An accurate Newtonian description of particle motion around a Schwarzschild black hole

A generalized Newtonian potential is derived from the geodesic motion of test particles in Schwarzschild spacetime. This potential reproduces several relativistic features with higher accuracy than commonly used pseudo-Newtonian approaches. The new potential reproduces the exact location of the marginally stable, marginally bound, and photon circular orbits, as well as the exact radial dependence of the binding energy and the angular momentum of these orbits. Moreover, it reproduces the orbital and epicyclic angular frequencies to better than 6%. In addition, the spatial projections of general trajectories coincide with their relativistic counterparts, while the time evolution of parabolic-like trajectories and the pericentre advance of elliptical-like trajectories are both reproduced exactly. We apply this approach to a standard thin accretion disc and find that the efficiency of energy extraction agrees to within 3% with the exact relativistic value, while the energy flux per unit area as a function of radius is reproduced everywhere to better than 7%. As a further astrophysical application we implement the new approach within a smoothed particle hydrodynamics code and study the tidal disruption of a main-sequence star by a supermassive black hole. The results obtained are in very good agreement with previous relativistic simulations of tidal disruptions in Schwarzschild spacetime. The equations of motion derived from this potential can be implemented easily within existing Newtonian hydrodynamics codes with hardly any additional computational effort.Comment: 11 pages, 8 figures, minor corrections to match version accepted for publication in MNRA

Dynamos, Super-pulsars and Gamma-ray bursts

The remnant of a neutron star binary coalescence is expected to be temporarily stabilised against gravitational collapse by its differential rotation. We explore the possibility of dynamo activity in this remnant and assess the potential for powering a short-duration gamma-ray burst (GRB). We analyse our three-dimensional hydrodynamic simulations of neutron star mergers with respect to the flow pattern inside the remnant. If the central, newly formed super-massive neutron star remains stable for a good fraction of a second an efficient low-Rossby number $\alpha-\Omega$-dynamo will amplify the initial seed magnetic fields exponentially. We expect that values close to equipartition field strength will be reached within several tens of milliseconds. Such a super-pulsar could power a GRB via a relativistic wind, with an associated spin-down time scale close to the typical duration of a short GRB. Similar mechanisms are expected to be operational in the surrounding torus formed from neutron star debris.Comment: 5 pages, 1 figure, Proceedings of the Gamma-ray Burst Symposium 2003, Santa Fe; Reference adde

Disk formation in the collapse of supramassive neutron stars

Short gamma-ray bursts (sGRBs) show a large diversity in their properties. This suggests that the observed phenomenon can be caused by different "central engines" or that the engine produces a variety of outcomes depending on its parameters, or possibly both. The most popular engine scenario, the merger of two neutron stars, has received support from the recent Fermi and INTEGRAL detection of a burst of gamma rays (GRB170817A) following the neutron star merger GW170817, but at the moment it is not clear how peculiar this event potentially was. Several sGRBs engine models involve the collapse of a supramassive neutron star that produces a black hole plus an accretion disk. We study this scenario for a variety of equations of states both via angular momentum considerations based on equilibrium models and via fully dynamical Numerical Relativity simulations. We obtain a broader range of disk forming configurations than earlier studies but we agree with the latter that none of these configurations is likely to produce a phenomenon that would be classified as an sGRB.Comment: accepted by MNRA

The long-term evolution of neutron star merger remnants - II. Radioactively powered transients

We use 3D hydrodynamic simulations of the long-term evolution of neutron star merger ejecta to predict the light curves of electromagnetic transients that are powered by the decay of freshly produced r-process nuclei. For the dynamic ejecta that are launched by tidal and hydrodynamic interaction, we adopt grey opacities of 10 cm$^2$/g, as suggested by recent studies. For our reference case of a 1.3-1.4 $M_\odot$ merger, we find a broad IR peak 2-4 d after the merger. The peak luminosity is $\approx 2\times 10^{40}$ erg/s for an average orientation, but increased by up to a factor of 4 for more favourable binary parameters and viewing angles. These signals are rather weak and hardly detectable within the large error box (~100 deg$^2$) of a gravitational wave trigger. A second electromagnetic transient results from neutrino-driven winds. These winds produce `weak' r-process material with $50 < A < 130$ and abundance patterns that vary substantially between different merger cases. For an adopted opacity of 1 cm$^2$/g, the resulting transients peak in the UV/optical about 6 h after the merger with a luminosity of $\approx 10^{41}$ erg/s (for a wind of 0.01 $M_\odot$) These signals are marginally detectable in deep follow-up searches (e.g. using Hypersuprime camera on Subaru). A subsequent detection of the weaker but longer lasting IR signal would allow an identification of the merger event. We briefly discuss the implications of our results to the recent detection of an nIR transient accompanying GRB 130603B.Comment: 14 pages, 11 figures, 5 tables, accepted to MNRA

On the diversity of short GRBs

Hydrodynamical simulations of the last inspiral stages and the final coalescence of a double neutron star system are used to investigate the power of the neutrino-driven wind, the energy and momentum of the fireball produced via $\nu \bar{\nu}$-annihilation, and the intensity and character of their interaction. It is argued that the outflow that derives from the debris will have enough pressure to collimate the relativistic fireball that it surrounds. The low luminosity relativistic jet will then appear brighter to an observer within the beam although most of the energy of the event is in the unseen, less collimated and slower wind. This model leads to a simple physical interpretation of the isotropic luminosities implied for short GRBs at cosmological distances. A wide variety of burst phenomenology could be attributable to the dependence of the neutrino luminosity on the initial mass of the double NS binary.Comment: accepted for publication in MNRAS Letters, 6 pages, 3 figure

A fast recursive coordinate bisection tree for neighbour search and gravity

We introduce our new binary tree code for neighbour search and gravitational force calculations in an N-particle system. The tree is built in a "top-down" fashion by "recursive coordinate bisection" where on each tree level we split the longest side of a cell through its centre of mass. This procedure continues until the average number of particles in the lowest tree level has dropped below a prescribed value. To calculate the forces on the particles in each lowest-level cell we split the gravitational interaction into a near- and a far-field. Since our main intended applications are SPH simulations, we calculate the near-field by a direct, kernel-smoothed summation, while the far field is evaluated via a Cartesian Taylor expansion up to quadrupole order. Instead of applying the far-field approach for each particle separately, we use another Taylor expansion around the centre of mass of each lowest-level cell to determine the forces at the particle positions. Due to this "cell-cell interaction" the code performance is close to O(N) where N is the number of used particles. We describe in detail various technicalities that ensure a low memory footprint and an efficient cache use. In a set of benchmark tests we scrutinize our new tree and compare it to the "Press tree" that we have previously made ample use of. At a slightly higher force accuracy than the Press tree, our tree turns out to be substantially faster and increasingly more so for larger particle numbers. For four million particles our tree build is faster by a factor of 25 and the time for neighbour search and gravity is reduced by more than a factor of 6. In single processor tests with up to 10^8 particles we confirm experimentally that the scaling behaviour is close to O(N). The current Fortran 90 code version is OpenMP-parallel and scales excellently with the processor number (=24) of our test machine.Comment: 12 pages, 16 figures, 1 table, accepted for publication in MNRAS on July 28, 201