Yasuharu Kohyama

Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies

We have succeeded in obtaining a precision analytic fitting formula for the exact numerical results of the relativistic corrections to the thermal Sunyaev-Zeldovich effect for clusters of galaxies which has a 1% accuracy for the crossover frequency region where the thermal thermal Sunyaev-Zeldovich effect signal changes from negative to positive sign. The fitting has been carried out for the ranges 0.020 < theta < 0.035 and 0 < X < 15, where theta= kTe/mc^{2}, X = omega/kT0, Te is the electron temperature, omega is the angular frequency of the photon, and T0 is the temperature of the cosmic microwave background radiation. The overall accuracy of the fitting is better than 0.1%. The present analytic fitting formula will be useful for accurate analyses of the thermal Sunyaev-Zeldovich effect for clusters of galaxies.We present an accurate numerical table for the relativistic corrections to the thermal Sunyaev-Zeldovich 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 numerical table is provided for the ranges 0.002 <= theta_e <= 0.100 and 0 <= X <= 20, where theta_e = kT_e/mc^2, X = hbar omega/kT_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. We also present an accurate analytic fitting formula that reproduces the numerical results with high precision.

Neutrino energy loss in stellar interiors. III. Pair, photo-, plasma, and bremsstrahlung processes

Detailed results of the calculation of the neutrino energy-loss rates due to pair, photo-, plasma, and bremsstrahlung processes corresponding to the density-temperature regime 1-10 to the 14th g/cu cm, 10 to the 7th - 10 to the 11th K are presented. The calculation is based on the Weinberg-Salam theory. The present calculation is the most accurate calculation to date covering the widest density-temperature regime. The discrepancies with the previous works are carefully examined. Extensive tables are prepared to show the detailed results of the photo-neutrino energy-loss rate. 26 refs.

Neutrino energy loss in stellar interiors

The energy loss rates due to pair, photo-, and plasma neutrino processes are calculated in the framework of the Weinberg-Salam theory for wide ranges of densities and temperatures. Accurate analytic fitting formulas are presented to facilitate the application of the result. It is found that the present calculation gives a neutrino energy loss rate which is substantially lower than that of Beaudet, Petrosian, and Salpeter (1967). The reduction factor alpha is in the range 0.35-0.88 depending on the neutrino masses, density, and temperature. 13 references.

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

We extend the formalism of the relativistic thermal Sunyaev-Zeldovich effect to a system moving with a velocity β ≡ /c with respect to the cosmic microwave background radiation. In the present formalism, the kinematic Sunyaev-Zeldovich effect for the cluster of galaxies with a peculiar velocity β is derived in a straightforward manner by the Lorentz boost of the generalized Kompaneets equation. We give an analytic expression for the kinematic Sunyaev-Zeldovich effect, which is valid up to O(β2) with the power series expansion approximation in terms of θe ≡ kBTe/mc2, where Te and m are the electron temperature and the electron mass, respectively. It is found that the relativistic corrections to the kinematic Sunyaev-Zeldovich effect are significant. For a typical electron temperature kBTe = 10 keV, one obtains -8.2% and +1.3% corrections from the O(βθe) and O(βθ2e) contributions, respectively. The O(β2) correction is extremely small: +0.2% for β = 1/300 at kBTe = 10 keV. Therefore it can be safely neglected. These relativistic corrections are directly reflected on the determination of the peculiar velocity β of the cluster of galaxies with the observation of the kinematic Sunyaev-Zeldovich effect.

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. 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.

Neutrino reaction cross sections on 12C target

Abstract In view of the importance of 12 C targets as detectors of astrophysical neutrinos, we present new estimates of the cross sections for the neutrino-induced superallowed transitions on 12 C, with a particular emphasis on the neutral-current induced reactions. The present calculation is made in a model-independent manner with a direct evaluation of the nuclear matrix element from the experimental data. Application to the astrophysical neutrino detection is also briefly discussed.

Neutrino energy loss in stellar interiors. IV: Plasma neutrino process for strongly degenerate electrons

The neutrino energy-loss rates due to plasma neutrino process are calculated for strongly degenerate electrons by using the accurate relativistic dispersion relations for the longitudinal and transverse plasmons. The calculated plasma neutrino energy loss rates are generally valid for relativistically degenerate electrons as well as for nonrelativistically degenerate electrons. The ratio of the result of the present calculation to that of the previous calculations ranges between 0.39 and 3.22 depending upon densities and temperatures. The results of the calculation are expressed by an analytical fitting formula

Relativistic Corrections to the Sunyaev-Zeldovich 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-Zeldovich 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 ≤ θe ≤ 0.05 and 0 ≤ X ≤ 20, where θe ≡ kBTe/mec2, X ≡ ω/kBT0, Te is the electron temperature, ω is the angular frequency of the photon, and T0 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-Zeldovich effect for high-temperature galaxy clusters.

Electrical and thermal conductivities of dense matter in the crystalline lattice phase. II: Impurity scattering

The impurity scattering contributions to the electrical and thermal resistivities of the dense matter in the crystalline lattice phase are calculated. This is the dominant contribution to the resistivity at sufficiently low temperatures. The calculated results nicely reproduce the empirical rules observed for terrestrial binary alloys. The numerical results are written in the form of analytic formulae to facilitate applications

Electrical and thermal conductivities of dense matter in the crystalline lattice phase. III: Inclusion of lower densities

The electrical and thermal conductivities of dense matter in the crystalline lattice phase due to phonon scattering are calculated including the lower densities 10 0 -10 4 g cm −3 . By this inclusion the data on the electrical and thermal conductivities of dense matter in the crystalline lattice phase will be complete for the density range 10 0.0 -10 12.7 g cm −3 . Analytic fitting formulae are given to facilitate applications of the present numerical results