Transportation Costs and the National Debt

Haensel, Vladimir

doi:10.1126/science.262.5131.163

Cited by 23 publications

(45 citation statements)

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“…Non-equilibrium beta processes in normal (non superfluid) neutron star cores have already been the subject of several studies (Haensel 1992;Reisenegger 1995). In this section, we shall not discuss the astrophysical conditions in which the breaking of chemical equilibrium can occur, but focus on its microphysical description.…”

Section: Out-of-equilibrium Beta Processes Without Superfluiditymentioning

confidence: 99%

“…While in beta equilibrium only the non-zero value of the temperature T determines the size of the available phase-space, and consequently all reactions rates, δµ 0 opens additional volume in the phase-space for beta processes. This results in an increase of the neutrino emissivity, and as beta reactions occurring off-equilibrium produce entropy and therefore heat neutron star matter, the net effect is the matter heating (Haensel 1992;Gourgoulhon & Haensel 1993;Reisenegger 1995Reisenegger , 1997Fernández & Reisenegger 2005).…”

Section: Introductionmentioning

confidence: 99%

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Non-equilibrium beta processes in superfluid neutron star cores

Villain

Haensel²

2005

A&A

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The influence of nucleons superfluidity on the beta relaxation time of degenerate neutron star cores, composed of neutrons, protons and electrons, is investigated. We numerically calculate the implied reduction factors for both direct and modified Urca reactions, with isotropic pairing of protons or anisotropic pairing of neutrons. We find that due to the non-zero value of the temperature and/or to the vanishing of anisotropic gaps in some directions of the phase-space, superfluidity does not always completely inhibit beta relaxation, allowing for some reactions if the superfluid gap amplitude is not too large in respect to both the typical thermal energy and the chemical potential mismatch. We even observe that if the ratio between the critical temperature and the actual temperature is very small, a suprathermal regime is reached for which superfluidity is almost irrelevant. On the contrary, if the gap is large enough, the composition of the nuclear matter can stay frozen for very long durations, unless the departure from beta equilibrium is at least as important as the gap amplitude. These results are crucial for precise estimation of the superfluidity effect on the cooling/slowing-down of pulsars and we provide online subroutines to be implemented in codes for simulating such evolutions.

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Section: Out-of-equilibrium Beta Processes Without Superfluiditymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-equilibrium beta processes in superfluid neutron star cores

Villain

Haensel²

2005

A&A

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“…In order to have different rotation rates in a stationary state, one therefore has to exclude β-reactions altogether, or at least assume that their characteristic timescale is much longer than the timescale at which we want to consider the configuration to be approximately stationary, for example the dynamical timescale (of order ms). In practice this assumption seems physically well justified by the slowness of these reactions (Haensel 1992), which operate on timescales of months to years for mature neutron stars.…”

Section: Stationary Two-fluid Neutron Star Modelsmentioning

confidence: 99%

Slowly rotating superfluid Newtonian neutron star model with entrainment

Prix

Comer

Andersson

2002

A&A

173

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Abstract. We develop a formalism that can be used to model slowly rotating superfluid Newtonian neutron stars. A simple two-fluid model is used to describe the matter, where one fluid consists of the superfluid neutrons that are believed to exist in the inner crust and core of mature neutron stars, while the other fluid is a charge neutral conglomerate of the remaining constituents (crust nuclei, core superconducting protons, electrons, etc.). We include the entrainment effect, which is a non-dissipative interaction between the two fluids whereby a momentum induced in one of the fluids will cause part of the mass of the other fluid to be carried along. The equations that describe rotational equilibria (i.e. axisymmetric and stationary configurations) are approximated using the slow-rotation approximation; an expansion in terms of the rotation rates of the two fluids where only terms up to second-order are kept. Our formalism allows the neutrons to rotate at a rate different from that of the charged constituents. For a particular equation of state that is quadratic in the two mass-densities and relative velocities of the fluids, we find an analytic solution to the slow-rotation equations. This result provides an elegant generalisation to the two-fluid problem of the standard expressions for the one-fluid polytrope E ∝ ρ 2 . The model equation of state includes entrainment and is general enough to allow for realistic values for, say, mass and radius of the star. It also includes a mixed term in the mass densities that can be related to "symmetry energy" terms that appear in more realistic equations of state. We use the analytic solution to explore how relative rotation between the two fluids, the "symmetry energy" term, and entrainment affect the neutron star's local distribution of particles, as well as global quantities as the Kepler limit, ellipticity, and moments of inertia.

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“…This EoS is fitted to a Skyrme-Lyon EoS [39] and to experimental data for neutron-rich nuclei according to Refs. [34,40]. In the following, we refer to this crust EoS as "SLy".…”

Section: Neutron Star Equation Of State: Constraints From Observablesmentioning

confidence: 99%

“…In the previous section the transition region from the hadronic to the quark phase was chosen by means of the parameters (Γ,¯ ) of the interpolating functions (40). In this section a different approach is taken assuming a first-order phase transition from hadronic to quark matter with an extended coexistence region of the two phases.…”

Section: Hadron-quark First-order Phase Transitionmentioning

confidence: 99%

Dense baryonic matter: Constraints from recent neutron star observations

Hell

Weise

2014

Phys. Rev. C

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Updated constraints from neutron star masses and radii impose stronger restrictions on the equation of state for baryonic matter at high densities and low temperatures. The existence of two-solar-mass neutron stars rules out many soft equations of state with prominent "exotic" compositions. The present work reviews the conditions required for the pressure as a function of baryon density in order to satisfy these constraints. Several scenarios for sufficiently stiff equations of state are evaluated. The common starting point is a realistic description of both nuclear and neutron matter based on a chiral effective field theory approach to the nuclear many-body problem. Possible forms of hybrid matter featuring a quark core in the center of the star are discussed using a threeflavor Polyakov-Nambu-Jona-Lasinio (PNJL) model. It is found that a conventional equation of state based on nuclear chiral dynamics meets the astrophysical constraints. Hybrid matter generally turns out to be too soft unless additional strongly repulsive correlations, e.g. through vector current interactions between quarks, are introduced. The extent to which strangeness can accumulate in the equation of state is also discussed.

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Transportation Costs and the National Debt

Cited by 23 publications

References 0 publications

Non-equilibrium beta processes in superfluid neutron star cores

Non-equilibrium beta processes in superfluid neutron star cores

Slowly rotating superfluid Newtonian neutron star model with entrainment

Dense baryonic matter: Constraints from recent neutron star observations

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