Boltzmann equations for neutrinos with flavor mixings

With a view of applications to the simulations of supernova explosion and proto neutron star cooling, we derive the Boltzmann equations for the neutrino transport with the flavor mixing based on the real time formalism of the nonequilibrium field theory and the gradient expansion of the Green function. The relativistic kinematics is properly taken into account. The advection terms are derived in the mean field approximation for the neutrino self-energy whiles the collision terms are obtained in the Born approximation. The resulting equations take the familiar form of the Boltzmann equation with corrections due to the mixing both in the advection part and in the collision part. These corrections are essentially the same as those derived by Sirera et al. for the advection terms and those by Raffelt et al. for the collision terms, respectively, though the formalism employed here is different from theirs. The derived equations will be easily implemented in numerical codes employed in the simulations of supernova explosions and proto neutron star cooling.Comment: 14 pages, 2 figures, REVTeX, to be published in Physical Review

Linear analysis on the growth of non-spherical perturbations in supersonic accretion flows

We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind the application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch & Ott (2013) demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without the fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 $\mathrm{M_\odot}$ progenitor model by Woosley & Heger (2007), which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically showed that the growth rate is proportional to $l$, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.Comment: 11 pages, 9 figures, accepted for publication in The Astrophysical Journa

The Evolution and Impacts of Magnetorotational Instability in Magnetized Core-Collapse Supernovae

We carried out 2D-axisymmetric MHD simulations of core-collapse supernovae for rapidly-rotating magnetized progenitors. By changing both the strength of the magnetic field and the spatial resolution, the evolution of the magnetorotational instability (MRI) and its impacts upon the dynamics are investigated. We found that the MRI greatly amplifies the seed magnetic fields in the regime where not the Alfv\'en mode but the buoyant mode plays a primary role in the exponential growth phase. The MRI indeed has a powerful impact on the supernova dynamics. It makes the shock expansion faster and the explosion more energetic, with some models being accompanied by the collimated-jet formations. These effects, however, are not made by the magnetic pressure except for the collimated-jet formations. The angular momentum transfer induced by the MRI causes the expansion of the heating region, by which the accreting matter gain an additional time to be heated by neutrinos. The MRI also drifts low-$Y_p$ matter from the deep inside of the core to the heating region, which makes the net neutrino heating rate larger by the reduction of the cooling due to the electron capture. These two effects enhance the efficiency of the neutrino heating, which is found to be the key to boost the explosion. Indeed we found that our models explode far more weakly when the net neutrino heating is switched off. The contribution of the neutrino heating to the explosion energy could reach 60\% even in the case of strongest magnetic field in the current simulations.Comment: 17 pages, 18 figures, ApJ in pres

Possible Signatures of Ejecta-Companion Interaction in iPTF 13bvn

We investigate the possible effects of the supernova ejecta hitting the companion star in iPTF 13bvn, focusing on the observable features when it becomes visible. iPTF 13bvn is a type Ib supernova that may become the first case that its progenitor is identified as a binary by near future observations. According to calculations by Bersten et al. (2014), the progenitor should have a mass $\approx3.5M_\odot$ to reproduce the supernova light curve, and such compact stars could only be produced via binary evolution. This is one of the reasons that we expect the progenitor to be a binary, but it should be confirmed by observing the remaining companion after the supernova. Their evolutionary calculations suggest that the companion star will be an overluminous OB star at the moment of supernova. With a combination of hydrodynamical and evolutionary simulations, we find that the secondary star will be heated by the supernova ejecta and expand to have larger luminosities and lower surface effective temperatures. The star will look rather like a red super giant, and this should be taken into account when searching for the companion star in the supernova ejecta in future observations.Comment: few corrections made, published in Ap

Regular and non-regular solutions of the Riemann problem in ideal magnetohydrodynamics

We have built a code to numerically solve the Riemann problem in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition to investigate a variety of solutions more thoroughly. The code can handle not only regular solutions, in which no intermediate shocks are involved, but also all types of non-regular solutions if any. As a first application, we explored the neighborhood of the initial condition that was first picked up by Brio & Wu (1988) and has been frequently employed in the literature as a standard problem to validate numerical codes. Contrary to the conventional wisdom that there will always be a regular solution, we found an initial condition, for which there is no regular solution but a non-regular one. The latter solution has only regular solutions in its neighborhood and actually sits on the boundary of regular solutions. This implies that the regular solutions are not sufficient to solve the ideal MHD Riemann problem and suggests that at least some types of non-regular solutions are physical. We also demonstrate that the non-regular solutions are not unique. In fact, we found for the Brio & Wu initial condition that there are uncountably many non-regular solutions. This poses an intriguing question: why a particular non-regular solution is always obtained in numerical simulations? This has important ramifications to the discussion of which intermediate shocks are really admissible.Comment: 32 pages, 12 figures, accepted for publication in Journal of Plasma Physic

Systematic Analysis of the Effects of Mode Conversion on Thermal Radiation from Neutron Stars

In this paper, we systematically calculate the polarization in soft X-rays emitted from magnetized neutron stars, which are expected to be observed by the next-generation X-ray satellites. Magnetars are one of the targets for these observations. This is because thermal radiation is normally observed in the soft X-ray band, and it is thought to be linearly polarized because of different opacities for two polarization modes of photons in the magnetized atmosphere of neutron stars and the dielectric properties of the vacuum in strong magnetic fields. In their previous study, Taverna et al. illustrated how strong magnetic fields influence the behavior of the polarization observables for radiation propagating in vacuo without addressing a precise, physical emission model. In this paper, we pay attention to the conversion of photon polarization modes that can occur in the presence of an atmospheric layer above the neutron star surface, computing the polarization angle and fraction and systematically changing the magnetic field strength, radii of the emission region, temperature, mass, and radii of the neutron stars. We confirmed that if plasma is present, the effects of mode conversion cannot be neglected when the magnetic field is relatively weak, $B \sim 10^{13} \mathrm{G}$. Our results indicate that strongly magnetized ($B \gtrsim 10^{14} \mathrm{G}$) neutron stars are suitable to detect polarizations, but not-so-strongly magnetized ($B \sim 10^{13} \mathrm{G}$) neutron stars will be the ones to confirm the mode conversion.Comment: 34 pages, 29 figures, published in The Astrophysical Journa

Vacuum Polarization and Photon Propagation in an Electromagnetic Plane Wave

The QED vacuum polarization in external monochromatic plane-wave electromagnetic fields is calculated with spatial and temporal variations of the external fields being taken into account. We develop a perturbation theory to calculate the induced electromagnetic current that appears in the Maxwell equations, based on Schwinger's proper-time method, and combine it with the so-called gradient expansion to handle the variation of external fields perturbatively. The crossed field, i.e., the long wavelength limit of the electromagnetic wave is first considered. The eigenmodes and the refractive indices as the eigenvalues associated with the eigenmodes are computed numerically for the probe photon propagating in some particular directions. In so doing, no limitation is imposed on the field strength and the photon energy unlike previous studies. It is shown that the real part of the refractive index becomes less than unity for strong fields, the phenomenon that has been known to occur for high-energy probe photons. We then evaluate numerically the lowest-order corrections to the crossed-field resulting from the field variations in space and time. It is demonstrated that the corrections occur mainly in the imaginary part of the refractive index.Comment: 50 pages, 17 figures, accepted for publication in Progress of Theoretical and Experimental Physic

Exact Riemann solver for ideal magnetohydrodynamics that can handle all types of intermediate shocks and switch-on/off waves

We have built a code to obtain the exact solutions of Riemann problems in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code can handle not only regular waves but also switch-on/off rarefactions and all types of non-regular shocks: intermediate shocks and switch-on/off shocks. Furthermore, the initial conditions with vanishing normal or transverse magnetic fields can be handled although the code is partly based on the algorithm proposed by Torrilhon (2002) (Torrilhon 2002 Exact Solver and Uniqueness Condition for Riemann problems of Ideal Magnetohydrodynamics. Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich), which cannot deal with all types of non-regular waves nor the initial conditions without normal or transverse magnetic fields. Our solver can find all the solutions for a given Riemann problem and hence, as demonstrated in this paper, one can investigate the structure of the solution space in detail. Therefore the solver is a powerful instrument to solve the outstanding problem of the existence and uniqueness of solutions of MHD Riemann problems. Moreover, the solver may be applied to numerical MHD schemes like the Godunov scheme in the future.Comment: 32 pages, 9 figures, accepted for publication in Journal of Plasma Physic

A Hydrodynamical Study on the Conversion of Hadronic Matter to Quark Matter: I. Shock-Induced Conversion

We study transitions of hadronic matter (HM) to 3-flavor quark matter (3QM) locally, regarding the conversion processes as combustion and describing them hydrodynamically. Not only the jump condition on both sides of the conversion front but the structures inside the front are also considered by taking into account what happens during the conversion processes on the time scale of weak interactions as well as equations of state (EOS's) in the mixed phase. Under the assumption that HM is metastable with their free energies being larger than those of 3QM but smaller than those of 2-flavor quark matter (2QM), we consider the transition via 2QM triggered by a rapid density rise in a shock wave. Based on the results, we discuss which combustion modes (strong/weak detonation) may be realized. HM is described by an EOS based on the relativistic mean field theory and 2, 3QM's are approximated by the MIT bag model. We demonstrate for a wide range of bag constant and strong coupling constant in this combination of EOS's that the combustion may occur in the so-called endothermic regime, in which the Hugoniot curve for combustion runs below the one for the shock wave in P-V plane, and which has no terrestrial counter part. We find that strong detonation always occurs. Depending on the EOS of quark matter (QM) as well as the density of HM and the Mach number of the detonation front, deconfinement from HM to 2QM is either completed or not completed in the shock wave. In the latter case, which is more likely if the EOS of QM ensures that deconfinement occurs above the nuclear saturation density and that the maximum mass of cold quark stars is larger than two solar mass, the conversion continues further via the mixing state of HM and 3QM on the time scale of weak interactions.Comment: 44 pages, 18 figures, accepted for publication in PR

A Hydrodynamical Study on the Conversion of Hadronic Matter to Quark Matter: II. Diffusion-Induced Conversion

We study transitions of hadronic matter (HM) to 3-flavor quark matter (3QM), regarding the conversion processes as combustion and describing them hydrodynamically. Under the assumption that HM is metastable with their free energies being larger than those of 3QM but smaller than those of 2-flavor quark matter (2QM), we consider in this paper the conversion induced by diffusions of seed 3QM. This is a sequel to our previous paper, in which the shock-induced conversion was studied in the same frame work. We not only pay attention to the jump condition on both sides of the conversion front but the structures inside the front are also considered by taking into account what happens during the conversion processes on the time scale of weak interactions. We employ for HM the Shen's EOS, which is based on the relativistic mean field theory, and the bag model-based EOS for QM just as in the previous paper. We demonstrated in that paper that in this combination of EOS's the combustion will occur for a wide range of the bag constant and strong coupling constant in the so-called endothermic regime, in which the Hugoniot curve for combustion runs below the initial state. We find that weak deflagration nearly always occurs and that weak detonation is possible only when the diffusion constant is (unrealistically) large and the critical strange fraction is small. The velocities of the conversion front are ~ $10^3-10^7$ cm/s depending on the initial temperature and density as well as the parameters in the QM EOS and become particularly small when the final state is in the mixed phase. Finally we study linear stability of the laminar weak-deflagration front and find that it is unstable in the exothermic regime (Darrius-Landau instability) but stable in the endothermic regime, which is quite contrary to the ordinary combustions.Comment: 36 pages, 21 figures, accepted for publication in PR