Surface asymmetries of accreting neutron stars are investigated for their mass quadrupole moment content. Though the amplitude of the gravitational waves from such asymmetries seem to be beyond the limit of detectability of the present generation of detectors, it appears that rapidly rotating neutron stars with strong magnetic fields residing in HMXBs would be worth considering for targeted search for continuous gravitational waves with the next generation of instruments.
Rapidly rotating Neutron Stars (NSs) in Low Mass X-ray Binaries (LMXBs) are thought to be interesting sources of Gravitational Waves (GWs) for current and next generation ground based detectors, such as Advanced LIGO and the Einstein Telescope. The main reason is that many of the NS in these systems appear to be spinning well below their Keplerian breakup frequency, and it has been suggested that torques associated with GW emission may be setting the observed spin period. This assumption has been used extensively in the literature to assess the strength of the likely gravitational wave signal.…
Magnetically confined mountains on accreting neutron stars are candidates for producing continuous gravitational waves. We formulate a magnetically confined mountain on a neutron star with strong multipole magnetic fields and obtain some sequences of numerical solutions. We find that the mass ellipticity of the mountain increases by one order of magnitude if the neutron star has strong multipole magnetic fields. As matter accretes on to the magnetic pole, the size of the mountain increases and the magnetic fields are buried. If the neutron star has a dipole magnetic field, the dipole magnetic …
We perform ideal-magnetohydrodynamic axisymmetric simulations of magnetically confined mountains on an accreting neutron star, with masses less than ~0.12 solar masses. We consider two scenarios, in which the mountain sits atop a hard surface or sinks into a soft, fluid base. We find that the ellipticity of the star, due to a mountain grown on a hard surface, approaches ~2e-4 for accreted masses greater than ~1.2e-3 solar masses, and that sinking reduces the ellipticity by between 25% and 60%. The consequences for gravitational radiation from low-mass x-ray binaries are discussed.
With the remarkable advent of gravitational-wave astronomy, we have shed light on previously shrouded events: compact binary coalescences. Neutron stars are promising (and confirmed) sources of gravitational radiation and it proves timely to consider the ways in which these stars can be deformed. Gravitational waves provide a unique window through which to examine neutron-star interiors and learn more about the equation of state of ultra-dense nuclear matter. In this work, we study two relevant scenarios for gravitational-wave emission: neutron stars that host (non-axially symmetric) mountains…
Many low-mass X-ray binary (LMXB) systems are observed to contain rapidly spinning neutron stars. The spin frequencies of these systems may be limited by the emission of gravitational waves. This can happen if their mass distribution is sufficiently non-axisymmetric. It has been suggested that such `mountains' may be created via temperature non-axisymmetries, but estimates of the likely level of temperature asymmetry have been lacking. To remedy this, we examine a simple symmetry breaking mechanism, where an internal magnetic field perturbs the thermal conductivity tensor, making it direction-…
The elastic crust of a neutron star fractures repeatedly as it spins down electromagnetically. An idealised, macroscopic model of inhomogeneous crustal failure is presented based on a cellular automaton with nearest-neighbour tectonic interactions involving strain redistribution and thermal dissipation. Predictions are made of the size and waiting-time distributions of failure events, as well as the rate of failure as the star spins down. The last failure event typically occurs when the star spins down to approximately 1% of its birth frequency with implications for rotational glitch activity.…
Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to $τ_\mathrm{I} \sim 10^5 - 10^8$ yr (depending on the conductivity of the neutron star crust) for an accreted mass of $M_a = 1.2 \times 10^{-4} M_…
A magnetically confined mountain on the surface of an accreting neutron star simultaneously reduces the global magnetic dipole moment through magnetic burial and generates a mass quadrupole moment, which emits gravitational radiation. Previous mountain models have been calculated for idealized isothermal and adiabatic equations of state. Here these models are generalised to include non-zero, finite thermal conduction. Grad-Shafranov equilibria for three representative, polytropic equations of state are evolved over many conduction time-scales with the magnetohydrodynamic solver PLUTO. It is sh…
Continuous gravitational waves are nearly monochromatic signals emitted by asymmetries in rotating neutron stars. These signals have not yet been detected. Deep all-sky searches for continuous gravitational waves from isolated neutron stars require significant computational expense. Deep searches for neutron stars in binary systems are even more expensive, but potentially these targets are more promising emitters, especially in the hundreds-Hz region, where ground-based gravitational wave detectors are most sensitive. We present here an all-sky search for continuous signals with frequency betw…
Cyclotron resonance scattering features (CRSFs) in the X-ray spectrum of an accreting neutron star are modified differently by accretion mounds sustained by magnetic and thermocompositional gradients. It is shown that one can discriminate, in principle, between mounds of different physical origins by studying how the line energy, width, and depth of a CRSF depend on the orientation of the neutron star, accreted mass, surface temperature distribution, and equation of state. CRSF signatures including gravitational light bending are computed for both phase-resolved and phase-averaged spectra on t…
We give an improved estimate of the detectability of gravitational waves from magnetically confined mountains on accreting neutron stars. The improved estimate includes the following effects for the first time: three-dimensional hydromagnetic ("fast") relaxation, three-dimensional resistive ("slow") relaxation, realistic accreted masses $M_a \la 2 \times 10^{-3} M_\odot$, (where the mountain is grown ab initio by injection), and verification of the curvature rescaling transformation employed in previous work. Typically, a mountain does not relax appreciably over the lifetime of a low-mass X-ra…
Mountains on rapidly rotating neutron stars efficiently radiate gravitational waves. The maximum possible size of these mountains depends on the breaking strain of neutron star crust. With multi-million ion molecular dynamics simulations of Coulomb solids representing the crust, we show that the breaking strain of pure single crystals is very large and that impurities, defects, and grain boundaries only modestly reduce the breaking strain to around 0.1. Due to the collective behavior of the ions during failure found in our simulations, the neutron star crust is likely very strong and can suppo…
Rapidly rotating neutron stars in Low Mass X-ray Binaries have been proposed as an interesting source of gravitational waves. In this chapter we present estimates of the gravitational wave emission for various scenarios, given the (electromagnetically) observed characteristics of these systems. First of all we focus on the r-mode instability and show that a 'minimal' neutron star model (which does not incorporate exotica in the core, dynamically important magnetic fields or superfluid degrees of freedom), is not consistent with observations. We then present estimates of both thermally induced …
Magnetically confined mountains on accreting neutron stars are promising sources of continuous-wave gravitational radiation and are currently the targets of directed searches with long-baseline detectors like the Laser Interferometer Gravitational Wave Observatory (LIGO). In this paper, previous ideal-magnetohydrodynamic models of isothermal mountains are generalized to a range of physically motivated, adiabatic equations of state. It is found that the mass ellipticity drops substantially, from ε~ 3e-4 (isothermal) to ε~ 9e-7 (non-relativistic degenerate neutrons), 6e-8 (relativistic degenerat…
We compute the continuous part of the ideal-magnetohydrodynamic (ideal-MHD) frequency spectrum of a polar mountain produced by magnetic burial on an accreting neutron star. Applying the formalism developed by Hellsten & Spies (1979), extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfvén part and a cusp part. The eigenfunctions are chirped and anharmonic with an exponential envelope, and the eigenfrequencies cover the whole spectrum above a minimum $ω_\mathrm{low}$. For equilibria with accreted mass …
Accreting neutron stars are one of the main targets for continuous gravitational wave searches, as asymmetric accretion may lead to quadrupolar deformations, or `mountains', on the crust of the star, which source gravitational wave emission at twice the rotation frequency. The gravitational wave torque may also impact on the spin evolution of the star, possibly dictating the currently observed spin periods of neutron stars in Low Mass X-ray Binaries and leading to the increased spindown rate observed during accretion in PSR J1023+0038. Previous studies have shown that deformed reaction layers …
One of the key differences between normal neutron and (bare) quark stars is relevant to the fact that the former are gravitationally bound while the latter self-confined unless their masses approach the maximum mass. This difference results in the possibility that quark stars could be very low massive whereas neutron stars cannot. Mountains could also be build on quark stars if realistic cold quark matter is in a solid state, and an alternative estimation of the mountain building is present. As spinning compact objects with non-axisymmetric mass distribution will radiate gravitational waves, t…
In this paper we study the spin-evolution and gravitational-wave luminosity of a newly born millisecond magnetar, formed either after the collapse of a massive star or after the merger of two neutron stars. In both cases we consider the effect of fallback accretion, and consider the evolution of the system due to the different torques acting on the star, namely the spin up torque due to accretion and spin-down torques due to magnetic dipole radiation, neutrino emission, and gravitational wave emission linked to the formation of a `mountain' on the accretion poles. Initially the spin period is …
Modelling mountains on accreting magnetized neutron stars
Università di Pisa（比萨大学）；Scuola Normale Superiore（比萨高等师范学院）；Università di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所，米兰分部）；INFN, Sezione di Pisa（意大利国家核物理研究所，比萨分部）；INFN, Sezione di Ferrara（意大利国家核物理研究所，费拉拉分部）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）
This work explores whether gravitational waves (GWs) from neutron star (NS) mountains can be detected with current 2nd-generation and future 3rd-generation GW detectors. In particular, we focus on a scenario where transient mountains are formed immediately after a NS glitch. In a glitch, a NS's spin frequency abruptly increases and then often exponentially recovers back to, but never quite reaches, the spin frequency prior to the glitch. If the recovery is ascribed to an additional torque due to a transient mountain, we find that GWs from that mountain are marginally-detectable with Advanced L…
With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar "mountain" deformation, the excitation of oscillations during magnetar flares and the possible gravit…
Neutron rich matter is central to many fundamental questions in nuclear physics and astrophysics. Moreover, this material is being studied with an extraordinary variety of new tools such as the Facility for Rare Isotope Beams (FRIB) and the Laser Interferometer Gravitational Wave Observatory (LIGO). We describe the Lead Radius Experiment (PREX) that uses parity violating electron scattering to measure the neutron radius in $^{208}$Pb. This has important implications for neutron stars and their crusts. We discuss X-ray observations of neutron star radii. These also have important implications f…
At very high densities, electrons react with protons to form neutron rich matter. This material is central to many fundamental questions in nuclear physics and astrophysics. Moreover, neutron rich matter is being studied with an extraordinary variety of new tools such as the Facility for Rare Isotope Beams (FRIB) and the Laser Interferometer Gravitational Wave Observatory (LIGO). We describe the Lead Radius Experiment (PREX) that uses parity violating electron scattering to measure the neutron radius in $^{208}$Pb. This has important implications for neutron stars and their crusts. We discuss …
With the first detections of binary neutron star mergers by gravitational-wave detectors, it proves timely to consider how the internal structure of neutron stars affects the way in which they can be asymmetrically deformed. Such deformations may leave measurable imprints on gravitational-wave signals and can be sourced through tidal interactions or the formation of mountains. We detail the formalism that describes fully-relativistic neutron star models with elastic crusts undergoing static perturbations. This formalism primes the problem for studies into a variety of mechanisms that can defor…
At very high densities, electrons react with protons to form neutron rich matter. This material is central to many fundamental questions in nuclear physics and astrophysics. Moreover, neutron rich matter is being studied with an extraordinary variety of new tools such as the Facility for Rare Isotope Beams (FRIB) and the Laser Interferometer Gravitational Wave Observatory (LIGO). We describe the Lead Radius Experiment (PREX) that uses parity violating electron scattering to measure the neutron radius of 208Pb. This has important implications for neutron stars and their crusts. We discuss X-ray…
Gravitational waves astronomy allows us to study objects and events invisible in electromagnetic waves. It is crucial to validate the theories and models of the most mysterious and extreme matter in the Universe: the neutron stars. In addition to inspirals and mergers of neutrons stars, there are currently a few proposed mechanisms that can trigger radiation of long-lasting gravitational radiation from neutron stars, such as e.g., elastically and/or magnetically driven deformations: mountains on the stellar surface supported by the elastic strain or magnetic field, free precession, or unstable…
The light curve of many supernovae (SNe) and gamma-ray bursts (GRBs) can be explained by a sustained injection of extra energy from its possible central engine, a rapidly rotating strongly magnetic neutron star (i.e. magnetar). The magnetic dipole radiation power that the magnetar supplies comes at the expense of the star's rotational energy. However, radiation by gravitational waves (GWs) can be more efficient than magnetic dipole radiation because of its stronger dependence on neutron star spin rate Omega, i.e. Omega^6 (for a static 'mountain') or Omega^8 (for a r-mode fluid oscillation) ver…
Continuous Gravitational Waves from Thermo-Elastic Mountains in Ultraluminous X-ray Pulsars
Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou 730000, China（兰州理论物理中心，甘肃省理论物理重点实验室，教育部量子理论与应用重点实验室，甘肃省量子物理基础学科研究中心）；Institute of Theoretical Physics & Research Center of Gravitation, School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China（兰州大学物理科学与技术学院理论物理与引力研究中心）；Department of Astronomy, School of Physics, Peking University, Beijing 100871, China（北京大学物理学院天文学系）；Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China（北京大学科维理天文与天体物理研究所）；National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China（中国科学院国家天文台）
By virtue of their sub-hour orbital periods, ultra-compact X-ray binaries are promising sources for the space-borne gravitational-wave interferometers LISA, Taiji, and TianQin. Some of these systems contain a neutron star primary, whose spin period can be measured directly via pulse timing, or indirectly through rotational modulations of burst phenomena. It is pointed out here that since actively accreting stars, with spin frequencies in the hundreds of Hz, may continuously emit appreciable gravitational waves due to the presence of accretion-built mountains, toroidal magnetic fields, and/or $…
We define `astromaterial science' as the study of materials in astronomical objects that are qualitatively denser than materials on earth. Astromaterials can have unique properties related to their large density, though they may be organized in ways similar to more conventional materials. By analogy to terrestrial materials, we divide our study of astromaterials into hard and soft and discuss one example of each. The hard astromaterial discussed here is a crystalline lattice, such as the Coulomb crystals in the interior of cold white dwarfs and in the crust of neutron stars, while the soft ast…
The pulsar J1203+0038 rotates with a frequency $ν\approx 592$ Hz and has been observed to transition between a radio state, during which it is visible as a millisecond radio pulsar, and and a Low Mass X-ray Binary state, during which accretion powered X-ray pulsations are visible. Timing during the two phases reveals that during the LMXB phase the neutron star is spinning down at a rate of $\dotν\approx -3 \times 10^{-15}$ Hz/s, which is approximately 27\% faster than the rate measured during the radio phase, $\dotν\approx -2.4 \times 10^{-15}$ Hz/s, and at odds with the predictions of accreti…
Sco X-1 as a continuous gravitational waves source: modelling the secular evolution using MESA
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Department of Physics, Norwegian University of Science and Technology（挪威科技大学物理系）
