Neutrino transport with isoenergetic and neutrino-electron scattering

Solution to steady-state, bigroup neutrino transport with isoenergetic and neutrino-electron scattering have been obtained for idealized conditions representative of the outer core or envelope of a star whose inner core is undergoing gravitational collapse. The solutions are presented in a form suitable for comparison with other numerical schemes. The incident neutrino distribution was chosen to be nonequilibrium, and the solutions clearly show the tendency of the neutrinos to equilibrate via neutrino-electron scattering as they propagate through the material. Care is taken to compare solutions obtained by two completely different techniques to ensure that the solutions presented here are accurate and error free. The solutions are compared with those obtained by a simple diffusion scheme, and by a flux limited diffusion scheme. The solutions given by the latter agree well with the solutions derived here, except when the neutrino angular distribution becomes oblate.     

Exact solution of the equation for the problem of diffuse reflection and transmission with a scattering function ω0(1 +x cos⊙) by the method of laplace transform and theory of linear singular integral equation

Neutrinos couple through a weak neutral current to the density of matter, in particular to the neutron density. Density fluctuations, or phonons, in the neutron fluid may be emitted or absorbed by neutrinos passing through the matter. At high densities, temperatures and neutrino energies the neutrino mean free paths for phonon emission and absorption can be 10⁶ cm. Significant changes in the neutrino momentum and energy accompany these processes. We present a model calculation for neutrino scattering by phonons, and representative numerical results for the neutrino mean free path and mean energy and momentum changes fork _B T andE _v both ranging from 1 to 27 MeV.Research supported by the National Research Council of Canada.     

A numerical model for Type II supernovae — The collapse stage

We use the following numerical model for the collapse stage of a Type II supernova of 15 M_⊙. Our electron capture rate includes the effects of the inverse reaction and the neutron-proton mass difference. This decreases the electron density at the collapse stage and led to rather large values of the maximum inward velocity and of the corresponding mass (Umax = 3.06 × 10⁹cm/s, Mmax=0.76 M_⊙). These larger values are more favourable for the propagation of shock after the rebounce and the triggering-off of a Type-II supernova explosion. For neutrino transport, we use a leakage model and an equilibrium diffusion model, respectively, for the thin and thick stages and a grey atmosphere model to assess the effect of neutrino precipitation on the collapse. We found this effect to be small, the energy precipitation to be not more than 10^?5 the neutrino energy loss and the momentum precipitation not more than 10^?6 the gravitational acceleration.     

The neutrino radiation for a hot neutron star formation and the envelope outburst problem

With the equations of neutrino heat conductivity being used, the neutrino light curve is calculated for the spherically symmetrical collapse of an iron-oxygen 2M star (Figure 1) up to the formation of a hot hydrostatically equilibrium neutron star. The total energy, radiated in the form of muon and electron neutrinos, is 5.8×10⁵³ erg (0.16Mc ²). The mean neutrino particle energy is 12 MeV for all the time the collapse proceeds. The maximum neutrino luminosity value is equal to 3×10⁵³ erg s^–1. For a 10M star collapse, the luminosity maximum 3×10⁵⁴ erg s^–1 takes place just at the moment of the formation of a black hole inside the collapsing star. The total radiated energy in this case is about 0.08Mc ². The set of calculations, allowing for the deposition of momentum by means of neutrino-nuclear coherent scattering, brings us to a conclusion that the envelope outburst is only possible if the scattering cross-section is 50 times larger than the value experimentally accepted (inequality 20)).     

Neutrino chemical potential and neutrino heat conductivity with allowance for neutrino scattering

The equations of neutrino hydrodynamics are derived in two different approximations taking into consideration the neutrino scattering from stellar material. In a thermal-conductivity approximation which holds good when neutrino optical depth with respect to absorption exceeds 1, the neutrino scattering is taken into account, analogously with photon radiative conductivity, by introducing the transport cross-section in the neutrino mean free path. In a practically important case when the neutrino optical thickness with respect to scattering is high enough, whereas that concerning absorption is sufficiently low, another approximation of Comptonized neutrinos is valid. In this case, the neutrino and antineutrino chemical potentials are independent of each other. They have to be calculated from equations of continuity established for neutrino and antineutrino alongside with the diffusion equation expressing the law of lepton-charge conservation. The equations of neutrino hydrodynamics are written out both with and without inclusion of muon neutrinos and antineutrinos.The equations obtained are established to deal properly with neutrino diffusion inside collapsing stars.     

Non-zero rest mass neutrinos and the cosmological constant

Recently it was pointed out that a non-zero cosmological constant can play a role in the formation of neutrino halos only in the case of neutrinos of very low rest mass (m _v <-0.1eV). However, phase-space considerations would requirem _v >50 eV if neutrinos dominate the missing mass in halos of large spiral galaxies and moreoverm _v >200 eV is implied in the case of dwarf spheroidals. These larger neutrino masses would be in conflict with observed constraints on the age of the Universe unless a cosmological constant is invoked.     

Dirac neutrino magnetic moment and possible time evolution of the neutrino signal from a supernova

We analyze the influence of neutrino helicity conversion, ν _L → ν _R, on the neutrino flux from a supernova attributable to the interaction of the Dirac neutrino magnetic moment with a magnetic field.We show that if the neutrino has a magnetic moment in the interval 10⁻¹³μ_B < μ_ν < 10⁻¹²μ_B and provided that a magnetic field of ∼10¹³–10¹⁴ G exists in the supernova envelope, a peculiar kind of time evolution of the neutrino signal from the supernova attributable to the resonance transition ν _L → ν _R in the magnetic field of the envelope can appear.     

Revision and recalibration of existing shock classifications for quartzose rocks using low‐shock pressure (2.5–20 GPa) recovery experiments and mesoscale numerical modeling

A combination of shock recovery experiments and numerical modeling of shock deformation in the low‐shock pressure range from 2.5 to 20 GPa for two dry sandstone types of different porosity, a completely water‐saturated sandstone, and a well‐indurated quartzite provides new insights into strongly heterogeneous distribution of different shock features. (1) For nonporous quartzo‐feldspathic rocks, the traditional classification scheme (Stöffler 1984 ) is suitable with slight changes in pressure calibration. (2) For water‐saturated quartzose rocks, a cataclastic texture (microbreccia) seems to be typical for the shock pressure range up to 20 GPa. This microbreccia does not show formation of PDFs but diaplectic quartz glass/SiO₂ melt is formed at 20 GPa (~1 vol%). (3) For porous quartzose rocks, the following sequence of shock features is observed with progressive increase in shock pressure (1) crushing of pores, (2) intense fracturing of quartz grains, and (3) increasing formation of diaplectic quartz glass/SiO₂ melt replacing fracturing. The formation of diaplectic quartz glass/SiO₂ melt, together with SiO₂ high‐pressure phases, is a continuous process that strongly depends on porosity. This experimental observation is confirmed by our concomitant numerical modeling. Recalibration of the shock classification scheme results in a porosity versus shock pressure diagram illustrating distinct boundaries for the different shock stages.     

The neutrino radiation of collapsing stellar cores and the neutrino burst detected from SN 1987 A

The properties of the neutrino burst generated by massive 1.5–2M collapsing stellar iron-oxygen cores are discussed. Special attention is given to the neutrino heat conductivity theory which allows us to calculate the transport of neutrinos through the collapsing stellar core up to the formation and during the first seconds of cooling of a hot hydrostatic neutron star. The theoretical predictions seem to be in good agreement with both the KAMIOKANDE II and IMB data on the neutrino burst detected from SN 1987A. The most reliable constraint on the neutrino rest mass is shown to bem _v <20–30eV, while the safest upper limit on the neutrino magnetic moment, µ _v < 10^–11 Bohr magnetons, results rather from the cooling of white dwarfs than from the SN 1987A neutrino data.Presented to the 13th International Conference Neutrino-88, Boston, U.S.A., 5–11 June, 1988.     

Chemical potential effects on neutrino diffusion in supernovae

Typically collapsing supernova hydrodynamic computations assume LTE neutrino transport andimpose photon-like behavior, i.e., fix the neutrino chemical potentials at zero. The validity of the latter condition is investigated in the diffusion approximation to transport. A coupled system of diffusion equations for energy and lepton number is solved in a collapsing supernova ambience. The results indicate a substantial growth in the neutrino chemical potential for densities above 10¹² gm cm^?3. The rate of energy transport is affected significantly by the concomitant increases in Fermi integrals and gradients in chemical potential counter to those of temperature. It is found that the extent of neutrino particle/antiparticle interaction also affects energy diffusion rates. Thus the photon-like condition on neutrino transport may misrepresent supernova energetics substantially. An extension of the usual Sn transport to include lepton characteristics is deemed necessary for a definitive answer to the neutrino transport supernova question.     

Novel Diagnostic of Shock Fronts in Low-Z Dense Plasmas

We performed an experiment using high-energy protons to characterize in situ the spatial and temporal evolution of a laser-driven shock propagating through a low-Z material. Radiography of the shock propagating through the low-Z transparent material (Lexan, quartz, diamond) enabled estimation of density under compression. In order to discriminate the influence of the shocked matter on the protons trajectory, a Monte-Carlo simulation was developed. This code describes the protons trajectory through the matter, calculating the scattering angle and the loss of energy.     

Dark matter-systematics of its distribution

The dynamical masses of dwarf-spheroidals, spiral and elliptical galaxies, dwarf irregular binaries, groups of galaxies and clusters are shown to lie in a band about the M ∼ ρR³ line. The value of ρ is approximately the same as that estimated for unseen matter in the solar neighbourhood. The clusters themselves lie about theM ∼ R ^-3 line derived for a self-gravitating neutrino gas; their masses are distributed around the maximum Jeans-mass, M_Jmax. corresponding to m_v - 10 eV in an expanding universe. The present day length scales of clusters and the dispersion in the velocities observed within them are understood in terms of a 100-fold expansion subsequent to the initial growth of the fluctuations at M_Jmax. These systematics on theR-M plane imply that the initial condensations in the expanding universe are on the scale of the rich clusters of galaxies, these condensations were triggered dominantly by the gravitation of the neutrinos and the constant density of al systems arises naturally due to the embedding of these systems in the large scale neutrino condensations. If the neutrino density falls off asr ^-2 beyond the cluster edge till the distributions from different clusters overlap, then the mean density of the neutrinos approximately equals the closure density of the universe.     

New constraints on neutrino masses from cosmology

By combining data from cosmic microwave background (CMB) experiments (including the recent WMAP third year results), large scale structure (LSS) and Lyman-α forest observations, we derive upper limits on the sum of neutrino masses of Σm_ν < 0.17 eV at 95% c.l. We then constrain the hypothesis of a fourth, sterile, massive neutrino. For the third massless +1 massive neutrino case we bound the mass of the sterile neutrino to m_s < 0.26 eV at 95% c.l. These results exclude at high significance the sterile neutrino hypothesis as an explanation of the LSND anomaly. We then generalize the analysis to account for active neutrino masses which tightens the limit to m_s < 0.23 eV and the possibility that the sterile abundance is not thermal. In the latter case, the constraints in the (mass, density) plane are non-trivial. For a mass of >1 eV or <0.05 eV the cosmological energy density in sterile neutrinos is always constrained to be ω_ν < 0.003 at 95% c.l. However, for a sterile neutrino mass of 0.25 eV, ω_ν can be as large as 0.01.     

Neutrino mass,luminosity variation,and spectrum of SN1987A

In this paper, the neutrino mass has been determined from SN1987a observation in a manner that the simultaneity of neutrino emission is not regarded as the starting point, but is itself defined through the analysis by Monte-Carlo simulation. The result is that the neutrino mass lies in 3–4 eV, possiblym _v 3.6 eV. Neutrino luminosity variation and neutrino spectrum are also obtained. Comparison with theories gives further support to the mass determination, and also predicts the mass of progenitor star of SN1987a to be in the range of 12–25M .The project supported by the National Natural Science Foundation of China.     

Quasi-elastic neutrino scattering by nuclei in superdense matter of a collapsing star

The interaction of neutrinos with nuclei in the superdense matter of a collapsing star is studied, taking into account the collective modes and thermal fluctuations of the medium density. It is shown that the elastic neutrino scattering by nuclei with a momentum transfer less than or of the order of the inverse distance between the ions in the nonideal Coulomb plasma, differs considerably from the analogous scattering by a single nucleus. The weak A interaction screening by medium electrons is taken into account. The collision integral and transport cross section of neutrino scattering by nuclei are calculated in terms of macroscopic medium parameters.     

Neutrinooszillationen in Neutronensternmaterie

According to the suggestion of T. J. Mazurek (1979) neutrino oscillations occuring during the dynamic stellar collapse (M ≥ 10M) could be result in a transfer of leptonic zero-point energy to baryons. Then the adiabatic index increases above γ ≥ 4/3, and such an increase is necessary to reverse the collapse. From the theory of neutrino oscillations of B. Pontekorvo (1967) we derive the oszillation length L of neutrinos in vacuum and the characteristic oscillation lengh L^* of neutrinos taking into consideration the refraction index n_e of neutron star matter. The comparison of both oscillation lenghts shows that for electron densities, characteristically of neutron star matter, the oscillation lenght L is considerable larger than the oscillation lenght L^*. Therefore neutrino oscillations cannot influence the scenario for neutrino emission of the neutron star.     

The complete solution for the scattering of polarized light in a Rayleigh and isotropically scattering atmosphere

TheF _N method is used to solve, in a concise manner, the complete problem concerning the diffusion of polarized light in a plane-parallel Rayleigh and isotropically scattering atmosphere.     

Energetic protons from the solar flare of March 24, 1966

Ten to 100 meV protons from the solar flare of March 24, 1966 were observed on the University of California scintillation counter on OGO-I. The short rise and decay times observed in the count rates of the 32 channels of pulse-height analysis show that scattering of the protons by the interplanetary field was much less important in this event than in previously observed proton flares. A diffusion theory in which D = M _r is found to be inadequate to account for the time behavior of the count rates of this event. Small fluctuations of the otherwise smooth decay phase may be due to flare protons reflected from the back of a shock front, which passed the earth on March 23.     

Neutrino processes in dense matter

Expressions for the source and collision terms of the neutrino transport equation relevant to the neutrino transport supernova model are derived in the framework of the theory of neutral currents. In particular we study the capture and emission of neutrini (and anti-neutrini) by free nucleos, the inelastic scattering by free nucleons, the coherent scattering by nuclei, as well as the corresponding muonic processes.We also derive an analytical formula for the neutrino scatteringrate on electrons, valid for large electron degeneracy.     

Time-dependent neutrino transport out of dense stellar cores

Time-dependent neutrino transport out of an optically thick neutronized stellar core is calculated to study the effects of neutrino degeneracy and of source depletion. Neutrino trapping inhibits further neutrino emission until neutrinos peel out of the outer zones of the core, exposing successively inner zones. This inwardly propagating neutrino rarefaction wave can lead toe ^–+pv+n oscillations in chemical composition. The effect of neutrino Fermi statistics is to retard considrably and disperse neutrino leakage out of the core, making neutrino transport insignificant during fast stages of core collapse.Supported in part by the U.S. Department of Energy under Contract EY-76-C-02-3071.