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The influence of magnetic fields on the Sunyaev Zeldovich effect in clusters of galaxies

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 Added by Patrick Michel Koch
 Publication date 2002
  fields Physics
and research's language is English




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We study the influence of intracluster large scale magnetic fields on the thermal Sunyaev-Zeldovich (SZ) effect. In a macroscopic approach we complete the hydrostatic equilibrium equation with the magnetic field pressure component. Comparing the resulting mass distribution with a standard one, we derive a new electron density profile. For a spherically symmetric cluster model, this new profile can be written as the product of a standard ($beta$-) profile and a radius dependent function, close to unity, which takes into account the magnetic field strength. For non-cooling flow clusters we find that the observed magnetic field values can reduce the SZ signal by $sim 10%$ with respect to the value estimated from X-ray observations and the $beta$-model. If a cluster harbours a cooling flow, magnetic fields tend to weaken the cooling flow influence on the SZ-effect.



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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 Wrights 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.
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.
We present new measurements of the Sunyaev-Zeldovich (SZ) effect from clusters of galaxies using the Sunyaev-Zeldovich Infrared Experiment (SuZIE II). We combine these new measurements with previous cluster observations with the SuZIE instrument to form a sample of 15 clusters of galaxies. For this sample we calculate the central Comptonization, y, and the integrated SZ flux decrement, S, for each of our clusters. We find that the integrated SZ flux is a more robust observable derived from our measurements than the central Comptonization due to inadequacies in the spatial modelling of the intra-cluster gas with a standard Beta model. This is highlighted by comparing our central Comptonization results with values calculated from measurements using the BIMA and OVRO interferometers. On average, the SuZIE calculated central Comptonizations are approximately 60% higher in the cooling flow clusters than the interferometric values, compared to only approximately 12% higher in the non-cooling flow clusters. We believe this discrepancy to be in large part due to the spatial modelling of the intra-cluster gas. From our cluster sample we construct y-T and S-T scaling relations. The y-T scaling relation is inconsistent with what we would expect for self-similar clusters; however this result is questionable because of the large systematic uncertainty in the central Comptonization. The S-T scaling relation has a slope and redshift evolution consistent with what we expect for self-similar clusters with a characteristic density that scales with the mean density of the universe. We rule out zero redshift evolution of the S-T relation at 90% confidence.
In the present universe, magnetic fields exist with various strengths and on various scales. One possible origin of these cosmic magnetic fields is the primordial magnetic fields (PMFs) generated in the early universe. PMFs are considered to contribute to matter density evolution via Lorentz force and the thermal history of intergalactic medium (IGM) gas due to ambipolar diffusion. Therefore, information about PMFs should be included in the temperature anisotropy of the Cosmic Microwave Background through the thermal Sunyaev-Zeldovich (tSZ) effect in IGM. In this article, given an initial power spectrum of PMFs, we show the spatial fluctuation of mass density and temperature of the IGM and tSZ angular power spectrum created by the PMFs. Finally, we find that the tSZ angular power spectrum induced by PMFs becomes significant on small scales, even with PMFs below the observational upper limit. Therefore, we conclude that the measurement of tSZ anisotropy on small scales will provide the most stringent constraint on PMFs.
The presence of ubiquitous magnetic fields in the universe is suggested from observations of radiation and cosmic ray from galaxies or the intergalactic medium (IGM). One possible origin of cosmic magnetic fields is the magnetogenesis in the primordial universe. Such magnetic fields are called primordial magnetic fields (PMFs), and are considered to affect the evolution of matter density fluctuations and the thermal history of the IGM gas. Hence the information of PMFs is expected to be imprinted on the anisotropies of the cosmic microwave background (CMB) through the thermal Sunyaev-Zeldovich (tSZ) effect in the IGM. In this study, given an initial power spectrum of PMFs as $P(k)propto B_{rm 1Mpc}^2 k^{n_{B}}$, we calculate dynamical and thermal evolutions of the IGM under the influence of PMFs, and compute the resultant angular power spectrum of the Compton $y$-parameter on the sky. As a result, we find that two physical processes driven by PMFs dominantly determine the power spectrum of the Compton $y$-parameter; (i) the heating due to the ambipolar diffusion effectively works to increase the temperature and the ionization fraction, and (ii) the Lorentz force drastically enhances the density contrast just after the recombination epoch. These facts result in making the tSZ angular power spectrum induced by the PMFs more remarkable at $ell >10^4$ than that by galaxy clusters even with $B_{rm 1Mpc}=0.1$ nG and $n_{B}=-1.0$ because the contribution from galaxy clusters decreases with increasing $ell$. The measurement of the tSZ angular power spectrum on high $ell$ modes can provide the stringent constraint on PMFs.
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