Neutrino Transport Research Articles

NUCLEOSYNTHESIS IN CORE-COLLAPSE SUPERNOVA EXPLOSIONS TRIGGERED BY A QUARK-HADRON PHASE TRANSITION

We explore heavy element nucleosynthesis in the explosion of massive stars which are triggered by a quark-hadron phase transition during the early post bounce phase of core-collapse supernovae. The present study is based on general relativistic radiation hydrodynamics simulations with three-flavor Boltzmann neutrino transport in spherical symmetry, which utilize a quark-hadron hybrid equation of state based on the MIT bag model for strange quark matter. The quark-hadron phase transition inside the stellar core forms a shock wave propagating towards the surface of the proto-neutron star. The shock wave results in an explosion and ejects neutron-rich matter which is piled up or accreting on the proto-neutron star. Later, during the cooling phase, the proto-neutron star develops a proton-rich neutrino-driven wind. We present a detailed analysis of the nucleosynthesis outcome in both neutron-rich and proton-rich ejecta and compare our integrated nucleosynthesis with observations of metal poor stars.

Neutral-current neutrino-nucleus cross sections based on relativistic nuclear energy density functional

Background: Inelastic neutrino-nucleus scattering through the weak neutral-current plays an important role in a stellar environment where the transport of neutrinos determines the rate of cooling. Since there are no direct experimental data on neutral-current neutrino-nucleus cross sections available, only the modeling of these reactions provides the relevant input for supernova simulations.Purpose: To establish a fully self-consistent framework for neutral-current neutrino-nucleus reactions based on a relativistic nuclear energy density functional.Methods: Neutrino-nucleus cross sections are calculated using a weak Hamiltonian and nuclear properties of initial and excited states are obtained with a relativistic Hartree-Bogoliubov model and a relativistic quasiparticle random phase approximation that is extended to include pion contributions for unnatural parity transitions.Results: Inelastic neutral-current neutrino-nucleus cross sections for ${}^{12}$C, ${}^{16}$O, ${}^{56}$Fe, ${}^{56}$Ni, and even isotopes ${}^{92\ensuremath{-}100}$Mo as well as respective cross sections averaged over distribution of supernova neutrinos.Conclusions: The present study provides insight into neutrino-nucleus scattering cross sections in the neutral channel, their theoretical uncertainty in view of recently developed microscopic models, and paves the way for systematic self-consistent large-scale calculations involving open-shell target nuclei.

PROGENITOR-EXPLOSION CONNECTION AND REMNANT BIRTH MASSES FOR NEUTRINO-DRIVEN SUPERNOVAE OF IRON-CORE PROGENITORS

We perform hydrodynamic supernova simulations in spherical symmetry for over 100 single stars of solar metallicity to explore the progenitor-explosion and progenitor-remnant connections established by the neutrino-driven mechanism. We use an approximative treatment of neutrino transport and replace the high-density interior of the neutron star (NS) by an inner boundary condition based on an analytic proto-NS core-cooling model, whose free parameters are chosen such that explosion energy, nickel production, and energy release by the compact remnant of progenitors around 20 solar masses are compatible with Supernova 1987A. Thus we are able to simulate the accretion phase, initiation of the explosion, subsequent neutrino-driven wind phase for 15-20 s, and the further evolution of the blast wave for hours to days until fallback is completed. Our results challenge long-standing paradigms. We find that remnant mass, launch time, and properties of the explosion depend strongly on the stellar structure and exhibit large variability even in narrow intervals of the progenitors' zero-age-main-sequence mass. While all progenitors with masses below about 15 solar masses yield NSs, black hole (BH) as well as NS formation is possible for more massive stars, where partial loss of the hydrogen envelope leads to weak reverse shocks and weak fallback. Our NS baryonic masses of ~1.2-2.0 solar masses and BH masses >6 solar masses are compatible with a possible lack of low-mass BHs in the empirical distribution. Neutrino heating accounts for SN energies between some 10^{50} erg and about 2*10^{51} erg, but can hardly explain more energetic explosions and nickel masses higher than 0.1-0.2 solar masses. These seem to require an alternative SN mechanism.

A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE. II. RELATIVISTIC EXPLOSION MODELS OF CORE-COLLAPSE SUPERNOVAE

We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the CoCoNuT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the spacetime metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 solar mass progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared to Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong non-radial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.

A NEW CODE FOR PROTO-NEUTRON STAR EVOLUTION

A new code for following the evolution and emissions of proto-neutron stars during the first minute of their lives is developed and tested. The code is one dimensional, fully implicit, and general relativistic. Multi-group, multi-flavor neutrino transport is incorporated that makes use of variable Eddington factors obtained from a formal solution of the static general relativistic Boltzmann equation with linearized scattering terms. The timescales of neutrino emission and spectral evolution obtained using the new code are broadly consistent with previous results. Unlike other recent calculations, however, the new code predicts that the neutrino-driven wind will be characterized, at least for part of its existence, by a neutron excess. This change, potentially consequential for nucleosynthesis in the wind, is due to an improved treatment of the charged-current interactions of electron flavored neutrinos and anti-neutrinos with nucleons. A comparison is also made between the results obtained using either variable Eddington factors or simple equilibrium flux-limited diffusion. The latter approximation, which has been frequently used in previous studies of proto-neutron star cooling, accurately describes the total neutrino luminosities (to within 10%) for most of the evolution, until the proto-neutron star becomes optically thin.

A NEW MONTE CARLO METHOD FOR TIME-DEPENDENT NEUTRINO RADIATION TRANSPORT

Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are relatively easy to extend to multiple spatial dimensions, which makes them potentially interesting in modeling complex multi-dimensional astrophysical phenomena such as core-collapse supernovae. The aim of this paper is to explore Monte Carlo methods for modeling neutrino transport in core-collapse supernovae. We generalize the Implicit Monte Carlo photon transport scheme of Fleck & Cummings and gray discrete-diffusion scheme of Densmore et al. to energy-, time-, and velocity-dependent neutrino transport. Using our 1D spherically-symmetric implementation, we show that, similar to the photon transport case, the implicit scheme enables significantly larger timesteps compared with explicit time discretization, without sacrificing accuracy, while the discrete-diffusion method leads to significant speed-ups at high optical depth. Our results suggest that a combination of spectral, velocity-dependent, Implicit Monte Carlo and discrete-diffusion Monte Carlo methods represents a robust approach for use in neutrino transport calculations in core-collapse supernovae. Our velocity-dependent scheme can easily be adapted to photon transport.

FULLY GENERAL RELATIVISTIC SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE WITH AN APPROXIMATE NEUTRINO TRANSPORT

We present results from the first generation of multi-dimensional hydrodynamic core-collapse simulations in full general relativity (GR) that include an approximate treatment of neutrino transport. Using a M1 closure scheme with an analytic variable Eddington factor, we solve the energy-independent set of radiation energy and momentum based on the Thorne's momentum formalism. To simplify the source terms of the transport equations, a methodology of multiflavour neutrino leakage scheme is partly employed. Our newly developed code is designed to evolve the Einstein field equation together with the GR radiation hydrodynamic equations. We follow the dynamics starting from the onset of gravitational core-collapse of a 15 $M_{\odot}$ star, through bounce, up to about 100 ms postbounce in this study to study how the spacial multi-dimensionality and GR would affect the dynamics in the early postbounce phase. Our 3D results support the anticipation in previous 1D results that the neutrino luminosity and average neutrino energy of any neutrino flavor in the postbounce phase increase when switching from SR to GR hydrodynamics. This is because the deeper gravitational well of GR produces more compact core structures, and thus hotter neutrino spheres at smaller radii. By analyzing the residency timescale to the neutrino-heating timescale in the gain region, we show that the criterion to initiate neutrino-driven explosions can be most easily satisfied in 3D models, irrespective of SR or GR hydrodynamics. Our results suggest that the combination of GR and 3D hydrodynamics provides the most favorable condition to drive a robust neutrino-driven explosion.

Explosion Mechanisms of Core-Collapse Supernovae

Supernova theory, numerical and analytic, has made remarkable progress in the past decade. This progress was made possible by more sophisticated simulation tools, especially for neutrino transport, improved microphysics, and deeper insights into the role of hydrodynamic instabilities. Violent, large-scale nonradial mass motions are generic in supernova cores. The neutrino-heating mechanism, aided by nonradial flows, drives explosions, albeit low-energy ones, of O-Ne-Mg-core and some Fe-core progenitors. The characteristics of the neutrino emission from newborn neutron stars were revised, new features of the gravitational-wave signals were discovered, our notion of supernova nucleosynthesis was shattered, and our understanding of pulsar kicks and explosion asymmetries was significantly improved. But simulations also suggest that neutrino-powered explosions might not explain the most energetic supernovae and hypernovae, which seem to demand magnetorotational driving. Now that modeling is being advanced from two to three dimensions, more realism, new perspectives, and hopefully answers to long-standing questions are coming into reach.

Effects of the temperature dependence of the in-medium nucleon mass on core-collapse supernovae

Aims. A complete description of the core collapse supernova mechanism requires an appropriate treatment of both the hydrodynamics and the microphysics. We study the influence of a nuclear physics input, namely the temperature dependence of the nucleon effective mass in nuclei induced by the in-medium effects, in the core collapse of a massive star.Methods. We present here the first implementation of this nuclear input in a hydrodynamical one-dimensional simulation. The simulations are performed with a spherically symmetric Newtonian model, with neutrino transport treated in the multi-group flux-limited diffusion approximation.Results. The inclusion of the temperature dependence of the in-medium nucleon mass has an impact on the equation of state of the system and reduces the deleptonisation during the collapse. This results in a non-negligible effect on the shock wave energetics. The shock wave is formed more outwards, and in the first few milliseconds after bounce the shock front has propagated further out.

MAGNETOROTATIONALLY DRIVEN SUPERNOVAE AS THE ORIGIN OF EARLY GALAXY r -PROCESS ELEMENTS?

We examine magnetorotationally driven supernovae as sources of $r$-process elements in the early Galaxy. On the basis of thermodynamic histories of tracer particles from a three-dimensional magnetohydrodynamical core-collapse supernova model with approximated neutrino transport, we perform nucleosynthesis calculations with and without considering the effects of neutrino absorption reactions on the electron fraction ($Y_{e}$) during post-processing. We find that the peak distribution of $Y_{e}$ in the ejecta is shifted from $\sim0.15$ to $\sim0.17$ and broadened toward higher $Y_{e}$ due to neutrino absorption. Nevertheless, in both cases the second and third peaks of the solar $r$-process element distribution can be well reproduced. The rare progenitor configuration that was used here, characterized by a high rotation rate and a large magnetic field necessary for the formation of bipolar jets, could naturally provide a site for the strong $r$-process in agreement with observations of the early galactic chemical evolution.

Neutrino spectra evolution during protoneutron star deleptonization

The neutrino-driven wind, which occurs after the onset of a core-collapse supernova explosion, has long been considered as the possible site for the synthesis of heavy $r$-process elements in the Universe. Only recently, it has been possible to simulate supernova explosions up to $\ensuremath{\sim}10\text{ }\text{ }\mathrm{seconds}$, based on three-flavor Boltzmann neutrino transport. These simulations show that the neutrino luminosities and spectra of all flavors are very similar and their difference even decreases during the deleptonization of the proto-neutron star. As a consequence, the ejecta are always proton rich which rules out the possible production of heavy $r$-process elements ($Z>56$). We perform a detailed analysis of the different weak processes that determine the neutrino spectra. Nonelectron flavor (anti)neutrinos are produced and interact only via neutral-current processes, while electron (anti)neutrinos have additional contributions from charge-current processes. The latter are dominated by ${\ensuremath{\nu}}_{e}$-absorption on neutrons and ${\overline{\ensuremath{\nu}}}_{e}$-absorption on protons. At early times, charge-current processes are responsible for spectral differences between ${\ensuremath{\nu}}_{e}$, ${\overline{\ensuremath{\nu}}}_{e}$ and ${\ensuremath{\nu}}_{\ensuremath{\mu}/\ensuremath{\tau}}$. However, as the region of neutrino decoupling moves to higher densities during deleptonization, charge-current reactions are suppressed by final state Pauli blocking. ${\overline{\ensuremath{\nu}}}_{e}$ absorption on protons is suppressed due to the continuously increasing chemical potential of the neutrons. ${\ensuremath{\nu}}_{e}$ absorption on neutrons is blocked by the increasing degeneracy of the electrons. These effects result in negligible contributions from charge-current reactions on time scales on the order of tens of seconds, depending on the progenitor star. Hence, the neutrino spectra are mainly determined from neutral-current processes which do not distinguish between the different flavors and result in the convergence of the spectra. These findings are independent of the charge-current reaction rates used. It rules out the possibility of neutron-rich ejecta at late times and the production of heavy $r$-process elements from nonrotating and not magnetized proto-neutron stars.

THREE-DIMENSIONAL HYDRODYNAMIC CORE-COLLAPSE SUPERNOVA SIMULATIONS FOR AN 11.2M☉STAR WITH SPECTRAL NEUTRINO TRANSPORT

We present numerical results on three-dimensional (3D) hydrodynamic core-collapse simulations of an $11.2 M_{\odot}$ star. By comparing one-(1D) and two-dimensional(2D) results with those of 3D, we study how the increasing spacial multi-dimensionality affects the postbounce supernova dynamics. The calculations were performed with an energy-dependent treatment of the neutrino transport that is solved by the isotropic diffusion source approximation scheme. By performing a tracer-particle analysis, we show that the maximum residency time of material in the gain region is shown to be longer for 3D due to non-axisymmetric flow motions than 2D, which is one of advantageous aspects of 3D models to obtain neutrino-driven explosions. Our results show that convective matter motions below the gain radius become much more violent in 3D than 2D, making the neutrino luminosity larger for 3D. Nevertheless the emitted neutrino energies are made smaller due to the enhanced cooling. Our results indicate whether these advantages for driving 3D explosions could or could not overwhelm the disadvantages is sensitive to the employed numerical resolutions. An encouraging finding is that the shock expansion tends to become more energetic for models with finer resolutions. To draw a robust conclusion, 3D simulations with much more higher numerical resolutions and also with more advanced treatment of neutrino transport as well as of gravity is needed, which could be hopefully practicable by utilizing forthcoming Petaflops-class supercomputers.

NEW EQUATIONS OF STATE IN SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE

We discuss three new equations of state (EOS) in core-collapse supernova simulations. The new EOS are based on the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects and relativistic mean-field (RMF) interactions. We consider the RMF parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport. The results obtained for the new EOS are compared with the widely used EOS of H. Shen et al. and Lattimer & Swesty. The systematic comparison shows that the model description of inhomogeneous nuclear matter is as important as the parameterization of the nuclear interactions for the supernova dynamics and the neutrino signal. Furthermore, several new aspects of nuclear physics are investigated: the HS EOS contains distributions of nuclei, including nuclear shell effects. The appearance of light nuclei, e.g., deuterium and tritium is also explored, which can become as abundant as alphas and free protons. In addition, we investigate the black hole formation in failed core-collapse supernovae, which is mainly determined by the high-density EOS. We find that temperature effects lead to a systematically faster collapse for the non-relativistic LS EOS in comparison to the RMF EOS. We deduce a new correlation for the time until black hole formation, which allows to determine the maximum mass of proto-neutron stars, if the neutrino signal from such a failed supernova would be measured in the future. This would give a constraint for the nuclear EOS at finite entropy, complementary to observations of cold neutron stars.

Neutrino and anti-neutrino transport in accretion disks

We numerically solve the one dimensional Boltzmann equation of the neutrino and anti-neutrino transport in accretion disks and obtain the fully energy dependent and direction dependent neutrino and anti-neutrino emitting spectra, under condition that the distribution of the mass density,temperature and chemical components are given. Then, we apply the resulting neutrino and anti-neutrino emitting spectra to calculate the corresponding annihilation rate of neutrino pairs above the neutrino dominated accretion disk and find that the released energy resulting from the annihilation of neutrino pairs can not provide sufficient energy for the most energetic short gamma ray bursts whose isotropic luminosity can be as high as $10^{52}$ ergs/s unless the high temperature zone where the temperature is beyond 10 MeV can stretch over 200 km in the disk. We also compare the resulting luminosity of neutrinos and anti-neutrinos with the results from the two commonly used approximate treatment of the neutrino and anti-neutrino luminosity: the Fermi-Dirac black body limit and a simplified model of neutrino transport, i.e., the gray body model, and find that both of them overestimate the neutrino/anti-neutrino luminosity and their annihilation rate greatly. Additionally, as did in Sawyer (2003), we also check the validity of the two stream approximation, and find that it is a good approximation to high accuracy.

Computations of the collapse of a stellar iron core allowing for the absorption, emission, and scattering of electron neutrinos and anti-neutrinos

The collapse of the iron core of a star with mass 1.4M⊙ is computed. The initial model was chosen to be polytropic, P ∝ ρ1+1/n, with n = 3. The equation of state takes into account the equilibrium radiation of photons, a mixture of Fermi gases comprised of free nucleons and ideal gases comprised of nuclei (Fe, He) in equilibrium with respect to nuclear reactions, and electron-positron gas. The transport equation for electron neutrinos and anti-neutrinos is also included. The absorption and emission of neutrinos and anti-neutrinos with the participation of free nucleons and nuclei is taken into account, as well as scattering on electrons. The main goal of this study is to develop a numerical method for the joint solution of the gas-dynamical equations formatter and the Boltzmann kinetic equations for the distribution functions of various types of neutrinos in both optically thin and optically thick regions. The spherically symmetrical case is considered, but the dependences of the distribution functions on all the phase-space variables—the mass coordinate, particle energy, cosine of the angle between the radius vector and the particle momentum, and time, (m, e, µ, t)—are retained in the description of the neutrino transport. When computing reaction rates, the exact quantum-mechanical expressions for the probabilities of processes are used, with integration over the entire momentum phase space. The gas-dynamical variables depend on the mass coordinate and time, (m, t). The solution yields neutrino light curves, which have narrow maximum with characteristic widths ≈10 ms. This makes it possible to place constraints on the mass of the electron neutrino based on the detection of short bursts of radiation, ≲4 eV. Part of the neutrino energy is absorbed in the envelope of the stellar core (∼1050 erg). This is associated with the higher mean neutrino energies in this model, which is more exact than models with neutrino thermal conductivity. This approach is of interest for the application of multi-dimensional models taking into account large-scale convection.

Core-collapse supernovae as supercomputing science: A status report toward six-dimensional simulations with exact Boltzmann neutrino transport in full general relativity

This is a status report on our endeavor to reveal the mechanism of core-collapse supernovae (CCSNe) by large-scale numerical simulations. Multi-dimensionality of the supernova engine, general relativistic magnetohydrodynamics, energy and lepton number transport by neutrinos emitted from the forming neutron star, aswell as nuclear interactions there, are all believed to play crucial roles in repelling infalling matter and producing energetic explosions. These ingredients are non-linearly coupled with one another in the dynamics of core collapse, bounce, and shock expansion. Serious quantitative studies of CCSNe hence make extensive numerical computations mandatory. Since neutrinos are neither in thermal nor in chemical equilibrium in general, their distributions in the phase space should be computed. This is a six-dimensional (6D) neutrino transport problem and quite a challenge, even for those with access to the most advanced numerical resources such as the “K computer”. To tackle this problem, we have embarked on efforts on multiple fronts. In particular, we report in this paper our recent progresses in the treatment of multidimensional (multi-D) radiation hydrodynamics. We are currently proceeding on two different paths to the ultimate goal. In one approach, we employ an approximate but highly efficient scheme for neutrino transport and treat 3D hydrodynamics and/or general relativity rigorously; some neutrino-driven explosions will be presented and quantitative comparisons will be made between 2D and 3D models. In the second approach, on the other hand, exact, but so far Newtonian, Boltzmann equations are solved in two and three spatial dimensions; we will show some example test simulations. We will also address the perspectives of exascale computations on the next generation supercomputers.

Asymmetric Neutrino Reaction in Magnetized Proto-Neutron Stars in Fully Relativistic Approach

We calculate asymmetric neutrino absorption and scattering cross sections on hot and dense magnetized neutron-star matter including hyperons in fully relativistic mean-field theory. The absorption/scattering cross sections are suppressed/enhanced incoherently in the direction of the magnetic field B = Bẑ . The asymmetry is 2–4% at the matter density ρ0 ≤ ρB ≤ 3ρ0 and temperature T ≤ 40MeV for B = 2 × 1017 G. Then we solve the Boltzmann equation for the neutrino transport in 1D attenuation approximation, and get the result that the kick velocity becomes about 300 km/s for the proto-neutron star with 168 solar mass at T = 20MeV.

Parametrized 3D models of neutrino-driven supernova explosions

Time-dependent and direction-dependent neutrino and gravitational-wave (GW) signatures are presented for a set of 3D hydrodynamic models of parametrized, neutrino-driven supernova explosions of non-rotating 15 and 20 solar mass stars. We employ an approximate treatment of neutrino transport. Due to the excision of the high-density core of the proto-neutron star and the use of an axis-free overset grid, the models can be followed from the post-bounce accretion phase for more than one second without imposing any symmetry restrictions. GW and neutrino emission exhibit the generic time-dependent features known from 2D models. Non-radial hydrodynamic mass motions in the accretion layer and their interaction with the outer layers of the proto-neutron star together with anisotropic neutrino emission give rise to a GW signal with an amplitude of ~5-20 cm and frequencies 100--500 Hz. The GW emission from mass motions reaches a maximum before the explosion sets in. Afterwards the GW signal exhibits a low-frequency modulation, in some cases describing a quasi-monotonic growth, associated with the non-spherical expansion of the explosion shock wave and the large-scale anisotropy of the escaping neutrino flow. Variations of the mass-quadrupole moment due to convective activity inside the nascent neutron star contribute a high-frequency component to the GW signal during the post-explosion phase. The GW signals exhibit strong variability between the two polarizations, different explosion simulations and different observer directions, and does not possess any template character. The neutrino emission properties show fluctuations over the neutron star surface on spatial and temporal scales that reflect the different types of non-spherical mass motions. The modulation amplitudes of the measurable neutrino luminosities and mean energies are significantly smaller than predicted by 2D simulations.

No Collective Neutrino Flavor Conversions during the Supernova Accretion Phase

We perform a dedicated study of the supernova (SN) neutrino flavor evolution during the accretion phase, using results from recent neutrino radiation hydrodynamics simulations. In contrast to what was expected in the presence of only neutrino-neutrino interactions, we find that the multiangle effects associated with the dense ordinary matter suppress collective oscillations. The matter suppression implies that neutrino oscillations will start outside the neutrino decoupling region and therefore will have a negligible impact on the neutrino heating and the explosion dynamics. Furthermore, the possible detection of the next galactic SN neutrino signal from the accretion phase, based on the usual Mikheyev-Smirnov-Wolfenstein effect in the SN mantle and Earth matter effects, can reveal the neutrino mass hierarchy in the case that the mixing angle θ(13) is not very small.

The neutrino signal at HALO: learning about the primary supernova neutrino fluxes and neutrino properties

Core-collapse supernova neutrinos undergo a variety of phenomena when they travel from the high neutrino density region and large matter densities to the Earth. We perform analytical calculations of the supernova neutrino fluxes including collective effects due to the neutrino-neutrino interactions, the Mikheev-Smirnov-Wolfenstein (MSW) effect due to the neutrino interactions with the background matter and decoherence of the wave packets as they propagate in space. We predict the numbers of one- and two-neutron charged and neutral-current electron-neutrino scattering on lead events. We show that, due to the energy thresholds, the ratios of one- to two-neutron events are sensitive to the pinching parameters of neutrino fluxes at the neutrinosphere, almost independently of the presently unknown neutrino properties. Besides, such events have an interesting sensitivity to the spectral split features that depend upon the presence/absence of energy equipartition among neutrino flavors. Our calculations show that a lead-based observatory like the Helium And Lead Observatory (HALO) has the potential to pin down important characteristics of the neutrino fluxes at the neutrinosphere, and provide us with information on the neutrino transport in the supernova core.