Neutrino transport in type II supernovae: Boltzmann solver vs. Monte Carlo method

We have coded a Boltzmann solver based on a finite difference scheme (S_N method) aiming at calculations of neutrino transport in type II supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been made for realistic atmospheres of post bounce core models under the assumption of a static background. We have also investigated in detail the dependence of the results on the numbers of radial, angular, and energy grid points and the way to discretize the spatial advection term which is used in the Boltzmann solver. A general relativistic calculation has been done for one of the models. We find overall good agreement between the two methods. However, because of a relatively small number of angular grid points (which is inevitable due to limitations of the computation time) the Boltzmann solver tends to underestimate the flux factor and the Eddington factor outside the (mean) ``neutrinosphere'' where the angular distribution of the neutrinos becomes highly anisotropic. This fact suggests that one has to be cautious in applying the Boltzmann solver to a calculation of the neutrino heating in the hot-bubble region because it might tend to overestimate the local energy deposition rate. A comparison shows that this trend is opposite to the results obtained with a multi-group flux-limited diffusion approximation of neutrino transport. The accuracy of the Boltzmann solver can be considerably improved by using a variable angular mesh to increase the angular resolution in the semi-transparent regime.Comment: 19 pages, 17 figures, submitted to A&

Exploring Hadron Physics in Black Hole Formations: a New Promising Target of Neutrino Astronomy

The detection of neutrinos from massive stellar collapses can teach us a lot not only about source objects but also about microphysics working deep inside them. In this study we discuss quantitatively the possibility to extract information on the properties of dense and hot hadronic matter from neutrino signals coming out of black-hole-forming collapses of non-rotational massive stars. Based on our detailed numerical simulations we evaluate the event numbers for SuperKamiokande with neutrino oscillations being fully taken into account. We demonstrate that the event numbers from a Galactic event are large enough not only to detect it but also to distinguish one hadronic equation of state from another by our statistical method assuming the same progenitor model and non-rotation. This means that the massive stellar collapse can be a unique probe into hadron physics and will be a promising target of the nascent neutrino astronomy.Comment: 7 pages, 3 figures, accepted for publication in PR

A new baryonic equation of state at sub-nuclear densities for core-collapse simulations

We calculate a new equation of state for baryons at sub-nuclear densities meant for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with the thermodynamic quantities. The formulation is the NSE description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with the atomic number up to ~ 1000. We have also taken into account the pasta phase, thanks to which the transition to uniform nuclear matter in our EOS occurs in the conventional manner: nuclei are not dissociated to nucleons but survive right up to the transition to uniform nuclear matter. We find that the free energy and other thermodynamical quantities are not very different from those given in the Shen's EOS, one of the standard EOS's that adopt the single nucleus approximation. The average mass is systematically different, on the other hand, which may have an important ramification to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far. The EOS table is currently under construction, which will include the weak interaction rates.Comment: 34 pages, 11 figures, Accepted for publication Ap

A CONSIDERATION OF QUANTITATIVE EVALUATION OF DEXTERITY IN SPORTS EXERCISE

The aim of this study was to quantitatively evaluate dexterity on athletic motions. Subjects were three skilled and three non-skilled weight lifters. They performed power clean that is a strength-training motion. We measured trajectories of joints by using motion capture system, and calculated joint torque according to dynamical equations using only kinematic data. In order to evaluate the strength of stretch reflex and that of proprioceptive feedbacks, we employed curve fitting with the recursive least squares method in our proposed torque model that includes a term caused by stretch reflex and feedback terms with respect to the COP and COM position. The results show that the calculated coefficients reflect some dexterous behavior of skilled motions