Accurate evolutions of inspiralling neutron-star binaries: prompt and delayed collapse to black hole

TL;DR

This work presents long, fully general-relativistic simulations of equal-mass binary neutron stars using high-resolution hydrodynamics and adaptive mesh refinement to follow inspiral, merger, and the formation of a rotating black hole surrounded by a torus. By comparing polytropic (isentropic) and ideal-fluid (non-isentropic) equations of state across high- and low-mass binaries, the study reveals prompt BH formation for high-mass cases and delayed collapse via a hypermassive neutron star for low-mass cases, with Kelvin-Helmholtz instabilities developing at the shear interface. Gravitational waves are extracted using two independent methods, enabling robust waveform analyses that show how EOS and merger dynamics imprint distinct signals, including high-frequency content from HMNS oscillations and BH ringdown. The results have implications for GW astronomy and short GRB central-engine models, while highlighting the need for magnetic fields and neutrino transport in future, more realistic simulations.

Abstract

Binary neutron-star (BNS) systems represent primary sources for the gravitational-wave (GW) detectors. We present a systematic investigation in full GR of the dynamics and GW emission from BNS which inspiral and merge, producing a black hole (BH) surrounded by a torus. Our results represent the state of the art from several points of view: (i) We use HRSC methods for the hydrodynamics equations and high-order finite-differencing techniques for the Einstein equations; (ii) We employ AMR techniques with "moving boxes"; (iii) We use as initial data BNSs in irrotational quasi-circular orbits; (iv) We exploit the isolated-horizon formalism to measure the properties of the BHs produced in the merger; (v) Finally, we use two approaches, based either on gauge-invariant perturbations or on Weyl scalars, to calculate the GWs. These techniques allow us to perform accurate evolutions on timescales never reported before (ie ~30 ms) and to provide the first complete description of the inspiral and merger of a BNS leading to the prompt or delayed formation of a BH and to its ringdown. We consider either a polytropic or an ideal fluid EOS and show that already with this idealized EOSs a very interesting phenomenology emerges. In particular, we show that while high-mass binaries lead to the prompt formation of a rapidly rotating BH surrounded by a dense torus, lower-mass binaries give rise to a differentially rotating NS, which undergoes large oscillations and emits large amounts of GWs. Eventually, also the NS collapses to a rotating BH surrounded by a torus. Finally, we also show that the use of a non-isentropic EOS leads to significantly different evolutions, giving rise to a delayed collapse also with high-mass binaries, as well as to a more intense emission of GWs and to a geometrically thicker torus.

Figures (29)

• Figure 1: Isodensity contours on the $(x,y)$ (equatorial) plane for the evolution of the high-mass binary with the polytropic EOS (i.e. model $1.62$-$45$-${\rm P}$ in Table \ref{['table:ID']}). The time stamp in ${\rm ms}$ is shown on the top of each panel the color-coding bar is shown on the right in units of ${\rm g/cm}^3$ and the thick dashed line represents the AH. A high-resolution version of this figure can be found at weblink.
• Figure 2: Evolution of the maximum rest-mass density normalized to its initial value for the high-mass binary. Indicated with a dotted vertical line is the time at which the stars merge, while a vertical dashed line shows the time at which an AH is first found and which is a few ${\rm ms}$ only after the merger in this case. After this time, the maximum rest-mass density is computed in a region outside the AH and therefore it refers to the density of the oscillating torus. It is only a few orders of magnitude smaller. Note that the non-normalised value of the maximum rest-mass density at $t=0$ is $5.91\times10^{14}\,{\rm g}/{\rm cm^3}$ (see Table \ref{['table:ID']}). The binary has been evolved using the polytropic EOS.
• Figure 3: Isodensity contours on the $(x,z)$ plane highlighting the formation of a torus surrounding the central BH, whose AH is indicated with a thick dashed line. The data refers to the high-mass binary evolved with the polytropic EOS. A high-resolution version of this figure can be found at weblink.
• Figure 4: Evolution of the proper separation (top part) and of the coordinate separation (bottom part) for binaries with initial coordinate separation of either $45$ or $60\,{\rm km}$ (i.e. models $1.62$-$45$-${\rm P}$ and $1.62$-$60$-${\rm P}$ in Table \ref{['table:ID']}). Indicated with a dashed line is the proper separation for the binary starting at $45\,{\rm km}$ and suitably shifted in time.
• Figure 5: Coordinate (dashed line) and proper (solid line) trajectory of one of the stars for the high-mass binary from a coordinate distance of $45\,{\rm km}$ (about $2.2$ orbits).