Figure 1:
Schematic pictures of various neutron star surfaces. 

Figure 2:
Different parameter domains in the plane for ^{56}Fe plasma with magnetic field B = 10^{12} G. Dashdot line: melting temperature . Solid lines: – Fermi temperature for the electrons (noted in the main text); – ion plasma temperature. Longdash lines: and relevant for the quantized regime of the electrons (Section 2.2); for comparison we also show, by dotted lines, , and for B = 0. For further explanation see the text. From [184]. 

Figure 3:
Left panel: melting temperature versus density. Right panel: electron and ion plasma temperature versus density. Solid lines: the groundstate 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. Dotdash 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. 

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. 

Figure 5:
In the Wigner–Seitz approximation the crystal (represented here as a twodimensional 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 , where is the density of lattice sites (ions). 

Figure 6:
Surface tension of the nuclei in neutron star crusts versus neutron excess parameter inside the nuclear cluster, in the plane interface approximation with different Skyrme models [123]. 

Figure 7:
Structure of the ground state of the inner crust. Radius of the Wigner–Seitz cell, proton radius of spherical nuclei, and fraction of volume filled by nuclear clusters (in percent), versus average baryon number density as calculated by Douchin & Haensel [124]. 

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 as calculated by Douchin & Haensel [124]. is the number of neutrons adsorbed on the surface of the clusters. 

Figure 9:
Proton number Z of the nuclear clusters vs. density in the ground state of the inner crust of neutron stars, calculated by various authors from different liquid drop models based on manybody theories with effective interactions: RBP(Ravenhall, Bennett and Pethick) [344], Douchin & Haensel [124], Pethick & Ravenhall [326]. For comparison, the results of the quantum calculations of Negele & Vautherin [303] (diamonds) are also shown. 

Figure 10:
Proton number Z of the nuclear clusters vs. the mass density in the ground state of the inner crust, calculated by different semiclassical models: Buchler & Barkat [61], Ogasawara & Sato [308], Oyamatsu [314], Sumiyoshi et al. [400], Goriely et al. [171]. For comparison the results of the quantum calculations of Negele & Vautherin [303] (diamonds) are also shown. 

Figure 11:
Proton number Z of the nuclear clusters vs. the mass density in the ground state of the inner crust, calculated by different quantum models: Negele & Vautherin [303], the model P2 from Baldo et al. [31, 32] and the recent calculations of Onsi et al [311]. 

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 (in cm^{–3}), as calculated by Negele & Vautherin [303]. 

Figure 13:
Wigner–Seitz cell of a bodycentered cubic lattice. 

Figure 14:
First Brillouin zone of the bodycentered cubic lattice (whose Wigner–Seitz is shown in Figure 13). The directions x, y and z denote the Cartesian axis in space. 

Figure 15:
Single particle energy spectrum of unbound neutrons in the ground state of the inner crust composed of ^{200}Zr, at 7 10^{11} g cm^{–3}, obtained by Chamel et al. [96]. Left: calculation in the Wigner–Seitz approximation. Right: full band structure calculation (reduced zone scheme) assuming that the crust is a bodycentered cubic lattice with nuclear clusters (solid line) and without (dashed line). The capital letters on the horizontal axis refer to lines or points in kspace, as indicated in Figure 14. 

Figure 16:
Structures formed by selfassembled surfactants in aqueous solutions, depending on the volume ratio of the hydrophilic and hydrophobic parts. Adapted from [226]. 

Figure 17:
Sketch of the sequence of pasta phases in the bottom layers of groundstate crusts with an increasing nuclear volume fraction, based on the study of Oyamatsu and collaborators [315]. 

Figure 18:
The artist’s view of a lowmass Xray 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. 

Figure 19:
Model of an accreting neutron star crust. The total mass of the star is . Stable hydrogen burning takes place in the Hburning shell, and produces helium, which accumulates in the Heshell. Helium ignites at 10^{7} g cm^{–3}, leading to a helium flash and explosive burning of all matter above the bottom of the Helayer into ^{56}Ni, which captures electrons to become ^{56}Fe. After 1 h, the cycle of accretion, burning of hydrogen and explosion triggered by a helium flash repeats again and the layer of iron from the previous burst is pushed down. Based on the unpublished results of calculations by P. Haensel and J.L. Zdunik. Accreted crust model of [186, 185]. The core model of [125]. 

Figure 20:
Electron capture processes. 

Figure 21:
Z and N of nuclei vs. matter density in an accreted crust, for different models of dense matter. Solid line: ; dotted line: . Every change of N and Z, which takes place at a constant pressure, is accompanied by a jump in density: it is represented by small steep (but not perpendicular!) segments of the curves. These segments connect the top and the bottom density of a thin reaction shell. Arrows indicate positions of the neutron drip point. From Haensel & Zdunik [187]. 

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. 

Figure 23:
Integrated heat released in the crust, (per one accreted nucleon) versus , assuming initial ashes of pure ^{56}Fe. Solid line: HZ* model of Haensel & Zdunik [188], with . Dashdotted line: with pycnonuclear fusion blocked until . Based on Haensel & Zdunik [188]. Figure made by J.L. Zdunik. 

Figure 24:
Baryon chemical potential at , vs. pressure for different models of neutron star crust. Black solid line: for the groundstate crust. Lines with discontinuous drops: for four evolution models in the accreted crust with . Upper four smooth lines, which nearly coincide: . For an explanation see the text. Based on Haensel & Zdunik [188]. Figure made by J.L. Zdunik. 

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, ) in a steady thermal state, with standard cooling of the core (no fast cooling of the direct Urca type). Upper solid curve – . Lower solid curve – . H and He burning shells are indicated by asterisks. Deep crustal heating is included. Dashed line – temperature profile without deep crustal heating. Based on Figure 3b of MiraldaEscudé el al. [292]. 

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 MiraldaEscudé et al. [292]. 

Figure 27:
EoS of the ground state of the outer crust for various nuclear models. From Rüster et al. [357]. A zoomedin segment of the EoS just before the neutron drip can be seen in Figure 28. 

Figure 28:
EoS of the ground state of the outer crust just before neutron drip for various nuclear models. From Rüster et al. [357]. 

Figure 29:
Comparison of the SLy and FPS EoSs. From [184]. 

Figure 30:
Comparison of the SLy and FPS EoSs near the crustcore transition. Thick solid line: inner crust with spherical nuclei. Dashed line corresponds to “exotic nuclear shapes”. Thin solid line: uniform npe matter. From [184]. 

Figure 31:
Adiabatic index for various EoSs of the groundstate outer crust below neutron drip. The horizontal line corresponds to . The neutron drip point 4 10^{11} g cm^{–3} depends slightly on the EoS model used and, therefore, is not marked. From Rüster et al. [357]. 

Figure 32:
Adiabatic index for the EoS of the groundstate crust. Dotted vertical lines correspond to the neutron drip and crustcore interface points. Calculations performed using the SLy EoS of Douchin & Haensel [125]. 

Figure 33:
The SLy EoS. Dotted vertical lines correspond to the neutron drip and crustcore transition. From [184]. 

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. 

Figure 35:
Variation of the adiabatic index of supernova matter with mass density for three different EoSs with trapped neutrinos: Lattimer and Swesty [255] (compressible liquid drop model), Shen [374, 375] (relativistic mean field theory in the local density approximation) and Wolff [197] (Hartree–Fock with Skyrme nucleonnucleon interaction). The lepton fraction is and the entropy per nucleon is equal to . 

Figure 36:
Variation of the adiabatic index of supernova matter, , with pressure in the nuclear pasta phases for a fixed electron fraction and the entropy per nucleon , from the Thomas–Fermi calculations with the Skyrme interaction SkM of Lassaut et al. [252]. 

Figure 37:
Mass of the crust for the SLy EoS [125]. The neutron star mass is . For this EoS, spherical nuclei persist down to the crustcore interface. Left panel: fractional mass of the crust shell, , vs. its bottom density . Right panel: proper depth below the star surface, z vs. mass density . 

Figure 38:
Mass of the crust for the FPS EoS [274]. The neutron star mass is . Notice the presence of the pasta layer, which are absent for the SLy EoS. The pasta phases occupy a thin density layer, but contain about 48% of the crust mass. Left panel: fractional mass of the crust shell, , vs. its bottom density . Right panel: proper depth below the star surface, z vs. mass density . 

Figure 39:
Mass of the crust shell for the groundstate crust and for the accreted crust. The total stellar mass is . Accreted crust: EoS of Haensel & Zdunik [185]. Groundstate crust: same compressible liquid drop model of atomic nuclei of Mackie & Baym [277], but full thermodynamic equilibrium (cold catalyzed matter). The black dots indicate the neutron drip transition. Left panel: fractional mass of the crust shell, , vs. its bottom density . Right panel: versus depth below the star surface, z. 

Figure 40:
Cross section in the plane passing through the rotation axis of a neutron star of , rotating at 1200 Hz. The SLy EoS for crust and core [125] is used. The coordinates are defined by: and , while , , and are metric coordinates, Equation (106). The contours are lines of constant density. Inner contour: crustcore interface. Intermediate contour: outerinner crust interface. Outer contour: stellar surface. Figure made by J.L. Zdunik. 

Figure 41:
Nonmagnetized and magnetized pure ^{56}Fe crust in a neutron star with and R = 10 km and at T = 0. Matter density (left vertical scale) and the mass of the outer shell (right vertical axis) versus depth below the surface z, for B = 0, B = 10^{12} G, and B = 10^{13} G. Arrows indicate densities (kinks) at which the n = 1 Landau level starts to be populated with increasing depth. Figure 6.15 from [184]. 

Figure 42:
Nonmagnetized (solid line), and magnetized crust (dashdotted line) calculated with ground state composition calculated at . The dashed magenta line in the bottomright panel corresponds to the compressible liquid drop model of [125], and is smooth due to its quasiclassical nature, while the curve with discontinuous drops in pressure as obtained using the groundstate model of [183]. Figure made by A.Y. Potekhin. 

Figure 43:
Effective shear modulus versus density, for a bcc lattice. Solid line – cold catalyzed matter (Haensel and Pichon 1994 model [183] for the outer crust (Section 3.1), and that of Negele and Vautherin 1973 [303] for the inner crust (Section 3.2.3)). Dashdotted line – cold catalyzed matter calculated by Douchin and Haensel 2000 [126] (compressible liquid drop model, based on SLy effective NN interaction, Section 3.2.1). Dotted line – accreted crust model of Haensel and Zdunik 1990 [185] (Section 4). Figure made by A.Y. Potekhin. 

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. 

Figure 45:
Typical pairing gap in pure neutron matter as a function of the neutron number density, obtained in the BCS approximation with a bare nucleonnucleon potential and the free energy spectrum (taken from Figure 7 of [271]). 

Figure 46:
pairing gap in pure neutron matter as a function of the neutron number density obtained from microscopic calculations with different approximations to account for medium effects. 

Figure 47:
Melting temperature of the crust and critical temperature for the onset of neutron superfluidity as a function of the density . The model of the inner crust is based on Negele & Vautherin[303]. Three representative cases (as shown in Figure 46) are: the BCS pairing gap and the more realistic pairing gaps of Cao et al. [69] and Schwenk et al. [366]. 

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), assuming that the neutron superfluid is uniform with the density of unbound neutrons denoted by in [303]. Three representative cases have been considered: the BCS pairing gap , and the more realistic pairing gaps of Cao et al. [69] and Schwenk et al. [366]. The gaps are shown in Figure 46. For comparison, we also show the radius of the Wigner–Seitz sphere and the mean interneutron spacing . 

Figure 49:
Neutron pairing fields in the inner crust, calculated by Baldo et al. [32]. Results are shown inside the Wigner–Seitz sphere. is the average Fermi momentum defined by , where is the baryon density. 

Figure 50:
Schematic picture illustrating collective motions of particles associated with a low momentum quasiparticle (phonon). 

Figure 51:
Schematic picture illustrating collective motions of particles associated with a roton quasiparticle according to Feynman’s interpretation. 

Figure 52:
Momentum induced at a position by the vortex line with circulation . 

Figure 53:
Thermal conductivity vs. mass density at T = 10^{7} K for four types of ions in the neutron star envelope. Lower curves: for each composition, electronion and electronelectron collisions included. Upper curves: electronion collisions only. Based on Figure 6 from [339]. 

Figure 54:
Electrical conductivity and thermal conductivity of the outer and inner crust, calculated for the groundstate model of Negele & Vautherin [303]. Labels 7 and 8 refer to and 8, respectively. The thin line with label 7 corresponds to an impure crust, which contains in the lattice sites 5% impurities – nuclei with . Based on a figure made by A.Y. Potekhin. 

Figure 55:
The same as in Figure 54 but calculated for the accretedcrust model of Haensel & Zdunik [185]. Results obtained assuming 5% of nuclei – impurities with . Based on a figure made by A.Y. Potekhin. 

Figure 56:
Electron shear viscosity of the crust and the upper layer of the core for . Calculated by Chugunov & Yakovlev [101] with a smooth composition model of the groundstate (Appendix B of Haensel, Potekhin, and Yakovlev [184]). 

Figure 57:
Electron contribution to crust viscosity and effect of impurities. Solid lines – perfect onecomponent plasma. Dashed line – admixture of impurities with and . Curves are labeled by . Impurity contribution to becomes dominant for : this is visible for a curve. Groundstate crust model of Negele & Vautherin [303] is used. Figure made by A.Y. Potekhin. 

Figure 58:
Schematic picture of torsional oscillations in neutron star crust. Left: equilibrium structure of the solid crust, represented as a twodimensional square lattice. Right: shear flow in the crust (the shear velocity is indicated by arrows). 

Figure 59:
Longitudinal () and transverse () electrical and thermal conductivities in the outer envelope composed of ^{56}Fe for B = 10^{12} G and . Quantum calculations (solid lines) are compared with classical ones (dash lines). Vertical bars: liquidsolid transition at T = 10^{7} K. Based on Figure 5 from [338]. 

Figure 60:
Sketch of the 2surface swept out by a quantized vortex line moving with the 4velocity ; is the superfluid angular velocity. 

Figure 61:
Neutrino emissivities associated with different mechanisms of neutrino emission acting in a neutron star crust, versus , at temperature T = 3 10^{9} K. Numbers in parentheses indicate . Effect of B = 10^{14} G (and a fortiori – effect of a lower B) on is insignificant. , , and were calculated at B = 0. Label “syn (14)” – synchrotron radiation by electrons in constant magnetic field B = 10^{14} G, etc. Groundstate composition of the crust is assumed: Haensel & Pichon [183] model for the outer crust, and Negele & Vautherin [303] model for the inner crust. For further explanations see the text. From [428]. 

Figure 62:
Same as for Figure 61, but at T = 10^{9} K. is increased by B, as shown by the labels (14), (13), (12). Notice, that at B = 0 is too low to be seen. From [428]. 

Figure 63:
Same as in Figure 61, but calculated at T = 3 10^{8} K. and are too small to be seen. From [428]. 

Figure 64:
Neutrino emissivity from the Cooper pair formation mechanism, calculated for strong (uniform) neutron superfluidity with the maximum critical temperature (a model from [231]). For comparison, from two most efficient other mechanisms, plasmon decay and electron Bremsstrahlung, are also plotted. The smooth composition groundstate crust model of Kaminker et al. [231] is used; it predicts a specific in the inner crust. This crust model is described in detail in Appendix B.2 of Haensel et al. [184]). From [428]. 

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 10^{11} g cm^{–3}. Solid, dashed, dotted, and dotdashed 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. 

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. 

Figure 67:
Luminosities of , , and 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 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. 

Figure 68:
Redshifted surface temperatures (as seen by an observer at infinity) vs. age of neutron stars with different masses as compared with observation. Dotdashed curves are calculated with only proton superfluidity in the core. Solid curves also include neutron superfluidity in the crust and outer core [428]. 

Figure 69:
Neutron star specific heat at T = 10^{9} 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]. 

Figure 70:
Effective surface temperature (as seen by an observer at infinity) of a neutron star during the first hundred years for different crust models. Dotted lines: cooling without neutrino emission from the crust (upper line), infinite at . Solid line: cooling curve for the best values of , , and . Dashed line : dripped neutrons heat capacity removed. Dashed curve : thermal conductivity calculated assuming pointlike nuclei. Two other dashed lines: neutrino emission processes removed except for plasmon decay (pl) or electronnucleus Bremsstrahlung (). See also line in Table 2 of [167]. 

Figure 71:
Magnetic field lines and temperature distribution in a neutron star crust for an axisymmetric dipolar magnetic field B = 3 10^{12} G and an isothermal core with temperature T_{core} = 10^{6} K. The temperature is measured in units of T_{core}. The magnetic field is confined to the crust. From [158]. 

Figure 72:
Relationship between the effective surface temperature , as measured by an observer at infinity, and the local temperature at the bottom of the heatblanketing envelope, (at ). Calculations performed for the groundstate (Fe) and partlyaccreted envelopes of mass . Numbers indicate for a star with surface gravity (in units of 10^{14} cm s^{–2}). Symbols in parentheses indicate chemical composition of accreted envelope. 

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 relements. From [23]. 

Figure 74:
Glitch observed in the Crab pulsar by Wong et al. [425] 

Figure 75:
Amplitudes of 97 pulsar glitches, including the very large glitch observed in PSR J1806–2125 [199]. 

Figure 76:
Schematic picture showing the variations and of the pulsar angular frequency , during a glitch and in the interglitch period, respectively. 

Figure 77:
Coupling parameter for selected glitching pulsars. From [269]. 

Figure 78:
The moment of inertia I vs. the deformation parameter for the Crab pulsar over the S5 run of the LIGO detector. The areas to the right of the diagonal lines are the experimentally excluded regions. The horizontal lines represent theoretical upper and lower limits on the moment of inertia. The lines labelled “uniform prior” and “restricted prior” are the results obtained respectively without and with prior information on the gravitational wave signal parameters. From [2]. 

Figure 79:
Constraints on the mass and radius of SGR 1806–20 obtained from the seismic analysis of quasiperiodic oscillations in Xray emission during the December 27, 2004 giant flare. For comparison, the massradius relation for several equations of state is shown (see [359] for further details). 

Figure 80:
Constraints on the mass and radius of SGR 1900+14 obtained from the seismic analysis of the quasiperiodic oscillations in the Xray emission during the August 27, 1998 giant flare. For comparison, the massradius relation for several equations of state is shown (see [359] for further details). From [359]. 

Figure 81:
Oscillations detected in an Xray burst from 4U 1728–34 at frequency 363 Hz [399]. 

Figure 82:
Spreading of a thermonuclear burning hotspot on the surface of a rotating neutron star simulated by Spitkovsky [386] (from http://www.astro.princeton.edu/~anatoly/). 

Figure 83:
Xray luminosities of SXTs in quiescence vs. timeaveraged accretion rates. The heating curves correspond to different neutron star masses, increasing from the top to the bottom, with a step of . The EoS of the core is moderately stiff, with [340]. The model of a strong proton and a weak neutron superfluidity is assumed [261]. The highest curve (hottest stars) corresponds to , and the lowest one (coldest stars) to . The upper bundle of coalescing curves corresponds to masses , where a star of mass has a central density equal to the threshold for the direct Urca process. The red dotted line represents thermal states of a “basic model” (nonsuperfluid core, slow cooling via a modified Urca process). Total deep heat released per accreted nucleon is . Figure made by K.P. Levenfish. For a further description of neutron star models and observational data see Levenfish & Haensel [261]. 

Figure 84:
Same as Figure 83 but assuming ten times smaller . Such a low crustal heating is contradicted by the measured luminosities of three SXTs: Aql X–1, RXJ1709–2639, and 4U 1608–52. Figure made by K.P. Levenfish. 

Figure 85:
Left vertical axis: thermal conductivity of neutron star crust vs. density, at and 8. GS – pure ground state crust. A – pure accreted crust. GS (low ) – amorphous ground state crust. Right vertical axis – deep crustal heating per accreted nucleon in a thin heating shell, vs. density, according to model of Haensel & Zdunik [188]. From Shternin et al. [379]. Figure made by P.S. Shternin. 

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, . Curves 1 and 4 were obtained for pure crystal accreted crust with two different models of superfluidity of neutrons in the inner crust (strong and weak). Curves 1 and 4 give best fit to data points. Line 5 – amorphous ground state crust; line 2 – ground state crust without neutron superfluidity: both are ruled out by observations. From Shternin et al. [379]. Figure made by P.S. Shternin. 
http://www.livingreviews.org/lrr200810 
This work is licensed under a Creative Commons License. Problems/comments to 