Neutrino Equation Research Articles

Current status of numerical-relativity simulations in Kyoto

We describe the current status of our numerical simulations for the collapse of a massive stellar core to a black hole (BH) and the merger of binary neutron stars (BNS), performed in the framework of full general relativity incorporating finite-temperature equations of state (EOS) and neutrino cooling. For the stellar core collapse simulation, we present the latest numerical results. We employed a purely nucleonic EOS derived by Shen et al. [Nucl. Phys. A 637, 435 (1998)]. As an initial condition, we adopted a 100 M presupernova model calculated by Umeda and Nomoto [Astrophys. J. 637, 1014 (2008)], which has a massive core (M ≈ 3M) with a high value of entropy per baryon (s ≈ 4kB). Changing the degree of rotation for the initial condition, we clarify the strong dependence of the outcome of the collapse on this. When the rotation is rapid enough, the shock wave formed at the core bounce is deformed to a torus-like shape. Then, the infalling matter accumulates in the central region due to the oblique shock at the torus surface, hitting the proto-neutron star and dissipating the kinetic energy there. As a result, outflows can be launched. The proto-neutron eventually collapses to a BH and an accretion torus is formed around it.We also found that the evolution of the BH and torus depends strongly on the rotation initially given. In the BNS merger simulations, we employ an EOS incorporating a degree of freedom for hyperons derived by Shen et al. [Astrophys. J. Suppl. 197, 20 (2011)], in addition to the purely nucleonic EOS. The numerical simulations show that for the purely nucleonic EOS, a hypermassive neutron star (HMNS) with a long lifetime (10 ms) is the outcome for the total mass M ≤ 3.0M. In contrast, the formed HMNS collapses to a BH in a shorter time scale with the hyperonic EOS for M ≥ 2.7M. It is shown that the typical total neutrino luminosity of the HMNS is ∼(3–10)×1053 ergs/s and the effective amplitude of gravitational waves from the HMNS is (2–6)×10−22 at f ≈ 2–2.5 kHz for a source distance of 100 Mpc.

Effects of Hyperons in Binary Neutron Star Mergers

Numerical simulations for the merger of binary neutron stars are performed in full general relativity incorporating both nucleonic and hyperonic finite-temperature equations of state (EOS) and neutrino cooling. It is found that even for the hyperonic EOS, a hypermassive neutron star is first formed after the merger for the typical total mass ≈2.7M(⊙), and subsequently collapses to a black hole (BH). It is shown that hyperons play a substantial role in the postmerger dynamics, torus formation around the BH, and emission of gravitational waves (GWs). In particular, the existence of hyperons is imprinted in GWs. Therefore, GW observations will provide a potential opportunity to explore the composition of neutron star matter.

Dirac equation for massive neutrinos in a Schwarzschild–de Sitter spacetime from a 5D vacuum

Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild–de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.

General relativistic ray-tracing algorithm for the determination of the electron-positron energy deposition rate from neutrino pair annihilation around rotating neutron and quark stars

We present a full general relativistic numerical code for estimating the energy–momentum deposition rate (EMDR) from neutrino pair annihilation (⁠⁠). The source of the neutrinos is assumed to be a neutrino-cooled accretion disc around neutron and quark stars. We calculate the neutrino trajectories by using a ray-tracing algorithm with the general relativistic Hamilton's equations for neutrinos and derive the spatial distribution of the EMDR due to the annihilations of neutrinos and antineutrinos around rotating neutron and quark stars. We obtain the EMDR for several classes of rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the Massachusetts Institute of Technology (MIT) bag model equation of state and in the colour–flavour-locked (CFL) phase. The distribution of the total annihilation rate of the neutrino–antineutrino pairs around rotating neutron and quark stars is studied for isothermal discs and accretion discs in thermodynamical equilibrium. We demonstrate both the differences in the equations of state for neutron and quark matter and rotation with the general relativistic effects significantly modify the EMDR of the electrons and positrons generated by the neutrino–antineutrino pair annihilation around compact stellar objects, as measured at infinity.

A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes

We present the new open-source spherically symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by Romero–Ibáñez–Gourgoulhon and employs radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify substantially. We discretize the GRHD equations with a finite-volume scheme, employing piecewise-parabolic reconstruction and an approximate Riemann solver. GR1D is intended for the simulation of stellar collapse to neutron stars and black holes and will also serve as a testbed for modeling technology to be incorporated in multi-D GR codes. Its GRHD part is coupled to various finite-temperature microphysical equations of state in tabulated form that we make available with GR1D. An approximate deleptonization scheme for the collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch are included and described. We also derive the equations for effective rotation in 1D and implement them in GR1D. We present an array of standard test calculations and also show how simple analytic equations of state in combination with presupernova models from stellar evolutionary calculations can be used to study qualitative aspects of black hole formation in failing rotating core-collapse supernovae. In addition, we present a simulation with microphysical equations of state and neutrino leakage/heating of a failing core-collapse supernova and black hole formation in a presupernova model of a 40 M⊙ zero-age main-sequence star. We find good agreement on the time of black hole formation (within 20%) and last stable protoneutron star mass (within 10%) with predictions from simulations with full Boltzmann neutrino radiation hydrodynamics.

Coupling active and sterile neutrinos in the cosmon plus seesaw framework

The cosmological evolution of neutrino energy densities driven by cosmon-type field equations is introduced assuming that active and sterile neutrinos are intrinsically connected by cosmon fields through the seesaw mechanism. Interpreting sterile neutrinos as dark matter adiabatically coupled with dark energy results in a natural decoupling of (active) mass varying neutrino (MaVaN) equations. Identifying the dimensionless scale of the seesaw mechanism, m/M, with a power of the cosmological scale factor, a, allows for embedding the resulting masses into the generalized Chaplygin gas (GCG) scenario for the dark sector. Without additional assumptions, our findings establish a precise connection among three distinct frameworks: the cosmon field dynamics for MaVaN's, the seesaw mechanism for dynamical mass generation and the GCG scenario. Our results also corroborate with previous assertions that mass varying particles can be the right responsible for the stability issue and for the cosmic acceleration of the universe.

Generalized Symmetries of Massless Free Fields on Minkowski Space

A complete and explicit classification of generalized, or local, symmetries of massless free fields of spin s 1/2 is carried out. Up to equivalence, these are found to consists of the conformal symmetries and their duals, new chiral symmetries of order 2s, and their higher-order extensions obtained by Lie differentiation with respect to confor- mal Killing vectors. In particular, the results yield a complete classification of generalized symmetries of the Dirac-Weyl neutrino equation, Maxwell's equations, and the linearized gravity equations.

Neutrino oscillations in matter and in twisting magnetic fields

We find the solution to the Dirac equation for a massive neutrino with a magnetic moment propagating in background matter and interacting with the twisting magnetic field. In frames of the relativistic quantum mechanics approach to the description of neutrino evolution we use the obtained solution to derive neutrino wavefunctions satisfying the given initial condition. We apply the results to the analysis of neutrino spin oscillations in matter under the influence of the twisting magnetic field. Then on the basis of the yielded results we describe spin-flavor oscillations of Dirac neutrinos that mix and have non-vanishing matrix of magnetic moments. We again formulate the initial condition problem, derive neutrinos wavefunctions and calculate the transition probabilities for different magnetic moment matrices. The consistency of the obtained results with the quantum-mechanical treatment of spin-flavor oscillations is discussed. We also consider several applications to astrophysical and cosmological neutrinos.

PLASMA WAKES DRIVEN BY NEUTRINOS, PHOTONS AND ELECTRON BEAMS

There is considerable interest in the propagation dynamics of intense electron and photon neutrino beams in a background dispersive medium such as dense plasmas, particularly in the search for a mechanism to explain the dynamics of type II supernovae. Neutrino interactions with matter are usually considered as single particle interactions. All the single particle mechanisms describing the dynamical properties of neutrino's in matter are analogous with the processes involving single electron interactions with a medium such as Compton scattering, and Cerenkov radiation etc. However, it is well known that beams of electrons moving through a plasma give rise to a new class of processes known as collective interactions such as two stream instabilities which result in either the absorption or generation of plasma waves. Intense photon beams also drive collective interactions such as modulational type instabilities. In both cases relativistic electron beams of electrons and photon beams can drive plasma wakefields in plasmas. Employing the relativistic kinetic equations for neutrinos interacting with dense plasmas via the weak force we explore collective plasma streaming instabilities driven by Neutrino electron and photon beams and demonstrate that all three types of particles can drive wakefields.

Neutrino quantum states and spin light in matter

On the basis of the exact solutions of the modified Dirac equation for a massive neutrino moving in matter we develop the quantum theory of the spin light of neutrino (SLν). The expression for the emitted photon energy is derived as a function of the density of matter for different matter compositions. The dependence of the photon energy on the helicities of the initial and final neutrino states is shown explicitly. The rate and radiation power of the SLν in matter are obtained with the emitted photon linear and circular polarizations being accounted for. The developed quantum approach to the SLν in matter (which is similar to the Furry representation of electrodynamics) can be used in the studies of other processes with neutrinos in the presence of matter.

Neutrino plasma coupling in dense astrophysical plasmas

There is considerable interest in the propagation dynamics of intense neutrino beams in a background dispersive medium such as dense plasmas, particularly in the search for a mechanism to explain the dynamics of type II supernovae. Neutrino interactions with matter are usually considered as single particle interactions. All the single particle mechanisms describing the dynamical properties of neutrinos in matter are analogous with the processes involving single electron interactions with a medium such as Compton scattering, Cerenkov radiation, etc. However, it is well known that beams of electrons moving through a plasma give rise to a new class of processes known as collective interactions, such as two stream instabilities, which result in either the absorption or generation of plasma waves. Employing the relativistic kinetic equations for neutrinos interacting with dense plasmas via the weak force, we explore collective plasma streaming instabilities driven by neutrino beams. We examine the anomalous transfer between neutrinos and dense plasma via excitation of electron plasma waves. The nonlinear coupling between an intense neutrino beam and a plasma reveals the presence of two regimes, a hydrodynamic regime and a kinetic regime. The latter is responsible for Landau damping or growth of electron plasma waves. In dense fusion stellar plasmas neutrino Landau damping can play a significant role as an additional stellar plasma cooling process. Another interesting result is an asymmetry in the momentum balance imported by the neutrinos to the core of the exploding star due to symmetry breaking by the collapsed star's magnetic fields. This results in a directed velocity of the resulting neutron star or pulsar, explaining the so called ‘birth’ velocity.

Transport in nanostructures and nanotubes

In two-dimensional honeycomb lattices, electronic states are described by Weyl's equation for a massless neutrino when each site is occupied by an electron on average. The system has a topological singularity at the origin k=0 of the wave vector, giving rise to nontrivial Berry's phase when k is rotated around the origin. The singularity causes discrete jumps in the conductivity at the energy corresponding to k=0 in honeycomb lattices and leads to the absence of backscattering and a perfect conductance in carbon nanotubes.

Nonlocal Transport Phenomena and Various Structure Formations in Plasmas. Nonlocal Transport in Laser Implosion and Supernova Explosion.

Nonlocal transport becomes important in a variety of situations in physics. We briefly review under what conditions it appears to be important in modeling energy transport by neutral gas, neutrons, charged particles, photons, and neutrinos. In the cases of these last three, the cross-sections strongly depend upon particle energies. In such cases, nonlocal transport becomes important even when each mean free path is much shorter than the length of the change of its energy density. We mainly review the research that has been done on nonlocal electron energy transport in relation to laser-produced plasmas and the way in which precise calculation of neutrino transport changes the properties of a shock wave, which is used as a driver to explode a massive star such as a supernova, by solving Boltzmann-type equations for neutrinos and anti-neutrinos.

Neutrino beam plasma instability

We derive relativistic fluid set of equations for neutrinos and electrons from relativistic Vlasov equations with Fermi weak interaction force. Using these fluid equations, we obtain a dispersion relation describing neutrino beam plasma instability, which is little different from normal dispersion relation of streaming instability. It contains new, nonelectromagnetic, neutrino-plasma (or electroweak) stable and unstable modes also. The growth of the instability is weak for the highly relativistic neutrino flux, but becomes stronger for weakly relativistic neutrino flux in the case of parameters appropriate to the early universe and supernova explosions. However, this mode is dominant only for the beam velocity greater than 0.25c and in the other limit electroweak unstable mode takes over.

Boltzmann equations for neutrinos with flavor mixings

With a view of applications to the simulations of supernova explosions and protoneutron star cooling, we derive the Boltzmann equations for the neutrino transport with 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 while the collision terms are obtained in the Born approximation. The resulting equations take the familiar form of the Boltzmann equation with corrections due to 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 protoneutron star cooling.

Neutrino Landau damping

The kinetic regime of the collective interaction between neutrinos and electron plasma waves is described via the coupled kinetic equations for neutrinos and electrons. It is shown that neutrinos can Landau damp electron plasma waves. In dense stellar plasmas, this novel mechanism can play a significant role as an additional and much stronger turbulent plasma cooling process.

QUANTUM EQUATIONS FOR MASSLESS PARTICLES OF ANY SPIN

By decomposing the mass squared operator for zero mass particles of spin s we obtain one-particle quantum equations for any spin on which 2s−1 subsidiary conditions are imposed. The derived equations are consistent with the two component neutrino equation and the Maxwell equations. Subsidiary conditions for the spins 1, \(\frac{3}{2}\), and 2 are presented.

Neutrino Driven Streaming Instabilities in a Dense Plasma

The nonlinear self-consistent propagation of neutrinos in a dense plasma is described using the relativistic kinetic equations for neutrinos and electrons. The general nonlinear dispersion relation for a neutrino fluid coupled with a plasma is derived. For scenarios close to realistic astrophysical conditions, neutrino driven streaming instabilities can develop, with growth rates which scale with the Fermi constant ${G}_{F}$, thus leading to significant energy transfer from the neutrinos to the plasma.

On a class of consistent linear higher spin equations on curved manifolds

We analyse a class of linear wave equations for odd half spin that have a well-posed initial value problem. We demonstrate consistency of the equations in curved space-times. They generalise the Weyl neutrino equation. We show that there exists an associated invariant exact set of spinor fields indicating that the characteristic initial value problem on a null cone is formally solvable, even for the system coupled to general relativity. We derive the general analytic solution in flat space by means of Fourier transforms. Finally, we present a twistor contour integral description for the general analytic solution and assemble a representation of the group O(4, 4) on the solution space.

Maxwell’s Equations as the One-Photon Quantum Equation

Maxwell’s equations (the Faraday and Ampere-Maxwell laws) can be presented as a three-component equation in a way similar to the two-component neutrino equation. However, in this case, the electric and magnetic Gauss laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. We have also shown that equations for massless particles, derived by Dirac in 1936, lead to the same result. The complex wave function, being a linear combination of the electric and magnetic fields, is a locally measurable and well understood quantity. Therefore Maxwell equations should be used as a guideline for proper interpretations of quantum theories.