Cosmology using numerical relativity

Almost all hydrodynamic accretion disk models parametrize viscosity with the dimensionless parameter alpha. There is no detailed model for alpha, so it is usually taken to be a constant. However, global simulations of magnetohydrodynamic disks find that alpha varies with distance from the central object. Also, Newtonian simulations tend to find smaller alpha's than general relativistic simulations. We seek a one-dimensional model for alpha that can reproduce these two observations. We are guided by data from six general relativistic magnetohydrodynamic accretion disk simulations. The variation of alpha in the inner, laminar regions of the flow results from stretching of mean magnetic field lines by the flow. The variation of alpha in the outer, turbulent regions results from the dependence of the magnetorotational instability on the dimensionless shear rate. We give a one-dimensional prescription for alpha(r) that captures these two effects and reproduces the radial variation of alpha observed in the simulations. For thin disks, the prescription simplifies to the formula alpha(r)=0.025[q(r)/1.5]^6, where the shear parameter, q(r), is an analytical function of radius in the Kerr metric. The coefficient and exponent are inferred from our simulations and will change as better simulation data becomes available. We conclude that the alpha-viscosity prescription can be extended to the radially varying alpha's observed in simulations. It is possible that Newtonian simulations find smaller alpha's than general relativistic simulations because the shear parameter is lower in Newtonian flows.

Using general relativistic neutrino-radiation hydrodynamics simulations with the multi-group M1 scheme in one dimension, we investigate the collapse of massive, fully convective, and non-rotating white dwarfs (WDs), which are formed by accretion-induced collapse or merger-induced collapse, and the subsequent explosion. We produce initial WDs in hydrostatic equilibrium, which have super-Chandrasekhar mass and are about to collapse. The WDs have masses of $1.6\, M_{\odot }$ with different initial central densities specifically at $1.0\times 10^{10}$, $4.0\times 10^{9}$, $2.0\times 10^{9}$, and $1.0\times 10^{9}\:\mbox{g}\:\mbox{cm}^{-3}$. First, we examine the stability of initial WD in case weak interactions are turned off. Secondly, we calculate the collapse of WDs with weak interactions. We employ hydrodynamics simulations with Newtonian gravity in the first and second steps. Thirdly, we calculate the formation of neutron stars and accompanying explosions with general relativistic simulations. As a result, WDs with the highest density of $10^{10}\:\mbox{g}\:\mbox{cm}^{-3}$ collapse not by weak interactions but by the photodissociation of the iron, and three WDs with low central densities collapse by the electron capture as expected at the second step and succeed in the explosion with a small explosion energy of $\sim\! 10^{48}\:$erg at the third step. By changing the surrounding environment of WDs, we find that there is a minimum value of ejecta masses, which is $\sim\! 10^{-5}\, M_{\odot }$. With the most elaborate simulations of this kind so far, this value is one to two orders of magnitude smaller than previously reported values and is compatible with the estimated ejecta mass from FRB 121102.

We consider numerical simulations in general relativity in ADM formalism with cosmological ansatz for the metric. This ansatz is convenient for investigations of the Universe creation in laboratory with Galileons. Here we consider toy model for the software: spherically symmetric scalar field minimally coupled to the gravity with asymmetric double well potential. We studied the dependence of radius of critical bubble on the parameters of the theory. It demonstrates the wide applicability of thin-wall approximation. We did not find any kind of stable bubble solution.

We present the first fully general relativistic dynamical simulations of Abelian Higgs cosmic strings using 3+1D numerical relativity. Focusing on cosmic string loops, we show that they collapse due to their tension and can either (i) unwind and disperse or (ii) form a black hole, depending on their tension $G\mu$ and initial radius. We show that these results can be predicted using an approximate formula derived using the hoop conjecture, and argue that it is independent of field interactions. We extract the gravitational waveform produced in the black hole formation case and show that it is dominated by the $l=2$ and $m=0$ mode. We also compute the total gravitational wave energy emitted during such a collapse, being $0.5\pm 0.2~ \%$ of the initial total cosmic string loop mass, for a string tension of $G\mu=1.6\times 10^{-2}$ and radius $R=100~M_{pl}^{-1}$. We use our results to put a bound on the production rate of planar cosmic strings loops as $N \lesssim 10^{-2}~\mathrm{Gpc}^{-3}~\mathrm{yr}^{-1}$.

We present a new open-source axisymmetric general relativistic hydrodynamics code Gmunu (general-relativistic multigrid numerical solver) which uses a multigrid method to solve the elliptic metric equations in the conformally flat condition (CFC) approximation on a spherical grid. Most of the existing relativistic hydrodynamics codes are based on formulations which rely on a free-evolution approach of numerical relativity, where the metric variables are determined by hyperbolic equations without enforcing the constraint equations in the evolution. On the other hand, although a fully constrained-evolution formulation is theoretical more appealing and should lead to more stable and accurate simulations, such an approach is not widely used because solving the elliptic-type constraint equations during the evolution is in general more computationally expensive than hyperbolic free-evolution schemes. Multigrid methods solve differential equations with a hierarchy of discretizations and its computational cost is generally lower than other methods such as direct methods, relaxation methods, successive over-relaxation. With multigrid acceleration, one can solve the metric equations on a comparable time scale as solving the hydrodynamics equations. This would potentially make a fully constrained-evolution formulation more affordable in numerical relativity simulations. As a first step to assess the performance and robustness of multigrid methods in relativistic simulations, we develop a hydrodynamics code that makes use of standard finite-volume methods coupled with a multigrid metric solver to solve the Einstein equations in the CFC approximation. In this paper, we present the methodology and implementation of our code Gmunu and its properties and performance in some benchmarking relativistic hydrodynamics problems.

This is the first in a series of papers devoted to fully general-relativistic N-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization method and time-integration algorithm that provides satisfyingly stable evolution. More precisely, we show that it is able to pass a robustness test and to follow scalar linear modes around an expanding homogeneous and isotropic space-time. Most importantly, it is able to evolve typical cosmological initial conditions on comoving scales down to tenths of megaparsecs with controlled constraint and energy-momentum conservation violations all the way down to the regime of strong inhomogeneity.

We present a new approach for achieving high-order convergence in fully general-relativistic hydrodynamic simulations. The approach is implemented in WhiskyTHC, a new code that makes use of state-of-the-art numerical schemes and was key in achieving, for the first time, higher than second-order convergence in the calculation of the gravitational radiation from inspiraling binary neutron stars (Radice et al 2014 Mon. Not. R. Astron. Soc. 437 L46–L50). Here, we give a detailed description of the algorithms employed and present results obtained for a series of classical tests involving isolated neutron stars. In addition, using the gravitational-wave emission from the late-inspiral and merger of binary neutron stars, we make a detailed comparison between the results obtained with the new code and those obtained when using standard second-order schemes commonly employed for matter simulations in numerical relativity. We find that even at moderate resolutions and for binaries with large compactness, the phase accuracy is improved by a factor 50 or more.

With the first generation of ground-based gravitational wave laser interferometers already taking data, the availability of reliable waveform templates from astrophysical sources, which may help extract the signal from the anticipated noisy data, is urgently required. Gravitational stellar core collapse supernova has traditionally been considered among the most important astrophysical sources of potentially detectable gravitational radiation. Only very recently the first multidimensional simulations of relativistic rotational core collapse have been possible (albeit for models with simplified input physics), thanks to the use of conservative formulations of the hydrodynamics equations and advanced numerical methodology, as well as stable formulations of Einstein's equations. In this paper, the current status of relativistic core collapse simulations is discussed, with the emphasis given to the modelling of the collapse dynamics and to the computation of the gravitational radiation in the existing numerical approaches. Work employing the conformally-flat approximation (CFC) of the 3+1 Einstein's equations is reported, as well as extensions of this approximation (CFC+) and investigations within the framework of the so-called BSSN formulation of the 3+1 gravitational field equations (with no approximation for the spacetime dynamics). On the other hand, the incorporation of magnetic fields and the MHD equations in numerical codes to improve the realism of core collapse simulations in general relativity, is currently an emerging field where significant progress is bound to be soon achieved. The paper also contains a brief discussion of magneto-rotational simulations of core collapse, aiming at addressing the effects of magnetic fields on the collapse dynamics and on the gravitational waveforms.

The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve a given problem under this grid structure, one must ensure the suitable transfer of information among the different grids involved. In this work, we discuss a technique that allows one to construct finite-difference schemes of arbitrary high order which are guaranteed to satisfy linear numerical and strict stability. The method relies on the use of difference operators satisfying summation by parts and penalty terms to transfer information between the grids. This allows the derivation of semi-discrete energy estimates for problems admitting such estimates at the continuum. We analyse several aspects of this technique when used in conjunction with high-order schemes and illustrate its use in one-, two- and three-dimensional numerical relativity model problems with non-trivial topologies, including truly spherical black hole excision.

Obituary for Péter Csizmadia

We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation as well as the hydrodynamic equations are fully solved. This paper is especially devoted to simulations of test problems such as spherical dust collapse, stability test of perturbed spherical stars, and preservation of (approximate) equilibrium states of rapidly rotating neutron star and/or corotating binary neutron stars. These test simulations confirm that simulations of coalescing binary neutron stars are feasible in a numerical relativity code. It is illustrated that using our numerical code, simulations of these problems, in particular those of corotating binary neutron stars, can be performed stably and fairly accurately for a couple of dynamical timescales. These numerical results indicate that our formulation for solving the Einstein field equation and hydrodynamic equations are robust and make it possible to perform a realistic simulation of coalescing binary neutron stars for a long time from the innermost circular orbit up to formation of a black hole or neutron star.

We study the stability of standing shock waves in advection-dominated accretion flows into a Schwarzschild black hole by 2D general relativistic hydrodynamic simulations as well as linear analysis in the equatorial plane. We demonstrate that the accretion shock is stable against axisymmetric perturbations but becomes unstable to non-axisymmetric perturbations. The results of dynamical simulations show good agreement with linear analysis on the stability, oscillation and growing time scales. The comparison of different wave-travel times with the growth time scales of the instability suggests that the instability is likely to be of the Papaloizou-Pringle type, induced by the repeated propagations of acoustic waves. However, the wavelengths of perturbations are too long to clearly define the reflection point. By analyzing the non-linear phase in the dynamical simulations, it is shown that quadratic mode couplings precede the non-linear saturation. It is also found that not only short-term random fluctuations by turbulent motions but also quasi periodic oscillations take place on longer time scales in the non-linear phase. We give some possible implications of the instability for quasi periodic oscillations (QPOs) and the central engine for gamma ray bursts (GRBs).

A selection of results from the general relativistic MHD accretion simulations described in the previous talk are presented. We find that the magnetic field strength increases sharply with decreasing radius and is also enhanced near rapidly-spinning black holes. The greater magnetic field strength associated with rapid black hole rotation leads to a large outward electromagnetic angular momentum flux that substantially reduces both the mean accretion rate and the net accreted angular momentum per unit rest-mass. This electromagnetic stress strongly violates the traditional guess that the accretion stress vanishes at and inside the marginally stable orbit. Possible observational consequences include a constraint on the maximum spin of black holes, enhancement to the radiative efficiency, and concentration of fluorescent Fe Kα to the innermost part of the accretion disk.

Contact. Comparing horizon-scale observations of Sgr A* and M 87* with numerical simulations has provided considerable insight into their interpretation. Most of these simulations are variations of the same physical scenario consisting of a rotation-supported torus seeded with poloidal magnetic fields. However, this approach has several well-known limitations such as secular decreasing trends in mass-accretion rates that render long-term variability studies difficult; a lack of connection with the large-scale accretion flow, which is replaced by an artificial medium emulating vacuum; and significant differences with respect to the predictions of models of accretion onto Sgr A* fed by stellar winds. Aims. We aim to study the flow patterns that arise on horizon scales in more general accretion scenarios that have a clearer connection with the large-scale flow, and are at the same time controlled by a reduced set of parameters. Methods. As a first step in this direction, we performed three-dimensional general relativistic hydrodynamic simulations of rotating transonic flows with velocity perturbations injected from a spherical boundary located far away from the central object (1000 gravitational radii). We studied the general properties of these flows with varying perturbation amplitudes and angular momentum. We analyzed time series of mass and angular-momentum radial fluxes, angle- and time-averaged profiles, and synthetic bremsstrahlung light curves, as well as the three-dimensional structure of the flow, and quantified shock and sonic transitions in the solutions. Results. We observe a rich phenomenology in accretion patterns, which includes smooth Bondi-like flows, turbulent torus-like structures, shocks, filaments, and complex sonic structures. For sufficiently large perturbations and angular momentum, radial profiles deviate from the constant entropy and constant angular-momentum profiles used for initialization and resemble those of advection-dominated accretion flows, showing evidence of entropy generation and angular-momentum redistribution not mediated by magnetic fields. Time series do not show the secular decreasing trend and are suitable for long-term variability studies. We see that the fluctuations are amplified and extend further in frequency than the injected spectrum, producing a red noise spectrum both for the mass-accretion rate and the synthetic light curves. Conclusions. We present a simulation setup that can produce a wide variety of flow patterns at horizon scales and incorporate information from large scale accretion models. The future inclusion of magnetic fields and radiative cooling could make this type of simulation a viable alternative for the numerical modeling of general low-luminosity active galactic nuclei (AGNs).

We perform general relativistic radiation magnetohydrodynamics simulations of super-Eddington accretion flows around a neutron star with a dipole magnetic field for modeling the Galactic ultraluminous X-ray source exhibiting X-ray pulsations, Swift J0243.6+6124. Our simulations show the accretion columns near the magnetic poles, the accretion disk outside the magnetosphere, and the outflows from the disk. It is revealed that the effectively optically thick outflows, consistent with the observed thermal emission at ∼107 K, are generated if the mass accretion rate is much higher than the Eddington rate and the magnetospheric radius is smaller than the spherization radius. In order to explain the blackbody radius (∼100–500 km) without contradicting the reported spin period (9.8 s) and spin-up rate (), a mass accretion rate of is required. Since the thermal emission was detected in two observations with of −2.22 × 10−8 s s−1 and −1.75 × 10−8 s s−1 but not in another with , the surface magnetic field strength of the neutron star in Swift J0243.6+6124 is estimated to be between 3 × 1011 G and 4 × 1012 G. From this restricted range of magnetic field strength, the accretion rate would be when the thermal emission appears and when it is not detected. Our results support the hypothesis that the super-Eddington phase in the 2017–2018 giant outburst of Swift J0243.6+6124 is powered by highly super-Eddington accretion flows onto a magnetized neutron star.