Naoki Itoh

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.

The r-Process in Supernova Explosions from the Collapse of O-Ne-Mg Cores

While the origin of r-process nuclei remains a long-standing mystery, recent spectroscopic studies of extremely metal poor stars in the Galactic halo strongly suggest that it is associated with core-collapse supernovae. In this study we examine r-process nucleosynthesis in a prompt supernova explosion from an 8-10 M☉ progenitor star as an alternative scenario to the neutrino wind mechanism, which has also been considered a promising site of the r-process. In the present model, the progenitor star has formed an oxygen-neon-magnesium (O-Ne-Mg) core (of mass 1.38 M☉) at its center. Its smaller gravitational potential, as well as the smaller core that is in nuclear statistical equilibrium at the time of core bounce, as compared with the iron cores in more massive stars, may allow the star to explode hydrodynamically rather than by delayed neutrino heating. The core-collapse simulations are performed with a one-dimensional, Newtonian hydrodynamic code. We obtain a very weak prompt explosion in which no r-processing occurs. We further simulate energetic prompt explosions by enhancement of the shock-heating energy in order to investigate conditions necessary for the production of r-process nuclei in such events. The r-process nucleosynthesis is calculated using a nuclear reaction network code including relevant neutron-rich isotopes with reactions among them. The highly neutronized ejecta (Ye ≈ 0.14-0.20) lead to robust production of r-process nuclei; their relative abundances are in excellent agreement with the solar r-process pattern. Our results suggest that prompt explosions of 8-10 M☉ stars with O-Ne-Mg cores can be a promising site of r-process nuclei. The mass of the r-process material per event is about 2 orders of magnitude larger than that expected from Galactic chemical evolution studies. We propose, therefore, that only a small fraction of r-process material is ejected via mixing-fallback mechanism of the core matter, wherein most of the r-process material falls back onto the proto-neutron star. A lower limit on the age of the universe is derived by application of the uranium-thorium (U-Th) chronometer pair by comparison with the observed ratio of these species in the highly r-process-enhanced, extremely metal poor star CS 31082-001. The inferred age is 14.1 ± 2.4 Gyr—the same as that obtained previously based on the neutrino wind scenario with the same nuclear mass formula. This suggests that chronometric estimates obtained using the U-Th pair are independent of the astrophysical conditions considered.

THE r-PROCESS IN THE NEUTRINO WINDS OF CORE-COLLAPSE SUPERNOVAE AND U-Th COSMOCHRONOLOGY

The discovery of the second highly r-process-enhanced, extremely metal poor star, CS 31082-001 ([Fe/H] = -2.9) has provided a powerful new tool for age determination by virtue of the detection and measurement of the radioactive species uranium and thorium. Because the half-life of 238U is one-third that of 232Th, the U-Th pair can, in principle, provide a far more precise cosmochronometer than the Th-Eu pair that has been used in previous investigations. In the application of this chronometer, the age of (the progenitor of) CS 31082-001 can be regarded as the minimum age of the Galaxy, and hence of the universe. One of the serious limitations of this approach, however, is that predictions of the production ratio of U and Th have not been made in the context of a realistic astrophysical model of the r-process. We have endeavored to produce such a model, based on the neutrino winds that are expected to arise from the nascent neutron star of a core-collapse supernova. In this model, the proto-neutron star mass and the (asymptotic) neutrino sphere radius are assumed to be 2.0 M☉ and 10 km, respectively. Recent hydrodynamic studies indicate that there may exist difficulties in obtaining such a compact (massive and/or small in radius) remnant. Nevertheless, we utilize this set of parameter choices since previous work suggests that the third r-process peak (and thus U and Th) is hardly reached when one adopts a less compact proto-neutron star in the framework of the neutrino-wind scenario. The temperature and density histories of the material involved in the neutron-capture processes are obtained with the assumption of a steady flow of the neutrino-powered winds, with general relativistic effects taken into account. The electron fraction is taken to be a free parameter, constant with time. The r-process nucleosynthesis in these trajectories is calculated with a nuclear reaction network code including actinides up to Z = 100. The mass-integrated r-process yields, obtained by assuming a simple time evolution of the neutrino luminosity, are compared to the available spectroscopic elemental abundance data of CS 31082-001. As a result, the age of this star is determined to be 14.1 ± 2.5 Gyr, in excellent agreement with lower limits on the age of the universe estimated by other dating techniques, as well as with other stellar radioactive age estimates. Future measurements of Pt and Pb in this star, as well as expansion of searches for additional r-process-enhanced, metal-poor stars (especially those in which both U and Th are measurable), are of special importance to constrain the current astrophysical models for the r-process.

Relativistic corrections to the Sunyaev-Zeldovich effect for extremely hot 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 ≤ θ e ≤ 0.100 and 0 ≤ X < 20, where θ e ≡ k B T e /m e c 2 , X ≡ hω/k B T 0 , T e is the electron temperature, ω 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.

SCREENING CORRECTIONS TO THE ELECTRON CAPTURE RATES IN DENSE STARS BY THE RELATIVISTICALLY DEGENERATE ELECTRON LIQUID

We calculate the screening corrections to the electron capture rates in dense stars by the relativistically degenerate electron liquid. In order to calculate the screening corrections we adopt the linear response theory, which is widely used in the field of solid-state physics and liquid-metal physics. In particular, we use the longitudinal dielectric function for the relativistically degenerate electron liquid derived by Jancovici. We calculate the screening potential at the position of the nucleus. By using this screening potential one can calculate the screening corrections to the electron capture rates. We present accurate analytic fitting formulae which summarize our numerical results. These fitting formulae will facilitate the application of the present results. The screening corrections to the electron capture rates are typically a few percent.

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 semianalytical 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 semianalytical approach is that this approach allows us to obtain the results with a 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, 0.05, 0.1, 0.2, 0.4, 0.7, 1, 2, 4, and 10 MeV. 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 the form of analytic formulae that would facilitate practical use of the results. We also extend our calculations to the case of mixtures of nuclear species.

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

ABSTRA C T 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 kBT e < 15 keV; the ratio of both the contributions is 20.2 per cent in the Wien region. In the Rayleigh ‐ Jeans region the ratio is 20.03 per cent. Therefore the multiple scattering contribution is safely neglected for the observed galaxy clusters.

Evolution of Low-Mass Population III Stars

We present the evolutionary models of metal-free stars in the mass range from 0.8 to 1.2 M☉ with up-to-date input physics. The evolution is followed to the onset of hydrogen mixing into a convection, driven by the helium flash at the red giant or asymptotic giant branch phase. The models of mass M ≥ 0.9 M☉ undergo a central hydrogen flash, triggered by carbon production due to the triple-α reaction. We find that the border of the off-center and central ignition of the helium core flash falls between 1.1 and 1.2 M☉; the models of mass M ≤ 1.1 M☉ experience hydrogen mixing at the tip of the red giant branch, while the models of M = 1.2 M☉ during the helium shell flashes on the asymptotic giant branch. The equation of state for the Coulomb liquid region, where electron conduction and radiation compete, is shown to be important since it affects the thermal state in the helium core and influences the red giant branch evolution. It is also found that the nonresonant term of the triple-α reaction plays an important role, although it has negligible effect on the evolution of stars of younger populations. We compare our models with the computations by several other sets of authors and confirm good agreement, except for one study that finds helium ignition much closer to the center, with important consequences for subsequent evolution.

An improved formula for the relativistic corrections to the kinematical Sunyaev-Zeldovich effect for clusters of galaxies

We improve the calculation of Nozawa, Itoh, and Kohyama (1998) to provide a formula for relativistic corrections to the thermal and kinematical Sunyaev-Zeldovich effects that is accurate to fourth order in theta_e = kT_e/m_ec^2, T_e and m_e being the electron temperature and electron mass, respectively. We also carry out a direct numerical integration of the Boltzmann collision term and confirm the excellent accuracy of the analytic formula. This formula will be useful for the analysis of the observational data of the forthcoming experiments of the kinematical Sunyaev-Zeldovich effect for clusters of galaxies.

Ion-Ion Correlation Effect on the Neutrino-Nucleus Scattering in Supernova Cores

We calculate the ion-ion correlation effect on the neutrino-nucleus scattering in supernova cores, which is an important opacity source for the neutrinos and plays a vital role in supernova explosions. In order to calculate the ion-ion correlation effect we use the results of the improved hypernetted-chain-method calculations of the classical one-component plasma. As in the preceding studies on this effect, we find a dramatic decrease of the effective neutrino-nucleus scattering cross section for relatively low energy neutrinos with Eν ≤ 20 MeV. As a matter of fact, our calculation shows a much more dramatic reduction of the effective neutrino-nucleus scattering cross section for the low-energy neutrinos with Eν ≤ 10 MeV than the results of Horowitz. Therefore, the ion-ion correlation effect will be more important than has hitherto been recognized. We present an accurate analytic fitting formula that summarizes our numerical results. This fitting formula will facilitate the application of the present results to supernova explosion simulations.