Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

Rosswog S.

We review the current status of compact object simulations that are based on the smooth particle hydrodynamics (SPH) method. The first main part of this review is dedicated to SPH as a numerical method. We begin by discussing relevant kernel approximation techniques and discuss the performance of different kernel functions. Subsequently, we review a number of different SPH formulations of Newtonian, special- and general relativistic ideal fluid dynamics. We particularly point out recent developments that increase the accuracy of SPH with respect to commonly used techniques. The second main part of the review is dedicated to the application of SPH in compact object simulations. We discuss encounters between two white dwarfs, between two neutron stars and between a neutron star and a stellar-mass black hole. For each type of system, the main focus is on the more common, gravitational wave-driven binary mergers, but we also discuss dynamical collisions as they occur in dense stellar systems such as cores of globular clusters.

Porth O., Komissarov S.S.

In stark contrast to their laboratory and terrestrial counterparts, the cosmic jets appear to be very stable. We propose that the reason behind this remarkable property is the loss of causal connectivity across these jets, caused by their rapid expansion in response to fast decline of external pressure with the distance from the "jet engine". In atmospheres with power-law pressure distribution, the total loss of causal connectivity occurs, when the power index k>2 - the steepness which is expected to be quite common for many astrophysical environments. This conclusion does not seem to depend on the physical nature of jets - it applies both to relativistic and non-relativistic flows, both magnetically-dominated and unmagnetized jets. In order to verify it, we have carried out numerical simulations of moderately magnetized and moderately relativistic jets. Their results give strong support to our hypothesis and provide with valuable insights. In particular, we find that the z-pinched inner cores of magnetic jets expand slower than their envelopes and become susceptible to instabilities even when the whole jet is stable. This may result in local dissipation and emission without global disintegration of the flow. Cosmic jets may become globally unstable when they enter flat sections of external atmospheres. We propose that the Fanaroff-Riley morphological division of extragalactic radio sources into two classes is related to this issue. In particular, we argue that the low power FR-I jets become re-confined, causally connected and globally unstable on the scale of galactic X-ray coronas, whereas more powerful FR-II jets re-confine much further out and remain largely intact until they terminate at hot spots. Using this idea, we derived the relationship between the critical jet power and the optical luminosity of the host galaxy, which is in a very good agreement with the observations.

Martí J.

Despite the success of the combination of conservative schemes and staggered constrained transport algorithms in the last fifteen years, the accurate description of highly magnetized, relativistic flows with strong shocks represents still a challenge in numerical RMHD. The present paper focusses in the accuracy and robustness of several correction algorithms for the conserved variables, which has become a crucial ingredient in the numerical simulation of problems where the magnetic pressure dominates over the thermal pressure by more than two orders of magnitude. Two versions of non-relativistic and fully relativistic corrections have been tested and compared using a magnetized cylindrical explosion with high magnetization ($ \ge 10^4$) as test. In the non-relativistic corrections, the total energy is corrected for the difference in the classical magnetic energy term between the average of the staggered fields and the conservative ones, before (CA1) and after (CA1') recovering the primitive variables. These corrections are unable to pass the test at any numerical resolution. The two relativistic approaches (CA2 and CA2'), correcting also the magnetic terms depending on the flow speed in both the momentum and the total energy, reveal as much more robust. These algorithms pass the test succesfully and with very small deviations of the energy conservation ($\le 10^{-4}$), and very low values of the total momentum ($\le 10^{-8}$). In particular, the algorithm CA2' (that corrects the conserved variables after recovering the primitive variables) passes the test at all resolutions. The numerical code used to run all the test cases is briefly described.

Ibáñez J., Cordero-Carrión I., Aloy M., Martí J., Miralles J.

We analyze the influence of the magnetic field in the convexity properties of the relativistic magnetohydrodynamics system of equations. To this purpose we use the approach of Lax, based on the analysis of the linearly degenerate/genuinely non-linear nature of the characteristic fields. Degenerate and non-degenerate states are discussed separately and the non-relativistic, unmagnetized limits are properly recovered. The characteristic fields corresponding to the material and Alfv\'en waves are linearly degenerate and, then, not affected by the convexity issue. The analysis of the characteristic fields associated with the magnetosonic waves reveals, however, a dependence of the convexity condition on the magnetic field. The result is expressed in the form of a generalized fundamental derivative written as the sum of two terms. The first one is the generalized fundamental derivative in the case of purely hydrodynamical (relativistic) flow. The second one contains the effects of the magnetic field. The analysis of this term shows that it is always positive leading to the remarkable result that the presence of a magnetic field in the fluid reduces the domain of thermodynamical states for which the EOS is non-convex.

Zanotti O., Dumbser M.

We present a high order one-step ADER–WENO finite volume scheme with space–time adaptive mesh refinement (AMR) for the solution of the special relativistic hydrodynamic and magnetohydrodynamic equations. By adopting a local discontinuous Galerkin predictor method, a high order one-step time discretization is obtained, with no need for Runge–Kutta sub-steps. This turns out to be particularly advantageous in combination with space–time adaptive mesh refinement, which has been implemented following a “cell-by-cell” approach. As in existing second order AMR methods, also the present higher order AMR algorithm features time-accurate local time stepping (LTS), where grids on different spatial refinement levels are allowed to use different time steps. We also compare two different Riemann solvers for the computation of the numerical fluxes at the cell interfaces. The new scheme has been validated over a sample of numerical test problems in one, two and three spatial dimensions, exploring its ability in resolving the propagation of relativistic hydrodynamical and magnetohydrodynamical waves in different physical regimes. The astrophysical relevance of the new code for the study of the Richtmyer–Meshkov instability is briefly discussed in view of future applications.

Porth O., Komissarov S.S., Keppens R.

In this paper we discuss the development of Rayleigh-Taylor filaments in axisymmetric simulations of Pulsar wind nebulae (PWN). High-resolution adaptive mesh refinement magnetohydrodynamic (MHD) simulations are used to resolve the non-linear evolution of the instability. The typical separation of filaments is mediated by the turbulent flow in the nebula and hierarchical growth of the filaments. The strong magnetic dissipation and field-randomization found in recent global three-dimensional simulations of PWN suggests that magnetic tension is not strong enough to suppress the growth of RT filaments, in agreement with the observations of prominent filaments in the Crab nebula. The long-term axisymmetric results presented here confirm this finding.

Bühler R., Blandford R.

The Crab nebula and its pulsar (referred to together as "Crab") have historically played a central role in astrophysics. True to their legacy, several unique discoveries have been made recently. The Crab was found to emit gamma-ray pulsations up to energies of 400 GeV, beyond what was previously expected from pulsars. Strong gamma-ray flares, of durations of a few days were discovered from within the nebula, while the source was previously expected to be stable in flux on these time scales. Here we review these intriguing and suggestive developments. In this context we give an overview of the observational properties of the Crab and our current understanding of pulsars and their nebulae.

Perucho M., Martí J.M., Laing R.A., Hardee P.E.

Jets in low-luminosity radio galaxies are known to decelerate from relativistic speeds on parsec scales to mildly or sub-relativistic speeds on kiloparsec scales. Several mechanisms have been proposed to explain this effect, including strong reconfinement shocks and the growth of instabilities (both leading to boundary-layer entrainment) and mass loading from stellar winds or molecular clouds. We have performed a series of axisymmetric simulations of the early evolution of jets in a realistic ambient medium to probe the effects of mass loading from stellar winds using the code Ratpenat. We study the evolution of Fanaroff-Riley Class I (FRI) jets, with kinetic powers L_j \sim 1.e41-1.e44 erg/s, within the first 2 kpc of their evolution, where deceleration by stellar mass loading should be most effective. Mass entrainment rates consistent with present models of stellar mass loss in elliptical galaxies produce deceleration and effective decollimation of weak FRI jets within the first kiloparsec. However, powerful FRI jets are not decelerated significantly. In those cases where the mass loading is important, the jets show larger opening angles and decollimate at smaller distances, but the overall structure and dynamics of the bow-shock are similar to those of unloaded jets with the same power and thrust. According to our results, the flaring observed on kpc scales is initiated by mass loading in the weaker FRI jets and by reconfinement shocks or the growth of instabilities in the more powerful jets. The final mechanism of decollimation and deceleration is always the development of disruptive pinching modes.

Walg S., Achterberg A., Markoff S., Keppens R., Porth O.

Various radio galaxies show signs of having gone through episodic jet outbursts in the past. An example is the class of double-double radio galaxies (DDRGs). However, to follow the evolution of an individual source in real-time is impossible due to the large time scales involved. Numerical studies provide a powerful tool to investigate the temporal behavior of episodic jet outbursts in a (magneto-)hydrodynamical setting. We simulate the injection of two jets from active galactic nuclei (AGN), separated by a short interruption time. Three different jet models are compared. We find that an AGN jet outburst cycle can be divided into four phases. The most prominent phase occurs when the restarted jet is propagating completely inside the hot and inflated cocoon left behind by the initial jet. In that case, the jet-head advance speed of the restarted jet is significantly higher than the initial jet-head. While the head of the initial jet interacts strongly with the ambient medium, the restarted jet propagates almost unimpeded. As a result, the restarted jet maintains a strong radial integrity. Just a very small fraction of the amount of shocked jet material flows back through the cocoon compared to that of the initial jet and much weaker shocks are found at the head of the restarted jet. We find that the features of the restarted jet in this phase closely resemble the observed properties of a typical DDRG.

Porth O., Komissarov S.S., Keppens R.

In this paper we give a detailed account of the first 3D relativistic magnetohydrodynamic (MHD) simulations of Pulsar Wind Nebulae (PWN), with parameters most suitable for the Crab Nebula. In order to clarify the new features specific to 3D models, reference 2D simulations have been carried out as well. Compared to the previous 2D simulations, we considered pulsar winds with much stronger magnetisation, up to \sigma=3, and accounted more accurately for the anticipated magnetic dissipation in the striped zone of these winds. While the 3D models preserve the separation of the post termination shock flow into the equatorial and polar components, their relative strength and significance differ. Whereas the highly magnetised 2D models produce highly coherent and well collimated polar jets capable of efficient "drilling" through the supernova shell, in the corresponding 3D models the jets are disrupted by the kink mode current driven instability and "dissolve" into the main body of PWN after propagation of several shock radii. Our results show that contrary to the expectations based on 1D analytical and semi-analytical models, our numerical solutions with highly magnetized pulsar winds still produce termination shocks with radii comparable to those deduced from the observations. We present polarized synchrotron maps constructed from the 3D simulations, showing that the wealth of morphological features observed with Hubble and Chandra can well be reproduced with 3D-MHD models.

Takahashi K., Yamada S.

AbstractWe have built a code to obtain the exact solutions of Riemann problems in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code can handle not only regular waves but also switch-on/off rarefactions and all types of non-regular shocks: intermediate shocks and switch-on/off shocks. Furthermore, the initial conditions with vanishing normal or transverse magnetic fields can be handled, although the code is partly based on the algorithm proposed by Torrilhon (2002) (Torrilhon, M. 2002 Exact solver and uniqueness condition for Riemann problems of ideal magnetohydrodynamics. Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich, Switzerland), which cannot deal with all types of non-regular waves nor the initial conditions without normal or transverse magnetic fields. Our solver can find all the solutions for a given Riemann problem, and hence, as demonstrated in this paper, one can investigate the structure of the solution space in detail. Therefore, the solver is a powerful instrument to solve the outstanding problem of existence and uniqueness of solutions of MHD Riemann problems. Moreover, the solver may be applied to numerical MHD schemes like the Godunov scheme in the future.

Mizuta A., Ioka K.

We investigate the jet propagation and breakout from the stellar progenitor for gamma-ray burst (GRB) collapsars by performing two-dimensional relativistic hydrodynamic simulations and analytical modeling. We find that the jet opening angle is given by $\theta_j \sim 1/5 \Gamma_{0}$, and infer the initial Lorentz factor of the jet at the central engine, $\Gamma_0$, is a few for existing observations of $\theta_j$. The jet keeps the Lorentz factor low inside the star by converging cylindrically via collimation shocks under the cocoon pressure, and accelerates at jet breakout before the free expansion to a hollow-cone structure. In this new picture the GRB duration is determined by the sound crossing time of the cocoon, after which the opening angle widens, reducing the apparent luminosity. Some bursts violating the maximum opening angle $\theta_{j,\max}\sim 1/5 \sim 12^{\circ}$ imply the existence of a baryon-rich sheath or a long-acting jet. We can explain the slopes in both Amati and Yonetoku spectral relations using an off-centered photosphere model, if we make only one assumption that the total jet luminosity is proportional to the initial Lorentz factor of the jet. We also numerically calibrate the pre-breakout model (Bromberg et al.) for later use.

Lamberts A., Fromang S., Dubus G., Teyssier R.

Gamma-ray binaries are composed of a massive star and a rotation-powered pulsar with a highly relativistic wind. The collision between the winds from both objects creates a shock structure where particles are accelerated, resulting in the observed high energy emission. We study the impact of special relativity on the structure and stability of the colliding wind region and highlight the differences with colliding winds from massive stars. We focus on evolution with increasing values of the Lorentz factor of the pulsar wind, keeping in mind that current simulations are unable to reach the expected values of the pulsar wind Lorentz factors by orders of magnitude. We use high resolution numerical simulations with a relativistic extension to the hydrodynamics code RAMSES we have developed. Using 2D simulations, we focus on the region close to the binary, neglecting orbital motion. We use different values of the Lorentz factor of the pulsar wind, up to 16. We find analytic scaling relations between stellar wind collisions and gamma-ray binaries. They provide the position of the contact discontinuity. The position of the shocks strongly depends on the Lorentz factor, the relativistic wind is more collimated than expected based on non-relativistic simulations. Beyond a certain distance, the shocked flow is accelerated to its initial velocity and follows adiabatic expansion. We provide guidance for extrapolation towards more realistic values of the Lorentz factor of the pulsar wind. We extended the adaptive mesh refinement code RAMSES to relativistic hydrodynamics. This code is suited for the study of astrophysical objects such as pulsar wind nebulae, gamma-ray bursts or relativistic jets and will be part of the next public release of RAMSES. Using this code we performed simulations of gamma-ray binaries, highlighting the limits and possibilities of current hydrodynamic models of such systems.

Rezzolla L., Zanotti O.

Abstract The book provides a lively and approachable introduction to the main concepts and techniques of relativistic hydrodynamics in a form which will appeal to physicists at advanced undergraduate and postgraduate levels. The book is divided into three parts. The first part deals with the physical aspects of relativistic hydrodynamics, touching on fundamental topics such as kinetic theory, equations of state, mathematical aspects of hyperbolic partial differential equations, linear and nonlinear waves in fluids, reaction fronts, and the treatment of non-ideal fluids. The second part provides an introductory but complete description of those numerical methods currently adopted in the solution of the relativistic-hydrodynamic equations. Starting from traditional finite-difference methods, modern high-resolution shock-capturing methods are discussed with special emphasis on Godunov upwind schemes based on Riemann solvers. High-order schemes are also treated, focusing on essentially non-oscillatory and weighted non-oscillatory methods, Galerkin methods and on modern ADER approaches. Finally, the third part of the book is devoted to applications and considers several physical and astrophysical systems for which relativistic hydrodynamics plays a crucial role. Several non-self-gravitating systems are first studied, including self-similar flows, relativistic blast waves, spherical flows onto a compact object, relativistic accreting disks, relativistic jets and heavy-ion collisions. Self-gravitating systems are also considered, from isolated stars, to more dynamical configurations such as the collapse to a black hole or the dynamics of binary systems. The book is especially recommended to astrophysicists, particle physicists and applied mathematicians.

Keppens R., Porth O., Galsgaard K., Frederiksen J.T., Restante A.L., Lapenta G., Parnell C.

In this paper, we address the long-term evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (grid-adaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shock-capturing, conservative, grid-adaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco-)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shock-capturing, high order finite differences, and particle in cell-like methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.

Basak S., Babbar A., Kumar H., Chandrashekar P.

Cao H., Peng M., Wu K.

Mizuno Y., Rezzolla L.

Cai C., Qiu J., Wu K.

The relativistic hydrodynamics (RHD) equations have three crucial intrinsic physical constraints on the primitive variables: positivity of pressure and density, and subluminal fluid velocity. However, numerical simulations can violate these constraints, leading to nonphysical results or even simulation failure. Designing genuinely physical-constraint-preserving (PCP) schemes is very difficult, as the primitive variables cannot be explicitly reformulated using conservative variables due to relativistic effects. In this paper, we propose three efficient Newton–Raphson (NR) methods for robustly recovering primitive variables from conservative variables. Importantly, we rigorously prove that these NR methods are always convergent and PCP, meaning they preserve the physical constraints throughout the NR iterations. The discovery of these robust NR methods and their PCP convergence analyses are highly nontrivial and technical. Our NR methods are versatile and can be seamlessly incorporated into any RHD schemes that require the recovery of primitive variables. As an application, we apply them to design PCP finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes for solving the RHD equations. Our PCP HWENO schemes incorporate high-order HWENO reconstruction, a PCP limiter, and strong-stability-preserving time discretization. We rigorously prove the PCP property of the fully discrete schemes using convex decomposition techniques. Moreover, we suggest the characteristic decomposition with rescaled eigenvectors and scale-invariant nonlinear weights to enhance the performance of the HWENO schemes in simulating large-scale RHD problems. Several demanding numerical tests are conducted to demonstrate the robustness, accuracy, and high resolution of the proposed PCP HWENO schemes and to validate the efficiency of our NR methods.

Xu L., Ding S., Wu K.

All the existing entropy stable (ES) schemes for relativistic hydrodynamics (RHD) in the literature were restricted to the ideal equation of state (EOS), which however is often a poor approximation for most relativistic flows due to its inconsistency with the relativistic kinetic theory. This paper develops high-order ES finite difference schemes for RHD with general Synge-type EOS, which encompasses a range of special EOSs. We first establish an entropy pair for the RHD equations with general Synge-type EOS in any space dimensions. We rigorously prove that the found entropy function is strictly convex and derive the associated entropy variables, laying the foundation for designing entropy conservative (EC) and ES schemes. Due to relativistic effects, one cannot explicitly express primitive variables, fluxes, and entropy variables in terms of conservative variables. Consequently, this highly complicates the analysis of the entropy structure of the RHD equations, the investigation of entropy convexity, and the construction of EC numerical fluxes. By using a suitable set of parameter variables, we construct novel two-point EC fluxes in a unified form for general Synge-type EOS. We obtain high-order EC schemes through linear combinations of the two-point EC fluxes. Arbitrarily high-order accurate ES schemes are achieved by incorporating dissipation terms into the EC schemes, based on (weighted) essentially non-oscillatory reconstructions. Additionally, we derive the general dissipation matrix for general Synge-type EOS based on the scaled eigenvectors of the RHD system. We also define a suitable average of the dissipation matrix at the cell interfaces to ensure that the resulting ES schemes can resolve stationary contact discontinuities accurately. Several numerical examples are provided to validate the accuracy and effectiveness of our schemes for RHD with four special EOSs.

Lioutas G., Bauswein A., Soultanis T., Pakmor R., Springel V., Röpke F.K.

ABSTRACT We implement general relativistic hydrodynamics in the moving-mesh code arepo. We also couple a solver for the Einstein field equations employing the conformal flatness approximation. The implementation is validated by evolving isolated static neutron stars using a fixed metric or a dynamical space–time. In both tests, the frequencies of the radial oscillation mode match those of independent calculations. We run the first moving-mesh simulation of a neutron star merger. The simulation includes a scheme to adaptively refine or derefine cells and thereby adjusting the local resolution dynamically. The general dynamics are in agreement with independent smoothed particle hydrodynamics and static-mesh simulations of neutron star mergers. Coarsely comparing, we find that dynamical features like the post-merger double-core structure or the quasi-radial oscillation mode persist on longer time scales, possibly reflecting a low numerical diffusivity of our method. Similarly, the post-merger gravitational wave emission shows the same features as observed in simulations with other codes. In particular, the main frequency of the post-merger phase is found to be in good agreement with independent results for the same binary system, while, in comparison, the amplitude of the post-merger gravitational wave signal falls off slower, i.e. the post-merger oscillations are less damped. The successful implementation of general relativistic hydrodynamics in the moving-mesh arepo code, including a dynamical space–time evolution, provides a fundamentally new tool to simulate general relativistic problems in astrophysics.

Kulikov I.M.

Relativistic jets are major sources of radio-frequency radiation in the Universe. Their study is complicated by the fact that the relativistic gas flows interact with interstellar space, with the formation of complex flows that are smaller than the jets but can affect the evolution of the entire jets. Adaptive grids have traditionally been used to simulate such multi-scale phenomena with high spatial resolution in the zone of complex jets and low resolution to reproduce the unperturbed gas flows. In this paper, a Patch-Block-Structured Adaptive-Mesh-Refinement technique is proposed for modeling multi-scale relativistic jets. To use this technique, mathematical tools for numerically solving the equations of special relativistic hydrodynamics are updated in a particular manner. The approach is applied to the evolution of a jet in interstellar space.

Bhoriya D., Biswas B., Kumar H., Chandrashekhar P.

This article proposes entropy stable discontinuous Galerkin schemes (DG) for two-fluid relativistic plasma flow equations. These equations couple the flow of relativistic fluids via electromagnetic quantities evolved using Maxwell’s equations. The proposed schemes are based on the Gauss–Lobatto quadrature rule, which has the summation by parts property. We exploit the structure of the equations having the flux with three independent parts coupled via nonlinear source terms. We design entropy stable DG schemes for each flux part, coupled with the fact that the source terms do not affect entropy, resulting in an entropy stable scheme for the complete system. The proposed schemes are then tested on various test problems in one and two dimensions to demonstrate their accuracy and stability.

Perucho M., López-Miralles J.

In this paper, we review recent and ongoing work by our group on numerical simulations of relativistic jets. Relativistic outflows in astrophysics are related to dilute, high energy plasmas, with physical conditions out of the reach of current laboratory capabilities. Simulations are thus imperative for the study of these objects. We present a number of such scenarios that have been studied by our group at the Universitat de València. In particular, we have focused on the evolution of extragalactic outflows through galactic and intergalactic environments, deceleration by interaction with stars or clouds or the propagation of jets in X-ray binaries and interaction with stellar winds from massive companions. All also share their role as particle acceleration sites and production of non-thermal radiation throughout the electromagnetic spectrum. Therefore, our work is not only aimed at understanding the impact of outflows on their environments and thus their role in galaxy and cluster evolution, but also the nature and capabilities of these sites as generators of high- and very-high-energy radiation and cosmic rays.

Janka H., Bauswein A.

Neutron stars (NSs) and black holes (BHs) are born when the final collapse of the stellar core terminates the lives of stars more massive than about nine solar masses. This can trigger the powerful ejection of a large fraction of the star’s material in a core-collapse supernova (CCSN), whose extreme luminosity is energized mostly by the decay of radioactive isotopes such as 56Ni and its daughter nucleus 56Co. When evolving in close binary systems, the compact relics of such infernal catastrophes spiral towards each other on orbits gradually decaying by gravitational wave emission. Ultimately, the violent collision of the two components forms a more massive, rapidly spinning remnant, again accompanied by the ejection of considerable amounts of matter. These merger events can be observed by high-energy bursts of gamma rays with afterglows and electromagnetic transients called kilonovae, which radiate the energy released in radioactive decays of freshly assembled rapid neutron-capture elements. By means of their mass ejection and the nuclear and neutrino reactions taking place in the ejecta, both CCSNe and compact object mergers (COMs) are prominent sites of heavy-element nucleosynthesis and play a central role in the cosmic cycle of matter and the chemical enrichment history of galaxies. The nuclear equation of state (EoS) of NS matter, from neutron-rich to proton-dominated conditions and with temperatures ranging from about 0 to roughly 100 MeV, is a crucial ingredient in these astrophysical phenomena. It determines their dynamical processes, their remnant properties even at the level of deciding between NS or BH, and the properties of the associated emission of neutrinos, whose interactions govern the thermodynamic conditions and the neutron-to-proton ratio for nucleosynthesis reactions in the innermost ejecta. This chapter discusses corresponding EoS-dependent effects of relevance in CCSNe as well as COMs.

López-Miralles J., Martí J.M., Perucho M.

Radiative transfer plays a major role in high-energy astrophysics. In multiple scenarios and in a broad range of energy scales, the coupling between matter and radiation is essential to understand the interplay between theory, observations and numerical simulations. In this paper, we present a novel scheme for solving the equations of radiation relativistic magnetohydrodynamics within the parallel code L\'ostrego. These equations, which are formulated taking successive moments of the Boltzmann radiative transfer equation, are solved under the gray-body approximation and the M1 closure using an IMEX time integration scheme. The main novelty of our scheme is that we introduce for the first time in the context of radiation magnetohydrodynamics a family of Jacobian-free Riemann solvers based on internal approximations to the Polynomial Viscosity Matrix, which were demonstrated to be robust and accurate for non-radiative applications. The robustness and the limitations of the new algorithms are tested by solving a collection of one-dimensional and multi-dimensional test problems, both in the free-streaming and in the diffusion radiation transport limits. Due to its stable performance, the applicability of the scheme presented in this paper to real astrophysical scenarios in high-energy astrophysics is promising. In future simulations, we expect to be able to explore the dynamical relevance of photon-matter interactions in the context of relativistic jets and accretion discs, from microquasars and AGN to gamma-ray bursts.

Bégué D., Pe’er A., Zhang G.-., Zhang B.-., Pevzner B.

Abstract We introduce a new GPU-accelerated general relativistic magnetohydrodynamic code based on HARM, which we call cuHARM. The code is written in CUDA-C and uses OpenMP to parallelize multi-GPU setups. Our code allows us to run high-resolution simulations of accretion disks and the formation and structure of jets without a need for multinode supercomputer infrastructure. A 2563 simulation is well within the reach of an Nvidia DGX-V100 server, with the computation being about 10 times faster than if only the CPU is used. We use this code to examine several disk structures all in the SANE state. We find that (i) increasing the magnetic field in the SANE state does not affect the mass accretion rate; (ii) simultaneously increasing the disk size and the magnetic field, while keeping the ratio of energies fixed, leads to the destruction of the jet once the magnetic flux through the horizon decreases below a certain limit (this demonstrates that the existence of a jet is a function of the initial mass distribution, and not of the initial intensity of the magnetic field, since the magnetorotational instability dictates the evolution of the magnetic field); and (iii) the structure of the jet is a weak function of the adiabatic index of the gas, with relativistic gas tending to have a wider jet.

Janka H., Bauswein A.

Neutron stars (NSs) and black holes (BHs) are born when the final collapse of the stellar core terminates the lives of stars more massive than about nine solar masses. This can trigger the powerful ejection of a large fraction of the star’s material in a core-collapse supernova (CCSN), whose extreme luminosity is energized mostly by the decay of radioactive isotopes such as 56Ni and its daughter nucleus 56Co. When evolving in close binary systems, the compact relics of such infernal catastrophes spiral towards each other on orbits gradually decaying by gravitational wave emission. Ultimately, the violent collision of the two components forms a more massive, rapidly spinning remnant, again accompanied by the ejection of considerable amounts of matter. These merger events can be observed by high-energy bursts of gamma rays with afterglows and electromagnetic transients called kilonovae, which radiate the energy released in radioactive decays of freshly assembled rapid neutron-capture elements. By means of their mass ejection and the nuclear and neutrino reactions taking place in the ejecta, both CCSNe and compact object mergers (COMs) are prominent sites of heavy-element nucleosynthesis and play a central role in the cosmic cycle of matter and the chemical enrichment history of galaxies. The nuclear equation of state (EoS) of NS matter, from neutron-rich to proton-dominated conditions and with temperatures ranging from about 0 to roughly 100 MeV, is a crucial ingredient in these astrophysical phenomena. It determines their dynamical processes, their remnant properties even at the level of deciding between NS or BH, and the properties of the associated emission of neutrinos, whose interactions govern the thermodynamic conditions and the neutron-to-proton ratio for nucleosynthesis reactions in the innermost ejecta. This chapter discusses corresponding EoS-dependent effects of relevance in CCSNe as well as COMs.

Ambruş V.E., Molnár E., Rischke D.H.

We derive the transport coefficients of second-order fluid dynamics with 14 dynamical moments using the method of moments and the Chapman-Enskog method in the relaxation-time approximation for the collision integral of the relativistic Boltzmann equation. Contrary to results previously reported in the literature, we find that the second-order transport coefficients derived using the two methods are in perfect agreement. Furthermore, we show that, unlike in the case of binary hard-sphere interactions, the diffusion-shear coupling coefficients ${\ensuremath{\ell}}_{V\ensuremath{\pi}}$, ${\ensuremath{\lambda}}_{V\ensuremath{\pi}}$, and ${\ensuremath{\tau}}_{V\ensuremath{\pi}}$ actually diverge in some approximations when the expansion order ${N}_{\ensuremath{\ell}}\ensuremath{\rightarrow}\ensuremath{\infty}$. Here we show how to circumvent such a problem in multiple ways, recovering the correct transport coefficients of second-order fluid dynamics with 14 dynamical moments. We also validate our results for the diffusion-shear coupling by comparison to a numerical solution of the Boltzmann equation for the propagation of sound waves in an ultrarelativistic ideal gas.

Chen Y., Wu K.

This paper presents a highly robust third-order accurate finite volume weighted essentially non-oscillatory (WENO) method for special relativistic hydrodynamics on unstructured triangular meshes. We rigorously prove that the proposed method is physical-constraint-preserving (PCP), namely, always preserves the positivity of the pressure and the rest-mass density as well as the subluminal constraint on the fluid velocity. The method is built on a highly efficient compact WENO reconstruction on unstructured meshes, a simple PCP limiter, the provably PCP property of the Harten--Lax--van Leer flux, and third-order strong-stability-preserving time discretization. Due to the relativistic effects, the primitive variables (namely, the rest-mass density, velocity, and pressure) are highly nonlinear implicit functions in terms of the conservative variables, making the design and analysis of our method nontrivial. To address the difficulties arising from the strong nonlinearity, we adopt a novel quasilinear technique for the theoretical proof of the PCP property. Three provable convergence-guaranteed iterative algorithms are also introduced for the robust recovery of primitive quantities from admissible conservative variables. We also propose a slight modification to an existing WENO reconstruction to ensure the scaling invariance of the nonlinear weights and thus to accommodate the homogeneity of the evolution operator, leading to the advantages of the modified WENO reconstruction in resolving multi-scale wave structures. Extensive numerical examples are presented to demonstrate the robustness, expected accuracy, and high resolution of the proposed method.