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We present an analytical and numerical study of a system composed of a stellar binary pair and a massless, locally isothermal viscous accretion disk that is coplanar to the binary orbital plane. Analytically, we study the effect of the binary’s gravitational potential over short timescales through the stability of epicyclic orbits, and over long timescales by revisiting the concept of resonant torques. Numerically, we perform two-dimensional Newtonian simulations of the disk-binary system over a range of binary mass ratios. We find that the results of our simulations are consistent with those of previous numerical studies. We additionally show, by comparison of the analytical and numerical results, that the circumbinary gap is maintained on the orbital timescale through the driving of epicyclic instabilities, and does not depend on resonant torquing, contrary to the standard lore. While our results are applicable to any disk-binary system, we highlight the importance of this result in the search for electromagnetic and gravitational-wave signatures from supermassive black hole binaries.

To gain insight into the dynamical influence of a supermassive black hole binary on a circumbinary accretion disk, we investigate the binary and viscous torque densities throughout such a disk, with emphasis on the final density distribution, particularly the size and stability of the central gap between the binary and the inner edge of the disk. We limit ourselves to the simplified case of a massless viscous thin accretion disk under the influence of the gravitational potential from a binary system whose orbital plane is inclined relative to the disk. We employ two-dimensional Newtonian hydrodynamics simulations to examine the influence of two model parameters: the mass ratio of the binary and the inclination angle between the binary and the disk. We investigate their impact on the density and torque distribution. In our analytical approach, we consider the stability of epicycles induced by the perturbative effect of the asymmetric inclined binary gravitational potential on Keplerian circular orbits. Through our simulations, we observe that certain configurations never attain a quasi-steady state, where the density profile averaged over many orbits stabilizes. This instability occurs when the inclination is close to 45°. Furthermore, we identify configurations where there is never a persistent balance between the dynamical and viscous torque densities, as well as cases where the location of this balance oscillates or exhibits other time-dependent behavior over viscous timescales. These findings have implications for understanding both the expected gravitational-wave signal and electromagnetic counterparts from supermassive black hole binaries.

We have performed numerical calculations of a binary interacting with a gas disk, using 11 different numerical methods and a standard binary−disk setup. The goal of this study is to determine whether all codes agree on a numerically converged solution and to determine the necessary resolution for convergence and the number of binary orbits that must be computed to reach an agreed-upon relaxed state of the binary−disk system. We find that all codes can agree on a converged solution (depending on the diagnostic being measured). The zone spacing required for most codes to reach a converged measurement of the torques applied to the binary by the disk is roughly 1% of the binary separation in the vicinity of the binary components. For our disk model to reach a relaxed state, codes must be run for at least 200 binary orbits, corresponding to about a viscous time for our parameters, 0.2(a 2Ω B /ν) binary orbits, where ν is the kinematic viscosity. The largest discrepancies between codes resulted from the dimensionality of the setup (3D vs. 2D disks). We find good agreement in the total torque on the binary between codes, although the partition of this torque between the gravitational torque, orbital accretion torque, and spin accretion torque depends sensitively on the sink prescriptions employed. In agreement with previous studies, we find a modest difference in torques and accretion variability between 2D and 3D disk models. We find cavity precession rates to be appreciably faster in 3D than in 2D.

We investigated hydrodynamical post-Newtonian models of selfgravitating stationary black-hole-disk systems. The post-Newtonian scheme presented here and also in our recent paper is a continuation of previous, purely Newtonian studies of selfgravitating hydrodynamical disks rotating according to the Keplerian rotation law. The post-Newtonian relativistic corrections are significant even at the 1PN level. The 1PN correction to the angular velocity can be of the order of 10% of its Newtonian value. It can be expressed as a combination of geometric and hydrodynamical terms. Moreover, in contrast to the Newtonian Poincaré-Wavre theorem, it depends both on the distance from the rotation axis and the distance from the equatorial plane. In the technical part of this note we derive virial relations valid up to 1PN order. We show that they are indeed satisfied by our numerical solutions.

We present an analytical and numerical study of a system composed of a stellar binary pair and a massless, locally isothermal viscous accretion disk that is coplanar to the binary orbital plane. Analytically, we study the effect of the binary's gravitational potential over short timescales through the study of stability for epicyclic orbits, and over long timescales by revisiting the concept of resonant torques. Numerically, we perform two-dimensional Newtonian numerical simulations of the disk-binary system over a range of binary mass ratios. We find that the results of our simulations are consistent with previous numerical studies. We additionally show, by comparison of the analytical and numerical results, that the circumbinary gap is maintained on the orbital timescale through the driving of epicyclic instabilities, and does not depend on resonant torquing, contrary to standard lore. While our results are applicable to any disk-binary system, we highlight the importance of this result in the search for electromagnetic and gravitational-wave signatures from supermassive black-hole binaries.

Interpreting gravitational wave observations and understanding the physics of astrophysical compact objects such as black holes or neutron stars requires accurate theoretical models. Here, we present a new numerical relativity computer program, called Nmesh, that has the design goal to become a next generation program for the simulation of challenging relativistic astrophysics problems such as binary black hole or neutron star mergers. In order to efficiently run on large supercomputers, Nmesh uses a discontinuous Galerkin method together with a domain decomposition and mesh refinement that parallelizes and scales well. In this work, we discuss the various numerical methods we use. We also present results of test problems such as the evolution of scalar waves, single black holes and neutron stars, as well as shock tubes. In addition, we introduce a new positivity limiter that allows us to stably evolve single neutron stars without an additional artificial atmosphere, or other more traditional limiters.

(Abridged) To gain insight into the dynamical influence of a supermassive black hole binary on a circumbinary accretion disk, we investigate the binary and viscous torque densities throughout such a disk, with emphasis on the final density distribution, particularly the size and stability of the central gap between the binary and the inner edge of the disk. We limit ourselves to the simplified case of a massless viscous thin accretion disk under the influence of the gravitational potential from a binary system whose orbital plane is inclined relative to the disk. The orbital plane could be inclined if it is not coeval with the disk, or the black holes have spin angular momentum misaligned with respect to the disk's orbital angular momentum, so that the binary can precess to an inclined orientation. We employ 2D Newtonian hydrodynamics simulations to examine the influence of two model parameters: the mass ratio of the binary and the inclination angle between the binary and the disk. We investigate their impact on the density and torque distribution. In our analytical approach, we consider the stability of epicycles induced by the perturbative effect of the asymmetric inclined binary gravitational potential on Keplerian circular orbits. Through our simulations, we observe that certain configurations never attain a quasi-steady state, where the density profile averaged over many orbits stabilizes. This instability occurs when the inclination is close to 45 degrees. Furthermore, we identify configurations where there is never a persistent balance between the dynamical and viscous torque densities, as well as cases where the location of this balance oscillates or exhibits other time-dependent behavior over viscous timescales. These findings have implications for understanding both the expected gravitational-wave signal and electromagnetic counterparts from supermassive black hole binaries.

(Abridged) To gain insight into the dynamical influence of a supermassive black hole binary on a circumbinary accretion disk, we investigate the binary and viscous torque densities throughout such a disk, with emphasis on the final density distribution, particularly the size and stability of the central gap between the binary and the inner edge of the disk. We limit ourselves to the simplified case of a massless viscous thin accretion disk under the influence of the gravitational potential from a binary system whose orbital plane is inclined relative to the disk. The orbital plane could be inclined if it is not coeval with the disk, or the black holes have spin angular momentum misaligned with respect to the disk's orbital angular momentum, so that the binary can precess to an inclined orientation. We employ 2D Newtonian hydrodynamics simulations to examine the influence of two model parameters: the mass ratio of the binary and the inclination angle between the binary and the disk. We investigate their impact on the density and torque distribution. In our analytical approach, we consider the stability of epicycles induced by the perturbative effect of the asymmetric inclined binary gravitational potential on Keplerian circular orbits. Through our simulations, we observe that certain configurations never attain a quasi-steady state, where the density profile averaged over many orbits stabilizes. This instability occurs when the inclination is close to 45 degrees. Furthermore, we identify configurations where there is never a persistent balance between the dynamical and viscous torque densities, as well as cases where the location of this balance oscillates or exhibits other time-dependent behavior over viscous timescales. These findings have implications for understanding both the expected gravitational-wave signal and electromagnetic counterparts from supermassive black hole binaries.

We investigate stationary, self-gravitating, magnetised disks (or tori) around black holes. The models are obtained by numerically solving the coupled system of the Einstein equations and the equations of ideal general-relativistic magnetohydrodynamics. The mathematical formulation and numerical aspects of our approach are similar to those reported in previous works modeling stationary self-gravitating perfect-fluid tori, but the inclusion of magnetic fields represents a new ingredient. Following previous studies of purely hydrodynamical configurations, we construct our models assuming Keplerian rotation in the disks and both spinning and spinless black holes. We focus on the case of a toroidal distribution of the magnetic field and build a large set of models corresponding to a wide range of values of the magnetisation parameter, starting with weakly magnetised disks and ending at configurations in which the magnetic pressure dominates over the thermal one. In all our models, the magnetic field affects the equilibrium structure of the torus mainly due to the magnetic pressure. In particular, an increasing contribution of the magnetic field shifts the location of the maximum of the rest-mass density towards inner regions of the disk. The total mass of the system and the angular momentum are affected by the magnetic field in a complex way, that depends on the black hole spin and the location of the inner radius of the disk. The non-linear dynamical stability of the solutions presented in this paper will be reported elsewhere.

We consider stationary, axially symmetric toroids rotating around spinless black holes, assuming the general-relativistic Keplerian rotation law, in the first post-Newtonian approximation. Numerical investigation shows that the angular momentum accumulates almost exclusively within toroids. It appears that various types of dragging (anti-dragging) effects are positively correlated with the ratio \\(M_D/m\\) (\\(M_D\\) is the mass of a toroid and \\(m\\) is the mass of the black hole) - moreover, their maxima are proportional to \\(M_D/m\\). The horizontal sizes of investigated toroids range from c. 50 to c. 450 of Schwarzschild radii \\(R_S\\) of the central black hole; their mass \\(M_D ın (10^-4m, 40m)\\) and the radial size of the system is c. 500 \\(R_S\\). We found that the relative strength of various dragging (anti-dragging) effects does not change with the mass ratio, but it depends on the size of toroids. Several isoperimetric inequalities involving angular momentum are shown to hold true.