Quadrupole moment of a magnetically confined mountain on an accreting neutron star: effect of the equation of state

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 \epsilon ~ 3e-4 (isothermal) to \epsilon ~ 9e-7 (non-relativistic degenerate neutrons), 6e-8 (relativistic degenerate electrons) and 1e-8 (non-relativistic degenerate electrons) (assuming a magnetic field of 3e12 G at birth). The characteristic mass M_{c} at which the magnetic dipole moment halves from its initial value is also modified, from M_{c}/M_{\sun} ~ 5e-4 (isothermal) to M_{c}/M_{\sun} ~ 2e-6, 1e-7, and 3e-8 for the above three equations of state, respectively. Similar results are obtained for a realistic, piecewise-polytropic nuclear equation of state. The adiabatic models are consistent with current LIGO upper limits, unlike the isothermal models. Updated estimates of gravitational-wave detectability are made. Monte Carlo simulations of the spin distribution of accreting millisecond pulsars including gravitational-wave stalling agree better with observations for certain adiabatic equations of state, implying that X-ray spin measurements can probe the equation of state when coupled with magnetic mountain models.Comment: 20 pages, 15 figures, to be published in MNRA

Gravitational waves from an accreting neutron star with a magnetic mountain

We calculate the amplitude of gravitational waves from a neutron star accreting symmetrically at its magnetic poles. The magnetic field, which is compressed into an equatorial belt during accretion, confines accreted matter in a mountain at the magnetic pole, producing gravitational waves. We compute hydromagnetic equilibria and the corresponding quadrupole moment as a function of the accreted mass, Ma, finding the polarization- and orientation- averaged wave strain at Earth to be h_c = 6.3 × 10^(–25)(M_a/10^(–5)M_☉)(ƒ/0.6kHz)^2(d/1kpc)^(–1) for a range of conditions, where ƒ is the wave frequency and d is the distance to the source. This is ~ 10^2 times greater than previous estimates, which failed to treat the mass-flux distribution self-consistently with respect to flux-freezin

Frequency spectrum of gravitational radiation from global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star

Recent time-dependent, ideal-magnetohydrodynamic (ideal-MHD) simulations of polar magnetic burial in accreting neutron stars have demonstrated that stable, magnetically confined mountains form at the magnetic poles, emitting gravitational waves at $f_{*}$ (stellar spin frequency) and $2 f_{*}$. Global MHD oscillations of the mountain, whether natural or stochastically driven, act to modulate the gravitational wave signal, creating broad sidebands (full-width half-maximum $\sim 0.2f_*$) in the frequency spectrum around $f_{*}$ and $2 f_{*}$. The oscillations can enhance the signal-to-noise ratio achieved by a long-baseline interferometer with coherent matched filtering by up to 15 per cent, depending on where $f_*$ lies relative to the noise curve minimum. Coherent, multi-detector searches for continuous waves from nonaxisymmetric pulsars should be tailored accordingly.Comment: 4 figures, accepted for publication in Ap

Componential coding in the condition monitoring of electrical machines Part 2: application to a conventional machine and a novel machine

This paper (Part 2) presents the practical application of componential coding, the principles of which were described in the accompanying Part 1 paper. Four major issues are addressed, including optimization of the neural network, assessment of the anomaly detection results, development of diagnostic approaches (based on the reconstruction error) and also benchmarking of componential coding with other techniques (including waveform measures, Fourier-based signal reconstruction and principal component analysis). This is achieved by applying componential coding to the data monitored from both a conventional induction motor and from a novel transverse flux motor. The results reveal that machine condition monitoring using componential coding is not only capable of detecting and then diagnosing anomalies but it also outperforms other conventional techniques in that it is able to separate very small and localized anomalies

Some remarks on the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians

We consider the problem of minimising the $k$th eigenvalue, $k \geq 2$, of the ($p$-)Laplacian with Robin boundary conditions with respect to all domains in $\mathbb{R}^N$ of given volume $M$. When $k=2$, we prove that the second eigenvalue of the $p$-Laplacian is minimised by the domain consisting of the disjoint union of two balls of equal volume, and that this is the unique domain with this property. For $p=2$ and $k \geq 3$, we prove that in many cases a minimiser cannot be independent of the value of the constant $\alpha$ in the boundary condition, or equivalently of the volume $M$. We obtain similar results for the Laplacian with generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$.Comment: 16 page

Higher Order Chemistry Models in the CFD Simulation of Laser-Ablated Carbon Plumes

Production of single-walled carbon nanotubes (SWNT) has taken place for a number of years and by a variety of methods such as laser ablation, chemical vapor deposition, and arc-jet ablation. Yet, little is actually understood about the exact chemical kinetics and processes that occur in SWNT formation. In recent time, NASA Johnson Space Center has devoted a considerable effort to the experimental evaluation of the laser ablation production process for SWNT originally developed at Rice University. To fully understand the nature of the laser ablation process it is necessary to understand the development of the carbon plume dynamics within the laser ablation oven. The present work is a continuation of previous studies into the efforts to model plume dynamics using computational fluid dynamics (CFD). The ultimate goal of the work is to improve understanding of the laser ablation process, and through that improved understanding, refine the laser ablation production of SWNT