arXiv subjects

A. Melatos

Publications and source records attributed to A. Melatos.

At least 73 records · Page 4Linked to original sources

arXiv2009

Sinking of a magnetically confined mountain on an accreting neutron star

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.

astro-ph.HE↗

arXiv2009

An unstable superfluid Stewartson layer in a differentially rotating neutron star

Experimental and numerical evidence is reviewed for the existence of a Stewartson layer in spherical Couette flow at small Ekman and Rossby numbers ($\Ek \lsim 10^{-3}$, $\Ro \lsim 10^{-2}$), the relevant hydrodynamic regime in the superfluid outer core of a neutron star. Numerical simulations of a superfluid Stewartson layer are presented for the first time, showing how the layer is disrupted by nonaxisymmetric instabilities. The unstable ranges of $\Ek$ and $\Ro$ are compared with estimates of these quantities in radio pulsars that exhibit glitches. It is found that glitching pulsars lie on the stable side of the instability boundary, allowing differential rotation to build up before a glitch.

astro-ph.SR↗

arXiv2009

Improved estimate of the detectability of gravitational radiation from a magnetically confined mountain on an accreting neutron star

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.

astro-ph.HE↗

arXiv2009

Resistive relaxation of a magnetically confined mountain on an accreting neutron star

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 $M_a = 1.2 \times 10^{-4} M_\odot$. The magnetic dipole moment simultaneously reemerges as the screening currents dissipate over $τ_\mathrm{I}$. For nonaxisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfvén time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease $τ_\mathrm{I}$ by \change{one order of magnitude} relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.

astro-ph.HE↗

arXiv2009

Continuous frequency spectrum of the global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star

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 $1.2 \times 10^{-6} \la M_a/M_\odot \la 1.7 \times 10^{-4}$ and surface magnetic fields $10^{11} \la B_\ast/\mathrm{G} \la 10^{13}$, $ω_\mathrm{low}$ is approximately independent of $B_\ast$, and increases with $M_a$. The results are consistent with the Alfvén spectrum excited in numerical simulations with the \textsc{zeus-mp} solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than $\sim 100$ Hz. The implications for gravitational wave searches for low-mass X-ray binaries are considered briefly.

astro-ph.HE↗

arXiv2008

Does the accreting millisecond pulsar XTE J1814-338 precess?

Precession in an accretion-powered pulsar is expected to produce characteristic variations in the pulse properties. Assuming surface intensity maps with one and two hotspots, we compute theoretically the periodic modulation of the mean flux, pulse-phase residuals and fractional amplitudes of the first and second harmonic of the pulse profiles. These quantities are characterised in terms of their relative precession phase offsets. We then search for these signatures in 37 days of X-ray timing data from the accreting millisecond pulsar XTE J1814-338. We analyse a 12.2-d modulation observed previously and show that it is consistent with a freely precessing neutron star only if the inclination angle is < 0.1 degrees, an a priori unlikely orientation. We conclude that if the observed flux variations are due to precession, our model incompletely describes the relative precession phase offsets (e.g. the surface intensity map is over-simplified). We are still able to place an upper limit on εof 3.0 x 10^{-9} independently of our model, and estimate the phase-independent tilt angle θ; to lie roughly between 5 and 10 degrees. On the other hand, if the observed flux variations are not due to precession, the detected signal serves as a firm upper limit for any underlying precession signal. We then place an upper limit on the product εcos(θ) of \leq 9.9 x 10^{-10}. The first scenario translates into a maximum gravitational wave strain of 10^{-27} from XTE J1814-338 (assuming a distance of 8 kpc), and a corresponding signal-to-noise ratio of \leq 10^{-3} (for a 120 day integration time) for the advanced LIGO ground-based gravitational wave detector.

astro-ph↗

arXiv2008

Gravitational radiation from pulsar glitches

The nonaxisymmetric Ekman flow excited inside a neutron star following a rotational glitch is calculated analytically including stratification and compressibility. For the largest glitches, the gravitational wave strain produced by the hydrodynamic mass quadrupole moment approaches the sensitivity range of advanced long-baseline interferometers. It is shown that the viscosity, compressibility, and orientation of the star can be inferred in principle from the width and amplitude ratios of the Fourier peaks (at the spin frequency and its first harmonic) observed in the gravitational wave spectrum in the plus and cross polarizations. These transport coefficients constrain the equation of state of bulk nuclear matter, because they depend sensitively on the degree of superfluidity.

gr-qc↗

arXiv2008

Collapse times of dipolar Bose-Einstein condensates

We investigate the time taken for global collapse by a dipolar Bose-Einstein condensate. Two semi-analytical approaches and exact numerical integration of the mean-field dynamics are considered. The semi-analytical approaches are based on a Gaussian ansatz and a Thomas-Fermi solution for the shape of the condensate. The regimes of validity for these two approaches are determined, and their predictions for the collapse time revealed and compared with numerical simulations. The dipolar interactions introduce anisotropy into the collapse dynamics and predominantly lead to collapse in the plane perpendicular to the axis of polarization.

cond-mat.other↗

arXiv2008

A Cellular Automaton Model of Pulsar Glitches

A cellular automaton model of pulsar glitches is described, based on the superfluid vortex unpinning paradigm. Recent analyses of pulsar glitch data suggest that glitches result from scale-invariant avalanches \citep{Melatos07a}, which are consistent with a self-organized critical system (SOCS). A cellular automaton provides a computationally efficient means of modelling the collective behaviour of up to $10^{16}$ vortices in the pulsar interior, whilst ensuring that the dominant aspects of the microphysics are not lost. The automaton generates avalanche distributions that are qualitatively consistent with a SOCS and with glitch data. The probability density functions of glitch sizes and durations are power laws, and the probability density function of waiting times between successive glitches is Poissonian, consistent with statistically independent events. The output of the model depends on the physical and computational paramters used. The fitted power law exponents for the glitch sizes ($a$) and durations ($b$) decreases as the strength of the vortex pinning increases. Similarly the exponents increase as the fraction of vortices that are pinned decreases. For the physical and computational parameters considered, one finds $-4.3\leq a \leq -2.0$ and $-5.5\leq b\leq -2.2$, and mean glitching rates in the range $0.0023\leqλ\leq0.13\$ in units of inverse time.

astro-ph↗

arXiv2008

Superfluid spherical Couette flow

We solve numerically for the first time the two-fluid, Hall--Vinen--Bekarevich--Khalatnikov (HVBK) equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette flow (SCF) and superfluid Taylor--Couette flow. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as $\Rey$ increases, and their shapes become more complex, especially in the superfluid component, with multiple secondary cells arising for $\Rey > 10^3$. The torque exerted by the normal component is approximately three times greater in a superfluid with anisotropic Hall--Vinen (HV) mutual friction than in a classical viscous fluid or a superfluid with isotropic Gorter-Mellink (GM) mutual friction. HV mutual friction also tends to "pinch" meridional circulation cells more than GM mutual friction. The boundary condition on the superfluid component, whether no slip or perfect slip, does not affect the large-scale structure of the flow appreciably, but it does alter the cores of the circulation cells, especially at lower $\Rey$. As $\Rey$ increases, and after initial transients die away, the mutual friction force dominates the vortex tension, and the streamlines of the superfluid and normal fluid components increasingly resemble each other. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants.

cond-mat.other↗

arXiv2008

Three-dimensional stability of magnetically confined mountains on accreting neutron stars

We examine the hydromagnetic stability of magnetically confined mountains, which arise when material accumulates at the magnetic poles of an accreting neutron star. We extend a previous axisymmetric stability analysis by performing three-dimensional simulations using the ideal-magnetohydrodynamic (ideal-MHD) code \textsc{zeus-mp}, investigating the role played by boundary conditions, accreted mass, stellar curvature, and (briefly) toroidal magnetic field strength. We find that axisymmetric equilibria are susceptible to the undular sub-mode of the Parker instability but are not disrupted. The line-tying boundary condition at the stellar surface is crucial in stabilizing the mountain. The nonlinear three-dimensional saturation state of the instability is characterized by a small degree of nonaxisymmetry ($\la 0.1$ per cent) and a mass ellipticity of $ε\sim 10^{-5}$ for an accreted mass of $M_a = 10^{-5} M_\odot$. Hence there is a good prospect of detecting gravitational waves from accreting millisecond pulsars with long-baseline interferometers such as Advanced LIGO. We also investigate the ideal-MHD spectrum of the system, finding that long-wavelength poloidal modes are suppressed in favour of toroidal modes in the nonaxisymmetric saturation state.

astro-ph↗

arXiv2007

Superfluid turbulence and pulsar glitch statistics

Experimental evidence is reviewed for the existence of superfluid turbulence in a differentially rotating, spherical shell at high Reynolds numbers ($\Rey\gsim 10^3$), such as the outer core of a neutron star. It is shown that torque variability increases with $\Rey$, suggesting that glitch activity in radio pulsars may be a function of $\Rey$ as well. The $\Rey$ distribution of the 67 glitching radio pulsars with characteristic ages $τ_c \leq 10^6$ {\rm yr} is constructed from radio timing data and cooling curves and compared with the $\Rey$ distribution of all 348 known pulsars with $τ_c \leq 10^6$ {\rm yr}. The two distributions are different, with a Kolmogorov-Smirnov probability $\geq 1 - 3.9 \times 10^{-3}$. The conclusion holds for (modified) Urca and nonstandard cooling, and for Newtonian and superfluid viscosities.

astro-ph↗

arXiv2007

Avalanche dynamics of radio pulsar glitches

We test statistically the hypothesis that radio pulsar glitches result from an avalanche process, in which angular momentum is transferred erratically from the flywheel-like superfluid in the star to the slowly decelerating, solid crust via spatially connected chains of local, impulsive, threshold-activated events, so that the system fluctuates around a self-organised critical state. Analysis of the glitch population (currently 285 events from 101 pulsars) demonstrates that the size distribution in individual pulsars is consistent with being scale invariant, as expected for an avalanche process. The waiting-time distribution is consistent with being exponential in seven out of nine pulsars where it can be measured reliably, after adjusting for observational limits on the minimum waiting time, as for a constant-rate Poisson process. PSR J0537$-$6910 and PSR J0835$-$4510 are the exceptions; their waiting-time distributions show evidence of quasiperiodicity. In each object, stationarity requires that the rate $λ$ equals $- ε\dotν / <Δν>$, where $\dotν$ is the angular acceleration of the crust, $<Δν>$ is the mean glitch size, and $ε\dotν$ is the relative angular acceleration of the crust and superfluid. There is no evidence that $λ$ changes monotonically with spin-down age. The rate distribution itself is fitted reasonably well by an exponential for $λ\geq 0.25 {\rm yr^{-1}}$. For $λ< 0.25 {\rm yr^{-1}}$, its exact form is unknown; the exponential overestimates the number of glitching pulsars observed at low $λ$, where the limited total observation time exercises a selection bias.

astro-ph↗

arXiv2007

Pulsed X-ray Emission from Pulsar A in the Double Pulsar System J0737-3039

The double pulsar system J0737-3039 is not only a test bed for General Relativity and theories of gravity, but also provides a unique laboratory for probing the relativistic winds of neutron stars. Recent X-ray observations have revealed a point source at the position of the J0737-3039 system, but have failed to detect pulsations or orbital modulation. Here we report on Chandra X-ray Observatory High Resolution Camera observations of the double pulsar. We detect deeply modulated, double-peaked X-ray pulses at the period of PSR J0737-3039A, similar in appearance to the observed radio pulses. The pulsed fraction is ~70%. Purely non-thermal emission from pulsar A plausibly accounts for our observations. However, the X-ray pulse morphology of A, in combination with previously reported spectral properties of the X-ray emission, allows the existence of both non-thermal magnetospheric emission and a broad sinusoidal thermal emission component from the neutron star surface. No pulsations are detected from pulsar B, and there is no evidence for orbital modulation or extended nebular structure. The absence of orbital modulation is consistent with theoretical expectations of a Poynting-dominated relativistic wind at the termination shock between the magnetosphere of B and the wind from A, and with the small fraction of the energy outflow from A intercepted by the termination shock.

astro-ph↗

arXiv2007

Burial of the polar magnetic field of an accreting neutron star. II. Hydromagnetic stability of axisymmetric equilibria

The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad-Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as $\Ma = 6\times 10^{-4}\Msun$, by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to $\Ma < 10^{-4}\Msun$) into the time-dependent, ideal-magnetohydrodynamic code ZEUS-3D and loading additional mass onto the star dynamically. The rise of buoyant magnetic bubbles through the accreted layer is observed in these experiments. We also investigate the stability of the resulting hydromagnetic equilibria by perturbing them in ZEUS-3D. Surprisingly, it is observed that the equilibria are marginally stable for all $\Ma\leq 6\times 10^{-4}\Msun$; the mountain oscillates persistently when perturbed, in a combination of Alfvén and acoustic modes, without appreciable damping or growth, and is therefore not disrupted (apart from a transient Parker instability initially, which expels $< 1 %$ of the mass and magnetic flux).

astro-ph↗

arXiv2006

Three-dimensional hydrodynamic simulations of asymmetric pulsar wind bow shocks

We present three-dimensional, nonrelativistic, hydrodynamic simulations of bow shocks in pulsar wind nebulae. The simulations are performed for a range of initial and boundary conditions to quantify the degree of asymmetry produced by latitudinal variations in the momentum flux of the pulsar wind, radiative cooling in the postshock flow, and density gradients in the interstellar medium (ISM). We find that the bow shock is stable even when travelling through a strong ISM gradient. We demonstrate how the shape of the bow shock changes when the pulsar encounters density variations in the ISM. We show that a density wall can account for the peculiar bow shock shapes of the nebulae around PSR J2124-3358 and PSR B0740-28. A wall produces kinks in the shock, whereas a smooth ISM density gradient tilts the shock. We conclude that the anisotropy of the wind momentum flux alone cannot explain the observed bow shock morphologies but it is instead necessary to take into account external effects. We show that the analytic (single layer, thin shell) solution is a good approximation when the momentum flux is anisotropic, fails for a steep ISM density gradient, and ap- proaches the numerical solution for efficient cooling. We provide analytic expressions for the latitudinal dependence of a vacuum-dipole wind and the associated shock shape, and compare the results to a split-monopole wind. We find that we are unable to distinguish between these two wind models purely from the bow shock morphology.

astro-ph↗

arXiv2006

Magnetic burial and the harmonic content of millisecond oscillations in thermonuclear X-ray bursts

Matter accreting onto the magnetic poles of a neutron star spreads under gravity towards the magnetic equator, burying the polar magnetic field and compressing it into a narrow equatorial belt. Steady-state, Grad-Shafranov calculations with a self-consistent mass-flux distribution (and a semi-quantitative treatment of Ohmic diffusion) show that, for $\Ma \gtrsim 10^{-5}\Msun$, the maximum field strength and latitudinal half-width of the equatorial magnetic belt are $B_{\rm max} = 5.6\times 10^{15} (\Ma/10^{-4}\Msun)^{0.32}$ G and $Δθ= \max[3^{\circ} (\Ma/10^{-4}\Msun)^{-1.5},3^{\circ} (\Ma/10^{-4}\Msun)^{0.5}(\dot{M}_{\rm a}/10^{-8}\Msun {\rm yr}^{-1})^{-0.5}]$ respectively, where $\Ma$ is the total accreted mass and $\dot{M}_{\rm a}$ is the accretion rate. It is shown that the belt prevents north-south heat transport by conduction, convection, radiation, and ageostrophic shear. This may explain why millisecond oscillations observed in the tails of thermonuclear (type I) X-ray bursts in low-mass X-ray binaries are highly sinusoidal: the thermonuclear flame is sequestered in the magnetic hemisphere which ignites first. The model is also consistent with the occasional occurrence of closely spaced pairs of bursts. Time-dependent, ideal-magnetohydrodynamic simulations confirm that the equatorial belt is not disrupted by Parker and interchange instabilities.

astro-ph↗

arXiv2006

Transitions between turbulent and laminar superfluid vorticity states in the outer core of a neutron star

We investigate the global transition from a turbulent state of superfluid vorticity to a laminar state, and vice versa, in the outer core of a neutron star. By solving numerically the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations for a rotating superfluid in a differentially rotating spherical shell, we find that the meridional counterflow driven by Ekman pumping exceeds the Donnelly-Glaberson threshold throughout most of the outer core, exciting unstable Kelvin waves which disrupt the rectilinear vortex array, creating a vortex tangle. In the turbulent state, the torque exerted on the crust oscillates, and the crust-core coupling is weaker than in the laminar state. This leads to a new scenario for the rotational glitches observed in radio pulsars: a vortex tangle is sustained in the differentially rotating outer core by the meridional counterflow, a sudden spin-up event brings the crust and core into corotation, the vortex tangle relaxes back to a rectilinear vortex array, then the crust spins down electromagnetically until enough meridional counterflow builds up to reform a vortex tangle. The turbulent-laminar transition can occur uniformly or in patches; the associated time-scales are estimated from vortex filament theory. We calculate numerically the global structure of the flow with and without an inviscid superfluid component, for Hall-Vinen and Gorter-Mellink forms of the mutual friction. We also calculate the post-glitch evolution of the angular velocity of the crust and its time derivative, and compare the results with radio pulse timing data, predicting a correlation between glitch activity and Reynolds number.

astro-ph↗