# Neutron Star Binaries Produced by Binary-Driven Hypernovae, Their Mergers, and the Link between Long and Short GRBs

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*GIRG*, Escuela de Física, Universidad Industrial de Santander, Bucaramanga 680002, Colombia

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## Abstract

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## 1. Introduction

## 2. A BNS Left by a BdHN II

## 3. Inferences from Conservation Laws

#### 3.1. Baryon Number Conservation

#### 3.2. Angular Momentum Conservation

#### 3.3. Mass-Energy Conservation

## 4. A Specific Example of BNS Merger

#### 4.1. Maximal Disk Mass

#### 4.2. Zero Disk Mass

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BdHN | Binary-driven hypernova |

BH | Black hole |

BNS | Binary neutron star |

CO | Carbon-oxygen |

EOS | Equation of state |

GRB | Gamma-ray burst |

GW | Gravitational wave |

ISCO | Innermost stable circular orbit |

NS | Neutron star |

$\nu $NS | Newborn neutron star |

S-GRB | Short gamma-ray burst |

S-GRF | Short gamma-ray flash |

SN | Supernova |

U-GRB | Ultrashort gamma-ray burst |

U-GRF | Ultrashort gamma-ray flash |

ZAMS | Zero-age main-sequence |

## References

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**Figure 1.**Massdensity snapshots and velocity field on the orbital plane of a BdHN for a CO left by a ${M}_{\mathrm{zams}}=15\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}$ and a $1.4\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}$ NS companion, with an initial orbital period of about $4.5$ min. We follow the expansion of the SN ejecta in the presence of the NS companion and the $\nu -$NS with a smoothed particle hydrodynamic (SPH) code. It is clear that a disk with opposite spins has formed around both stars.

**Figure 2.**Disk mass versus central remnant (NS) mass. Selected values of the angular momentum loss (in units of $G{M}_{\odot}^{2}/c$) are shown as points. The initial BNS has a total gravitational mass of $2.909\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}$ and a mass fraction $q=0.933$, so we assume the merger starts at the contact point. The maximum mass along the Keplerian sequence for the GM1 EOS is $2.84\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}$ and for the TM1 EOS it is $2.62\phantom{\rule{4pt}{0ex}}{M}_{\odot}$ (see Table 2). Thus, for the former EOS, the central remnant is a massive fast-rotating NS, while the latter suggests a prompt collapse into a Kerr BH.

**Table 1.**BNS produced by a BdHN II originated in a CO-NS with an orbital period of $4.5$ min. The CO star mass is $3.06\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}$, obtained from the stellar evolution of a ZAMS star of ${M}_{\mathrm{zams}}=15\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}$, and the NS companion has $1.4\phantom{\rule{3.33333pt}{0ex}}{M}_{\odot}$. The numerical smoothed-particle hydrodynamic (SPH) simulation follows the SN produced by the CO core collapse and estimates the accretion rate onto the $\nu $NS and the NS companion. The structure parameters of the NSs are calculated for the GM1 and TM1 EOS. We refer to [43] for additional details.

m | j | $\mathbf{\Omega}$ | ${\mathit{R}}_{\mathbf{eq}}$ | I | $\mathbf{\Omega}$ | ${\mathit{R}}_{\mathbf{eq}}$ | I | |
---|---|---|---|---|---|---|---|---|

[${\mathit{M}}_{\odot}$] | [s${}^{-1}$] | [km] | [g cm${}^{2}$] | [s${}^{-1}$] | [km] | [g cm${}^{2}$] | ||

GM1 EOS | TM1 EOS | |||||||

$\nu $NS | $1.505$ | $0.259$ | $1114.6$ | $14.03$ | $2.04\times {10}^{45}$ | $1077.1$ | $14.47$ | $2.11\times {10}^{45}$ |

NS | $1.404$ | $-0.011$ | $-52.14$ | $14.01$ | $1.85\times {10}^{45}$ | $-56.6$ | $14.49$ | $1.93\times {10}^{45}$ |

**Table 2.**Properties of the selected EOS. From left to right: maximum stable mass of non-rotating configurations, uniformly rotating configurations, set by the maximum mass of the Keplerian/mass-shedding sequence and the corresponding angular velocity.

EOS | ${\mathit{M}}_{\mathbf{max}}^{\mathbf{j}=0}$ | ${\mathit{M}}_{\mathbf{max}}^{{\mathbf{j}}_{\mathbf{kep}}}$ | ${\mathbf{\Omega}}_{\mathbf{kep}}^{\mathbf{max}}$ |
---|---|---|---|

$\left[{\mathit{M}}_{\odot}\right]$ | $\left[{\mathit{M}}_{\odot}\right]$ | $\left[{\mathit{s}}^{-\mathbf{1}}\right]$ | |

GM1 | $2.38$ | $2.84$ | $1.001\times {10}^{4}$ |

TM1 | $2.19$ | $2.62$ | $8.83\times {10}^{3}$ |

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## Share and Cite

**MDPI and ACS Style**

Becerra, L.M.; Fryer, C.; Rodriguez, J.F.; Rueda, J.A.; Ruffini, R.
Neutron Star Binaries Produced by Binary-Driven Hypernovae, Their Mergers, and the Link between Long and Short GRBs. *Universe* **2023**, *9*, 332.
https://doi.org/10.3390/universe9070332

**AMA Style**

Becerra LM, Fryer C, Rodriguez JF, Rueda JA, Ruffini R.
Neutron Star Binaries Produced by Binary-Driven Hypernovae, Their Mergers, and the Link between Long and Short GRBs. *Universe*. 2023; 9(7):332.
https://doi.org/10.3390/universe9070332

**Chicago/Turabian Style**

Becerra, Laura M., Chris Fryer, Jose F. Rodriguez, Jorge A. Rueda, and Remo. Ruffini.
2023. "Neutron Star Binaries Produced by Binary-Driven Hypernovae, Their Mergers, and the Link between Long and Short GRBs" *Universe* 9, no. 7: 332.
https://doi.org/10.3390/universe9070332