# The Macro-Physics of the Quark-Nova: Astrophysical Implications

## Abstract

**:**

## 1. Introduction

#### 1.1. The Energetic Problem in Astrophysics

#### 1.2. Exploding Neutron Stars?

#### 1.3. The Hadron-Quark Transition: The Thermodynamics

#### 1.4. Quark-Nova: A Brief Review of the Microphysics

#### 1.5. The Burn-UD Code and Non-Premixed Combustion

## 2. Quark-Nova: The Macrophysics

#### 2.1. The Code

#### 2.2. The Hot Proto-Quark Star

- Short combustion timescale: We must assume that the combustion process is much faster than the neutrino evolution process. The reason we should make such an assumption is that, if the neutrino cooling is much longer, it can be assumed that the temperature profile produced by the combustion process “freezes” and is only affected by neutrino transport. Since, outside the combustion process, all other cooling processes that affect the partitioning of the energy budget are much slower than neutrino transport, the microphysical combustion problem can reasonably be decoupled from the large-scale evolution problem, if we assume that combustion is much faster than neutrino transport.This assumption of combustion may be supported by microphysical simulations (e.g., [37]). Numerical simulations show that laminar burning speeds can reach $0.001$c–$0.1$c. Assuming these speeds are sustained in the microscopic case, and that instabilities do not slow down the burning front too much, using these numbers would mean that the neutron star would combust into a quark star in a fraction of a second. This timescale must be smaller than the timescale for cooling/deleptonization. We can make a rough order-of-magnitude estimate of the timescale of deleptonization/cooling through dimensional analysis. For the high temperatures > 20 MeV and high densities of a quark star (a few times nuclear saturation density), the neutrino mean free path is about ${\lambda}_{\nu}$∼1 cm, much smaller than the radius of the PQS of ${R}_{\mathrm{PQS}}={10}^{6}$ cm. Through dimensional analysis, we find the timescale of cooling: ${\tau}_{\mathrm{cool}}$∼${R}_{\mathrm{PQS}}^{2}/\left({\lambda}_{\nu}c\right)$∼33 s. Since this cooling timescale is much larger than the estimated combustion timescale, this particular assumption is valid.
- Hydrostatic equilibrium: This assumption is justified if the timescales studied in the stellar evolution simulation are longer than the hydrodynamic timescales. This can be tested by looking at the sonic time, which is the time a sound wave takes to cross the whole length that is studied. The reason neutrino cooling needs to be slower than the hydrodynamic processes is that the time-steps of the simulation need to be large enough so that pressure gradients along the star are smoothed out by sound waves. In our case, the length-scale is the radius of the PQS. Because the sound speed of degenerate matter is of the order of the speed of light c, the sonic time will be ${\tau}_{s}$∼${R}_{\mathrm{PQS}}/c$∼$3\times {10}^{-5}$ s. Since the cooling timescale, as calculated above, is of the order of 10 s, we can argue that the neutrino cooling is much slower than the hydrodynamic processes, which justifies the hydrostatic assumption.
- Neutrino trapping: Most stellar evolution codes for compact stars assume neutrino trapping to be able to simulate neutrino transport with a simple application of Fick’s law. Since we know that the mean free path of neutrinos is about 1 cm, while the radius of the quark star is R∼10 km, the neutrino trapping assumption is reasonable.
- β-equilibrium: We must assume that the quarks in the PQS are in chemical equilibrium at each time-step. This assumption makes it possible not to have to keep track of the time-dependent reaction rates that regulate the chemical composition of quark matter. Since the weak interaction in the context of the conversion of two-flavoured to three-flavoured matter has a timescale of ∼10${}^{-8}$ s, we can effectively assume chemical equilibrium, since the cooling/deleptonization timescale, as calculated above, is ∼10 s.
- Thermal equilibrium: In order to assume thermodynamic variables such as pressure, temperature, and chemical potential, we must assume that the neutrinos are thermalized. By thermalized, we imply that the neutrinos have collided and scattered sufficiently so that they can be considered to be at thermal equilibrium. In much of the Universe, neutrinos are seldom thermalized, since their interaction cross-section is tiny; so, once emitted, they pass through matter mostly unperturbed. However, compact stars, such as quark stars, are the only existing systems in the Universe that emit a spectrum of thermal neutrinos. This is due to the extreme densities and temperatures of these objects; such thermodynamic conditions enlarge the cross-section of neutrinos to the point that they scatter and collide easily with other particles.

#### 2.3. Thermalized Neutrinos and Heat Transport

- Frozen initial temperature profile: Since the dominant process of cooling is neutrino emission/transport, we can assume that the initial temperature profile can be interpolated from local microscopic simulations that calculate the temperature for a given initial fuel density. This implies that we can decouple the problem into two sets of microphysical and macrophysical simulations: the former calculates the temperature profile through interpolation of temperature calculations for various initial densities, and the latter solves the global, macroscopic equations of neutrino transport. This decoupling simplifies the calculations considerably.
- Frozen lepton fraction: Since the combustion process happens at a much faster timescale than the neutrino transport, we can assume that the initial lepton fraction of the unburned neutron star is equivalent to the initial lepton fraction distribution of the hot quark star that is evolved in the code. Through this assumption, we can directly extract the initial lepton fraction from the EOS of a neutron star.
- Convergence of combustion temperature at low initial hadronic densities: Our simulations can only calculate the temperature for initial hadronic densities that are not lower than $0.05$ fm${}^{-3}$, since, otherwise, the density gradient would be too large, generating numerical instabilities. However, for lower initial densities, such as those found on the edge of the hadronic star, the temperatures of the ash will converge to a similar temperature of ∼20 MeV, as the ash will also converge to the same density, since the large confinement pressure of B forces the ash to have a non-zero density in the order of nuclear saturation. Therefore, even if we do not pursue a simulation, we can calculate the neutrinospheric temperature from the binding energy released through two-flavour to three-flavour quark matter equilibration using an analytical argument. Using a zero entropy MIT bag model, in previous sections, we found that the temperature of a baryon can increase to about ∼30 MeV. In the numerical scheme for $0.05$ fm${}^{-3}$ initial hadronic density, this quantity ends up lower, but of the same magnitude, around ∼20 MeV, mostly because of the effect of the s-quark mass, where a finite mass leads to less binding energy release.The temperature of a neutrinospheric baryon that is about ∼20 MeV will mostly cool through neutrino emission. To ensure that the neutrinospheric temperature will remain high for sufficiently long after the combustion process, in order to assume the same high initial neutrinospheric temperature, it is necessary to calculate the cooling timescale. Assuming neutrinos are not trapped in the neutrinosphere, then the neutrinos of neutrinospheric quark matter will automatically escape the moment they are emitted. We can calculate the timescale of cooling analytically with the following prescription obtained from Iwamoto et al. [44].$${\tau}_{\mathrm{cool}}\sim 3153\phantom{\rule{4pt}{0ex}}\mathrm{s}\times {\left(\frac{{Y}_{e}}{0.01}\right)}^{-1/3}\times ({{{T}_{f}}_{9}}^{-4}-{{{T}_{i}}_{9}}^{-4})\phantom{\rule{4pt}{0ex}}.$$In the above, ${{T}_{f}}_{9}$ and ${{T}_{i}}_{9}$ are the neutrinosphere’s final and initial temperatures in units of ${10}^{9}$ K. For an initial temperature of around 20 MeV, how long it will take for the temperature to cool off by 50 percent can be determined, assuming that there is no combustion to “reheat” the interface. Using the above equation, the time necessary for the neutrinosphere to lose 50 percent of its temperature is about ${\tau}_{\mathrm{cool}}$∼${10}^{-5}$ s. This timescale is actually a lower bound, as the emissivity is proportional to ${Y}_{e}^{1/3}$, and, therefore, the emissivity becomes less intense as the lepton fraction lowers due to deleptonization. In order to assume this neutrinosphere temperature, this timescale must be much longer than the time required for the combustion interface to cross its own width. We can calculate the minimum combustion speed where this approximation is valid through the estimate $v=l/{\tau}_{\mathrm{cool}}$. Assuming the reaction zone width is $l=0.1$ cm and $\tau $∼${10}^{-5}$ s, as calculated from Equation (15), we obtain $v={10}^{4}$ cm/s. As even the slowest burning speeds calculated in the literature (e.g., Olinto et al. [30] indicate a lower limit of 1 km/s), we can assume that the neutrinosphere remains “hot” throughout the combustion process.

#### 2.4. The Neutrino Spectrum

#### 2.5. The Ejecta

- Mechanical core bounce: In the case of supersonic core-collapse, the increasing density in the core would make it stiffer, eventually making the infalling matter bounce back. This mechanism has been used in supernova simulations with quark cores (e.g., [50]).
- Thermal photon fireball: The surface of a quark star can achieve very high temperatures of T∼20 MeV. This would generate an intense photon flux that could push the crust towards relativistic speeds. This picture is sustained by the fact that the crust “floats” on top of the quark star, leaving a gap between the quark surface and the crust. The photon flux would then act as a piston that pushes the crust outwards. The other issue that occurs in the case of a transition to CFL, is that neutrino emissivities are shut off, making photons the explosive mechanism [51].
- Detonation: it could be that instabilities accelerate the laminar flame into supersonic speeds. This would generate an effect referred to as a deflagration to detonation transition (DDT). This would generate a shock that could eject the outer layers of the compact star.
- Neutrino-induced ejection: Originally Keränen et al. [52] calculated the mass ejection that is induced by neutrino deposition. From this perspective, the core shrinks supersonically and at the same time emits neutrinos that are absorbed by the overlaying layers, unbounding them gravitationally. In this case, ${10}^{51}$ ergs are deposited into the outer hadronic layers.

## 3. Some Applications to High-Energy Astrophysics

#### 3.1. Superluminous SuperNovae (SLSNe)

#### 3.2. Gamma-Ray Bursts (GRBs)

#### 3.3. Fast Radio Bursts (FRBs)

#### 3.4. R-Process Nucleo-Synthesis

## 4. Discussion

#### 4.1. Quark-Novae and the EOS of Dense Matter

#### 4.2. Quark-Novae and Binary Neutron Star Mergers

#### 4.3. Quark-Novae and Gravitational Waves

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

- Janka, H.-T.; Melson, T.; Summa, A. Physics of core-collapse supernovae in three dimensions: A sneak preview. Annu. Rev. Nucl. Part. Sci.
**2016**, 66, 341–375. [Google Scholar] [CrossRef] [Green Version] - Kumar, P.; Zhang, B. The physics of gamma-ray bursts and relativistic jets. Phys. Rep.
**2015**, 561, 1–109. [Google Scholar] [CrossRef] [Green Version] - Abbott, B.; Abbott, R.; Abbott, T.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.; Adya, V.; et al. Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A. Astrophys. J. Lett.
**2017**, 848, L13. [Google Scholar] [CrossRef] - Sukhbold, T.; Woosley, S. The most luminous supernovae. Astrophys. J. Lett.
**2016**, 820, L38. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R.; Dey, J.; Dey, M. Quark-Nova. Astron. Astrophys.
**2002**, 390, L39–L42. [Google Scholar] [CrossRef] [Green Version] - Bodmer, A. Collapsed nuclei. Phys. Rev. D
**1971**, 4, 1601. [Google Scholar] [CrossRef] - Terazawa, H. Tokyo University Report INS336; Tokyo University: Tokyo, Japan, 1979. [Google Scholar]
- Witten, E. Cosmic separation of phases. Phys. Rev. D
**1984**, 30, 272. [Google Scholar] [CrossRef] - Weber, F. Strange quark matter and compact stars. Prog. Part. Nucl. Phys.
**2005**, 54, 193–288. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R. The micro-physics of the Quark-Nova: Recent developments. In Exploring the Astrophysics of the XXI Century with Compact Stars; World Scientific Publishing: Singapore, 2022; ISBN 978-981-122-093-7. [Google Scholar]
- Glendenning, N.K. First-order phase transitions with more than one conserved charge: Consequences for neutron stars. Phys. Rev. D
**1992**, 46, 1274. [Google Scholar] [CrossRef] [Green Version] - Alford, M.G.; Rajagopal, K.; Reddy, S.; Wilczek, F. Minimal color-flavor-locked–nuclear interface. Phys. Rev. D
**2001**, 64, 074017. [Google Scholar] [CrossRef] [Green Version] - Lugones, G.; Grunfeld, A.G.; Ajmi, M.A. Surface tension and curvature energy of quark matter in the Nambu–Jona-Lasinio model. Phys. Rev. C
**2013**, 88, 045803. [Google Scholar] [CrossRef] [Green Version] - Paschalidis, V.; Yagi, K.; Alvarez-Castillo, D.; Blaschke, D.B.; Sedrakian, A. Implications from GW170817 and I-Love-Q relations for relativistic hybrid stars. Phys. Rev. D
**2018**, 97, 084038. [Google Scholar] [CrossRef] [Green Version] - Alvarez-Castillo, D.E.; Blaschke, D.B.; Grunfeld, A.G.; Pagura, V.P. Third family of compact stars within a nonlocal chiral quark model equation of state. Phys. Rev. D
**2019**, 99, 063010. [Google Scholar] [CrossRef] [Green Version] - Bhattacharyya, A.; Mishustin, I.N.; Greiner, W. Deconfinement phase transition in compact stars: Maxwell versus Gibbs construction of the mixed phase. J. Phys. G Nucl. Phys.
**2010**, 37, 025201. [Google Scholar] [CrossRef] - Yasutake, N.; Lastowiecki, R.; Benic, S.; Blaschke, D.; Maruyama, T.; Tatsumi, T. Finite-size effects at the hadron-quark transition and heavy hybrid stars. Phys. Rev. C
**2014**, 89, 065803. [Google Scholar] [CrossRef] [Green Version] - Alford, M.G.; Han, S. Characteristics of hybrid compact stars with a sharp hadron-quark interface. Eur. Phys. J. A
**2016**, 52, 62. [Google Scholar] [CrossRef] - Glendenning, N.K. Phase transitions and crystalline structures in neutron star cores. Phys. Rept.
**2001**, 342, 393. [Google Scholar] [CrossRef] - Carroll, J.D.; Leinweber, D.B.; Williams, A.G.; Thomas, A.W. Phase transition from quark-meson coupling hyperonic matter to deconfined quark matter. Phys. Rev. C
**2009**, 79, 045810. [Google Scholar] [CrossRef] [Green Version] - Weissenborn, S.; Sagert, I.; Pagliara, G.; Hempel, M.; Schaffner-Bielich, J. Quark matter in massive compact stars. Astrophys. J.
**2011**, 740, L14. [Google Scholar] [CrossRef] - Fischer, T.; Sagert, I.; Pagliara, G.; Hempel, M.; Schaffner-Bielich, J.; Rauscher, T.; Liebendörfer, M. Core-collapse supernova explosions triggered by a quark–hadron phase transition during the early post-bounce phase. Astrophys. J. Suppl.
**2011**, 194, 39. [Google Scholar] [CrossRef] - Schulze, H.-J.; Rijken, T. Maximum mass of hyperon stars with the Nijmegen ESC08 model. Phys. Rev. C
**2011**, 84, 035801. [Google Scholar] [CrossRef] [Green Version] - Maruyama, T.; Chiba, S.; Schulze, H.-J.; Tatsumi, T. Hadron-quark mixed phase in hyperon stars. Phys. Rev. D
**2007**, 76, 123015. [Google Scholar] [CrossRef] [Green Version] - Masuda, K.; Hatsuda, T.; Takatsuka, T. Hadron–quark cross-over and massive hybrid stars. Prog. Theor. Exp. Phys.
**2013**, 7, 073. [Google Scholar] - Alvarez-Castillo, D.; Blaschke, D.; Typel, S. Mixed phase within the multi-polytrope approach to high-mass twins. Astron. Nachr.
**2017**, 338, 1048. [Google Scholar] [CrossRef] [Green Version] - Dexheimer, V.; Negreiros, R.; Schramm, S. Role of strangeness in hybrid stars and possible observables. Phys. Rev. C
**2015**, 91, 055808. [Google Scholar] [CrossRef] [Green Version] - McLerran, L.; Reddy, S. Quarkyonic Matter and Neutron Stars. Phys. Rev. Lett.
**2019**, 122, 122701. [Google Scholar] [CrossRef] [Green Version] - Prakash, M.; Bombaci, I.; Prakash, M.; Ellis, P.J.; Lattimer, J.M.; Knorren, R. Composition and structure of proto-neutron stars. Phys. Rept.
**1997**, 280, 1. [Google Scholar] [CrossRef] [Green Version] - Olinto, A.V. On the conversion of neutron stars into strange stars. Phys. Lett. B
**1987**, 192, 71–75. [Google Scholar] [CrossRef] [Green Version] - Perez-Garcia, M.A.; Silk, J.; Stone, J.R. Dark matter, neutron stars, and strange quark matter. Phys. Rev. Lett.
**2010**, 105, 141101. [Google Scholar] [CrossRef] [Green Version] - Benvenuto, O.; Horvath, J. Evidence for strange matter in super-novae? Phys. Rev. Lett.
**1989**, 63, 716. [Google Scholar] [CrossRef] - Drago, A.; Lavagno, A.; Parenti, I. Burning of a hadronic star into a quark or a hybrid star. Astrophys. J.
**2007**, 659, 1519. [Google Scholar] [CrossRef] - Ouyed, R.; Niebergal, B.; Jaikumar, P. Explosive Combustion of a Neutron Star into a Quark Star: The non-premixed scenario. In Proceedings of the Compact Stars in the QCD Phase Diagram III (CSQCD III), Guarujá, Brazil, 12–15 December 2012. [Google Scholar]
- Niebergal, B. Hadronic-to-Quark-Matter Phase Transition: Astrophysical Implications. Ph.D. Thesis, University of Calgary, Calgary, AB, Canada, 2011. Publication Number: AAT NR81856. [Google Scholar]
- Ouyed, A. The Neutrino Sector in Hadron-Quark Combustion: Physical and Astrophysical Implications. Ph.D. Thesis, University of Calgary, Calgary, AB, Canada, 2018. [Google Scholar]
- Niebergal, B.; Ouyed, R.; Jaikumar, P. Numerical simulation of the hydrodynamical combustion to strange quark matter. Phys. Rev. C
**2010**, 82, 062801. [Google Scholar] [CrossRef] [Green Version] - Ouyed, A.; Ouyed, R.; Jaikumar, P. Numerical simulation of the hydrodynamical combustion to strange quark matter in the trapped neutrino regime. Phys. Lett. B
**2018**, 777, 184–190. [Google Scholar] [CrossRef] - Lugones, G. From quark drops to quark stars. Eur. Phys. J. A
**2016**, 52, 53. [Google Scholar] [CrossRef] [Green Version] - Drago, A.; Pagliara, G. The scenario of two families of compact stars. Eur. Phys. J. A
**2016**, 52, 41. [Google Scholar] [CrossRef] - Hempel, M.; Schaffner-Bielich, J. A statistical model for a complete supernova equation of state. Nucl. Phys. A
**2010**, 837, 210–254. [Google Scholar] [CrossRef] [Green Version] - Furusawa, S.; Sanada, T.; Yamada, S. Hydrodynamical study on the conversion of hadronic matter to quark matter: I. shock-induced conversion. Phys. Rev. D
**2016**, 93, 043018. [Google Scholar] [CrossRef] [Green Version] - Pons, J.A.; Steiner, A.W.; Prakash, M.; Lattimer, J.M. Evolution of proto-neutron stars with quarks. Phys. Rev. Lett.
**2001**, 86, 5223. [Google Scholar] [CrossRef] - Iwamoto, N. Neutrino emissivities and mean free paths of degenerate quark matter. Ann. Phys.
**1982**, 141, 1–49. [Google Scholar] [CrossRef] - Gao, Z.-F.; Shan, H.; Wang, W.; Wang, N. Reinvestigation of the electron fraction and electron fermi energy of neutron star. Astron. Nachrichten
**2017**, 338, 1066–1072. [Google Scholar] [CrossRef] [Green Version] - Salmonson, J.D.; Wilson, J.R. Neutrino annihilation between binary neutron stars. Astrophys. J.
**2001**, 561, 950. [Google Scholar] [CrossRef] [Green Version] - Goodman, J.; Dar, A.; Nussinov, S. Neutrino annihilation in type ii supernovae. Astrophys. J.
**1987**, 314, L7–L10. [Google Scholar] [CrossRef] - Cooperstein, J.; Horn, L.V.D.; Baron, E. Neutrino pair energy deposition in supernovae. Astrophys. J.
**1987**, 321, L129–L132. [Google Scholar] [CrossRef] - Jaikumar, P.; Reddy, S.; Steiner, A.W. Strange star surface: A crust with nuggets. Phys. Rev. Lett.
**2006**, 96, 041101. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gentile, N.; Aufderheide, M.; Mathews, G.; Swesty, F.; Fuller, G. The QCD phase transition and supernova core collapse. Astrophys. J.
**1993**, 414, 701–711. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R.; Rapp, R.; Vogt, C. Fireballs from quark stars in the color-flavor locked phase: Application to gamma-ray bursts. Astrophys. J.
**2005**, 632, 1001. [Google Scholar] [CrossRef] [Green Version] - Keränen, P.; Ouyed, R.; Jaikumar, P. Neutrino emission and mass ejection in Quark-Novae. Astrophys. J.
**2005**, 618, 485. [Google Scholar] [CrossRef] - Ouyed, R.; Leahy, D. Dynamical and thermal evolution of the Quark-Nova ejecta. Astrophys. J.
**2009**, 696, 562. [Google Scholar] [CrossRef] - Ouyed, R.; Leahy, D.; Ouyed, A.; Jaikumar, P. Spallation Model for the Titanium-Rich Supernova Remnant Cassiopeia A. Phys. Rev. Lett.
**2011**, 107, 151103. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R.; Kostka, M.; Koning, N.; Leahy, D.A.; Steffen, W. Quark nova imprint in the extreme supernova explosion SN 2006gy. MNRAS
**2012**, 423, 1652. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R.; Staff, J.E. Quark-novae in neutron star—White dwarf binaries: A model for luminous (spin-down powered) sub-Chandrasekhar-mass Type Ia supernovae? Res. Astron. Astrophys.
**2013**, 13, 435. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R.; Leahy, D.; Koning, N. Quark-Novae in massive binaries: A model for double-humped, hydrogen-poor, superluminous Supernovae. Mon. Not. R. Astron. Soc.
**2015**, 454, 2353–2359. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R.; Leahy, D.; Koning, N. A Quark-Nova in the wake of a core-collapse supernova: A unifying model for long duration gamma-ray bursts and fast radio bursts. Res. Astron. Astrophys.
**2020**, 20, 27. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R.; Leahy, D.; Koning, N. Quark-Novae in the outskirts of galaxies: An explanation of the fast radio burst phenomenon. Mon. Not. R. Astron. Soc.
**2021**, 500, 4414–4421. [Google Scholar] [CrossRef] - Jaikumar, P.; Meyer, B.S.; Otsuki, K.; Ouyed, R. Nucleosynthesis in neutron-rich ejecta from quark-novae. A&A
**2007**, 471, 227–236. [Google Scholar] - Kostka, M. Investigating astrophysical r-process sites: Code (r-Java 2.0) and model (dual-shock Quark-Nova) development. Ph.D. Thesis, University of Calgary, Calgary, AB, Canada, 2014. [Google Scholar]
- Ouyed, R.; Pudritz, R.E.; Jaikumar, P. Quark-Novae, cosmic reionization, and early r-process element production. Astrophys. J.
**2009**, 702, 1575–1583. [Google Scholar] [CrossRef] [Green Version] - Ouyed, R.; Leahy, D.; Koning, N. Hints of a second explosion (a quark nova) in Cassiopeia A Supernova. Res. Astron. Astrophys.
**2015**, 15, 483. [Google Scholar] [CrossRef] [Green Version] - Weber, F.; Weigel, M. Neutron star properties and the relativistic nuclear equation of state of many-baryon matter. Nucl. Phys. A
**1989**, 493, 549–582. [Google Scholar] [CrossRef] - Camelio, G.; Lovato, A.; Gualtieri, L.; Benhar, O.; Pons, J.A.; Ferrari, V. Evolution of a proto-neutron star with a nuclear many-body equation of state: Neutrino luminosity and gravitational wave frequencies. Phys. Rev. D
**2017**, 96, 043015. [Google Scholar] [CrossRef] [Green Version] - Buballa, M. NJL-model analysis of dense quark matter. Phys. Rep.
**2005**, 407, 205–376. [Google Scholar] [CrossRef] [Green Version] - Shibata, M.; Taniguchi, K.; Uryu, K.K. Merger of binary neutron stars with realistic equations of state in full general relativity. Phys. Rev. D
**2005**, 71, 084021. [Google Scholar] [CrossRef] [Green Version] - Hotokezaka, K.; Kyutoku, K.; Okawa, H.; Shibata, M.; Kiuc, K. Binary Neutron Star Mergers: Dependence on the Nuclear Equation of State. Phys. Rev. D
**2011**, 83, 124008. [Google Scholar] [CrossRef] [Green Version] - Drago, A.; Pagliara, G.; Popov, S.B. The Merger of Two Compact Stars: A Tool for Dense Matter Nuclear Physics. Universe
**2018**, 4, 50. [Google Scholar] [CrossRef] [Green Version] - Staff, J.E.; Jaikumar, P.; Chan, V.; Ouyed, R. Spindown of Isolated Neutron Stars: Gravitational Waves or Magnetic Braking? Astrophys. J.
**2012**, 751, 24. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Free energy per baryon versus temperature for the hadronic EOS [41] and that of (u,d,s) (the MIT bag EOS with strong coupling constant corrections) used in this work. The free energy of (u,d,s) becomes higher around T∼40 MeV, which blocks the conversion from hadronic to quark matter. Reprinted from Ref. [36].

**Figure 2.**Evolution of the neutrinospheric temperature for the PQS. Each curve represents a different length of the mixed-phase d (in meters). Reprinted from Ref. [36].

**Figure 3.**Detector count rates for a quark-nova vs. proto-neutron star for Super-Kamiokande III and Halo 2. Reprinted from Ref. [36].

**Table 1.**Final temperatures of (u,d,s) ash for different initial hadronic number densities, as calculated by solving the reaction-diffusion-advection equations. Burning speed is also included for each initial hadronic number density. Reprinted from Ref. [36].

${\mathit{n}}_{\mathit{B}}$ [fm${}^{-3}$] | T [MeV] | $\mathit{v}/\mathit{c}$ |
---|---|---|

0.05 | 22.9 | 0.00083 |

0.1 | 23.1 | 0.0016 |

0.2 | 23.4 | 0.0025 |

0.3 | 26.4 | 0.0058 |

0.4 | 30.4 | 0.010 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ouyed, R.
The Macro-Physics of the Quark-Nova: Astrophysical Implications. *Universe* **2022**, *8*, 322.
https://doi.org/10.3390/universe8060322

**AMA Style**

Ouyed R.
The Macro-Physics of the Quark-Nova: Astrophysical Implications. *Universe*. 2022; 8(6):322.
https://doi.org/10.3390/universe8060322

**Chicago/Turabian Style**

Ouyed, Rachid.
2022. "The Macro-Physics of the Quark-Nova: Astrophysical Implications" *Universe* 8, no. 6: 322.
https://doi.org/10.3390/universe8060322