Linear Momentum Flux Research Articles

Multipolar invariants and the eccentricity enhancement function parametrization of gravitational radiation

Gravitational radiation can be decomposed as an infinite sum of radiative multipole moments, which parametrize the waveform at infinity. The multipolar-post-Minkowskian formalism provides a connection between these multipoles and the source multipole moments, known as explicit integrals over the matter source. The gravitational wave energy, angular momentum and linear momentum fluxes are then expressed as multipolar expansions containing certain combinations of the source moments. We compute several gauge-invariant quantities as "building blocks" entering the multipolar expansion of both radiated energy and angular momentum at the 2.5 post-Newtonian (PN) level of accuracy in the case of hyperboliclike motion, by completing previous studies through the calculation of tail effects up to the fractional 1PN order. We express such multipolar invariants in terms of certain eccentricity enhancement factor functions, which are the counterpart of the well known enhancement functions already introduced in the literature for ellipticlike motion. Finally, we use the complete 2.5PN-accurate averaged energy and angular momentum fluxes to study the associated adiabatic evolution of orbital elements under gravitational radiation reaction.

Momentum recoil in the relativistic two-body problem: Higher-order tails

In the description of the relativistic two-body interaction, together with the effects of energy and angular momentum losses due to the emission of gravitational radiation, one has to take into account also the loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. We compute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum flux for a nonspinning binary system either along hyperboliclike or ellipticlike orbits. The corresponding orbital averages are evaluated at their leading post-Newtonian approximation, using harmonic coordinates and working in the Fourier domain. The final expressions are given in a large-eccentricity (or large-angular momentum) expansion along hyperboliclike orbits and in a small-eccentricity expansion along ellipticlike orbits. We thus complete a previous analysis focusing on both energy and angular momentum losses [Phys. Rev. D \textbf{104}, no.10, 104020 (2021)], providing brick-type results which will be useful, e.g., in the high-accurate determination of the radiated impulses of the two bodies undergoing a scattering process.

Linear momentum flux from inspiralling compact binaries in quasielliptical orbits at 2.5 post-Newtonian order

Emission of anisotropic gravitational radiation from compact binary system leads to a flux of linear momentum. This results in the recoil of the system. We investigate the rate of loss of Linear momentum flux in the far zone of the source using various mass type and current type multipole moments for inspiralling compact binary mergers in quasi-elliptical orbits at 2.5 Post Newtonian order. We compute the linear momentum flux accurate up to $\mathcal{O}(e_t)$ in harmonic coordinate. A 2.5 Post Newtonian Quasi-Keplarian representation of the parametric solution to the Post Newtonian equation of motion for the compact binary system has been adopted here. We also provide a closed-form expression for the accumulated linear momentum from the remote past through the binary evolution.

Integrated Fluxes in Magneto-Hydrodynamic Mixed Convection in a Cavity Sustained by Conjugate Heat Transfer

Abstract A numerical study of magneto-hydrodynamic mixed convection in a cavity has been conducted to investigate the influence of magnetic field on integrated flux of thermal energy, linear momentum, and kinetic energy. Shear force through lid motion establishes the forced convection effect and buoyancy force due to differential heating of the moving lid and the stationary interface ensures the natural convection phenomenon. Additionally, conduction through the solid slab with prescribed temperature at the outer surface attached to the cavity induces conjugate heat transfer. Further, the top and bottom walls throughout the domain are kept insulated and a uniform horizontal magnetic field is applied on the interface toward left. Fluid flow and heat transfer characteristics are examined for a range of Hartmann number (Ha): 0, 10, 50, and 120 at fixed values of Reynolds number, Grashof number, and Prandtl number of 300, 9 × 104 and 0.71, respectively. The result shows that the transport of heat in the near wall regions of the fluid domain is primarily governed by diffusion, whereas advection appears stronger in the central region of the cavity. Increase in magnetic field strength from Ha = 0 to 120 gradually suppresses the recirculating structure of the flow signifying a reduction in advective strength as depicted by the decrease in the value of total integrated heat flux from 25.15×10-3 to 6.0×10-3. The reduction in heat flux, momentum fluxes, and kinetic energy fluxes with increase in magnetic field has been well correlated in the range of 0≤Ha≤120.

Black-hole kicks from numerical-relativity surrogate models

Binary black holes radiate linear momentum in gravitational waves as they merge. Recoils imparted to the black-hole remnant can reach thousands of km/s, thus ejecting black holes from their host galaxies. We exploit recent advances in gravitational waveform modeling to quickly and reliably extract recoils imparted to generic, precessing, black hole binaries. Our procedure uses a numerical-relativity surrogate model to obtain the gravitational waveform given a set of binary parameters, then from this waveform we directly integrate the gravitational-wave linear momentum flux. This entirely bypasses the need of fitting formulae which are typically used to model black-hole recoils in astrophysical contexts. We provide a thorough exploration of the black-hole kick phenomenology in the parameter space, summarizing and extending previous numerical results on the topic. Our extraction procedure is made publicly available as a module for the Python programming language named SURRKICK. Kick evaluations take ~0.1s on a standard off-the-shelf machine, thus making our code ideal to be ported to large-scale astrophysical studies.

Thermodynamic bounds for existence of normal shock in compressible fluid flow in pipes.

The present paper is concerned with the thermodynamic theory of the normal shock in compressible fluid flow in pipes, in the lights of the pioneering works of Lord Rayleigh and G. Fanno. The theory of normal shock in pipes is currently presented in terms of the Rayleigh and Fanno curves, which are shown to cross each other in two points, one corresponding to a subsonic flow and the other corresponding to a supersonic flow. It is proposed in this paper a novel differential identity, which relates the energy flux density, the linear momentum flux density, and the entropy, for constant mass flow density. The identity so obtained is used to establish a theorem, which shows that Rayleigh and Fanno curves become tangent to each other at a single sonic point. At the sonic point the entropy reaches a maximum, either as a function of the pressure and the energy density flux or as a function of the pressure and the linear momentum density flux. A Second Law analysis is also presented, which is fully independent of the Second Law analysis based on the Rankine-Hugoniot adiabatic carried out by Landau and Lifshitz (1959).

Reviewing the roots of continuum formulations in molecular systems. Part III: Stresses, couple stresses, heat fluxes

This contribution is the third part in a series devoted to the fundamental link between discrete particle systems and continuum descriptions. The basis for such a link is the postulation of the primary continuum fields such as density and kinetic energy in terms of atomistic quantities using space and probability averaging. In this part, solutions to the flux quantities (stress, couple stress, and heat flux), which arise in the balance laws of linear and angular momentum, and energy are discussed based on the Noll’s lemma. We show especially that the expression for the stress is not unique. Integrals of all the fluxes over space are derived. It is shown that the integral of both the microscopic Noll–Murdoch and Hardy couple stresses (more precisely their potential part) equates to zero. Space integrals of the Hardy and the Noll–Murdoch Cauchy stress are equal and symmetric even though the local Noll–Murdoch Cauchy stress is not symmetric. Integral expression for the linear momentum flux and the explicit heat flux are compared to the virial pressure and the Green–Kubo expression for the heat flux, respectively. It is proven that in the case when the Dirac delta distribution is used as kernel for spatial averaging, the Hardy and the Noll–Murdoch solution for all fluxes coincide. The heat fluxes resulting from both the so-called explicit and implicit approaches are obtained and compared for the localized case. We demonstrate that the spatial averaging of the localized heat flux obtained from the implicit approach does not equate to the expression obtained using a general averaging kernel. In contrast this happens to be true for the linear momentum flux, i.e. the Cauchy stress.

Erratum: 2.5PN linear momentum flux from inspiralling compact binaries in quasicircular orbits and associated recoil: Nonspinning case [Phys. Rev. D85, 044021 (2012)

Erratum: 2.5PN linear momentum flux from inspiralling compact binaries in quasicircular orbits and associated recoil: Nonspinning case [Phys. Rev. D<b>85</b>, 044021 (2012)

Erratum: Radial infall of two compact objects: 2.5-post-Newtonian linear momentum flux and associated recoil [Phys. Rev. D85, 104046 (2012)

Erratum: Radial infall of two compact objects: 2.5-post-Newtonian linear momentum flux and associated recoil [Phys. Rev. D<b>85</b>, 104046 (2012)

Radial infall of two compact objects: 2.5-post-Newtonian linear momentum flux and associated recoil

The loss rate of linear momentum from a binary system composed of compact objects (radially falling towards each other under mutual gravitational influence) has been investigated using the multipolar post-Minkowskian approach. The 2.5PN accurate analytical formula for the linear momentum flux is provided, in terms of the separation of the two objects, in harmonic coordinates, both for a finite and infinite initial separation. The 2.5PN formulas for the linear momentum flux are finally used to estimate the recoil velocity accumulated during a premerger phase of the binary evolution.

2.5PN linear momentum flux from inspiralling compact binaries in quasicircular orbits and associated recoil: Nonspinning case

Anisotropic emission of gravitational waves (GWs) from inspiralling compact binaries leads to the loss of linear momentum and hence gravitational recoil of the system. The loss rate of linear momentum in the far-zone of the source (a nonspinning binary system of black holes in quasicircular orbit) is investigated at the 2.5 post-Newtonian (PN) order and used to provide an analytical expression in harmonic coordinates for the 2.5PN accurate recoil velocity of the binary accumulated in the inspiral phase. We find that the recoil velocity at the end of the inspiral phase (i.e at the innermost stable circular orbit (ISCO)) is maximum for a binary with symmetric mass ratio of \nu~0.2 and is roughly about ~4.58 km/s. Going beyond inspiral, we also provide an estimate of the more important contribution to the recoil velocity from the plunge phase. Again the recoil velocity at the end of the plunge, involving contributions both from inspiral and plunge phase, is maximum for a binary with \nu~0.2 and is of the order of ~180 km/s.

Numerical Relativity in D dimensional space-times: Collisions of unequal mass black holes

We present unequal mass head-on collisions of black holes in D = 5 dimensional space-times. We have simulated BH systems with mass ratios q = 1,1/2, 1/3, 1/4. We extract the total energy radiated throughout the collision and compute the linear momentum flux and the recoil velocity of the final black hole. The numerical results show very good agreement with point particle calculations when extrapolated to this limit.

Perturbative effects of spinning black holes in the extreme mass-ratio limit

Recently, we proposed an enhancement of the Regge–Wheeler–Zerilli formalism for first-order perturbations about a Schwarzschild background that includes first-order corrections due to the background black-hole spin in the black-hole perturbation approach. Using this formalism, we analytically investigate gravitational wave emission and linear momentum flux from a head-on collision of two spinning black holes in the extreme mass-ratio limit. The result derived in the lowest slow-motion and weak-field approximations here is consistent with the post-Newtonian calculation.

Recoil velocity at second post-Newtonian order for spinning black hole binaries

We compute the flux of linear momentum carried by gravitational waves emitted from spinning binary black holes at second post-Newtonian (2PN) order for generic orbits. In particular we provide explicit expressions of three new types of terms, namely, next-to-leading order spin-orbit terms at 1.5 post-Newtonian (1.5PN) order, spin-orbit tail terms at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to quasicircular orbits, we integrate the linear-momentum flux over time to obtain the recoil velocity as function of orbital frequency. We find that in the so-called superkick configuration the higher-order spin corrections can increase the recoil velocity up to a factor $\ensuremath{\sim}3$ with respect to the leading-order PN prediction. Whereas the recoil velocity computed in PN theory within the adiabatic approximation can accurately describe the early inspiral phase, we find that its fast increase during the late inspiral and plunge, and the arbitrariness in determining until when it should be trusted, makes the PN predictions for the total recoil not very accurate and robust. Nevertheless, the linear-momentum flux at higher PN orders can be employed to build more reliable resummed expressions aimed at capturing the nonperturbative effects until merger. Furthermore, we provide expressions valid for generic orbits, and accurate at 2PN order, for the energy and angular momentum carried by gravitational waves emitted from spinning binary black holes. Specializing to quasicircular orbits we compute the spin-spin terms at 2PN order in the expression for the evolution of the orbital frequency and found agreement with Mik\'oczi, Vas\'uth, and Gergely. We also verified that in the limit of extreme mass ratio our expressions for the energy and angular momentum fluxes match the ones of Tagoshi, Shibata, Tanaka, and Sasaki obtained in the context of black hole perturbation theory.

The Infrared Afterglow of Supermassive Black Hole Mergers

We model the spectra and light curves of circumbinary accretion disks during the time after the central black holes merge. The most immediate effect of this merger is the dissipation of energy in the outer regions of the disk due to the gravitational wave energy and linear momentum flux released at merger. This has the effect of perturbing the gas in the disk, which then radiates the dissipated energy over a cooling timescale, giving a characteristic infrared signal for tens of thousands of years when the total black hole mass is M~10^8 M_sun. On the basis of a simple cosmological merger model in which a typical supermassive black hole undergoes a few major mergers during its lifetime, we predict that ~10^4-10^5 of these IR sources should be observable today and discuss the possibility of identifying them with multi-wavelength surveys such as SWIRE/XMM-LSS/XBootes and COSMOS.

Erratum: Gravitational recoil from binary black hole mergers: The close-limit approximation [Phys. Rev. D74, 124010 (2006)

[abridged] The coalescence of a binary black hole system is one of the main sources of gravitational waves that present and future detectors will study. Apart from the energy and angular momentum that these waves carry, for unequal-mass binaries there is also a net flux of linear momentum that implies a recoil velocity of the resulting final black hole in the opposite direction. We present a computation of the recoil velocity based on the close-limit approximation scheme, which gives excellent results for head-on and grazing collisions of black holes when compared to full numerical relativistic calculations. We obtain a maximum recoil velocity of ~ 64 km/s for a symmetric mass ratio eta = M_1 M_2/(M_1+M_2)^2 ~ 0.19 and an initial proper separation of 4 M, where M is the total ADM mass of the system. This separation is the maximum at which the close-limit approximation is expected to provide accurate results. If we supplement this estimate with PN calculations up to the innermost stable circular orbit, we obtain a lower bound for the recoil velocity, with a maximum around 84 km/s. This is a lower bound because it neglects the initial merger phase. We can however obtain a rough estimate by using PN methods or the close-limit approximation. Since both methods are known to overestimate the amount of radiation, we obtain in this way an upper bound for the recoil with maxima in the range of 220-265 km/s. We also provide non-linear fits to these estimated upper and lower bounds. These estimates are subject to uncertainties related to issues such as the choice of initial data and higher effects in perturbation theory. Nonetheless, our estimates are consistent with previous results in the literature and suggest a narrower range of possible recoil velocities.

The Distribution of Recoil Velocities from Merging Black Holes

We calculate the linear momentum flux from merging black holes (BHs) with arbitrary masses and spin orientations, using the effective-one-body (EOB) model. This model includes an analytic description of the inspiral phase, a short merger, and a superposition of exponentially damped quasi-normal ring-down modes of a Kerr BH. By varying the matching point between inspiral and ring-down, we can estimate the systematic errors generated with this method. Within these confidence limits, we find close agreement with previously reported results from numerical relativity. Using a Monte Carlo implementation of the EOB model, we are able to sample a large volume of BH parameter space and estimate the distribution of recoil velocities. For a range of mass ratios 1 ≤ m1/m2 ≤ 10, spin magnitudes of a1, 2 = 0.9, and uniform random spin orientations, we find that a fraction f500 = 0.12 of binaries have recoil velocities greater than 500 km s-1 and that a fraction f1000 = 0.027 of binaries have kicks greater than 1000 km s-1. These velocities likely are capable of ejecting the final BH from its host galaxy. Limiting the sample to comparable-mass binaries with m1/m2 ≤ 4, the typical kicks are even larger, with f500 = 0.31 and f1000 = 0.079.

Gravitational Recoil from Spinning Binary Black Hole Mergers

The inspiral and merger of binary black holes will likely involve black holes with both unequal masses and arbitrary spins. The gravitational radiation emitted by these binaries will carry angular as well as linear momentum. A net flux of emitted linear momentum implies that the black hole produced by the merger will experience a recoil or kick. Previous studies have focused on the recoil velocity from unequal mass, non-spinning binaries. We present results from simulations of equal mass but spinning black hole binaries and show how a significant gravitational recoil can also be obtained in these situations. We consider the case of black holes with opposite spins of magnitude $a$ aligned/anti-aligned with the orbital angular momentum, with $a$ the dimensionless spin parameters of the individual holes. For the initial setups under consideration, we find a recoil velocity of $V = 475 \KMS a$. Supermassive black hole mergers producing kicks of this magnitude could result in the ejection from the cores of dwarf galaxies of the final hole produced by the collision.

Angular Momentum Transport and Proton–Alpha‐Particle Differential Streaming in the Solar Wind

The effect of solar rotation on the proton-alpha differential flow speed, $v_{\alpha p}$, and consequently on the angular momentum transport in the solar wind, is explored. It is found that the force introduced by the azimuthal components plays an important role in the force balance in interplanetary space, bringing the radial flow speeds of the species considered closer to each other. For the fast solar wind, the model cannot account for the decrease of $v_{\alpha p}$ observed by Helios between 0.3 and 1 AU. However, it can reproduce the profile of $v_{\alpha p}$ measured by Ulysses beyond 2 AU, if the right value for $v_{\alpha p}$ is imposed at that distance. In the slow solar wind, the effect of solar rotation is more pronounced if one starts with the value measured by Helios at 0.3 AU. In this case, solar rotation introduces a relative change of 10-16% in the radial flow speed of the alpha particles between 1 and 4 AU. The model calculations also show that, although alpha particles consume only a small fraction of the energy and linear momentum fluxes of protons, they cannot be neglected when considering the proton angular momentum flux ${\cal L}_p$. In most examples, it is found that ${\cal L}_p$ is determined by $v_{\alpha p}$ for both the fast and the slow wind. In the slow solar wind, it is also found that the proton and alpha angular momentum fluxes ${\cal L}_p$ and ${\cal L}_\alpha$ can be several times larger in magnitude than the flux carried by the magnetic stresses ${\cal L}_M$. While the sum of the angular momentum fluxes ${\cal L}_P={\cal L}_p+{\cal L}_\alpha$ of both species is found to be smaller than the magnetic stress ${\cal L}_M$, for the fast and slow wind alike, this result is at variance with the Helios measurements.

Recipes for stellar jets: results of combined optical/infrared diagnostics

We examine the conditions of the plasma along a sample of 'classical' Herbig-Haro jets located in the Orion and Vela star forming regions, through combined optical-infrared spectral diagnostics. Our sample includes HH 111, HH 34, HH 83, HH 73, HH 24 C/E, HH 24 J, observed at moderate spatial/spectral resolution. The obtained spectra cover a wide wavelength range from 0.6-2.5 um, including many transitions from regions of different excitation conditions. This allows us to probe the density and temperature stratification which characterises the cooling zones behind the shock fronts along the jet. The derived physical parameters (such as the extinction, the electron density and temperature, the ionisation fraction, and the total density) are used to estimate the depletion onto dust grains of Calcium and Iron with respect to solar abundances. This turns out to be between 70% and 0% for Ca and ~90% for Fe, suggesting that the weak shocks present in the beams are not capable of completely destroying the dust grains. We then derive the mass flux rates (Mdot_jet is on average 5 10^-8 M_solar yr^-1) and the associated linear momentum fluxes. The latter are higher than, or of the same order as, those measured in the coaxial molecular flows, suggesting that the flows are jet driven. Finally, we discuss differences between jets in our sample.