arXiv subjects

Steven A. Balbus

Publications and source records attributed to Steven A. Balbus.

At least 19 recordsLinked to original sources

arXiv2024

Determining the difference between local acceleration and local gravity: applications of the equivalence principle to relativistic trajectories

We show by direct calculation that the common Equivalence Principle explanation for why gravity must deflect light is quantitatively incorrect by a factor of three in Schwarzschild geometry. It is therefore possible, at least as a matter of principle, to tell the difference between local acceleration and a true gravitational field by measuring the local deflection of light. We calculate as well the deflection of test particles of arbitrary energy, and construct a leading-order coordinate transformation from Schwarzschild to local inertial coordinates, which shows explicitly how the effects of spatial curvature manifest locally for relativistic trajectories of both finite and vanishing rest mass particles.

gr-qc↗

arXiv2021

A Poynting theorem formulation for the gravitational wave stress pseudo tensor

A very simple and physical derivation of the conservation equation for the propagation of gravitational radiation is presented. The formulation is exact. The result takes the readily recognisable and intuitive form of a Poynting-style equation, in which the outward propagation of stress-energy is directly related to the volumetric equivalent of a radiation reaction force acting back upon the sources, including the purely gravitational contribution to the sources. Upon averaging, the emergent pseudo tensor for the gravitational radiation is in exact agreement with that found by much more labour-intensive methods.

gr-qc↗

arXiv2020

The spectral evolution of disc dominated tidal disruption events

We perform a detailed numerical and analytical study of the properties of observed light curves from relativistic thin discs, focussing on observational bands most appropriate for comparison with tidal disruption events (TDEs). We make use of asymptotic expansion techniques applied to the spectral emission integral, using time dependent disc temperature profiles appropriate for solutions of the relativistic thin disc equation. Rather than a power law associated with bolometric disc emission $L \sim t^{-n}$, the observed X-ray flux from disc-dominated TDEs will typically have the form of a power law multiplied by an exponential (see eq. 91). While precise details are somewhat dependent on the nature of the ISCO stress and disc-observer orientational angle, the general form of the time-dependent flux is robust and insensitive to the exact disc temperature profile. We present numerical fits to the UV and X-ray light curves of ASASSN-14li, a particularly well observed TDE. This modelling incorporates strong gravity optics. The full 900 days of ASASSN-14li X-ray observations are very well fit by a simple relativistic disc model, significantly improving upon previous work. The same underlying model also fits the final 1000 days of ASASSN-14li observations in three different UV bandpasses. Finally, we demonstrate that the analytic formulae reproduce the properties of full numerical modelling at both UV and X-ray wavelengths with great fidelity.

astro-ph.HE↗

arXiv2019

How mergers magnetise massive stars

Magnetic fields are ubiquitous in the Universe. The Sun's magnetic field drives the solar wind and causes solar flares and other energetic surface phenomena that profoundly affect space weather here on Earth. The first magnetic field in a star other than the Sun was detected in 1947 in the peculiar A-type star 78 Vir. It is now known that the magnetic fields of the Sun and other low-mass stars (<1.5 solar masses) are generated in-situ by a dynamo process in their turbulent, convective envelopes. Unlike such stars, intermediate-mass and high-mass stars (>1.5 solar masses; referred to as "massive" stars here) have relatively quiet, radiative envelopes where a solar-like dynamo cannot operate. However, about 10% of them, including 78 Vir, have strong, large-scale surface magnetic fields whose origin has remained a major mystery. The massive star $τ$ Sco is a prominent member of this group and appears to be surprisingly young compared to other presumably coeval members of the Upper Scorpius association. Here, we present the first 3D magneto-hydrodynamical simulations of the coalescence of two massive main-sequence stars and 1D stellar evolution computations of the subsequent evolution of the merger product that can explain $τ$ Sco's magnetic field, apparent youth and other observed characteristics. We argue that field amplification in stellar mergers is a general mechanism to form strongly-magnetised massive stars. These stars are promising progenitors of those neutron stars that host the strongest magnetic fields in the Universe, so-called magnetars, and that may give rise to some of the enigmatic fast radio bursts. Strong magnetic fields affect the explosions of core-collapse supernovae and, moreover, those magnetic stars that have rapidly-rotating cores at the end of their lives might provide the right conditions to power long-duration gamma-ray bursts and super-luminous supernovae.

astro-ph.SR↗

arXiv2019

Evolution of relativistic thin discs with a finite ISCO stress: I. Stalled accretion

We present solutions to the relativistic thin disc evolutionary equation using an $α$-model for the turbulent stress tensor. Solutions with a finite stress at the innermost stable circular orbit (ISCO) give rise to bolometric light curves with a shallow power law time dependence, in good agreement with those observed in tidal disruption events. A self-similar model based on electron scattering opacity, for example, yields a power law index of $-11/14$, as opposed to $-19/16$ for the case of zero ISCO stress. These solutions correspond to an extended period of relaxation of the evolving disc which, like the light curves they produce, is not sustainable indefinitely. Cumulative departures from the approximation of exact circular orbits cause the power law index to evolve slowly with time, leading eventually to the steeper fall-off associated with traditional zero ISCO stress models. These modified solutions are discussed in detail in a companion paper.

astro-ph.HE↗

arXiv2019

Evolution of relativistic thin discs with a finite ISCO stress: II. Late time behaviour

We present solutions to the relativistic thin disc evolutionary equation using a modified description of the mean fluid flow within the disc. The model takes into account the effects of sub-circular velocities in the innermost disc regions, and resolves otherwise unsustainable behaviour present in simple finite ISCO stress disc models. We show that the behaviour of a relativistic thin disc evolving with a finite ISCO stress is comprised of three distinct stages which join the ordinarily distinct finite and vanishing ISCO stress solutions into a fully continuous model parameterisation. The most important prediction of our model is the existence of an intermediate stage of "stalled accretion", controlled by a single dimensionless parameter. The hallmarks of this evolutionary phase appear to have been seen in GRMHD simulations as well as in the late time X-ray observations of tidal disruption events, but dedicated simulations and extended observations are needed for a deeper understanding.

astro-ph.HE↗

arXiv2018

The evolution of Kerr discs and late-time tidal disruption event light curves

An encounter between a passing star and a massive black hole at the centre of a galaxy, a so-called tidal disruption event or TDE, may leave a debris disc that subsequently accretes onto the hole. We solve for the time evolution of such a TDE disc, making use of an evolutionary equation valid for both the Newtonian and Kerr regimes. The late time luminosity emergent from such a disc is of interest as a model diagnostic, as it tends to follow a power law decline. The original simple ballistic fallback model, with equal mass in equal energy intervals, produces a -5/3 power law, while standard viscous disc descriptions yield a somewhat more shallow decline, with an index closer to -1.2. Of four recent, well-observed tidal disruption event candidates however, all had fall-off power law indices smaller than 1 in magnitude. In this work, we revisit the problem of thin disc evolution, solving this reduced problem in full general relativity. Our solutions produce power law indices that are in much better accord with observations. The late time observational data from many TDEs are generally supportive, not only of disc accretion models, but of finite stress persisting down to the innermost stable circular orbit.

astro-ph.HE↗

arXiv2017

An accretion disc instability induced by a temperature sensitive $α$ parameter

In the standard thin disc formalism the dimensionless $α$ parameter is usually assumed to be constant. However, there are good theoretical reasons for believing, as well as evidence from simulations, that $α$ is dependent on intrinsic disc properties. In this paper we analyse the conditions for the stability of a thin accretion disc in which $α$ is a function of the magnetic Prandtl number, the ratio of collisional viscosity to resistivity. In the inner disc, where the free electron opacity and radiation viscosity dominate, the disc is unstable if $α$ is proportional to the magnetic Prandtl number with an exponent, $n$, and $6/13<n<10/3$. This is within the range of values for the power-law index found in MHD simulations with simple energetics. We calculate the evolution of the unstable disc within the $α$ formalism and show that the physically accessible solutions form a limit cycle, analogous to the behaviour seen in recurrent dwarf novae. It is noteworthy that the time-dependent global behaviour of the instability results in cyclic heating of the inner section of the disc, when parameters appropriate for an X-ray binary system are used. We calculate a model spectrum of the disc in the flaring and quiescent states and show that the behaviour is compatible with X-ray observations of the thermal accretion disc in flaring X-ray binary systems.

astro-ph.HE↗

arXiv2017

Demonstration of a magnetic Prandtl number disc instability from first principles

Understanding what determines the strength of MHD turbulence in accretion discs is a question of fundamental theoretical and observational importance. In this work we investigate whether the dependence of the turbulent accretion disc stress ($α$) on the magnetic Prandtl number (Pm) is sufficiently sensitive to induce thermal-viscous instability using 3D MHD simulations. We first investigate whether the $α$-Pm dependence, found by many previous authors, has a physical or numerical origin by conducting a suite of local shearing-box simulations. We find that a definite $α$-Pm dependence persists when simultaneously increasing numerical resolution and decreasing the absolute values of both the viscous and resistive dissipation coefficients. This points to a physical origin of the $α$-Pm dependence. Using a further set of simulations which include realistic turbulent heating and radiative cooling, and by giving Pm a realistic physical dependence on the plasma temperature and density, we demonstrate that the $α$-Pm dependence is sufficiently strong to lead to a local instability. We confirm that the instability manifests itself as an unstable limit cycle by mapping the local thermal-equilibrium curve of the disc. This is the first self-consistent MHD simulation demonstrating the Pm instability from first principles. This result is important because a physical Pm instability would lead to the global propagation of heating and cooling fronts and a transition between disc states on timescales compatible with the observed hard/soft state transitions in black hole binaries.

astro-ph.HE↗

arXiv2016

The Goldreich-Schubert-Fricke instability in stellar radiative zones

The Goldreich-Schubert-Fricke (GSF) instability is a rotational instability that is thought to contribute to the transfer of angular momentum in differentially rotating stars. It has been included in recent codes of stellar evolution in a diffusion-like approximation, under the assumption that the kinematic viscosity $ν$ is unimportant for the development of the instability. As noted previously by other authors, for most stellar applications this may not be a valid approximation. We discuss this issue in detail, solving the dispersion relation of the perturbed modes for realistic values of $ν$ in the bulk of the radiative zone of the Sun and of three red giant stars at various evolutionary stages. We find that the GSF instability is triggered only in layers of extremely strong shear. In a simple case study, we also investigate the effect of a small deviation from axisymmetry or a small background magnetic field. We find that, like the viscosity, these have a stabilising effect. We conclude that this instability is probably far less efficient in transporting angular momentum than is often assumed, and may not even be present.

astro-ph.SR↗

arXiv2016

Surprises in astrophysical gasdynamics

Much of astrophysics consists of the study of ionised gas under the influence of gravitational and magnetic fields. Thus, it is not possible to understand the astrophysical universe without a detailed knowledge of the dynamics of magnetised fluids. Fluid dynamics is, however, a notoriously tricky subject, in which it is all too easy for one's a priori intuition to go astray. In this review, we seek to guide the reader through a series of illuminating yet deceptive problems, all with an enlightening twist. We cover a broad range of topics including the instabilities acting in accretion discs, the hydrodynamics governing the convective zone of the Sun, the magnetic shielding of a cooling galaxy cluster, and the behaviour of thermal instabilities and evaporating clouds. The aim of this review is to surprise and intrigue even veteran astrophysical theorists with an idiosynchratic choice of problems and counterintuitive results. At the same time, we endeavour to bring forth the fundamental ideas, to set out important assumptions, and to describe carefully whatever novel techniques may be appropriate to the problem at hand. By beginning at the beginning, and analysing a wide variety of astrophysical settings, we seek not only to make this review suitable for fluid dynamic veterans, but to engage novice recruits as well with what we hope will be an unusual and instructive introduction to the subject.

astro-ph.HE↗

arXiv2016

The radiative zone of the Sun and the tachocline: stability of baroclinic patterns of differential rotation

Barotropic rotation and radiative equilibrium are mutually incompatible in stars. The issue is often addressed by allowing for a meridional circulation, but this is not devoid of theoretical complications. Models of rotation in the Sun which maintain strict radiative equilibrium, making use of the observation that the Sun is not in a state of barotropic rotation, have recently been suggested. To investigate the dynamical behaviour of these solutions, we study the local stability of stratified, weakly magnetized, differentially rotating fluids to non-axisymmetric perturbations. Finite heat conductivity, kinematic viscosity, and resistivity are present. The evolution of local embedded perturbations is governed by a set of coupled, ordinary differential equations with time-dependent coefficients. Two baroclinic models of rotation for the upper radiative zone and tachocline are studied: (i) an interpolation based on helioseismology data, (ii) a theoretical solution directly compatible with radiative equilibrium. The growth of the local Goldreich-Schubert-Fricke instability appears to be suppressed, largely because of the viscosity. An extensive exploration of wavenumber space is carried out, with and without a magnetic field. Although we easily find classical local instabilities when they ought formally to be present, for the Sun the analysis reveals neither unstable solutions, nor even solutions featuring a large transient growth. We have not ruled out larger scale or nonlinear instabilities, nor have we rigorously proven local stability. But rotational configurations in close agreement with observations, generally thought to be vulnerable to the classic local Goldreich-Schubert-Fricke instability, do appear to be locally stable under rather general circumstances.

astro-ph.SR↗

arXiv2015

Inefficient Driving of Bulk Turbulence by Active Galactic Nuclei in a Hydrodynamic Model of the Intracluster Medium

Central jetted active galactic nuclei (AGN) appear to heat the core regions of the intracluster medium (ICM) in cooling-core galaxy clusters and groups, thereby preventing a cooling catastrophe. However, the physical mechanism(s) by which the directed flow of kinetic energy is thermalized throughout the ICM core remains unclear. We examine one widely discussed mechanism whereby the AGN induces subsonic turbulence in the ambient medium, the dissipation of which provides the ICM heat source. Through controlled inviscid 3-d hydrodynamic simulations, we verify that explosive AGN-like events can launch gravity waves (g-modes) into the ambient ICM which in turn decay to volume-filling turbulence. In our model, however, this process is found to be inefficient, with less than 1% of the energy injected by the AGN activity actually ending up in the turbulence of the ambient ICM. This efficiency is an order of magnitude or more too small to explain the observations of AGN-feedback in galaxy clusters and groups with short central cooling times. Atmospheres in which the g-modes are strongly trapped/confined have an even lower efficiency since, in these models, excitation of turbulence relies on the g-modes' ability to escape from the center of the cluster into the bulk ICM. Our results suggest that, if AGN-induced turbulence is indeed the mechanism by which the AGN heats the ICM core, its driving may rely on physics beyond that captured in our ideal hydrodynamic model.

astro-ph.HE↗

arXiv2014

On the high frequency spectrum of a classical accretion disc

We derive simple and explicit expressions for the high frequency spectrum of a classical accretion disc. Both stress-free and finite stress inner boundaries are considered. A classical accretion disc spectrum with a stress-free inner boundary departs from a Wien spectrum at large $ν$, scaling as $ν^{2.5}$ (as opposed to $ν^3$) times the usual exponential cut-off. If there is finite stress at the inner disc boundary, the maximum disc temperature generally occurs at this edge, even at relatively modest values of the stress. In this case, the high frequency spectrum is proportional to $ν^2$ times the exponential cut-off. If the temperature maximum is a local hot spot, instead of an axisymmetric ring, then an interior maximum produces a $ν^2$ prefactor while an edge maximum yields $ν^{1.5}$. Because of beaming effects, these latter findings should pertain to a classical relativistic disc. The asymptotics are in general robust and independent of the detailed temperature profile, provided only that the liberated free energy of differential rotation is dissipated locally, and may prove useful beyond the strict domain of classical disc theory. As observations continue to improve with time, our findings suggest the possibility of using the high energy spectral component of black hole candidates as a signature prediction of classical theory, as well as an diagnostic of the stress at the inner regions of an accretion disc.

astro-ph.HE↗

arXiv2014

Dynamical, biological, and anthropic consequences of equal lunar and solar angular radii

The nearly equal lunar and solar angular sizes as subtended at the Earth is generally regarded as a coincidence. This is, however, an incidental consequence of the tidal forces from these bodies being comparable. Comparable magnitudes implies strong temporal modulation, as the forcing frequencies are nearly but not precisely equal. We suggest that on the basis of paleogeographic reconstructions, in the Devonian period, when the first tetrapods appeared on land, a large tidal range would accompany these modulated tides. This would have been conducive to the formation of a network of isolated tidal pools, lending support to A.S. Romer's classic idea that the evaporation of shallow pools was an evolutionary impetus for the development of chiridian limbs in aquatic tetrapodomorphs. Romer saw this as the reason for the existence of limbs, but strong selection pressure for terrestrial navigation would have been present even if the limbs were aquatic in origin. Since even a modest difference in the Moon's angular size relative to the Sun's would lead to a qualitatively different tidal modulation, the fact that we live on a planet with a Sun and Moon of close apparent size is not entirely coincidental: it may have an anthropic basis.

astro-ph.EP↗

arXiv2012

The stability of stratified, rotating systems and the generation of vorticity in the Sun

We examine the linear behavior of three-dimensional Lagrangian displacements in a stratified, shearing background. The isentropic and iso-rotation surfaces of the equilibrium flow are assumed to be axisymmetric, but otherwise fully two-dimensional. Three-dimensional magnetic fields are included in the perturbation equations; however the equilibrium is assumed to be well-described by purely hydrodynamic forces. The model, in principle very general, is used to study the behavior of fluid displacements in an environment resembling the solar convection zone. Some very suggestive results emerge. All but high-latitude displacements align themselves with the observed surfaces of constant angular velocity. The tendency for the angular velocity to remain constant with depth in the bulk of the convective zone, together with other critical features of the rotation profile, emerge from little more than a visual inspection of the governing equation. In the absence of a background axial angular velocity gradient, displacements exhibit no poleward bias, suggesting that solar convection "plays-off" of prexisting shear rather than creates it. We argue that baroclinic vorticity of precisely the right order is generated at the radiative/convective zone boundary due to centrifugal distortion of equipotential surfaces that is not precisely followed by isothermal surfaces. If so, many features of the Sun's internal rotation become more clear, including: i) the general appearance of the tachocline; ii) the extension of differential rotation well into the radiative zone; iii) the abrupt change of morphology of convective zone isorotation surfaces; and iv) the inability of current numerical simulations to reproduce the solar rotation profile without imposed entropy boundary conditions.

astro-ph.SR↗

arXiv2011

Global model of differential rotation in the Sun

The isorotation contours of the solar convective zone (SCZ) show three distinct morphologies, corresponding to two boundary layers (inner and outer), and the bulk of the interior. Previous work has shown that the thermal wind equation together with informal arguments on the nature of convection in a rotating fluid could be used to deduce the shape of the isorotation surfaces in the bulk of the SCZ with great fidelity, and that the tachocline contours could also be described by relatively simple phenomenology. In this paper, we show that the form of these surfaces can be understood more broadly as a mathematical consequence of the thermal wind equation and a narrow convective shell. The analysis does not yield the angular velocity function directly, an additional surface boundary condition is required. But much can already be deduced without constructing the entire rotation profile. The mathematics may be combined with dynamical arguments put forth in previous works to the mutual benefit of each. An important element of our approach is to regard the constant angular velocity surfaces as an independent coordinate variable for what is termed the "residual entropy," a quantity that plays a key role in the equation of thermal wind balance. The difference between the dynamics of the bulk of the SCZ and the tachocline is due to a different functional form of the residual entropy in each region. We develop a unified theory for the rotational behavior of both the SCZ and the tachocline, using the solutions for the characteristics of the thermal wind equation. These characteristics are identical to the isorotation contours in the bulk of the SCZ, but the two deviate in the tachocline. The outer layer may be treated, at least descriptively, by similar mathematical techniques, but this region probably does not obey thermal wind balance.

astro-ph.SR↗

arXiv2011

On linear dust-gas streaming instabilities in protoplanetary discs

We revisit, via a very simplified set of equations, a linear streaming instability (technically an overstability), which is present in, and potentially important for, dusty protoplanetary disks (Youdin & Goodman 2005). The goal is a better understanding of the physical origin of such instabilities, which are notoriously subtle. Rotational dynamics seem to be essential to this type of instability, which cannot be captured by one-dimensional Cartesian models. Dust `pileups' in moving pressure maxima are an important triggering mechanism of the instability, and drag feedback of dust upon the gas allows these maxima to be strengthened. Coriolis forces and the background drift counteract the effects of the pressure force.

astro-ph.EP↗