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.
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 …
Relaxation of magnetically-confined mountains on accreting neutron stars through cross-field mass transport
School of Physics, University of Melbourne（墨尔本大学物理学院）；ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav), University of Melbourne（引力波发现卓越研究中心（OzGrav），墨尔本大学）；Escola de Artes, Ciências e Humanidades, Universidade de São Paulo（圣保罗大学艺术、科学与人文学院）
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…
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…
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）
This is the fourth in a series of companion papers showing that, when an efficient dynamo can be maintained by accretion disks around supermassive black holes in Active Galactic Nuclei (AGNs), it will lead to the formation of a powerful, magnetically-collimated helix that could explain both the observed jet/radiolobe structures on very large scales and ultimately the enormous power inferred from the observed ultra high energy cosmic rays (UHECRs) with energies > 10^19 eV. Many timescales are involved in this process. Our hyper-resistive magnetohydrodynamic (MHD) model provides a bridge between…
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.
The electrical resistivity of the accreted mountain in a millisecond pulsar is limited by the observed spin-down rate of binary radio millisecond pulsars (BRMSPs) and the spins and X-ray fluxes of accreting millisecond pulsars (AMSPs). We find $η\ge 10^{-28}\,\mathrm{s}\, (τ_\mathrm{SD}/1\,\mathrm{Gyr})^{-0.8}$ (where $τ_\mathrm{SD}$ is the spin-down age) for BRMSPs and $η\ge 10^{-25}\,\mathrm{s}\,(\dot{M}_\mathrm{a}/\dot{M}_\mathrm{E})^{0.6}$ (where $\dot{M}_\mathrm{a}$ and $\dot{M}_\mathrm{E}$ are the actual and Eddington accretion rates) for AMSPs. These limits are inferred assuming that th…
Turbulent magnetic diffusivity plays an important role for accretion disks and the launching of disk winds. We have implemented magnetic diffusivity, respective resistivity in the general relativistic MHD code HARM. This paper describes the theoretical background of our implementation, its numerical realization, our numerical tests and preliminary applications. The test simulations of the new code rHARM are compared with an analytic solution of the diffusion equation and a classical shock tube problem. We have further investigated the evolution of the magneto-rotational instability (MRI) in to…
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.…
Magnetic reconnection is a plasma phenomenon where a topological rearrangement of magnetic field lines with opposite polarity results in dissipation of magnetic energy into heat, kinetic energy and particle acceleration. Such a phenomenon is considered as an efficient mechanism for energy release in laboratory and astrophysical plasmas. An important question is how to make the process fast enough to account for observed explosive energy releases. The classical model for steady state magnetic reconnection predicts reconnection times scaling as $S^{1/2}$ (where $S$ is the Lundquist number) and y…
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 …
We investigate the launching of jets and outflows from magnetically diffusive accretion disks. Using the PLUTO code we solve the time-dependent resistive MHD equations taking into account the disk and jet evolution simultaneously. The main question we address is which kind of disks do launch jets and which kind of disks do not? In particular, we study how the magnitude and distribution of the (turbulent) magnetic diffusivity affect mass loading and jet acceleration. We have applied a turbulent magnetic diffusivity based on α-prescription, but have also investigate examples where the scale heig…
