Proc. Neutrino Astrophysics - MPP Theory Group

Models of Coalescing Neutron Stars with Different
Masses and Impact Parameters
Maximilian Ruffert 1,2 , Hans-Thomas Janka 1
1 Max-Planck-Institut für Astrophysik, Postfach 1523, 85740 Garching, Germany
2 Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, U.K.
Abstract
We have simulated a variety of models, in order to shed light on the accessible physical
conditions during the mergers, on the amount of matter dynamically ejected during the
merging, on the timescales of mass accretion by the (forming) black hole, on the conversion of
energy into neutrino emission, on the amount of energy deposited by ν¯ν-annihilation, and on
the baryon loading of the created pair-plasma fireball. To this end, we varied the masses and
mass ratios as well as the initial spins of the neutron stars, changed the impact parameter
to consider spiral-in orbits and direct collisions, included a black hole (vacuum sphere) in
our simulations, and studied the dynamical evolution of the accretion torus around the black
hole formed after the neutron star merging until a (nearly) stationary state was reached.
While the neutrino emission during the dynamical phases of the mergings is definitely too
small to power gamma-ray bursts (GRBs), we find that the masses, lifetimes, and neutrino
luminosities of the accretion tori have values that might explain short (O(0.1–1s)) and not
too powerful (∼ 10 51 /(4π)erg/(s · sterad)) gamma-ray bursts.
Summary of Numerical Procedures and Initial Conditions
The hydrodynamical simulations were done with a code based on the Piecewise Parabolic
Method (PPM) developed by Colella & Woodward [1]. The code is basically Newtonian, but
contains the terms necessary to describe gravitational wave emission and the corresponding
back-reaction on the hydrodynamical flow (Blanchet et al. [2]). The terms corresponding to
the gravitational potential are implemented as source terms in the PPM algorithm. In order to
describe the thermodynamics of the neutron star matter, we use the equation of state (EOS) of
Lattimer & Swesty [3]. Energy loss and changes of the electron abundance due to the emission
of neutrinos and antineutrinos are taken into account by an elaborate “neutrino leakage
scheme” [4]. The energy source terms contain the production of all types of neutrino pairs by
thermal processes and of electron neutrinos and antineutrinos also by lepton captures onto
baryons. Matter is rendered optically thick to neutrinos due to the main opacity producing
reactions which are neutrino-nucleon scattering and absorption of neutrinos onto baryons.
More detailed information about the employed numerical procedures can be found in Ruffert
et al. [4]. The following modifications compared to the previously published simulations ([4]
and [5]) were made in addition. (a) The models were computed on multiply nested and refined
grids to increase locally the spatial resolution while at the same time computing a larger total
volume. Our grid handling is described in detail in Section 4 of Ruffert [7]. (b) An entropy
equation instead of the equation for the total specific energy (specific internal energy plus
specific kinetic energy) was used to calculate the temperature of the gas in order to be able
to determine low temperatures more accurately. (c) The equation of state table was extended
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