arXiv subjects

J. C. Miller

Publications and source records attributed to J. C. Miller.

17 recordsLinked to original sources

arXiv2016

Mean-field models for non-Markovian epidemics on networks: from edge-based compartmental to pairwise models

This paper presents a novel extension of the edge-based compartmental model for epidemics with arbitrary distributions of transmission and recovery times. Using the message passing approach we also derive a new pairwise-like model for epidemics with Markovian transmission and an arbitrary recovery period. The new pairwise-like model allows one to formally prove that the message passing and edge-based compartmental models are equivalent in the case of Markovian transmission and arbitrary recovery processes. The edge-based and message passing models are conjectured to also be equivalent for arbitrary transmission processes; we show the first step of a full proof of this. The new pairwise-like model encompasses many existing well-known models that can be obtained by appropriate reductions. It is also amenable to a relatively straightforward numerical implementation. We test the theoretical results by comparing the numerical solutions of the various pairwise-like models to results based on explicit stochastic network simulations.

q-bio.QM↗

arXiv2016

Accretion mode of the Ultra-Luminous X-ray source M82 X-2

Periodic pulsations have been found in emission from the ultra-luminous X-ray source (ULX) M82 X-2, strongly suggesting that the emitter is a rotating neutron star rather than a black hole. However, the radiation mechanisms and accretion mode involved have not yet been clearly established. In this paper, we examine the applicability to this object of standard accretion modes for high mass X-ray binaries (HMXBs). We find that spherical wind accretion, which drives OB-type HMXBs, cannot apply here but that there is a natural explanation in terms of an extension of the picture for standard Be-type HMXBs. We show that a neutron star with a moderately strong magnetic field, accreting from a disc-shaped wind emitted by a Be-companion, could be compatible with the observed relation between spin and orbital period. A Roche lobe overflow picture is also possible under certain conditions.

astro-ph.HE↗

arXiv2013

Magnetic field structure and torque in accretion discs around millisecond pulsars

Millisecond pulsars are rather weakly-magnetized neutron stars which are thought to have been spun up by disc accretion, with magnetic linkage between the star and the disc playing a key role. Their spin history depends sensitively on details of the magnetic field structure, but idealized models from the 1980s and 1990s are still commonly used for calculating the magnetic field components. This paper is the third in a series presenting results from a step-by-step analysis which we are making of the problem, starting with very simple models and then progressively including additional features one at a time, with the aim of gaining new insights into the mechanisms involved. In our first two papers, the magnetic field structure in the disc was calculated for a standard Shakura and Sunyaev model, by solving the magnetic induction equation numerically in the stationary limit within the kinematic approximation; here we consider a more general velocity field in the disc, including backflow. We find that the profiles of the poloidal and toroidal components of the magnetic field are fairly similar in the two cases but that they can be very different from those in the models mentioned above, giving important consequences for the torque exerted on the central object. In particular we find that, contrary to what is usually thought, some regions of the disc outward of the co-rotation point (rotating more slowly than the neutron star) may nevertheless contribute to spinning up the neutron star on account of the detailed structure of the magnetic field in those parts of disc.

astro-ph.SR↗

arXiv2012

The kinetic theory of quasi-stationary collisionless accretion disc plasmas

Astrophysical plasmas in accretion discs are usually treated in the framework of fluid or MHD approaches but there are some situations where these treatments become inadequate and one needs to revert to the more fundamental underlying kinetic theory. This occurs when the plasma becomes effectively collisionless or weakly-collisional such as, for example, in radiatively inefficient accretion flows onto black holes. In this paper, we lay down the basics of kinetic theory in these contexts. In particular, we formulate the kinetic theory for quasi-stationary collisionless accretion disc plasmas in the framework of a Vlasov-Maxwell description, taking the plasma to be non-relativistic, axisymmetric, gravitationally-bound and subject to electromagnetic fields. Quasi-stationary solutions for the kinetic distribution functions are constructed which are shown to admit temperature anisotropies. The physical implications of the theory are then investigated and the equations of state and angular momentum conservation law are discussed. Analysis of the Ampere equation reveals the existence of a quasi-stationary kinetic dynamo which gives rise to self-generation of poloidal and azimuthal magnetic fields and operates even in the absence of turbulence and/or instability phenomena.

astro-ph.HE↗

arXiv2012

Absolute stability of axisymmetric perturbations in strongly-magnetized collisionless axisymmetric accretion disk plasmas

The physical mechanism responsible for driving accretion flows in astrophysical accretion disks is commonly thought to be related to the development of plasma instabilities and turbulence. A key question is therefore the determination of consistent equilibrium configurations for accretion-disk plasmas and investigation of their stability properties. In the case of collisionless plasmas kinetic theory provides the appropriate theoretical framework. This paper presents a kinetic description of low-frequency and long-wavelength axisymmetric electromagnetic perturbations in non-relativistic, strongly-magnetized and gravitationally-bound axisymmetric accretion-disk plasmas in the collisionless regime. The analysis, carried out within the framework of the Vlasov-Maxwell description, relies on stationary kinetic solutions of the Vlasov equation which allow for the simultaneous treatment of non-uniform fluid fields, stationary accretion flows and temperature anisotropies. It is demonstrated that, for such solutions, no axisymmetric unstable perturbations can exist occurring on characteristic time and space scales which are long compared with the Larmor gyration time and radius. Hence, these stationary configurations are actually stable against axisymmetric kinetic instabilities of this type. As a fundamental consequence, this rules out the possibility of having the axisymmetric magneto-rotational or thermal instabilities to arise in these systems.

astro-ph.HE↗

arXiv2011

An investigation of magnetic field distortions in accretion discs around neutron stars - II. Analysis of the toroidal field component

Millisecond pulsars are believed to be old pulsars spun up by a surrounding accretion disc. Magnetic fields are thought to play a leading role in this, both by determining the location of the inner edge of the disc and by exerting an additional torque on the star (as a result of the interaction between the stellar magnetic field and the disc plasma motion, which creates a toroidal component B_phi). In some well-known analytic models, developed in the 1980s, the B_phi profile was taken to be proportional to the relative angular velocity between the disc plasma and the neutron star, multiplied by a vertical dipolar field. The present work stands in the line of improving those models, suggesting a new profile for B. In a previous paper, we discussed the poloidal component of the magnetic field and here we consider the toroidal component, again making the kinematic approximation and looking for steady solutions of the induction equation for axisymmetric models. The poloidal magnetic field is not assumed to be dipolar and the poloidal velocity field is not taken to be zero everywhere. We also do not use the thin disc approximation to simplify the induction equation but instead solve it numerically in full 2D. The profile obtained in the earlier analytic models is shown to have very limited validity and a more general semi-analytic solution is proposed.

astro-ph.SR↗

arXiv2010

An investigation of magnetic field distortions in accretion discs around neutron stars. I. Analysis of the poloidal field component

We report results from calculations investigating stationary magnetic field configurations in accretion discs around magnetised neutron stars. Our strategy is to start with a very simple model and then progressively improve it providing complementary insight into results obtained with large numerical simulations. In our first model, presented here, we work in the kinematic approximation and consider the stellar magnetic field as being a dipole aligned with the stellar rotation axis and perpendicular to the disc plane, while the flow in the disc is taken to be steady and axisymmetric. The behaviour in the radial direction is then independent of that in the azimuthal direction. We investigate the distortion of the field caused by interaction with the disc matter, solving the induction equation numerically in full 2D. The influence of turbulent diffusivity and fluid velocity on the poloidal field configuration is analysed, including discussion of outflows from the top and bottom of the disc. We find that the distortions increase with increasing magnetic Reynolds number R_m (calculated using the radial velocity). However, a single global parameter does not give an adequate description in different parts of the disc and we use instead a `magnetic distortion function' D_m(r,θ) (a magnetic Reynolds number defined locally). Where D_m<<1 (near to the inner edge of the disc) there is little distortion, but where D_m>1 (most of the rest of the disc), there is considerable distortion and the field becomes weaker than the dipole would have been. Between these two regions, there is a transition zone where the field is amplified and can have a local minimum and maximum. The location of this zone depends sensitively on the diffusivity. The results depend very little on the boundary conditions at the top of the disc.

astro-ph.SR↗

arXiv2010

Microscopic calculation of the equation of state of nuclear matter and neutron star structure

We present results for neutron star models constructed with a new equation of state for nuclear matter at zero temperature. The ground state is computed using the Auxiliary Field Diffusion Monte Carlo (AFDMC) technique, with nucleons interacting via a semi-phenomenological Hamiltonian including a realistic two-body interaction. The effect of many-body forces is included by means of additional density-dependent terms in the Hamiltonian. In this letter we compare the properties of the resulting neutron-star models with those obtained using other nuclear Hamiltonians, focusing on the relations between mass and radius, and between the gravitational mass and the baryon number.

nucl-th↗

arXiv2009

Relativistic simulations of the phase-transition-induced collapse of neutron stars

An increase in the central density of a neutron star may trigger a phase transition from hadronic matter to deconfined quark matter in the core, causing it to collapse to a more compact hybrid-star configuration. We present a study of this, building on previous work by Lin et al. (2006). We follow them in considering a supersonic phase transition and using a simplified equation of state, but our calculations are general relativistic (using 2D simulations in the conformally flat approximation) as compared with their 3D Newtonian treatment. We also improved the treatment of the initial phase transformation, avoiding the introduction of artificial convection. As before, we find that the emitted gravitational-wave spectrum is dominated by the fundamental quasi-radial and quadrupolar pulsation modes but the strain amplitudes are much smaller than suggested previously, which is disappointing for the detection prospects. However, we see significantly smaller damping and observe a nonlinear mode resonance which substantially enhances the emission in some cases. We explain the damping mechanisms operating, giving a different view from the previous work. Finally, we discuss the detectability of the gravitational waves, showing that the signal-to-noise ratio for current or second generation interferometers could be high enough to detect such events in our Galaxy, although third generation detectors would be needed to observe them out to the Virgo cluster, which would be necessary for having a reasonable event rate.

astro-ph↗

arXiv2008

Curvature singularities, tidal forces and the viability of Palatini f(R) gravity

In a previous paper we showed that static spherically symmetric objects which, in the vicinity of their surface, are well-described by a polytropic equation of state with 3/2<Gamma<2 exhibit a curvature singularity in Palatini f(R) gravity. We argued that this casts serious doubt on the validity of Palatini f(R) gravity as a viable alternative to General Relativity. In the present paper we further investigate this characteristic of Palatini f(R) gravity in order to clarify its physical interpretation and consequences.

gr-qc↗

arXiv2005

The Double Pulsar J0737--3039: Testing the Neutron Star Equation of State

The double pulsar J0737--3039 has become an important astrophysical laboratory for testing fundamental physics. Here we demonstrate that the low measured mass of Pulsar B can be used to constrain the equation of state of neutron star matter {\em under the assumption} that it formed in an electron-capture supernova. We show that the observed orbital parameters as well as the likely evolutionary history of the system support such a hypothesis and discuss future refinements that will improve the constraints this test may provide.

astro-ph↗

arXiv2004

General Relativistic Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star. I. Formulation of the equations

We present analytic solutions of Maxwell equations in the internal and external background spacetime of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat spacetime solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections due to the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections due both to the spacetime curvature and to the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.

astro-ph↗

arXiv2001

Stationary Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star in General Relativity

Following the general formalism presented by Rezzolla, Ahmedov and Miller (MNRAS, 322, 723 2001), we here derive analytic solutions of the electromagnetic fields equations in the internal and external background spacetime of a slowly rotating highly conducting magnetized neutron star. The star is assumed to be isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. Our results indicate that the electromagnetic fields of a slowly rotating neutron star are modified by general relativistic effects arising from both the monopolar and the dipolar parts of the gravitational field. The results presented here differ from the ones discussed by Rezzolla, Ahmedov and Miller (MNRAS, 322, 723 2001) mainly in that we here consider the interior magnetic field to be dipolar with the same radial dependence as the external one. While this assumption might not be a realistic one, it should be seen as the application of our formalism to a case often discussed in the literature.

gr-qc↗

arXiv1997

Are Q-stars a serious threat for stellar-mass black hole candidates?

We examine the status of the threat posed to stellar-mass black hole candidates by the possible existence of Q-stars (compact objects with an exotic equation of state which might have masses well above the normally-accepted maximum for standard neutron stars). We point out that Q-stars could be extremely compact (with radii less than 1.5 times the corresponding Schwarzschild radius) making it quite difficult to determine observationally that a given object is a black hole rather than a Q-star, unless there is direct evidence for the absence of a solid surface. On the other hand, in order for a Q-star to have a mass as high as that inferred for the widely-favoured black hole candidate V404 Cygni, it would be necessary for the Q-matter equation of state to apply already at densities an order of magnitude below that of nuclear matter and this might well be considered implausible on physical grounds. We also describe how rotation affects the situation and discuss the prospects for determining observationally that black hole candidates are not Q-stars.

astro-ph↗

arXiv1995

Evaporation of cosmological quark drops and relativistic radiative transfer

We discuss the results of a full relativistic treatment of the hydrodynamics of disconnected quark regions during the final stages of the cosmological quark-hadron transition. In this study, which represents a further development of a previous analysis of the evaporation of cosmological quark drops, the effects of long range energy and momentum transfer via electromagnetically interacting particles are consistently taken into account. For this purpose, a set of relativistic Lagrangian equations describing the evolution of the strongly interacting fluids is coupled to a system of equivalent equations accounting for the hydrodynamics of the fluid of electromagnetically interacting particles. The complete set of equations has then been solved numerically and results are presented from this. The inclusion of relativistic radiative transfer produces significantly different results, with the formation of high density regions at the end of the drop evaporation being particularly relevant. A comparison is made with results obtained for the previous radiation-free model and the cosmological implications concerning baryon number concentrations are briefly discussed.

astro-ph↗

arXiv1995

EVAPORATION OF QUARK DROPS DURING THE COSMOLOGICAL Q-H TRANSITION

We have carried out a study of the hydrodynamics of disconnected quark regions during the final stages of the cosmological quark-hadron transition. A set of relativistic Lagrangian equations is presented for following the evaporation of a single quark drop and results from the numerical solution of this are discussed. A self-similar solution is shown to exist and the formation of baryon number density inhomogeneities at the end of the drop contraction is discussed.

astro-ph↗

arXiv1994

Hydrodynamics of the Cosmological Quark-Hadron Transition in the Presence of Long-Range Energy and Momentum Transfer

Two previous papers in this series have presented a study of the growth of hadronic bubbles during the cosmological Quark--Hadron transition, treating the material within each phase as a single perfect fluid. Here, we extend the analysis to include the effects of long-range energy and momentum transfer by weakly and electromagnetically interacting particles. After a short review of the formalism adopted, we discuss the numerical strategies used in the computer code which has been constructed in order to solve this system of equations. Results for the growth of single hadronic bubbles are also presented.

astro-ph↗