arXiv subjects

John C. Miller

Publications and source records attributed to John C. Miller.

At least 19 recordsLinked to original sources

arXiv2026

Universal behaviour of $α$-viscosity in black hole accretion discs

The Shakura-Sunyaev $α$-viscosity coefficient, defined as the ratio of total stress to total pressure, $α= \mathbb{T}/p$, began to play an important role in the development of accretion disc theory in the early 1970s. The origin of the turbulence that causes the stress $\mathbb{T}$ was unknown at that time; Shakura and Sunyaev assumed $α=$ const. Today we know that this was not quite realistic - modern general relativistic magneto-hydrodynamic simulations (GRMHD) of black hole accretion discs have revealed that $α$ changes by about an order of magnitude within the disc, being smaller far away from the black hole and larger in the plunging region close in, and it has been found that the behaviour of $α$ reflects some underlying, fundamental properties of the stress $\mathbb{T}$. In particular, it has been argued by several authors, that $\mathbb{T}$ must be zero at the black hole horizon. We note that the stress calculated in three independent GRMHD simulations of accretion discs around non-rotating black holes, made by a variety of authors (including ourselves), each has its prominent maximum close to the location of the circular photon orbit. We propose a formula that accurately describes this 'universal' behaviour of $α$ in terms of the 'gyration radius', a physical characteristic of rotation well known in Newtonian dynamics and in the black hole case uniquely defined by the Kerr space-time geometry. Analytic and semi-analytic models of black hole accretion discs provide an invaluable insight into fundamental physics, and the GRMHD simulations do not aspire to replace them. Rather, simulations could help to improve analytic models by making them more realistic. For example, our $α$-formula, deduced from the GRMHD simulations, may be useful in the construction of improved versions of thin and slim disc models.

astro-ph.HE↗

arXiv2020

Trapping of null geodesics in slowly rotating spacetimes

Extremely compact objects containing a region of trapped null geodesics could be of astrophysical relevance due to trapping of neutrinos with consequent impact on cooling processes or trapping of gravitational waves. These objects have previously been studied under the assumption of spherical symmetry. In the present paper, we consider a simple generalization by studying trapping of null geodesics in the framework of the Hartle-Thorne slow-rotation approximation taken to first order in the angular velocity, and considering a uniform-density object with uniform emissivity for the null geodesics. We calculate effective potentials and escape cones for the null geodesics and how they depend on the parameters of the spacetimes, and also calculate the "local" and "global" coefficients of efficiency for the trapping. We demonstrate that due to the rotation the trapping efficiency is different for co-rotating and retrograde null geodesics, and that trapping can occur even for $R>3GM/c^2$, contrary to what happens in the absence of rotation.

gr-qc↗

arXiv2020

The outer crust of a cold, non-accreting neutron star within the Quark-Meson Coupling (QMC) model

The outer crust properties of cold non-accreting neutron stars are studied within the framework of the quark-meson coupling (QMC) model, which includes the effects of modifications of the quark structure inside individual nucleons when they are within a high-density nuclear medium. With a unique set of five well-constrained adjustable parameters, which have a clear physical basis, the QMC model gives predictions for the ground state observables of even-even nuclei which agree with experiment as well as traditional models. Furthermore, it gives improved theoretical values for nuclei thought to play a role in the outer crusts of neutron stars but for which experimental data is not available. Using the latest experimental data tables wherever possible but otherwise the predictions from the QMC model, we construct an equation of state for the outer crust which is then used within stellar model calculations to obtain an equilibrium sequence of crustal layers, each characterized by a particular neutron rich nuclei. Various properties of the layers are calculated for a range of neutron-star masses, and comparisons are made with alternative equations of state from the literature. This leads to the conclusion that the QMC model successfully predicts the outer crust properties and is fully comparable with the more traditional mass models, which all depend on a larger number of parameters.

nucl-th↗

arXiv2019

Epicyclic oscillations in the Hartle-Thorne external geometry

The external Hartle-Thorne geometry, which describes the space-time outside a slowly-rotating compact star, is characterized by the gravitational mass $M$, angular momentum $J$ and quadrupole moment $Q$ of the star and gives a convenient description which, for the rotation frequencies of more than 95 % of known pulsars, is sufficiently accurate for most purposes. We focus here on the motion of particles in these space-times, presenting a detailed systematic analysis of the frequency properties of radial and vertical epicyclic motion and of orbital motion. Our investigation is motivated by X-ray observations of binary systems containing a rotating neutron star which is accreting matter from its binary companion. In these systems, twin high-frequency quasi-periodic oscillations are sometimes observed with a frequency ratio approaching $3:2$ or $5:4$ and these may be explained by models involving the orbital and epicyclic frequencies of quasi-circular geodesic motion. In our analysis, we use realistic equations of state for the stellar matter and proceed in a self-consistent way, following the Hartle-Thorne approach in calculating both the corresponding values of $Q$, $M$ and $J$ for the stellar model and the properties of the surrounding spacetime. Our results are then applied to a range of geodetical models for QPOs. A key feature of our study is that it implements the recently-discovered universal relations among neutron star parameters so that the results can be directly used for models with different masses $M$, radii $R$ and rotational frequencies $f_\mathrm{rot}$.

astro-ph.HE↗

arXiv2017

Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse

In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those which then move outwards with respect to the matter have been proposed for use in defining black holes, replacing the global concept of an "event horizon" which has some serious drawbacks for practical applications. We here present results from a study of the properties of both outgoing and ingoing trapping horizons, assuming strict spherical symmetry throughout. We have investigated their causal nature (i.e. whether they are spacelike, timelike or null), making contact with the Misner-Sharp- Hernandez formalism, which has often been used for numerical calculations of spherical collapse. We follow two different approaches, one using a geometrical quantity related to expansions of null geodesic congruences, and the other using the horizon velocity measured with respect to the collapsing matter. After an introduction to these concepts, we then implement them within numerical simulations of stellar collapse, revisiting pioneering calculations from the 1960s where some features of the emergence and subsequent behaviour of trapping horizons could already be seen. Our presentation here is aimed firmly at "real world" applications of interest to astrophysicists and includes the effects of pressure, which may be important for the asymptotic behaviour of the ingoing horizon.

gr-qc↗

arXiv2017

Tidal disruptions by rotating black holes: relativistic hydrodynamics with Newtonian codes

We propose an approximate approach for studying the relativistic regime of stellar tidal disruptions by rotating massive black holes. It combines an exact relativistic description of the hydrodynamical evolution of a test fluid in a fixed curved spacetime with a Newtonian treatment of the fluid's self-gravity. Explicit expressions for the equations of motion are derived for Kerr spacetime using two different coordinate systems. We implement the new methodology within an existing Newtonian Smoothed Particle Hydrodynamics code and show that including the additional physics involves very little extra computational cost. We carefully explore the validity of the novel approach by first testing its ability to recover geodesic motion, and then by comparing the outcome of tidal disruption simulations against previous relativistic studies. We further compare simulations in Boyer--Lindquist and Kerr--Schild coordinates and conclude that our approach allows accurate simulation even of tidal disruption events where the star penetrates deeply inside the tidal radius of a rotating black hole. Finally, we use the new method to study the effect of the black hole spin on the morphology and fallback rate of the debris streams resulting from tidal disruptions, finding that while the spin has little effect on the fallback rate, it does imprint heavily on the stream morphology, and can even be a determining factor in the survival or disruption of the star itself. Our methodology is discussed in detail as a reference for future astrophysical applications.

astro-ph.HE↗

arXiv2016

Class numbers of large degree nonabelian number fields

If a number field has a large degree and discriminant, the computation of the class number becomes quite difficult, especially without the assumption of GRH. In this article, we will unconditionally show that a certain nonabelian number field of degree 120 has class number one. This field is the unique $A_5 \times C_2$ extension of the rationals that is ramified only at 653 with ramification index 2. It is the largest degree number field unconditionally proven to have class number 1. The proof uses the algorithm of Guàrdia, Montes and Nart to calculate an integral basis and then finds integral elements of small prime power norm to establish an upper bound for the class number; further algebraic arguments prove the class number is 1. It is possible to apply these techniques to other nonabelian number fields as well.

math.NT↗

arXiv2015

Class numbers in cyclotomic Z_p-extensions

For any prime p and any positive integer n, let B(p,n) denote the n-th layer of the cyclotomic Z_p-extension over the rationals. Based on the heuristics of Cohen and Lenstra, and refined by new results on class numbers of particular B(p,n), we provide evidence for the following conjecture: For all primes p and positive integers n, the ideal class group of B(p,n) is trivial.

math.NT↗

arXiv2014

Causal horizons and topics in structure formation

This is a write-up of a talk given at the Opava RAGtime meeting in 2011, but it has been updated to include some subsequent related developments. The talk focused on discussion of some aspects of black hole and cosmological horizons under rather general circumstances, and on two different topics related to formation of cosmological structures at different epochs of the universe: virialization of cold dark matter during standard structure formation in the matter-dominated era, and primordial black hole formation during the radiative era.

gr-qc↗

arXiv2014

Real cyclotomic fields of prime conductor and their class numbers

Surprisingly, the class numbers of cyclotomic fields have only been determined for fields of small conductor, e.g. for prime conductors up to 67, due to the problem of finding the "plus part," i.e. the class number of the maximal real subfield. Our results have improved the situation. We prove that the plus part of the class number is 1 for prime conductors between 71 and 151. Also, under the assumption of the generalized Riemann hypothesis, we determine the class number for prime conductors between 167 and 241. This technique generalizes to any totally real field of moderately large discriminant, allowing us to confront a large class of number fields not previously treatable.

math.NT↗

arXiv2014

Class numbers of totally real fields and applications to the Weber class number problem

The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root discriminant of the field can be too large to be treated by Odlyzko's discriminant bounds. We describe a new technique for determining the class number of such fields, allowing us to attack the class number problem for a large class of number fields not treatable by previously known methods. We give an application to Weber's class number problem, which is the conjecture that all real cyclotomic fields of power of 2 conductor have class number 1.

math.NT↗

arXiv2013

Primordial black hole formation in the early universe: critical behaviour and self-similarity

Following on after three previous papers discussing the formation of primordial black holes during the radiative era of the early universe, we present here a further investigation of the critical nature of the process involved, aimed at making contact with some of the basic underlying ideas from the literature on critical collapse. We focus on the intermediate state, which we have found appearing in cases with perturbations close to the critical limit, and examine the connection between this and the similarity solutions which play a fundamental role in the standard picture of critical collapse. We have derived a set of self-similar equations for the null-slicing form of the metric which we are using for our numerical calculations, and have then compared the results obtained by integrating these with the ones coming from our simulations for collapse of cosmological perturbations within an expanding universe. We find that the similarity solution is asymptotically approached in a region which grows to cover both the contracting matter and part of the semi-void which forms outside it. Our main interest is in the situation relevant for primordial black hole formation in the radiative era of the early universe, where the relation between the pressure $p$ and the energy density $e$ can be reasonably approximated by an expression of the form $p = we$ with $w=1/3$. However, we have also looked at other values of $w$, both because these have been considered in previous literature and also because they can be helpful for giving further insight into situations relevant for primordial black hole formation. As in our previous work, we have started our simulations with initial supra-horizon scale perturbations of a type which could have come from inflation.

gr-qc↗

arXiv2013

Quadrupole moments of rotating neutron stars and strange stars

We present results for models of neutron stars and strange stars constructed using the Hartle-Thorne slow-rotation method with a wide range of equations of state, focusing on the values obtained for the angular momentum $J$ and the quadrupole moment $Q$, when the gravitational mass $M$ and the rotational frequency $Ω$ are specified. Building on previous work, which showed surprising uniformity in the behaviour of the moment of inertia for neutron-star models constructed with widely-different equations of state, we find similar uniformity for the quadrupole moment. These two quantities, together with the mass, are fundamental for determining the vacuum space-time outside neutron stars. We study particularly the dimensionless combination of parameters $QM/J^2$ (using units for which $c=G=1$). This quantity goes to 1 in the case of a Kerr-metric black hole and deviations away from 1 then characterize the difference between neutron-star and black-hole space-times. It is found that $QM/J^2$ for both neutron stars and strange stars decreases with increasing mass, for a given equation of state, reaching a value of around 2 (or even less) for maximum-mass models, meaning that their external space-time is then rather well approximated by the Kerr metric. If $QM/J^2$ is plotter against compactness $R/2M$ (where $R$ is the radius), it is found that the relationship is nearly unique for neutron-star models, independent of the equation of state, while it is significantly different for strange stars. This gives a new way of possibly distinguishing between them.

astro-ph.SR↗

arXiv2012

An analytic toy model for relativistic accretion in Kerr spacetime

We present a relativistic model for the stationary axisymmetric accretion flow of a rotating cloud of non-interacting particles falling onto a Kerr black hole. Based on a ballistic approximation, streamlines are described analytically in terms of timelike geodesics, while a simple numerical scheme is introduced for calculating the density field. A novel approach is presented for describing all of the possible types of orbit by means of a single analytic expression. This model is a useful tool for highlighting purely relativistic signatures in the accretion flow dynamics coming from a strong gravitational field with frame-dragging. In particular, we explore the coupling due to this between the spin of the black hole and the angular momentum of the infalling matter. Moreover, we demonstrate how this analytic solution may be used for benchmarking general relativistic numerical hydrodynamics codes by comparing it against results of smoothed particle hydrodynamics simulations for a collapsar-like setup. These simulations are performed first for a ballistic flow (with zero pressure) and then for a hydrodynamical one where we measure the effects of pressure gradients on the infall, thus exploring the extent of applicability of the ballistic approximation.

astro-ph.HE↗

arXiv2012

Measuring the Effects of Artificial Viscosity in SPH Simulations of Rotating Fluid Flows

A commonly cited drawback of SPH is the introduction of spurious shear viscosity by the artificial viscosity term in situations involving rotation. Existing approaches for quantifying its effect include approximate analytic formulae and disc-averaged be- haviour in specific ring-spreading simulations, based on the kinematic effects produced by the artificial viscosity. These methods have disadvantages, in that they typically are applicable to a very small range of physical scenarios, have a large number of simplifying assumptions, and often are tied to specific SPH formulations which do not include corrective (e.g., Balsara) or time-dependent viscosity terms. In this study we have developed a simple, generally applicable and practical technique for evaluating the local effect of artificial viscosity directly from the creation of specific entropy for each SPH particle. This local approach is simple and quick to implement, and it al- lows a detailed characterization of viscous effects as a function of position. Several advantages of this method are discussed, including its ease in evaluation, its greater accuracy and its broad applicability. In order to compare this new method with ex- isting ones, simple disc flow examples are used. Even in these basic cases, the very roughly approximate nature of the previous methods is shown. Our local method pro- vides a detailed description of the effects of the artificial viscosity throughout the disc, even for extended examples which implement Balsara corrections. As a further use of this approach, explicit dependencies of the effective viscosity in terms of SPH and flow parameters are estimated from the example cases. In an appendix, a method for the initial placement of SPH particles is discussed which is very effective in reducing numerical fluctuations.

astro-ph.IM↗

arXiv2011

Role of electric charge in shaping equilibrium configurations of fluid tori encircling black holes

Astrophysical fluids may acquire non-zero electrical charge because of strong irradiation or charge separation in a magnetic field. In this case, electromagnetic and gravitational forces may act together and produce new equilibrium configurations, which are different from the uncharged ones. Following our previous studies of charged test particles and uncharged perfect fluid tori encircling compact objects, we introduce here a simple test model of a charged perfect fluid torus in strong gravitational and electromagnetic fields. In contrast to ideal magnetohydrodynamic models, we consider here the opposite limit of negligible conductivity, where the charges are tied completely to the moving matter. This is an extreme limiting case which can provide a useful reference against which to compare subsequent more complicated astrophysically-motivated calculations. To clearly demonstrate the features of our model, we construct three-dimensional axisymmetric charged toroidal configurations around Reissner-Nordström black holes and compare them with equivalent configurations of electrically neutral tori.

astro-ph.HE↗

arXiv2011

Analytic solutions to the accretion of a rotating finite cloud towards a central object - II. Schwarzschild spacetime

We construct a general relativistic model for the accretion flow of a rotating finite cloud of non-interacting particles infalling onto a Schwarzschild black hole. The streamlines start at a spherical shell, where boundary conditions are fixed, and are followed down to the point at which they either cross the black hole horizon or become incorporated into an equatorial thin disc. Analytic expressions for the streamlines and the velocity field are given, in terms of Jacobi elliptic functions, under the assumptions of stationarity and ballistic motion. A novel approach allows us to describe all of the possible types of orbit with a single formula. A simple numerical scheme is presented for calculating the density field. This model is the relativistic generalisation of the Newtonian one developed by Mendoza, Tejeda, Nagel, 2009 and, due to its analytic nature, it can be useful in providing a benchmark for general relativistic hydrodynamical codes and for exploring the parameter space in applications involving accretion onto black holes when the approximations of steady state and ballistic motion are reasonable ones.

astro-ph.HE↗

arXiv2011

Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations

A kinetic treatment is developed for collisionless magnetized plasmas occurring in high-temperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively-inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow collisionless dynamics of these plasmas is investigated, yielding a reduced gyrokinetic Vlasov equation for the kinetic distribution function. For doing this, an asymptotic quasi-stationary solution is first determined, represented by a generalized bi-Maxwellian distribution expressed in terms of the relevant adiabatic invariants. The existence of the solution is shown to depend on having suitable kinetic constraints and conditions leading to particle trapping phenomena. With this solution one can treat temperature anisotropy, toroidal and poloidal flow velocities and finite Larmor-radius effects. An asymptotic expansion for the distribution function permits analytic evaluation of all of the relevant fluid fields. Basic theoretical features of the solution and their astrophysical implications are discussed. As an application, the possibility of describing the dynamics of slowly time-varying accretion flows and the self-generation of magnetic field by means of a \textquotedblleft kinetic dynamo effect\textquotedblright\ is discussed. Both effects are shown to be related to intrinsically-kinetic physical mechanisms.

astro-ph.HE↗