HYDRODYNAMIC SIMULATION OF NEUTRON STAR MERGERS
Rubén Martín Cabezón Gómez (1) <ruben.cabezon@upc.es>
Domingo García - Senz (1) (2) <domingo.garcia@upc.es>
ABSTRACT
(1) Departament de Física i Enginyeria Nuclear (UPC). Barcelona.
(2) Institut d’Estudis Espacials de Catalunya (IEEC).
In the last years binary systems containing compact objects have been among the most promising scenarios to test diverse fields of physics in extreme conditions.
Besides their intrinsic scientifical interest, these systems have played a fundamental role in measuring and explaining different phenomenae such as gravitational waves
and gamma-ray bursts (GRB). Through the use of the Smooth Particle Hydrodynamics technique (SPH) we have followed the evolution of neutron stars binary system
mergers with different mass ratios, studied the mass loss and the gravitational wave emission using the quadrupole approximation. We present here a summary of our
calculations concerning the hydrodynamical evolution and the GW emission.
SMOOTH PARTICLE HYDRODYNAMICS (SPH)
The basic idea of SPH is to simulate a fluid through a group of free-moving interpolating points called pseudo-particles. The
physical properties of the system are evaluated just in the current position of each pseudo-particle as a weighted
interpolation of the physical properties of its closest pseudo-particles (fig. 1). The weight is calculated as a function of the
distance between the current pseudo-particle and its corresponding neighbours. This function typically has the form of a
peaked gaussian with a spatial limited range and is called Kernel. These pseudo-particles are moved at each time-step
according to the hydrodynamic equations (1,2).
We have developed a newtonian 3D-SPH code and applied it to the coallescing binary neutron stars scenario. Our SPH
includes:
• Calculation of gravity by multipolar expansion.
• Runge-Kutta integrator at second order.
• Realistic EOS based in a RMF approximation (3).
• Adaptative time-step.
• Nuclear network of 14 isotopes.
• Cubic spline Kernel.
• Evaluation of GW emission through the quadrupole approximation (4).
• Spatial and time variable smoothing-length.
• Neighbour pseudo-particles localization using an octal tree.
Fig. 1. Evaluating physical propierties in the
position of the red pseudo-particles. Only particles
inside a certain range (blue circle) have some
influence (i.e. weight greater for the closer ones).
NEUTRON STAR MERGERS
NS-NS mergers are scenarios with an important relevance
in different astrophysical events:
• Gravitational waves emission.
• Short gamma-ray bursts progenitors.
• Alternative site for the r-process elements.
A 3D hydrodynamical evolution calculated with our SPH
code can be seen in fig. 2. The system is formed by two
identical 1.4 solar masses neutron stars. The results
obtained are in a good agreement with those published in
the literature (5).
Fig. 2. Hydrodynamical evolution on density of a NS-NS merger of identical stars with 1.4 M. From left to right and from up to
down, in t0 unities (t0 = (GM/R3)-1/2 ~ 10-4 s): t = 1, 4, 13, 19, 24, 29, 36, 47, 78 and 104. Each image ranges a 60 Km square.
1.0
Walecka-Serot
q=1
GRAVITATIONAL WAVES
1.0
q = 0.85
Wiringa, Fiks & Fabrocini
CONCLUSIONS
(r0 / M) h+ / (R / M)
Gravitational emission during the coalescence is treated here as a
perturbation in the quadrupole approximation, calculated while solving
the Newtonian equations of hydrodynamics with our 3D-SPH.
Two different tests were performed to evaluate the influence of the
mass ratio and the EOS in the emission of gravitational waves:
1.- Using the same EOS for both stars we followed the merging of
a NS-NS system with a mass ratio of q=1 and q=0.85. (fig. 3)
2.- We followed the merging of a NS-NS system of two identical
stars with Waleka-Serot EOS and with Wiringa, Fiks & Fabrocini EOS,
being the first the stiffer one. (fig. 4).
(r0 / M) h+ / (R / M)
0.5
0.0
0.0
-0.5
-1.0
-1.0
0.0E+0
4.0E-3
8.0E-3
Time (s)
1.2E-2
1.6E-2
Fig. 3. “Plus” polarization mode of the gravitational
emission in a coallescing NS-NS system for two
different initial mass ratios. Both stars have the same
EOS (Shen et. al). Little deviation from unity of this
parameter leads to great changes in the GW emission.
0.0E+0
4.0E-3
8.0E-3
Time (s)
1.2E-2
1.6E-2
Fig. 4. “Plus” polarization mode of the gravitational
emission in a coallescing NS-NS system with mass
ratio q=1, using different EOS. The GW emission gets
dumped faster as the EOS becomes less stiffer due to
the increase in the compresibility of the material.
Three-dimensional hydrodynamical simulations are necessary to explore the evolution of compact objects in binary systems. Through the use of our hydro-code we have
followed the evolution of a binary neutron star coallescence. We have also estimated the influence of some parameters in the gravitational wave emission. We could see
that the stiffness of the EOS has some influence in the GW emission (fig. 4): the stiffer the EOS, the less compressible is the star, thus its configuration remains
ellipsoidal more time and its GW emission drops to zero more slowly with time. This effect could be useful to discriminate between different EOS in order to find one more
suitable to describe nuclear matter. However, we can see that the effect of the mass ratio seems to be also important (fig. 3) and may mask the effect of the EOS.
Therefore one must be careful when gravitational emission is used for imposing restrictions on the equation of state.
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