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-ray binary. The ellipticity reaches $ε\approx 2 \times 10^{-5}$ for $M_a=2\times 10^{-3} M_\odot$. The gravitational wave spectrum for triaxial equilibria contains an additional line, which, although weak, provides valuable information about the mountain shape. We evaluate the detectability of magnetic mountains with Initial and Advanced LIGO. For a standard, coherent matched filter search, we find a signal-to-noise ratio of $d = 28 (M_a/10^{-4} M_\odot)
(1+5.5 M_a/10^{-4} M_\odot)^{-1} (D/10 \mathrm{kpc})^{-1} (T_0/14
\mathrm{d})^{1/2}$ for Initial LIGO, where $D$ is the distance and $T_0$ is the observation time. From the nondetection of gravitational waves from low-mass X-ray binaries to date, and the wave strain limits implied by the spin frequency distribution of these objects (due to gravitational wave braking), we conclude that there are other, as yet unmodelled, physical effects that further reduce he quadrupole moment of a magnetic mountain, most notably sinking into the crust.
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.
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 …
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…
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_…
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 …
Magnetically Confined Mountains on Accreting White Dwarfs
Escola de Artes, Ciências e Humanidades, Universidade de São Paulo（圣保罗大学艺术、科学与人文学院）；Instituto de Física de São Carlos, Universidade de São Paulo（圣保罗大学圣卡洛斯物理研究所）
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-…
Protomagnetars spun up to millisecond rotation periods by supernova fallback are predicted to radiate gravitational waves via hydrodynamic instabilities for ~ 10^2 s before possibly collapsing to form a black hole. It is shown that magnetic funnelling of the accretion flow (i) creates a magnetically confined polar mountain, which boosts the gravitational wave signal, and (ii) "buries" the magnetic dipole moment, delaying the propeller phase and assisting black hole formation.
Extremely powerful magnetic fields are contained inside neutron stars. Their effect is to deform the shape of the star, leading to the emission of continuous gravitational waves. The magnetic deformation of neutron stars depends on the details of their magnetic field, that is its geometry and strength. Moreover, it depends on their composition, described by the equation of state. Unfortunately, both the configuration of the magnetic field and the equation of state of neutron stars are unkown, and assessing the detectability of continuous gravitational waves from neutron stars suffers from thes…
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.
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）
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.…
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…
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 …
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…
The viscosity-driven "spin-flip" instability in newborn magnetars with interior toroidal magnetic fields is re-examined. We calculate the bulk viscosity coefficient ($ζ$) of cold, $npe μ$ matter in neutron stars (NS), for selected values of the nuclear symmetry energy and in the regime where $β$-equilibration is slower than characteristic oscillation periods. We show that: i) $ζ$ is larger than previously assumed and the instability timescale correspondingly shorter; ii) for a magnetically-induced ellipticity $ε_B \lesssim 4 \times 10^{-3}$, typically expected in newborn magnetars, spin-flip o…
