## Pseudo-Newtonian simulations of black hole-neutron star mergers as possible progenitors of short-duration gamma-ray bursts

##### Abstract

Black hole-neutron star (BH-NS) mergers are promising candidates for the progenitors of
short-duration gamma-ray bursts (GRBs). With the right initial conditions, the neutron star
becomes tidally disrupted, eventually forming a dense, accreting disk around the black hole.
The thermal energy of this black hole-disk system can be extracted via neutrino processes,
while the spin energy of the black hole can be extracted via magnetic processes. Either (or
even a combination of these) processes could feasibly power a relativistic jet with energy
≥~ 10 49 erg and duration ≤~ 2 s, hence producing a short-duration GRB.
In this thesis, we investigate BH-NS mergers with three-dimensional, pseudo-Newtonian
simulations. We use the simulation code Charybdis, which uses a dimensionally-split,
reconstruct-solve-average scheme (i.e. using Riemann solvers) to solve the Euler equations of
hydrodynamics. Although the code is based on a Newtonian framework, it includes pseudo-
Newtonian approximations of local gravitational wave effects and the innermost stable circular
orbit of the BH, which are both general relativistic phenomena. The code also includes
the effects of global neutrino emission, shear viscosity and self-gravity.
This thesis comprises two main projects. The first project is a parameter study of the equation
of state, which encapsulates the relationship between the pressure of a fluid and its other
thermodynamic properties. Although the EOS is well understood at low densities, it is yet to
be constrained at supranuclear densities, and so must be treated as a parameter in numerical
studies of BH-NS mergers. We present simulations using three existing EOSs, in order to
investigate their effect on the merger dynamics. We find that the EOS strongly influences the
fate of the NS, the properties of the accretion disk, and the neutrino emission.
In the second project, we begin upgrading Charybdis to include magnetic field effects, in
order to investigate the magnetic processes described above. We implement existing reconstruction
and Riemann solver algorithms for the equations of magnetohydrodynamics, and
present 1D tests to compare them. When modelling magnetic fields in more than one dimension,
we must also deal with the divergence-free condition, ∇. B = 0. We develop a new
constrained transport algorithm to ensure our code maintains this condition, and present 2D
tests to confirm its accuracy. This algorithm has many advantages over existing ones, including
easier implementation, greater computational efficiency and better parallelisation. Finally,
we present preliminary tests that use these algorithms in simulations of BH-NS mergers.