The shear modulus of the neutron star crust and nonradial oscillations of neutron stars

AbstractUnderstanding the properties of the crust and the core as well as its interface is essential for accurate astrophysical modelling of phenomena such as glitches, X-ray bursts or oscillations in neutron stars. To study the crust–core properties, it is crucial to develop a unified and consistent scheme to describe both the clusterised matter in the crust and homogeneous matter in the core. The low density regime in the neutron star crust is accessible to terrestrial nuclear experiments. In order to develop a consistent description of the crust and the core of neutron stars within the same formalism, we use a density functional scheme, with the model coefficients in homogeneous matter related directly to empirical nuclear observables. In this work, we extend this scheme to non-homogeneous matter to describe nuclei in the crust. We then test this scheme against nuclear observables.

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Neutron star crust in Voigt approximation: general symmetry of the stress–strain tensor and an universal estimate for the effective shear modulus

Monthly Notices of the Royal Astronomical Society Letters ◽

10.1093/mnrasl/slaa173 ◽

2020 ◽

Vol 500 (1) ◽

pp. L17-L21

Author(s):

Andrey I Chugunov

Keyword(s):

Neutron Star ◽

Shear Modulus ◽

Strain Tensor ◽

Stress Strain ◽

Effective Shear Modulus ◽

General Symmetry ◽

Atomic Nuclei ◽

Neutron Star Crust ◽

Sphere Radius ◽

Composition I

ABSTRACT I discuss elastic properties of neutron star crust in the framework of static Coulomb solid model when atomic nuclei are treated as non-vibrating point charges; electron screening is neglected. The results are also applicable for solidified white dwarf cores and other materials, which can be modelled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress–strain tensor has additional symmetry: contraction Bijil = 0. It does not depend on the structure (crystalline or amorphous) and composition. I show as a result of this symmetry the effective (Voigt averaged) shear modulus of the polycrystalline or amorphous matter to be equal to −2/15 of the Coulomb (Madelung) energy density at undeformed state. This result is general and exact within the model applied. Since the linear mixing rule and the ion sphere model are used, I can suggest a simple universal estimate for the effective shear modulus: $\sum _Z 0.12\, n_Z Z^{5/3}e^2 /a_\mathrm{e}$. Here summation is taken over ion species, nZ is number density of ions with charge Ze. Finally, ae = (4πne/3)−1/3 is electron sphere radius. Quasi-neutrality condition ne = ∑ZZnZ is assumed.

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Structure and Shear Modulus of the Neutron Star Crust

Journal of Physics Conference Series ◽

10.1088/1742-6596/342/1/012005 ◽

2012 ◽

Vol 342 ◽

pp. 012005 ◽

Cited By ~ 2

Author(s):

Joseph Hughto

Keyword(s):

Neutron Star ◽

Shear Modulus ◽

Neutron Star Crust

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Modelling neutron star mountains

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3635 ◽

2020 ◽

Vol 500 (4) ◽

pp. 5570-5582

Author(s):

F Gittins ◽

N Andersson ◽

D I Jones

Keyword(s):

Neutron Star ◽

Neutron Stars ◽

Gravitational Radiation ◽

Continuous Wave ◽

Pressure Perturbation ◽

Will Emit ◽

Thermal Pressure ◽

The Core ◽

Neutron Star Crust ◽

Crucial Ingredient

ABSTRACT As the era of gravitational-wave astronomy has well and truly begun, gravitational radiation from rotating neutron stars remains elusive. Rapidly spinning neutron stars are the main targets for continuous-wave searches since, according to general relativity, provided they are asymmetrically deformed, they will emit gravitational waves. It is believed that detecting such radiation will unlock the answer to why no pulsars have been observed to spin close to the break-up frequency. We review existing studies on the maximum mountain that a neutron star crust can support, critique the key assumptions and identify issues relating to boundary conditions that need to be resolved. In light of this discussion, we present a new scheme for modelling neutron star mountains. The crucial ingredient for this scheme is a description of the fiducial force which takes the star away from sphericity. We consider three examples: a source potential which is a solution to Laplace’s equation, another solution which does not act in the core of the star and a thermal pressure perturbation. For all the cases, we find that the largest quadrupoles are between a factor of a few to two orders of magnitude below previous estimates of the maximum-mountain size.

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A Gravitational-Wave Perspective on Neutron-Star Seismology

Universe ◽

10.3390/universe7040097 ◽

2021 ◽

Vol 7 (4) ◽

pp. 97

Author(s):

Nils Andersson

Keyword(s):

Neutron Star ◽

Neutron Stars ◽

Gravitational Wave ◽

Fundamental Mode ◽

Compact Binaries

We provide a bird’s-eye view of neutron-star seismology, which aims to probe the extreme physics associated with these objects, in the context of gravitational-wave astronomy. Focussing on the fundamental mode of oscillation, which is an efficient gravitational-wave emitter, we consider the seismology aspects of a number of astrophysically relevant scenarios, ranging from transients (like pulsar glitches and magnetar flares), to the dynamics of tides in inspiralling compact binaries and the eventual merged object and instabilities acting in isolated, rapidly rotating, neutron stars. The aim is not to provide a thorough review, but rather to introduce (some of) the key ideas and highlight issues that need further attention.

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Aspects of the Collapse of Compact Objects

Publications of the Astronomical Society of Australia ◽

10.1017/s1323358000018750 ◽

1980 ◽

Vol 4 (1) ◽

pp. 49-50

Author(s):

R. A. Gingold ◽

J. J. Monaghan

Keyword(s):

Neutron Star ◽

Neutron Stars ◽

White Dwarf ◽

Compact Objects ◽

Dwarf Star

Misner Thorne and Wheeler (1973), (page 629) suggested that a freshly formed White Dwarf star of several solar masses would, if slowly — rotating, collapse to form a neutron star pancake which would become unstable and eventually produce several, possibly colliding, neutron stars.

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