Massive Proto-neutron Star Research Articles

Influence of the weakly interacting light U boson on the properties of massive protoneutron stars**Supported by National Natural Science Foundation of China (11175147)

Considering the octet baryons in relativistic mean field theory and selecting entropy per baryon S=1, we calculate and discuss the influence of U bosons on the equation of state, mass-radius, moment of inertia and gravitational redshift of massive protoneutron stars (PNSs). The effective coupling constant gU of U bosons and nucleons is selected from 0 to 70 GeV−2. The results indicate that U bosons will stiffen the equation of state (EOS). The influence of U bosons on the pressure is more obvious at low density than high density, while the influence of U bosons on the energy density is more obvious at high density than low density. The U bosons play a significant role in increasing the maximum mass and radius of PNS. When the value of gU changes from 0 to 70 GeV−2, the maximum mass of a massive PNS increases from 2.11M⊙ to 2.58M⊙, and the radius of a PNS corresponding to PSR J0348+0432 increases from 13.71 km to 24.35 km. The U bosons will increase the moment of inertia and decrease the gravitational redshift of a PNS. For the PNS of the massive PSR J0348+0432, the radius and moment of inertia vary directly with gU, and the gravitational redshift varies approximately inversely with gU.

ALPHA-CONSTRAINED QSE NUCLEOSYNTHESIS IN HIGH-ENTROPY AND FAST-EXPANDING MATERIAL

ABSTRACT We investigate the nucleosynthesis process in high-entropy ( s / k B ≳ 100 ?> ) and very fast expanding ( τ exp ∼ 10 − 3 s ?> ) materials. In such a material with the electron fraction near 0.5, an interesting nucleosynthesis process occurs. In this process, the abundance distribution of heavy nuclei of A > 100 ?> achieves quasi-statistical equilibrium (QSE) at high temperature and the abundances are frozen at the end of the nucleosynthesis. We explain this abundance distribution using the “alpha-constrained QSE” abundances formulated in this paper. We demonstrate that this nucleosynthesis would occur in neutrino-driven winds from massive proto-neutron stars in hypernovae, where A ∼ 140 ?> p-nuclei are synthesized.

NUCLEOSYNTHESIS IN NEUTRINO-DRIVEN WINDS IN HYPERNOVAE

We investigate the nucleosynthesis in the neutrino-driven winds blown off from a $3M_\odot$ massive proto-neutron star (mPNS) temporarily formed during the collapse of a $100M_\odot$ star. Such mPNSs would be formed in hypernovae. We construct steady and spherically symmetric wind solutions. We set large neutrino luminosities of $\sim 10^{53}\ {\rm erg\ s^{-1}}$ and average energies of electron neutrinos and antineutrinos in the ranges of $\epsilon_{\nu_e}=9-16\ {\rm MeV}$ and $\epsilon_{\bar{\nu}_e}=11-18\ {\rm MeV}$ based on a recent numerical relativity simulation. The wind solutions indicate much shorter temperature-decrease timescale than that of the winds from ordinary PNSs and, depending on $\epsilon_\nu$, the winds can be both neutron-rich and proton-rich. In the neutron-rich wind, the $r$-process occurs and the abundance distribution of a fiducial wind model of the mPNS gives an approximate agreement with the abundance pattern of metal-poor weak $r$ star HD~122563, although the third-peak elements are produced only when the $\bar{\nu}_e$ energy is much larger than the $\nu_e$ energy. In the proton-rich wind, the strong $\nu p$-process occurs and $A>100$ nuclides are synthesized. The synthesized nuclei can be neutron-rich in some cases because the large neutrino luminosity of the mPNS supplies a sufficient amount of neutrons.

THE r -PROCESS IN PROTO-NEUTRON-STAR WIND REVISITED

We examine the r-process in the neutrino-driven proto-neutron-star (PNS) wind of core-collapse supernovae in light of the recent findings of massive neutron stars in binaries as well as of an indication of neutron-richness in the PNS ejecta because of the nucleon potential corrections on neutrino opacities. To this end, a spherically symmetric, general relativistic, steady-state wind model is applied for a wide range of PNS masses between 1.2 M_sun and 2.4 M_sun with the latter reaching the causality limit. Nucleosynthesis calculations with these PNS models are performed by assuming a time evolution of electron fraction with its minimal value of Y_e = 0.4, which mimics recent hydrodynamical results. The fundamental nucleosynthetic aspect of the PNS wind is found to be the production of Sr, Y and Zr in quasi-equilibrium and of the elements with A = 90-110 by a weak r-process, which can be an explanation for the abundance signatures in r-process-poor Galactic halo stars. PNSs more massive than 2.0 M_sun can eject heavy r-process elements, however, with substantially smaller amount than what is needed to account for the solar content. PNS winds can be thus the major origin of light trans-iron elements but no more than 10% of those heavier than A ~ 110, although they may be the sources of the low-level abundances of Sr and Ba found in numerous metal-poor stars if the maximum mass of PNS exceeds 2.0 M_sun.

A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE OF CORE-COLLAPSE SUPERNOVAE. III. GRAVITATIONAL WAVE SIGNALS FROM SUPERNOVA EXPLOSION MODELS

We present a detailed theoretical analysis of the gravitational-wave (GW) signal of the post-bounce evolution of core-collapse supernovae (SNe), employing for the first time relativistic, two-dimensional (2D) explosion models with multi-group, three-flavor neutrino transport based on the ray-by-ray-plus approximation. The waveforms reflect the accelerated mass motions associated with the characteristic evolutionary stages that were also identified in previous works: A quasi-periodic modulation by prompt postshock convection is followed by a phase of relative quiescence before growing amplitudes signal violent hydrodynamical activity due to convection and the standing accretion shock instability during the accretion period of the stalled shock. Finally, a high-frequency, low-amplitude variation from proto-neutron star (PNS) convection below the neutrinosphere appears superimposed on the low-frequency trend associated with the aspherical expansion of the SN shock after the onset of the explosion. Relativistic effects in combination with detailed neutrino transport are shown to be essential for quantitative predictions of the GW frequency evolution and energy spectrum, because they determine the structure of the PNS surface layer and its characteristic g-mode frequency. Burst-like high-frequency activity phases, correlated with sudden luminosity increase and spectral hardening of electron (anti-)neutrino emission for some 10ms, are discovered as new features after the onset of the explosion. They correspond to intermittent episodes of anisotropic accretion by the PNS in the case of fallback SNe. We find stronger signals for more massive progenitors with large accretion rates. The typical frequencies are higher for massive PNSs, though the time-integrated spectrum also strongly depends on the model dynamics.

Nucleation rate of colour superconducting droplets in protoneutron stars

We analyse the nucleation of quark matter droplets under protoneutron star conditions. We adopt a two-phase framework in which the hadronic phase is described through a nonlinear Walecka model and the just deconfined matter by the MIT bag model including colour superconductivity. Surface tension and curvature energy are calculated self-consistently within the multiple reflection expansion formalism. We impose flavour conservation during the transition, which means that the just deconfined quark droplet is transiently out of equilibrium with respect to weak interactions. Our results show that trapped neutrinos slightly increase the critical density for deconfinement and that colour superconductivity significantly decreases such density at low temperatures. We also show that the nucleation rate is negligible for droplets larger than 100–200 fm and is huge for smaller droplets provided that the temperature is low enough. We compare our results with previous calculations using the Nambu–Jona–Lasinio model with colour superconductivity and the MIT bag model without colour superconductivity. We conclude that the deconfinement transition should be triggered instantaneously when a density slightly larger than the bulk transition density is reached at some layer of a protoneutron star. Since colour superconductivity lowers the transition density at low temperatures, the transition is likely to occur after significant cooling in a massive enough protoneutron star.

The Σ Well Depth and the Proto Neutron Star Matter

The effect of the Σ well depth \(U_{\varSigma}^{(N)}\) on a proto neutron star (PNS) is examined within the framework of relativistic mean field theory for the baryon octet system. It is found that the well depth \(U_{\varSigma}^{(N)}\) will affect the structures of the PNS. With the well depth \(U_{\varSigma}^{(N)}\) growing from 0 to 30 MeV, the field strength of meson ρ, the chemical potentials of electrons and neutrons, the relative number density of p, e, μ, Λ, Ξ0, the mass and the pressure of a PNS all increase while the relative number density of n, Ξ−, Σ−, Σ0, Σ+ decrease. It is also found that the larger changes of the hyperon coupling constants, which is connected to the Σ well depth \(U_{\varSigma}^{(N)}\), will lead to the smaller changes in the neutron star mass and this shows the mass of PNS is not very sensitive to the hyperon coupling constants.

Effect of collective neutrino oscillations on the neutrino mechanism of core-collapse supernovae

In the seconds after collapse of a massive star, the newborn proto-neutron star (PNS) radiates neutrinos of all flavors. The absorption of electron-type neutrinos below the radius of the stalled shockwave may drive explosions (the "neutrino mechanism"). Because the heating rate is proportional to the square of neutrino energy, flavor conversion of mu and tau neutrinos to electron-type neutrinos via collective neutrino oscillations (CnuO) may in principle increase the heating rate and drive explosions. In order to assess the potential importance of CnuO for the shock revival, we solve the steady-state boundary value problem of spherically-symmetric accretion between the PNS surface (r_nu) and the shock (r_S), including a scheme for flavor conversion via CnuO. For a given r_nu, PNS mass (M), accretion rate (Mdot), and assumed values of the neutrino energies from the PNS, we calculate the critical neutrino luminosity above which accretion is impossible and explosion results. We show that CnuO can decrease the critical luminosity by a factor of at most ~1.5, but only if the flavor conversion is fully completed inside r_S and if there is no matter suppression. The magnitude of the effect depends on the model parameters (M, Mdot, and r_nu) through the shock radius and the physical scale for flavor conversion. We quantify these dependencies and find that CnuO could lower the critical luminosity only for small M and Mdot, and large r_nu. However, for these parameter values CnuO are suppressed due to matter effects. By quantifying the importance of CnuO and matter suppression at the critical neutrino luminosity for explosion, we show in agreement with previous studies that CnuO are unlikely to affect the neutrino mechanism of core-collapse supernovae significantly.

Critical Conditions for Core-Collapse Supernovae

The explosion of a core-collapse supernova can be approximated by the breakdown of steady-state solutions for accretion onto a proto-neutron star (PNS). We analytically show that as the neutrino luminosity exceeds a critical value L(c), the neutrinosphere pressure exceeds the hydrostatic limit even for an optimal shock radius R. This yields L(c) [proportionally] M(2)T(2) (with logarithmic corrections) and R [proportionally] M/T, in agreement with numerical results, where M and T are the PNS mass and neutrino temperature, respectively. The near-critical flow can be approximated as a ballistic shell on top of an isothermal layer.

Potential Depth of Σ-hyperons in Saturated Nuclear Matter and Rotational Inertia of Proto Neutron Star†

In the framework of relativistic mean field theory and taking account of the baryon octet system {n, p,Λ,Σ−,Σ0,Σ+, Ξ−, Ξ0}, the influence of the potential depth U(N) Σ of Σ-hyperon in saturated nuclear matter on the rotational inertia of proto neutron star (PNS) is investigated. It is found that the rotational inertia corresponding to the maximum mass of PNS increases, respectively, by a factor of 0.44%, 0.29% and 0.08%, for the attractive potential depth U(N) Σ = -30 MeV, -20MeV, -10MeV and 0MeV, and increases by a factor of 0.06% and 0.08% for the repulsive potential depth U(N) Σ = + 10MeV, + 20MeV and + 30 MeV. The effect of the attractive (negative) potential depth U(N) Σ on the rotational inertia corresponding to the maximum mass of PNS is several times larger than that of the repulsive (positive) one.

BLACK HOLE FORMATION IN FAILING CORE-COLLAPSE SUPERNOVAE

We present results of a systematic study of failing core-collapse supernovae and the formation of stellar-mass black holes (BHs). Using our open-source general-relativistic 1.5D code GR1D equipped with a three-species neutrino leakage/heating scheme and over 100 presupernova models, we study the effects of the choice of nuclear equation of state (EOS), zero-age main sequence (ZAMS) mass and metallicity, rotation, and mass-loss prescription on BH formation. We find that the outcome, for a given EOS, can be estimated, to first order, by a single parameter, the compactness of the stellar core at bounce. By comparing protoneutron star (PNS) structure at the onset of gravitational instability with solutions of the Tolman-Oppenheimer-Volkof equations, we find that thermal pressure support in the outer PNS core is responsible for raising the maximum PNS mass by up to 25% above the cold NS value. By artificially increasing neutrino heating, we find the critical neutrino heating efficiency required for exploding a given progenitor structure and connect these findings with ZAMS conditions, establishing, albeit approximately, for the first time based on actual collapse simulations, the mapping between ZAMS parameters and the outcome of core collapse. We also study the effect of progenitor rotation and find that the dimensionless spin of nascent BHs may be robustly limited below a^* = Jc/GM^2 = 1 by the appearance of nonaxisymmetric rotational instabilities.

The maximum and minimum mass of protoneutron stars in the Brueckner theory

We study the structure of protoneutron stars within the finite-temperature Brueckner-Bethe-Goldstone theoretical approach, paying particular attention to how it is joined to a low-density nuclear equation of state (EOS). We find a slight sensitivity of the minimum value of the protoneutron star mass on the low-density equation of state, whereas the maximum mass is hardly affected.

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.

Effects of δ Meson on Thermal Protoneutron Star Matter

In the framework of the relativistic mean field theory, the effects of the δ meson on protoneutron star matter with hyperons at unite temperature are investigated. In thermal protoneutron star matter, the δ field potential increases with density first and then decreases. Fixing the density, the increase of the temperature suppresses the S field potential. With the inclusion of the δ meson, the threshold densities for hyperons become lower and the abundance of trapped neutrinos decreases. The most important effect of the δ meson is to increase the abundance of hyperons in the inner core range of protoneutron stars. With the rise of the temperature, the density range where the δ meson plays an important role is narrowed and the effects of the δ meson are suppressed. Moreover, the protoneutron star mass and radius are nearly not affected by the δ meson.

Dynamics and Neutrino Signal of Black Hole Formation in Nonrotating Failed Supernovae. II. Progenitor Dependence

We study the progenitor dependence of black hole formation and its associated neutrino signal due to the gravitational collapse of a nonrotating massive star, following on our previous study of a single progenitor model. We aim to clarify whether the dynamical evolution toward black hole formation occurs in the same manner for different progenitors and to examine whether the characteristic of neutrino bursts having short duration and rapidly increasing average energies is a general one. We perform numerical simulations using general relativistic neutrino radiation hydrodynamics to follow the dynamical evolution from the collapse of 40 and 50 M☉ presupernova models to black hole formation via contracting proto-neutron stars. For the three progenitor models studied in this paper, we find that black hole formation occurs ~0.4-1.5 s after core bounce through an increase of the proto-neutron star mass, accompanied by a short and energetic neutrino burst. The density profile of the progenitor is important in determining the accretion rate onto the proto-neutron star and, therefore, the duration of the neutrino burst. We compare the neutrino bursts of black hole-forming events from different progenitors and discuss whether they can be used to probe clearly the progenitor and the dense matter.

Neutrino crown of a protoneutron star and analysis of its convective instability

A numerical solution to the problem of the structure of the neutrino crown of a protoneutron star that is formed upon an iron-star-core collapse, which is peculiar to all massive stars at the end of their thermonuclear evolution, is given. The structure of a neutrino crown, which is semitransparent to neutrino radiation from a spherical layer between the neutrinosphere and the front of the accretion shock wave, is determined by a set of nonlinear ordinary differential equations of spherically symmetric neutrino hydrodynamics with allowance for a complete set of beta processes in a Boltzmann free-nucleon gas and an ultrarelativistic Fermi-Dirac electron-positron gas that form neutrino-crown matter. The problem of consistently taking into account nonequilibrium neutrino-absorption and neutrino-emission processes and the problem of formulating boundary conditions for a neutrino crown were the main problems in constructing the numerical solution in question, which was obtained by means of a dedicated algorithm. The problem at hand features a number of parameters: the protoneutron-star mass, M0; the rate of accretion of the outer layers of the collapsing star being considered, ⊙M0; the effective temperature of the neutrinosphere and the effective neutrino chemical potential there, Tveff and ψveff, respectively; and, finally, the total neutrino emissivity of the neutrinosphere, \(L_{v\tilde v} \). Two of these parameters, M0 and \(L_{v\tilde v} \), are varied within broad intervals in accordance with the hydrodynamic theory of a collapse. On one hand, the numerical solutions constructed in the present study give an idea of the physical conditions in the immediate vicinity of a protoneutron star in the course of its continuing gravitational collapse; on the other hand, they make it possible to obtain exhaustive information about its convective instability, which is the most important property of a so-called soundless collapse—that is, a collapse not accompanied by an explosion of a supernova scale. The increment of the development of a convective instability is obtained at a linear stage, this giving sufficient grounds to introduce the hypothesis that the instability in question plays a key role in the origin of observed gamma-ray bursts. More precisely, these bursts may result from the development of the instability at the subsequent nonlinear stage, which has yet to be studied theoretically—in particular, on the basis of non-one-dimensional numerical models of neutrino hydrodynamics.

PROTONEUTRON STAR MODEL WITH NONZERO STRANGENESS CORE

Protoneutron stars are hot and lepton rich objects formed in type II supernovae. It is natural to regard the evolution of these stars as taking place in several stages. This paper describes results of analysis of protoneutron star evolution for models incorporating an strangeness-rich, neutrino opaque matter equation of state. Of special interest in this paper is the comparison of protoneutron star models for two different phases. One characterized by neutrino trapping and by the value of entropy s=1 and the other, formed when neutrinos leak out of the system, described as a hot deleptonized star. The equation of state adequate for the protoneutron star has been constructed. It has been shown that the maximum stable protoneutron star mass is close to 1.44 M⊙.

The r-process in neutrino-driven winds from a typical neutron star with M = 1.4 M⊙

We study the effects of the outer boundary conditions in neutrino-driven winds on the r-process nucleosynthesis. Varying the boundary condition, we obtain various asymptotic thermal temperature of expanding material. As a result, we find that the slightly lower asymptotic temperature than those in the previous studies of the neutrino-driven winds can lead to a successful r-process even for the typical proto-neutron star mass M NS 1.4M ⊙. We also discuss the relation between the boundary condition and neutron star mass, which is related to the progenitor mass, for the successful r-process

ITAL][CLC]r[/CLC][/ITAL]-Process Nucleosynthesis in Neutrino-driven Winds from a Typical Neutron Star with [ITAL]M[/ITAL] = 1.4 [ITAL]M[/ITAL][TINF]⊙[/TINF

We study the effects of the outer boundary conditions in neutrino-driven winds on r-process nucleosynthesis. We perform numerical simulations of hydrodynamics of neutrino-driven winds and nuclear reaction network calculations. As an outer boundary condition of hydrodynamic calculations, we set a pressure upon the outermost layer of the wind, which is approaching toward the shock wall. Varying the boundary pressure, we obtain various asymptotic thermal temperatures of expanding material in the neutrino-driven winds for resulting nucleosynthesis. We find that a slightly lower asymptotic temperature reduces the charged particle reaction rates and the resulting amount of seed elements and leads to a high neutron-to-seed ratio for a successful r-process abundance pattern, which is in reasonable agreement with the solar system r-process abundance pattern. As a result, the asymptotic temperature, slightly lower than those in previous studies of neutrino-driven winds, can lead to a successful r-process even for the typical proto-neutron star mass MNS ~ 1.4 M☉. We also explore the relation between the boundary condition and the neutron star mass, which is related to the progenitor mass, for a successful r-process.

Ther‐Process in the Neutrino Winds of Core‐Collapse Supernovae and U‐Th Cosmochronology

The discovery of the second highly r-process-enhanced, extremely metal poor star, CS 31082-001 ([Fe/H] = -2.9) has provided a powerful new tool for determination by virtue of the detection and measurement of the radioactive species uranium and thorium. Because the half-life of 238U is one-third that of 232Th, the U-Th pair can, in principle, provide a far more precise cosmochronometer than the Th-Eu pair that has been used in previous investigations. In the application of this chronometer, the of (the progenitor of) CS 31082-001 can be regarded as the minimum of the Galaxy, and hence of the universe. One of the serious limitations of this approach, however, is that predictions of the production ratio of U and Th have not been made in the context of a realistic astrophysical model of the r-process. We have endeavored to produce such a model, based on the winds that are expected to arise from the nascent neutron star of a core-collapse supernova. In this model, the proto-neutron star mass and the (asymptotic) neutrino sphere radius are assumed to be 2.0 M☉ and 10 km, respectively. Recent hydrodynamic studies indicate that there may exist difficulties in obtaining such a compact (massive and/or small in radius) remnant. Nevertheless, we utilize this set of parameter choices since previous work suggests that the third r-process peak (and thus U and Th) is hardly reached when one adopts a less compact proto-neutron star in the framework of the neutrino-wind scenario. The temperature and density histories of the material involved in the neutron-capture processes are obtained with the assumption of a steady flow of the neutrino-powered winds, with general relativistic effects taken into account. The electron fraction is taken to be a free parameter, constant with time. The r-process nucleosynthesis in these trajectories is calculated with a nuclear reaction network code including actinides up to Z = 100. The mass-integrated r-process yields, obtained by assuming a simple time evolution of the neutrino luminosity, are compared to the available spectroscopic elemental abundance data of CS 31082-001. As a result, the age of this star is determined to be 14.1 ± 2.5 Gyr, in excellent agreement with lower limits on the of the universe estimated by other dating techniques, as well as with other stellar radioactive estimates. Future measurements of Pt and Pb in this star, as well as expansion of searches for additional r-process-enhanced, metal-poor stars (especially those in which both U and Th are measurable), are of special importance to constrain the current astrophysical models for the r-process.