 Impact Factor
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    ABSTRACT: Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the formal solutions in three different representation forms for the Sunyaev-Zeldovich effect. By expanding the formal solution in the operator representation in powers of both the derivative operator and electron velocity, we derive a formal solution that is equivalent to the Fokker-Planck expansion approximation. We extend the present formalism to the kinematical Sunyaev-Zeldovich effect. The properties of the frequency redistribution functions are studied. We find that the kinematical Sunyaev-Zeldovich effect is described by the redistribution function related to the electron pressure. We also solve the rate equations numerically. We obtain the exact numerical solutions, which include the full-order terms in powers of the optical depth. Comment: 13 pages, 5 figures, accepted by PRD for publication
    Physical review D: Particles and fields 04/2009; 79(12). DOI:10.1103/PhysRevD.79.123007 · 4.86 Impact Factor
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