Back-reaction Force Research Articles

Radiating particles accelerated by a weakly charged Schwarzschild black hole

It is well known that supermassive black holes in the centers of galaxies are capable of accelerating charged particles to very high energies. In many cases, the particle acceleration by black holes occurs electromagnetically through an electric field induced by the source. In such scenarios, the accelerated particles radiate electromagnetic waves, leading to the appearance of the backreaction force, which can considerably change the dynamics, especially, if the particles are relativistic. The effect of the radiation reaction force due to accelerating electric field of the central body in curved spacetime has not been considered previously. We study the dynamics of radiating charged particles in the field of the Schwarzschild black hole in the presence of an electric field associated with a small central charge of negligible gravitational influence. We use the DeWitt-Brehme equation and discuss the effect of the self-force, also known as the tail term, within the given approach. We also study the pure effect of the self-force to calculate the radiative deceleration of radially moving charged particles. In the case of bounded orbits, we find that the radiation reaction force can stabilize and circularize the orbits of oscillating charged particles by suppressing the oscillations or causing the particles to spiral down into the black hole depending on the sign of the electrostatic interaction. In all cases, we calculate the energy losses and exact trajectories of charged particles for different values and signs of electric charge.

General backreaction force of cosmological bubble expansion

The gravitational-wave energy-density spectra from cosmological first-order phase transitions crucially depend on the terminal wall velocity of asymptotic bubble expansion when the driving force from the effective potential difference is gradually balanced by the backreaction force from the thermal plasma. Much attention has previously focused on the backreaction force acting on the bubble wall alone but overlooked the backreaction forces on the sound shell and shock-wave front, if any, which have been both numerically and analytically accomplished in our previous studies but only for a bag equation of state. In this paper, we will generalize the backreaction force on bubble expansion beyond the simple bag model. Published by the American Physical Society 2024

Viscosity-modulated clustering of heated bidispersed particles in a turbulent gas

Clustering of externally and evenly heated particles is enhanced by the increased viscosity of heated fluid in the vicinity of these clusters – a phenomenon known as viscous capturing (VC). Herein we study, via direct numerical simulations of decaying turbulence, the effect of temperature-driven viscosity on clustering with different particle loading densities. We employ a two-way momentum and energy coupling, and gas viscosity is modelled by a power law to understand the role of the increased drag and particle back-reaction force on the clustering intensity. For the continuum and dispersed phases, Eulerian and Lagrangian point particle schemes have been used, neglecting inter-particle collisions. We found that the enhanced viscosity-driven clustering is a strong function of particle loading density, as the increase in particle number density enables the formation of large uneven clusters before heating, which is the main condition for VC to take effect. Higher number density should result in greater turbulence modulation and negate local temperature-based viscous effects leading to VC. However, due to higher local particle number density in the clusters and interphase heat transfer, increased drag force prevails in such cases and delivers excessive clustering. By sampling conditionally the particle velocity and temperature inside the clusters, it is found that the thermodynamic and kinematic properties of the particles in the clusters are highly correlated, and this correlation increases with the particle loading density. Therefore, based on the particle number density, temperature-based viscosity can enhance considerably the clustering of heated particles and alter the effect of particles on the underlying turbulence.

Hydrodynamic backreaction force of cosmological bubble expansion

As a promising probe for the new physics beyond the standard model of particle physics in the early Universe, the predictions for the stochastic gravitational wave background from a cosmological first-order phase transition heavily rely on the bubble wall velocity determined by the bubble expansion dynamics. The bubble expansion dynamics is governed by the competition between the driving force from the effective potential difference and the backreaction force from a sum of the thermal force and friction force induced by the temperature jumping and out-of-equilibrium effects across the bubble wall, respectively. In this paper, we propose a hydrodynamic evaluation on this total backreaction force for a non-runaway steady-state bubble expansion, which, after evaluated at the wall interface, exactly reproduces the pressure difference $\Delta_\mathrm{wall}[(\bar{\gamma}^2-1)w]$ obtained previously from the junction condition of the total energy-momentum tensor at the wall interface, where $w$ is the enthalpy and $\bar{\gamma}\equiv(1-\bar{v}^2)^{-1/2}$ is the Lorentz factor of the wall-frame fluid velocity $\bar{v}$.

Алгоритм для учёта потерь на гравитационное излучение при слиянии нейтронных звёзд

The stripping model of stripping in a pair of contact binary neutron stars is one of the promising explanations for short gamma-ray bursts. For correct modeling of the mass transfer stage, a self-consistent accounting for the loss of angular momentum due to the emission of gravitational waves is required. The paper presents a new algorithm for calculating the back-reaction force of gravitational radiation in a pair of binary neutron stars. The calculation is implemented by the smoothed-particle hydrodynamics method (SPH).

Non-linear evolution of instabilities between dust and sound waves

ABSTRACT We study the non-linear evolution of the acoustic ‘resonant drag instability’ (RDI) using numerical simulations. The acoustic RDI is excited in a dust–gas mixture when dust grains stream through gas, interacting with sound waves to cause a linear instability. We study this process in a periodic box by accelerating neutral dust with an external driving force. The instability grows as predicted by linear theory, eventually breaking into turbulence and saturating. As in linear theory, the non-linear behaviour is characterized by three regimes – high, intermediate, and low wavenumbers – the boundary between which is determined by the dust–gas coupling strength and the dust-to-gas mass ratio. The high and intermediate wavenumber regimes behave similarly to one another, with large dust-to-gas ratio fluctuations while the gas remains largely incompressible. The saturated state is highly anisotropic: dust is concentrated in filaments, jets, or plumes along the direction of acceleration, with turbulent vortex-like structures rapidly forming and dissipating in the perpendicular directions. The low-wavenumber regime exhibits large fluctuations in gas and dust density, but the dust and gas remain more strongly coupled in coherent ‘fronts’ perpendicular to the acceleration. These behaviours are qualitatively different from those of dust ‘passively’ driven by external hydrodynamic turbulence, with no back-reaction force from dust on to gas. The virulent nature of these instabilities has interesting implications for dust-driven winds in a variety of astrophysical systems, including around cool stars, in dusty torii around active-galactic-nuclei, and in and around giant molecular clouds.

Particle acceleration in relativistic magnetic reconnection with strong inverse-Compton cooling in pair plasmas

ABSTRACT Particle-in-cell (PIC) simulations have shown that relativistic collisionless magnetic reconnection drives non-thermal particle acceleration (NTPA), potentially explaining high-energy (X-ray/γ-ray) synchrotron and/or inverse Compton (IC) radiation observed from various astrophysical sources. The radiation back-reaction force on radiating particles has been neglected in most of these simulations, even though radiative cooling considerably alters particle dynamics in many astrophysical environments where reconnection may be important. We present a radiative PIC study examining the effects of external IC cooling on the basic dynamics, NTPA, and radiative signatures of relativistic reconnection in pair plasmas. We find that, while the reconnection rate and overall dynamics are basically unchanged, IC cooling significantly influences NTPA: the particle spectra still show a hard power law (index ≥ −2) as in non-radiative reconnection, but transition to a steeper power law that extends to a cooling-dependent cut-off. The steep power-law index fluctuates in time between roughly −3 and −5. The time-integrated photon spectra display corresponding power laws with indices ≈−0.5 and ≈−1.1, similar to those observed in hard X-ray spectra of accreting black holes.

Gravitomagnetic dynamical friction

A supermassive black hole moving through a field of stars will gravitationally scatter the stars, inducing a backreaction force on the black hole known as dynamical friction. In Newtonian gravity, the axisymmetry of the system about the black hole's velocity $\mathbf{v}$ implies that the dynamical friction must be anti-parallel to $\mathbf{v}$. However, in general relativity the black hole's spin $\mathbf{S}$ need not be parallel to $\mathbf{v}$, breaking the axisymmetry of the system and generating a new component of dynamical friction similar to the Lorentz force $\mathbf{F} = q\mathbf{v} \times \mathbf{B}$ experienced by a particle with charge $q$ moving in a magnetic field $\mathbf{B}$. We call this new force gravitomagnetic dynamical friction and calculate its magnitude for a spinning black hole moving through a field of stars with Maxwellian velocity dispersion $\sigma$, assuming that both $v$ and $\sigma$ are much less than the speed of light $c$. We use post-Newtonian equations of motion accurate to $\mathcal{O}(v^3/c^3)$ needed to capture the effect of spin-orbit coupling and also include direct stellar capture by the black hole's event horizon. Gravitomagnetic dynamical friction will cause a black hole with uniform speed to spiral about the direction of its spin, similar to a charged particle spiraling about a magnetic field line, and will exert a torque on a supermassive black hole orbiting a galactic center, causing the angular momentum of this orbit to slowly precess about the black-hole spin. As this effect is suppressed by a factor $(\sigma/c)^2$ in nonrelativistic systems, we expect it to be negligible in most astrophysical contexts but provide this calculation for its theoretical interest and potential application to relativistic systems.

Ultra-bright, high-energy-density γ-ray emission from a gas-filled gold cone-capillary

We propose a new scheme to obtain a compact ultra-bright, high-energy-density γ ray source by ultra-intense laser interaction with a near-critical-density (NCD) plasmas filled gold cone-capillary. By using the particle-in-cell code EPOCH, it is shown that NCD electrons are accelerated by the laser ponderomotive force in the gold cone and emit strong radiation. Considering the effect of large radiation back-reaction force, some electrons are kicked into the laser field. The trapped electrons oscillate significantly in the transverse direction and emit ultra-bright γ ray in the forward direction. By attaching a capillary to the gold cone, the trapped electrons are able to keep oscillating for a long distance and the radiation emission can be significantly enhanced. Three-dimensional simulations show that the total γ photon flux with the photon energy in the range of 3 MeV to 30 MeV is approximately 1013/shot, and the corresponding peak brightness is in the order of 1023 photons/s/mm2/mrad2/0.1%BW. The average energy-density of the radiated γ photons is about 1017J/m3, which is six orders of magnitude higher than the threshold of high-energy-density physics. The energy conversion efficiency from the laser to the γ photons is estimated to be about 5% at the irradiation of a laser with intensity ∼1.37×1022W/cm2.

Spin-1/2 Charged Particle in 1+4 dimensions with N=1-Supersymmetry

We study the dynamics of a charged spin-(1/2) particle in an external 5-dimensional electromagnetic field. We then consider that we are at the TeV scale, so that we can access the fifth dimension and carry out our physical considerations in a 5-dimensional brane. In this brane, we focus our attention to the quantum-mechanical dynamics of the charged particle minimally coupled to the 5-dimensional electromagnetic field. We propose a way to identify the Abraham-Lorentz back reaction force as an effect of the extra ( fifth ) dimension. In another regime of fields allowed by the model, a massive charged particle (CHAMP) behaviour can be, in which the bulk electric field play a crucial rôle.

Gravitational self-force on a particle in circular orbit around a Schwarzschild black hole

We calculate the gravitational self-force acting on a pointlike particle of mass $\ensuremath{\mu}$, set in a circular geodesic orbit around a Schwarzschild black hole. Our calculation is done in the Lorenz gauge: For given orbital radius, we first solve directly for the Lorenz-gauge metric perturbation using numerical evolution in the time domain; we then compute the (finite) backreaction force from each of the multipole modes of the perturbation; finally, we apply the ``mode-sum'' method to obtain the total, physical self-force. The temporal component of the self-force (which is gauge invariant) describes the dissipation of orbital energy through gravitational radiation. Our results for this component are consistent, to within the computational accuracy, with the total flux of gravitational-wave energy radiated to infinity and through the event horizon. The radial component of the self-force (which is gauge dependent) is calculated here for the first time. It describes a conservative shift in the orbital parameters away from their geodesic values. We thus obtain the $O(\ensuremath{\mu})$ correction to the specific energy and angular momentum parameters (in the Lorenz gauge), as well as the $O(\ensuremath{\mu})$ shift in the orbital frequency (which is gauge invariant).

Quantum Backreaction (Casimir) Effect II. Scalar and Electromagnetic Fields

Casimir effect in most general terms may be understood as a backreaction of a quantum system causing an adiabatic change of the external conditions under which it is placed. This paper is the second installment of a work scrutinizing this effect with the use of algebraic methods in quantum theory. The general scheme worked out in the first part is applied here to the discussion of particular models. We consider models of the quantum scalar field subject to external interaction with ``softened'' Dirichlet or Neumann boundary conditions on two parallel planes. We show that the case of electromagnetic field with softened perfect conductor conditions on the planes may be reduced to the other two. The ``softening'' is implemented on the level of the dynamics, and is not imposed ad hoc, as is usual in most treatments, on the level of observables. We calculate formulas for the backreaction energy in these models. We find that the common belief that for electromagnetic field the backreaction force tends to the strict Casimir formula in the limit of ``removed cutoff'' is not confirmed by our strict analysis. The formula is model dependent and the Casimir value is merely a term in the asymptotic expansion of the formula in inverse powers of the distance of the planes. Typical behaviour of the energy for large separation of the plates in the class of models considered is a quadratic fall-of. Depending on the details of the ``softening'' of the boundary conditions the backreaction force may become repulsive for large separations.

Doubly Helical Coronal Ejections from Dynamos and Their Role in Sustaining the Solar Cycle

Two questions about the solar magnetic field might be answered together once their connection is identified. The first is important for large-scale dynamo theory: what prevents the magnetic back-reaction forces from shutting down the dynamo cycle? The second question is, what determines the handedness of twist and writhe in magnetized coronal ejecta? Magnetic helicity conservation is important for answering both questions. Conservation implies that dynamo generation of large-scale writhed structures is accompanied by the oppositely signed twist along these structures. The latter is associated with the back-reaction force. We suggest that coronal mass ejections simultaneously liberate small-scale twist and large-scale writhe of opposite sign, helping to prevent the cycle from quenching and enabling a net magnetic flux change in each hemisphere. Solar observations and helicity spectrum measurements from our simulation of a rising flux tube support this idea. We show a new pictorial of dynamo flux generation that includes the back-reaction and magnetic helicity conservation and represents the field by a ribbon or tube rather than a line.

Back reaction of Einstein’s gravitational waves as the origin of natal pulsar kicks

At the early core bounce of a supernova collapse rapid convective overturn along with gradients in density and temperature in the neutrino-decoupling zone drives anisotropic neutrino flux. If then active-to-sterile $({\ensuremath{\nu}}_{\overline{\ensuremath{\tau}},\overline{\ensuremath{\mu}}}\ensuremath{\leftrightarrow}{\ensuremath{\nu}}_{s})$ neutrino oscillations in the dense core take place, gravitational radiation should be emitted the entire oscillation length. Since the oscillation feeds mass energy up into (or drains it from) the new species, the large neutrino mass-squared difference ${(10}^{4}$ ${\mathrm{eV}}^{2}\ensuremath{\lesssim}\ensuremath{\Delta}{m}^{2}\ensuremath{\lesssim}{10}^{8}$ ${\mathrm{eV}}^{2})$ implies that a huge amount of energy is released as gravity waves. This gravitational waves luminosity is larger than the one from either neutrino convection and cooling or perturbed matter distributions. I identify the back-reaction force (mass and current multipoles) of the gravitational wave burst generated over the oscillation time scale as the pulsar thruster.

Nucleosynthesis calculations for the ejecta of neutron star coalescences

We present the results of fully dynamical r-process network calculations for the ejecta of neutron star mergers (NSMs). The late stages of the inspiral and the final violent coalescence of a neutron star binary have been calculated in detail using a 3D hydrodynamics code (Newtonian gravity plus backreaction forces emerging from the emission of gravitational waves) and a realistic nuclear equation of state. The found trajectories for the ejecta serve as input for dynamical r-process calculations where all relevant nuclear reactions (including beta-decays depositing nuclear energy in the expanding material) are followed. We find that all the ejected material undergoes r-process. For an initial Ye close to 0.1 the abundance distributions reproduce very accurately the solar r-process pattern for nuclei with A above 130. For lighter nuclei strongly underabundant (as compared to solar) distributions are encountered. We show that this behaviour is consistent with the latest observations of very old, metal-poor stars, despite simplistic arguments that have recently been raised against the possibility of NSM as possible sources of Galactic r-process material.

Accretion of a Satellite onto a Spherical Galaxy: Binary Evolution and Orbital Decay

We study the dynamical evolution of a satellite (of mass M) orbiting around a companion spherical galaxy. The satellite is subject to a back-reaction force FΔ resulting from the density fluctuations excited in the primary stellar system. We evaluate this force using the linear response theory developed by Colpi & Pallavicini in 1998. FΔ is computed in the reference frame comoving with the primary galaxy and is expanded in multipoles. To lowest order, the force depends on a time integral involving a dynamical four-point correlation function of the unperturbed background. The equilibrium stellar system (of mass Nm) is described in terms of a Gaussian one-particle distribution function. To capture the relevant features of the physical process determining the evolution of the detached binary, we introduce in the Hamiltonian the harmonic potential as interaction potential among stars. The evolution of the composite system is derived solving for a set of ordinary differential equations; the dynamics of the satellite and of the stars is computed self-consistently. We determine the conditions for tidal capture of a satellite from an asymptotic free state and give an estimate of the maximum kinetic energy above which encounters do not end in a merger as a function of the mass ratio M/Nm. We find that capture always leads to final coalescence. If the binary forms as a bound pair, stability against orbital decay is lost if the pericentric distance is smaller than a critical value. This instability is interpreted in terms of a near-resonance condition and establishes when the orbital Keplerian frequency becomes comparable to the internal frequency ω of the stellar system. We show that before coalescence, eccentric orbits become progressively less eccentric; the circularization is explored as a function of mass ratio. The timescale of binary coalescence τb is a sensitive function of the eccentricity e for a fixed semimajor axis a and M/Nm ratio: the mismatch between τb at e ~ 0 and τb at e ~ 1 can be very large, typically τb(e 1) ~ 6ω-1, and the time ratio τb(0)/τb(1) 5 (for M/Nm = 0.05). In addition, we find that τb obeys a scaling relation with M/Nm for circular orbits: τb ∝ (M/Nm)-α, with α ~ 0.4. In grazing encounters, τb is nearly independent of mass.

Drag on a Satellite Moving across a Spherical Galaxy: Tidal and Frictional Forces in Short‐lived Encounters

The drag force on a satellite of mass M moving with speed V in the gravitational field of a spherically symmetric background of stars is computed. During the encounter, the stars are subject to a time-dependent force that alters their equilibrium. The resulting distortion in the stellar density field acts back to produce a force FΔ that decelerates the satellite. This force is computed using a perturbative technique known as linear response theory. In this paper, we extend the formalism of linear response to derive the correct expression for the back-reaction force FΔ that applies when the stellar system is described by an equilibrium one-particle distribution function. FΔ is expressed in terms of a suitable correlation function that couples the satellite dynamics to the unperturbed dynamics of the stars. At time t, the force depends upon the whole history of the composite system. In the formalism, we account for the shift of the stellar center of mass resulting from linear momentum conservation. The self-gravity of the response is neglected since it contributes to a higher order in the perturbation. Linear response theory applies also to the case of a satellite orbiting outside the spherical galaxy. The case of a satellite moving on a straight line, at high speed relative to the stellar dispersion velocity, is explored. We find that the satellite during its passage raises (1) global tides in the stellar distribution and (2) a wake, i.e., an overdense region behind its trail. If the satellite motion is external to the galaxy, it suffers a dissipative force that is not exclusively acting along V but acquires a component along R, the position vector relative to the center of the spherical galaxy. We derive the analytical expression of the force in the impulse approximation. In penetrating short-lived encounters, the satellite moves across the stellar distribution and the transient wake excited in the density field is responsible for most of the deceleration. We find that dynamical friction arises from a memory effect involving only those stars perturbed along the path. The force can be written in terms of an effective Coulomb logarithm that now depends upon time. The value of ln Λ is computed for two simple equilibrium density distributions; it is shown that the drag increases as the satellite approaches the denser regions of the stellar distribution and attains a maximum after pericentric passage. When the satellite crosses the edge of the galaxy, the force does not vanish since the galaxy keeps memory of the perturbation induced and declines on a time comparable to the dynamical time of the stellar system. In the case of a homogeneous cloud, we compute the total energy loss. In evaluating the contribution resulting from friction, we derive self-consistently the maximum impact parameter, which is found to be equal to the length traveled by the satellite within the system. Tides excited by the satellite in the galaxy reduce the value of the energy loss by friction; in close encounters, this value is decreased by a factor of ~1.5.