Relativistic Smoothed Particle Hydrodynamics Research Articles

Optical Appearance of Eccentric Tidal Disruption Events

Stars approaching supermassive black holes can be tidally disrupted. Despite being expected to emit X-rays, tidal disruption events (TDEs) have been largely observed in optical bands, which is poorly understood. In this Letter, we simulate the tidal disruption of a 1 M ⊙ main-sequence star on an eccentric (e = 0.95) orbit with a periapsis distance 1 or 5 times smaller than the tidal radius (β = 1 or 5) using general relativistic smoothed particle hydrodynamics. We follow the simulation for up to 1 yr postdisruption. We show that accretion disks in eccentric TDEs are masked by unbound material outflowing at ∼10,000 km s −1. Assuming electron scattering opacity, this material would be visible as a ∼100 au photosphere at ∼104 K, in line with observations of candidate TDEs.

Inhomogeneous cosmology using general relativistic smoothed particle hydrodynamics coupled to numerical relativity

Inhomogeneous cosmology using general relativistic smoothed particle hydrodynamics coupled to numerical relativity

Tidal disruptions by rotating black holes: effects of spin and impact parameter

Abstract We present the results of relativistic smoothed particle hydrodynamics simulations of tidal disruptions of stars by rotating supermassive black holes, for a wide range of impact parameters and black hole spins. For deep encounters, we find that: relativistic precession creates debris geometries impossible to obtain with the Newtonian equations; part of the fluid can be launched on plunging orbits, reducing the fallback rate and the mass of the resulting accretion disc; multiple squeezings and bounces at periapsis may generate distinctive X-ray signatures resulting from the associated shock breakout; disruptions can occur inside the marginally bound radius, if the angular momentum spread launches part of the debris on non-plunging orbits. Perhaps surprisingly, we also find relativistic effects important in partial disruptions, where the balance between self-gravity and tidal forces is so precarious that otherwise minor relativistic effects can have decisive consequences on the stellar fate. In between, where the star is fully disrupted but relativistic effects are mild, the difference resides in a gentler rise of the fallback rate, a later and smaller peak, and longer return times. However, relativistic precession always causes thicker debris streams, both in the bound part (speeding up circularization) and in the unbound part (accelerating and enhancing the production of separate transients). We discuss various properties of the disruption (compression at periapsis, shape and spread of the energy distribution) and potential observables (peak fallback rate, times of rise and decay, duration of super-Eddington fallback) as a function of the impact parameter and the black hole spin.

General relativistic smoothed particle hydrodynamics

We present a method for general relativistic smoothed particle hydrodynamics (GRSPH), based on an entropy-conservative form of the general relativistic hydrodynamic equations for a perfect fluid. We aim to replace approximate treatments of general relativity in current SPH simulations of tidal disruption events and accretion discs. We develop an improved shock capturing formulation that distinguishes between shock viscosity and conductivity in relativity. We also describe a new Hamiltonian time integration algorithm for relativistic orbital dynamics and GRSPH. Our method correctly captures both Einstein and spin-induced precession around black holes. We benchmark our scheme in 1D and 3D against mildly and ultra relativistic shock tubes, exact solutions for epicyclic and vertical oscillation frequencies, and Bondi accretion. We assume fixed background metrics (Minkowski, Schwarzschild and Kerr in Cartesian Boyer-Lindquist coordinates) but the method lays the foundation for future direct coupling with numerical relativity.

A Derivation of the Entropy-Based Relativistic Smoothed Particle Hydrodynamics by Variational Principle

In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the uid of high energy density but of low baryon density, the entropy is taken as the base quantity for the interpolation. The smoothed particle hydrodynamics algorithm employed in this study is of the second order, which guarantees better particle consistency. Furthermore, it is shown that the variational principle preserves the translational invariance of the system, and therefore improves the accuracy of the method. A brief discussion on the potential implications of the model in heavy ion physics as well as in general relativity are also presented.

Conservative, special-relativistic smoothed particle hydrodynamics

We present and test a new, special-relativistic formulation of smoothed particle hydrodynamics (SPH). Our approach benefits from several improvements with respect to earlier relativistic SPH formulations. It is self-consistently derived from the Lagrangian of an ideal fluid and accounts for the terms that stem from non-constant smoothing lengths, usually called “grad-h terms”. In our approach, we evolve the canonical momentum and the canonical energy per baryon and thus circumvent some of the problems that have plagued earlier formulations of relativistic SPH. We further use a much improved artificial viscosity prescription which uses the extreme local eigenvalues of the Euler equations and triggers selectively on (a) shocks and (b) velocity noise. The shock trigger accurately monitors the relative density slope and uses it to fine-tune the amount of artificial viscosity that is applied. This procedure substantially sharpens shock fronts while still avoiding post-shock noise. If not triggered, the viscosity parameter of each particle decays to zero. None of these viscosity triggers is specific to special relativity, both could also be applied in Newtonian SPH. The performance of the new scheme is explored in a large variety of benchmark tests where it delivers excellent results. Generally, the grad-h terms deliver minor, though worthwhile, improvements. As expected for a Lagrangian method, it performs close to perfect in supersonic advection tests, but also in strong relativistic shocks, usually considered a particular challenge for SPH, the method yields convincing results. For example, due to its perfect conservation properties, it is able to handle Lorentz factors as large as γ = 50,000 in the so-called wall shock test. Moreover, we find convincing results in a rarely shown, but challenging test that involves so-called relativistic simple waves and also in multi-dimensional shock tube tests.

Mergers of Black Hole–Neutron Star Binaries. I. Methods and First Results

We use a 3D relativistic SPH (smoothed particle hydrodynamics) code to study mergers of black hole-neutron star (BH-NS) binary systems with low mass ratios, adopting q ≡ MNS/MBH 0.1 as a representative case. The outcome of such mergers depends sensitively on both the magnitude of the BH spin and its obliquity (i.e., the inclination of the binary orbit with respect to the equatorial plane of the BH). In particular, only systems with sufficiently high BH spin parameter a and sufficiently low orbital inclinations allow any NS matter to escape or to form a long-lived disk outside the BH horizon after disruption. Mergers of binaries with orbital inclinations above ~60° lead to complete prompt accretion of the entire NS by the BH, even for the case of an extreme Kerr BH. We find that the formation of a significant disk or torus of NS material around the BH always requires a near-maximal BH spin and a low initial inclination of the NS orbit just prior to merger.

Gravitational Waves and X‐Ray Signals from Stellar Disruption by a Massive Black Hole

Gravitational waves and X-ray flares are expected from tidal disruption of stars by a massive black hole. Using a relativistic smoothed particle hydrodynamics code, we investigate the fate of main-sequence and helium stars in plunge orbits passing near Schwarzschild or Kerr black holes of mass ~105-106 M☉. We show that quadrupole gravitational waves emitted during the tidal disruption process are described reasonably well by a point-particle approximation even in the strong-encounter case. An additional hydrodynamic calculation based on the Godunov method indicates that shocks develop for sufficiently high tidal compressions. The shock heating results in an X-ray flare, which for solar-type stars disrupted by ~106 M☉ black holes is in the keV range associated with the gravitational wave signal. The hardness and duration of the X-ray flare may serve as a diagnostic of the mass of the central black hole.

Variational principles for relativistic smoothed particle hydrodynamics

In this paper we show how the equations of motion for the smoothed particle hydrodynamics (SPH) method may be derived from a variational principle for both non-relativistic and relativistic motion when there is no dissipation. Because the SPH density is a function of the coordinates the derivation of the equations of motion through variational principles is simpler than in the continuum case where the density is defined through the continuity equation. In particular, the derivation of the general relativistic equations is more direct and simpler than that of Fock. The symmetry properties of the Lagrangian lead immediately to the familiar additive conservation laws of linear and angular momentum and energy. In addition, we show that there is an approximately conserved quantity which, in the continuum limit, is the circulation.

Smoothed Particle Hydrodynamics Simulations of Ultrarelativistic Shocks with Artificial Viscosity

We present a fully Lagrangian conservation form of the general relativistic hydrodynamic equations for perfect fluids with artificial viscosity in a given arbitrary background spacetime. This conservation formulation is achieved by choosing suitable Lagrangian time evolution variables, from which the generic fluid variables of rest-mass density, 3-velocity, and thermodynamic pressure have to be determined. We present the corresponding equations for an ideal gas and show the existence and uniqueness of the solution. On the basis of the Lagrangian formulation we have developed a three-dimensional general relativistic smoothed particle hydrodynamics (SPH) code using the standard SPH formalism as known from nonrelativistic fluid dynamics. One-dimensional simulations of a shock tube and a wall shock are presented together with a two-dimensional test calculation of an inclined shock tube. With our method we can model ultrarelativistic fluid flows including shocks with Lorentz factors of even 1000.

A relativistic smoothed particle hydrodynamics method tested with the shock tube

The smoothed particle hydrodynamics method is applied to an ADM 3 + 1 formulation of the equations for relativistic fluid flow. In particular the one-dimensional shock tube is addressed. Three codes are described. The first is a straightforward extension of classic SPH, while the other two are modifications which allow for time-dependent smoothing lengths. The first of these modifications approximates the internal energy density, while the second approximates the total energy density. Two smoothing forms are tested: an artificial viscosity and the direct method of A.J. Baker [Finite Element Computation Fluid Mechanics (Hemisphere, New York, 1983)]. The results indicate that the classic SPH code with particle-particle based artificial viscosity is reasonably accurate and very consistent. It gives quite sharp edges and flat plateaus, but the velocity plateau is significantly overestimated, and an oscillation can appear in the rarefaction wave. The modified versions with Baker smoothing procedure better results for moderate initial conditions, but begin to show spikes when the initial density jump is large. Generally the results are comparable to simple finite element and finite difference methods.