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#### Black hole-neutron star mergers and short GRBs: a relativistic toy model to estimate the mass of the torus

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1007.4160

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APJ_727_2_95.pdf

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##### Citation

Pannarale, F., Tonita, A., & Rezzolla, L. (2011). Black hole-neutron star mergers
and short GRBs: a relativistic toy model to estimate the mass of the torus.* Astrophysical Journal,*
*727*(2): 95. doi:10.1088/0004-637X/727/2/95.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-CE7D-E

##### Abstract

The merger of a binary system composed of a black hole and a neutron star may
leave behind a torus of hot, dense matter orbiting around the black hole. While
numerical-relativity simulations are necessary to simulate this process
accurately, they are also computationally expensive and unable at present to
cover the large space of possible parameters, which include the relative mass
ratio, the stellar compactness and the black hole spin. To mitigate this and
provide a first reasonable coverage of the space of parameters, we have
developed a method for estimating the mass of the remnant torus from black
hole-neutron star mergers. The toy model makes use of the relativistic affine
model to describe the tidal deformations of an extended tri-axial ellipsoid
orbiting around a Kerr black hole and measures the mass of the remnant torus by
considering which of the fluid particles composing the star are on bound orbits
at the time of the tidal disruption. We tune the toy model by using the results
of fully general-relativistic simulations obtaining relative precisions of few
a percent and use it to investigate the space of parameters extensively. In
this way we find that the torus mass is largest for systems with highly
spinning black holes, small stellar compactnesses and large mass ratios. As an
example, tori as massive as $M_{b,\text{tor}} \simeq 1.33\,M_{\odot}$ can be
produced for a very extended star with compactness $C\simeq 0.1$ inspiralling
around a black hole with dimensionless spin $a=0.85$ and mass ratio $q\simeq
0.3$. However, for a more astrophysically reasonable mass ratio $q \simeq 0.14$
and a canonical value of the stellar compactness $C\simeq 0.145$, the toy model
sets a considerably smaller upper limit of $M_{b,\text{tor}} \lesssim
0.34\,M_{\odot}$.