arXiv subjects

Yasuharu Kohyama

Publications and source records attributed to Yasuharu Kohyama.

At least 19 recordsLinked to original sources

arXiv2014

Relativistic corrections to the Kompaneets equation

We study the Sunyaev-Zeldovich effect for clusters of galaxies. We explore the relativistic corrections to the Kompaneets equation in terms of two different expansion approximation schemes, namely, the Fokker-Planck expansion approximation and delta function expansion approximation. We show that two expansion approximation formalisms are equivalent under the Thomson approximation, which is extremely good approximation for the CMB photon energies. This will clarify the situation for existing theoretical methods to analyse observation data.

astro-ph.CO↗

arXiv2014

Analytical studies on the Sunyaev-Zeldovich effect in the cluster of galaxies for three Lorentz frames II: single integral formula

We study the Sunyaev-Zeldovich effect for clusters of galaxies. The Boltzmann equations for the cosmic microwave background photon distribution function are studied in three Lorentz frames. We extend the previous work and derive analytic expressions for the integrated photon redistribution functions over the photon frequency. We also derive analytic expressions in the power series expansion approximation. By combining two formulas, we offer a simple and accurate tool to analyse observation data. These formulas are applicable to the non-thermal electron distributions as well as the standard thermal distribution. The Boltzmann equation is reduced to a single integral form of the electron velocity.

astro-ph.CO↗

arXiv2013

Analytical studies on the Sunyaev Zeldovich effect in the cluster of galaxies for three Lorentz frames

We study the Sunyaev-Zeldovich effect for clusters of galaxies. The Boltzmann equations for the CMB photon distribution function are studied in three Lorentz frames. We clarify the relations of the SZ effects among the different Lorentz frames. We derive analytic expressions for the photon redistribution functions. These formulas are applicable to the nonthermal electron distributions as well as the standard thermal distribution. We show that the Fokker-Planck expansion of the Boltzmann equation can be expanded by the power series of the diffusion operator of the original Kompaneets equation.

astro-ph.CO↗

arXiv2011

Knee structure in high-energy inverse Compton scattering of CMB photons

We study the inverse Compton scattering of the CMB photons off nonthermal high-energy electrons. In the previous study, assuming the power-law distribution for electrons, we derived the analytic expression for the spectral intensity function $I(ω)$ in the Thomson approximation, which was applicable up to the photon energies of $ω<$ O(GeV). In the present paper, we extend the previous work to higher photon energies of $ω>$ O(GeV) by taking into account the terms dropped in the Thomson approximation, i.e., the Klein-Nishina formula. The analytic expression for $I(ω)$ is derived with the Klein-Nishina formula. It is shown that $I(ω)$ has a "knee" structure at $ω=$ O(PeV). The knee, if exists, should be accessible with gamma-ray observatories such as Fermi-LAT. We propose simple analytical formulae for $I(ω)$ which are applicable to wide photon energies from Thomson region to extreme Klein-Nishina region.

astro-ph.CO↗

arXiv2010

Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies. II. comparison of covariant formalisms

We study a covariant formalism for the Sunyaev-Zeldovich effects developed in the previous papers by the present authors, and derive analytic expressions for the redistribution functions in the Thomson approximation. We also explore another covariant formalism recently developed by Poutanen and Vurm. We show that the two formalisms are mathematically equivalent in the Thomson approximation which is fully valid for the cosmic microwave background photon energies. The present finding will establish a theoretical foundation for the analysis of the Sunyaev-Zeldovich effects for the clusters of galaxies.

astro-ph.CO↗

arXiv2010

Scaling Laws in High-Energy Inverse Compton Scattering. II. Effect of Bulk Motions

We study the inverse Compton scattering of the CMB photons off high-energy nonthermal electrons. We extend the formalism obtained by the previous paper to the case where the electrons have non-zero bulk motions with respect to the CMB frame. Assuming the power-law electron distribution, we find the same scaling law for the probability distribution function P_{1,K}(s) as P_{1}(s) which corresponds to the zero bulk motions, where the peak height and peak position depend only on the power-index parameter. We solved the rate equation analytically. It is found that the spectral intensity function also has the same scaling law. The effect of the bulk motions to the spectral intensity function is found to be small. The present study will be applicable to the analysis of the X-ray and gamma-ray emission models from various astrophysical objects with non-zero bulk motions such as radio galaxies and astrophysical jets.

astro-ph.CO↗

arXiv2010

Scaling Laws in High-Energy Inverse Compton Scattering

Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the inverse Compton scattering process for high-energy nonthermal electrons. Assuming the power-law electron distribution, we find a scaling law in the probability distribution function P_1(s), where the peak height and peak position depend only on the power index parameter. We solved the rate equation analytically. It is found that the spectral intensity function also has the scaling law, where the peak height and peak position depend only on the power index parameter. The present study will be particularly important to the analysis of the X-ray and gamma-ray emission models from various astrophysical objects such as radio galaxies and supernova remnants.

astro-ph.CO↗

arXiv2009

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

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.

astro-ph.CO↗

arXiv2009

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

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.

astro-ph.CO↗

arXiv2008

The Second Born Corrections to the Electrical and Thermal Conductivities of Dense Matter in the Liquid Metal Phase

The second Born corrections to the electrical and thermal conductivities are calculated for the dense matter in the liquid metal phase for various elemental compositions of astrophysical importance. Inclusion up to the second Born corrections is sufficiently accurate for the Coulomb scattering of the electrons by the atomic nuclei with Z < 26. Our approach is semi-analytical, and is in contrast to that of the previous authors who have used fully numerical values of the cross section for the Coulomb scattering of the electron by the atomic nucleus. The merit of the present semi-analytical approach is that this approach affords us to obtain the results with reliable Z-dependence and ρ-dependence. The previous fully numerical approach has made use of the numerical values of the cross section for the scattering of the electron off the atomic nucleus for a limited number of Z-values, Z=6, 13, 29, 50, 82, and 92, and for a limited number of electron energies, 0.05MeV, 0.1MeV, 0.2MeV, 0.4MeV, 0.7MeV, 1MeV, 2MeV, 4MeV, and 10MeV. Our study, however, has confirmed that the previous results are sufficiently accurate. They are recovered, if the terms higher than the second Born terms are taken into account. We make a detailed comparison of the present results with those of the previous authors. The numerical results are parameterized in a form of analytic formulae that would facilitate practical uses of the results. We also extend our calculations to the case of mixtures of nuclear species. The corresponding subroutine can be retrieved from http://www.ph.sophia.ac.jp/~itoh-ken/subroutine/subroutine.htm

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arXiv2007

Relativistic Thermal Bremsstrahlung Gaunt Factor for the Intracluster Plasma. III. Analytic Fitting Formula for the Nonrelativistic Exact Gaunt Factor

We present an accurate analytic fitting formula for the thermal bremsstrahlung Gaunt factor in the nonrelativistic limit. The fitting formula excellently reproduces the numerical results of the calculation carried out by the present authors using the method of Karzas and Latter. The present analytic fitting formula will be useful for the analysis of the X-ray emission which comes from the intracluster plasmas with relatively low temperatures as well as the other X-ray sources.

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arXiv2007

Relativistic Thermal Bremsstrahlung Gaunt Factor for the Intracluster Plasma. II. Analytic Fitting Formulae

We present accurate analytic fitting formulae which summarize the results of the recent calculation by Nozawa, Itoh and Kohyama on the relativistic thermal bremsstrahlung Gaunt factor for the intracluster plasma. The fitting is carried out for Z = 1 to 28, 6.0 < log T < 8.5, -4.0 < log (omega/kT) < 1.0, where Z is the charge number of the ion, T is the temperature, and omega is the angular frequency of the emitted photon. The present analytic fitting formulae will be useful for the analysis of the X-ray emission which comes from the intracluster plasma as well as the other X-ray sources.

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arXiv2005

Relativistic Corrections to the Sunyaev-Zeldovich Effect for Clusters of Galaxies. V. Effect of the Motion of the Observer

We extend the formalism of the relativistic thermal and kinematical Sunyaev-Zeldovich effects to the observer's system (the Solar System) moving with a velocity $β_{S}$ with respect to the cosmic microwave background radiation. We confirm the results recently obtained by Chluba, Huetsi, and Sunyaev in the lowest order of the observer's velocity $β_{S}. We give a more general analytic expression for the thermal and kinematical Sunyaev-Zeldovich effects corresponding to the observer's system with the power series expansion approximation in terms of $θ_{e}$. It is found that the effect of the motion of the observer on the Sunyaev-Zeldovich effect will become important in the future high precision observation projects of the Sunyaev-Zeldovich effect.

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arXiv2001

Relativistic corrections to the multiple scattering effect on the Sunyaev-Zel'dovich effect in the isotropic approximation

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 in the isotropic approximation. We present the results of the calculations by the Fokker-Planck expansion method as well as by the direct numerical integration of the collision term of the Boltzmann equation. The multiple scattering contribution is found to be very small compared with the single scattering contribution. For high-temperature galaxy clusters of kT=15keV, the ratio of the both contributions is -0.2% 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.

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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.

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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.

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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.

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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.

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