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Figure 1:
Schematic pictures of various neutron star surfaces. |
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Figure 2:
Different parameter domains in the ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 3:
Left panel: melting temperature versus density. Right panel: electron and ion plasma temperature versus density. Solid lines: the ground-state composition of the crust is assumed: Haensel & Pichon [183] for the outer crust, and Negele & Vautherin [303] for the inner crust. Dot lines: accreted crust, as calculated by Haensel & Zdunik [185]. Jumps result from discontinuous changes of Z and A. Dot-dash line: results obtained for the compressible liquid drop model of Douchin & Haensel [125] for the ground state of the inner crust; a smooth behavior (absence of jumps) results from the approximation inherent in the compressible liquid drop model. Thick vertical dashes: neutron drip point for a given crust model. Figure made by A.Y. Potekhin. |
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Figure 4:
Schematic picture of the ground state structure of neutron stars along the density axis. Note that the main part of this figure represents the solid crust since it covers about 14 orders of magnitude in densities. |
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Figure 5:
In the Wigner–Seitz approximation the crystal (represented here as a two-dimensional hexagonal lattice) is decomposed into independent identical spheres, centered around each site of the lattice. The radius of the sphere is chosen so that the volume of the sphere is equal to ![]() ![]() |
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Figure 6:
Surface tension of the nuclei in neutron star crusts versus neutron excess parameter ![]() |
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Figure 7:
Structure of the ground state of the inner crust. Radius ![]() ![]() ![]() ![]() |
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Figure 8:
Composition of nuclear clusters in the ground state of the inner crust. Baryon number A of spherical clusters and their proton number Z, versus average baryon number density ![]() ![]() |
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Figure 9:
Proton number Z of the nuclear clusters vs. density ![]() |
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Figure 10:
Proton number Z of the nuclear clusters vs. the mass density ![]() |
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Figure 11:
Proton number Z of the nuclear clusters vs. the mass density ![]() |
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Figure 12:
Nucleon number densities (in fm–3) along the axis joining two adjacent Wigner–Seitz cells of the ground state of the inner crust, for a few baryon densities ![]() |
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Figure 13:
Wigner–Seitz cell of a body-centered cubic lattice. |
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Figure 14:
First Brillouin zone of the body-centered cubic lattice (whose Wigner–Seitz is shown in Figure 13). The directions x, y and z denote the Cartesian axis in ![]() |
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Figure 15:
Single particle energy spectrum of unbound neutrons in the ground state of the inner crust composed of 200Zr, at ![]() ![]() |
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Figure 16:
Structures formed by self-assembled surfactants in aqueous solutions, depending on the volume ratio of the hydrophilic and hydrophobic parts. Adapted from [226]. |
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Figure 17:
Sketch of the sequence of pasta phases in the bottom layers of ground-state crusts with an increasing nuclear volume fraction, based on the study of Oyamatsu and collaborators [315]. |
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Figure 18:
The artist’s view of a low-mass X-ray binary. The companion of a neutron star fills its Roche lobe and loses its mass via plasma flow through the inner Lagrangian point. Due to its angular momentum, plasma orbits around the neutron star, forming an accretion disk. Gradually losing angular momentum due to viscosity within the accretion disk, plasma approaches the neutron star and eventually falls onto its surface. Figure by T. Piro. |
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Figure 19:
Model of an accreting neutron star crust. The total mass of the star is ![]() ![]() ![]() |
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Figure 20:
Electron capture processes. |
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Figure 21:
Z and N of nuclei vs. matter density in an accreted crust, for different models of dense matter. Solid line: ![]() ![]() |
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Figure 22:
Heat sources accompanying accretion, in the outer (upper panel) and inner (lower panel) accreted crust. Vertical lines, positioned at the bottom of every reaction shell, represent the heat per accreted nucleon. Based on Haensel & Zdunik [188]. Figure made by J.L. Zdunik. |
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Figure 23:
Integrated heat released in the crust, ![]() ![]() ![]() ![]() |
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Figure 24:
Baryon chemical potential at ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 25:
Temperature (local, in the reference frame of the star) vs. density within the crust of an accreting neutron star (soft EoS of the core, ![]() ![]() ![]() |
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Figure 26:
Same as in Figure 25, but for fast neutrino cooling due to pion condensation in the inner core. Based on Figure 3c of Miralda-Escudé et al. [292]. |
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Figure 27:
EoS of the ground state of the outer crust for various nuclear models. From Rüster et al. [357]. A zoomed-in segment of the EoS just before the neutron drip can be seen in Figure 28. |
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Figure 28:
EoS of the ground state of the outer crust just before neutron drip for various nuclear models. From Rüster et al. [357]. |
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Figure 29:
Comparison of the SLy and FPS EoSs. From [184]. |
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Figure 30:
Comparison of the SLy and FPS EoSs near the crust-core transition. Thick solid line: inner crust with spherical nuclei. Dashed line corresponds to “exotic nuclear shapes”. Thin solid line: uniform npe matter. From [184]. |
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Figure 31:
Adiabatic index ![]() ![]() ![]() ![]() |
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Figure 32:
Adiabatic index ![]() |
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Figure 33:
The SLy EoS. Dotted vertical lines correspond to the neutron drip and crust-core transition. From [184]. |
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Figure 34:
Comparison of the SLy EoS for cold catalyzed matter (dotted line) and the EoS of accreted crust (solid line). Figure by A.Y. Potekhin. |
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Figure 35:
Variation of the adiabatic index ![]() ![]() ![]() ![]() |
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Figure 36:
Variation of the adiabatic index of supernova matter, ![]() ![]() ![]() ![]() |
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Figure 37:
Mass of the crust for the SLy EoS [125]. The neutron star mass is ![]() ![]() ![]() ![]() |
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Figure 38:
Mass of the crust for the FPS EoS [274]. The neutron star mass is ![]() ![]() ![]() ![]() |
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Figure 39:
Mass of the crust shell for the ground-state crust and for the accreted crust. The total stellar mass is ![]() ![]() ![]() ![]() |
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Figure 40:
Cross section in the plane passing through the rotation axis of a neutron star of ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 41:
Nonmagnetized and magnetized pure 56Fe crust in a neutron star with ![]() ![]() |
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Figure 42:
Nonmagnetized (solid line), and magnetized crust (dash-dotted line) calculated with ground state composition calculated at ![]() ![]() |
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Figure 43:
Effective shear modulus ![]() |
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Figure 44:
Schematic picture illustrating the difference between the BCS regime (left) of overlapping loosely bound fermion pairs and the BEC regime (right) of strongly bound pairs. |
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Figure 45:
Typical ![]() |
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Figure 46:
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Figure 47:
Melting temperature ![]() ![]() ![]() ![]() |
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Figure 48:
Pippard’s coherence length for the neutron star crust model of Negele & Vautherin[303]. The coherence length has been calculated from Equation (138 ![]() ![]() ![]() ![]() ![]() |
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Figure 49:
Neutron pairing fields in the inner crust, calculated by Baldo et al. [32]. Results are shown inside the Wigner–Seitz sphere. ![]() ![]() ![]() |
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Figure 50:
Schematic picture illustrating collective motions of particles associated with a low momentum quasiparticle (phonon). |
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Figure 51:
Schematic picture illustrating collective motions of particles associated with a roton quasiparticle according to Feynman’s interpretation. |
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Figure 52:
Momentum ![]() ![]() ![]() |
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Figure 53:
Thermal conductivity vs. mass density at T = 107 K for four types of ions in the neutron star envelope. Lower curves: for each composition, electron-ion and electron-electron collisions included. Upper curves: electron-ion collisions only. Based on Figure 6 from [339]. |
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Figure 54:
Electrical conductivity ![]() ![]() ![]() ![]() |
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Figure 55:
The same as in Figure 54 but calculated for the accreted-crust model of Haensel & Zdunik [185]. Results obtained assuming 5% of nuclei – impurities with ![]() |
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Figure 56:
Electron shear viscosity of the crust and the upper layer of the core for ![]() |
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Figure 57:
Electron contribution to crust viscosity and effect of impurities. Solid lines – perfect one-component plasma. Dashed line – admixture of impurities with ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 58:
Schematic picture of torsional oscillations in neutron star crust. Left: equilibrium structure of the solid crust, represented as a two-dimensional square lattice. Right: shear flow in the crust (the shear velocity is indicated by arrows). |
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Figure 59:
Longitudinal ( ![]() ![]() ![]() |
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Figure 60:
Sketch of the 2-surface swept out by a quantized vortex line moving with the 4-velocity ![]() ![]() |
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Figure 61:
Neutrino emissivities associated with different mechanisms of neutrino emission acting in a neutron star crust, versus ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 62:
Same as for Figure 61, but at T = 109 K. ![]() ![]() |
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Figure 63:
Same as in Figure 61, but calculated at T = 3 ![]() ![]() ![]() |
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Figure 64:
Neutrino emissivity from the Cooper pair formation mechanism, calculated for strong (uniform) neutron superfluidity with the maximum critical temperature ![]() ![]() ![]() |
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Figure 65:
Mass fractions of different particles in a supernova core as a function of baryon mass coordinate at the time when the central density reaches 1011 g cm–3. Solid, dashed, dotted, and dot-dashed lines show mass fractions of protons, neutrons, nuclei, and alpha particles, respectively. The results are given for two equations of state: the compressible liquid drop model of Lattimer & Swesty [255] (thin lines) and the relativistic mean field theory in the local density approximation of Shen et al. [374, 375] (thick lines). See [402] for details. |
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Figure 66:
Radial positions of shock waves as a function of time after bounce (the moment of greatest compression of the central core corresponding to a maximum central density) for two different equations of states: the compressible liquid drop model of Lattimer & Swesty [255] (thin line) and the relativistic mean field theory in the local density approximation of Shen et al. [374, 375] (thick line). See [402] for details. Notice that these particular models failed to produce a supernova explosion. |
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Figure 67:
Luminosities of ![]() ![]() ![]() |
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Figure 68:
Redshifted surface temperatures (as seen by an observer at infinity) vs. age of neutron stars with different masses as compared with observation. Dot-dashed curves are calculated with only proton superfluidity in the core. Solid curves also include neutron superfluidity in the crust and outer core [428]. |
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Figure 69:
Neutron star specific heat at T = 109 K. Solid lines: partial heat capacities of ions (i), electrons (e) and free neutrons (n) in nonsuperfluid crusts, as well as of neutrons, protons (p) and electrons in nonsuperfluid cores. Dashed lines: heat capacities of free neutrons in the crust modified by superfluidity. Two particular models of weak and strong superfluidity are considered. The effects of the nuclear inhomogeneities on the free neutrons are neglected. From [167]. |
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Figure 70:
Effective surface temperature (as seen by an observer at infinity) of a ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 71:
Magnetic field lines and temperature distribution in a neutron star crust for an axisymmetric dipolar magnetic field B = 3 ![]() |
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Figure 72:
Relationship between the effective surface temperature ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 73:
Final composition of clumps of ejected neutron star crust with different initial densities (solid squares). The open circles correspond to the solar system abundance of r-elements. From [23]. |
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Figure 74:
Glitch ![]() |
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Figure 75:
Amplitudes of 97 pulsar glitches, including the very large glitch ![]() |
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Figure 76:
Schematic picture showing the variations ![]() ![]() ![]() |
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Figure 77:
Coupling parameter ![]() |
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Figure 78:
The moment of inertia I vs. the deformation parameter ![]() |
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Figure 79:
Constraints on the mass and radius of SGR 1806–20 obtained from the seismic analysis of quasi-periodic oscillations in X-ray emission during the December 27, 2004 giant flare. For comparison, the mass-radius relation for several equations of state is shown (see [359] for further details). |
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Figure 80:
Constraints on the mass and radius of SGR 1900+14 obtained from the seismic analysis of the quasi-periodic oscillations in the X-ray emission during the August 27, 1998 giant flare. For comparison, the mass-radius relation for several equations of state is shown (see [359] for further details). From [359]. |
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Figure 81:
Oscillations detected in an X-ray burst from 4U 1728–34 at frequency ![]() |
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Figure 82:
Spreading of a thermonuclear burning hotspot on the surface of a rotating neutron star simulated by Spitkovsky [386] (from ![]() |
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Figure 83:
X-ray luminosities of SXTs in quiescence vs. time-averaged accretion rates. The heating curves correspond to different neutron star masses, increasing from the top to the bottom, with a step of ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Figure 84:
Same as Figure 83 but assuming ten times smaller ![]() |
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Figure 85:
Left vertical axis: thermal conductivity of neutron star crust vs. density, at ![]() ![]() ![]() |
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Figure 86:
Theoretical cooling curves for KS 1731–260 relaxing toward a quiescent state; observations expressed in terms of effective surface temperature as measured by a distant observer, ![]() |
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