arXiv subjects

Satoshi Nozawa

Publications and source records attributed to Satoshi Nozawa.

43 records · Page 3Linked to original sources

arXiv2000

Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. V. Multiple Scattering

We extend the formalism for the calculation of the relativistic corrections to the Sunyaev-Zel'dovich effect for clusters of galaxies and include the multiple scattering effects. We present a systematic method for the inclusion of the multiple scattering effects. The multiple scattering contribution is found to be very small compared with the single scattering contribution. For high-temperature galaxy clusters of k_{B}T_{e} = 15keV, the ratio of the both contributions is -0.3% in the Wien region. In the Rayleigh--Jeans region the ratio is -0.03%. Therefore the multiple scattering contribution is safely neglected for the observed galaxy clusters.

astro-ph↗

arXiv2000

Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. IV. Analytic fitting formula for the Numerical Results

We present an accurate analytic fitting formula for the numerical results for the relativistic corrections to the thermal Sunyaev-Zel'dovich effect for clusters of galaxies. The numerical results for the relativistic corrections have been obtained by numerical integration of the collision term of the Boltzmann equation. The fitting is carried out for the ranges 0.02 < theta_{e} < 0.05 and 0 < X < 20, where theta_{e} = k_{B}T_{e}/m_{e}c^{2}, X = omega/k_{B}T_{0}, T_{e} is the electron temperature, omega is the angular frequency of the photon, and T_{0} is the temperature of the cosmic microwave background radiation. The accuracy of the fitting is generally better than 0.1%. The present analytic fitting formula will be useful for the analyses of the thermal Sunyaev-Zel'dovich effect for high-temperature galaxy clusters.

astro-ph↗

arXiv1998

Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies. II. Inclusion of Peculiar Velocities

We extend the formalism of the relativistic thermal Sunyaev-Zel'dovich effect to the system moving with a velocity beta (= v/c) with respect to the cosmic microwave background radiation. In the present formalism, the kinematic Sunyaev-Zel'dovich effect for the cluster of galaxies with a peculiar velocity is derived in a straightforward manner by the Lorentz boost of the generalized Kompaneets equation. We give an analytic expression for the kinematic Sunyaev-Zel'dovich effect which is valid up to O(beta^{2}) with the power series expansion approximation in terms of theta_{e} = k_{B} T_{e}/ mc^{2}, where T_{e} and m are the electron temperature and the electron mass, respectively. It is found that the relativistic corrections to the kinematic Sunyaev-Zel'dovich effect are significant. For a typical electron temperature 10keV, one obtains -8.2% and +1.3% corrections from the O(beta theta_{e}) and O(beta theta_{e}^{2}) contributions, respectively. The O(beta^{2}) correction is extremely small, +0.2% for beta=1/300 at 10keV. Therefore it can be safely neglected. These relativistic corrections are directly reflected on the determination of the peculiar velocity of the cluster of galaxies with the observation of the kinematic Sunyaev-Zel'dovich effect.

astro-ph↗

arXiv1998

Relativistic Thermal Bremsstrahlung Gaunt Factor for the Intracluster Plasma. II. Heavy Elements

We calculate the relativistic thermal bremsstrahlung Gaunt factor for the high-temperature plasma which exists in clusters of galaxies. We calculate the Gaunt factor by employing the Bethe-Heitler cross section corrected by the Elwert factor. The calculations in this paper are made for the fully ionized plasma for the following cases: Z = 10 (Ne), 12 (Mg), 14 (Si), 16 (S), 26 (Fe). We also calculate the Gaunt factor by using the Coulomb-distorted wave functions for nonrelativistic electrons following the method of Karzas and Latter. By comparing the Gaunt factors calculated by these two different methods, we carefully assess the accuracy of the calculation. We present the numerical results in the form of tables.

astro-ph↗

arXiv1998

Relativistic Thermal Bremsstrahlung Gaunt Factor for the Intracluster Plasma

We calculate the relativistic thermal bremsstrahlung Gaunt factor for the high-temperature plasma which exists in clusters of galaxies. We calculate the Gaunt factor by employing the Bethe-Heitler cross section corrected by the Elwert factor. We also calculate the Gaunt factor by using the Coulomb-distorted wave functions for nonrelativistic electrons following the method of Karzas and Latter. By comparing the Gaunt factors calculated by these two different methods, we carefully assess the accuracy of the calculation. We present the numerical results in the form of tables.

astro-ph↗

arXiv1998

Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies

We study the generalized Kompaneets equation (kinetic equation for the photon distribution function taking into account the Compton scattering by electrons) using a relativistically covariant formalism. Using the generalized Kompaneets equation, we derive an analytic expression for the Sunyaev-Zel'dovich effect, which takes into account up to O(theta**5) terms, where theta=kT/mc**2 is the relativistic expansion parameter and T is the electron temperature. We carefully study the applicable region of the obtained analytic expression by comparing with the result of the direct numerical integration. We conclude that the present analytic expression can be reliably applied to the calculation of the Sunyaev-Zel'dovich effect for kT < 15keV, which is the highest electron temperature in the presently known clusters of galaxies. Therefore, the present analytic expression can be applied to all known clusters of galaxies.

astro-ph↗

arXiv1997

Dissipative Field Theory with Caldeira-Leggett Method and its Application to Disoriented Chiral Condensation

The effective field theory including the dissipative effect is developed based on the Caldeira-Leggett theory at the classical level. After the integration of the small field fluctuations considered as the field radiation, the integro-differential field equation is given and shown to include the dissipative effects. In that derivation, special cares should be taken for the boundary condition of the integration. Application to the linear sigma model is given, and the decay process of the chiral condensate is calculated with it, both analytically in the linear approximation and numerically. With these results, we discuss the stability of chiral condensates within the quenched approximation.

nucl-th↗