Implosion-explosion in supernovae

Chavanis, Pierre‐Henri; Denet, Bruno; Berre, Martine Le; Pomeau, Yves

doi:10.1209/0295-5075/129/30003

Cited by 13 publications

(23 citation statements)

References 14 publications

(55 reference statements)

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“…The caloric curve depends on a unique parameter µ which is a measure of the mass M h of the DM halo [see Eq. (98)]. We then used the fact that the DM halos are virialized so that the dimensionless inverse temperature η = βGM m/R is of order unity.…”

Section: B Methodologymentioning

confidence: 99%

“…Together with the relation (98) between µ and M h , Eq. ( 108) determines the core mass-halo mass relation M c (M h ).…”

Section: The MC − M H Relation For the Ch Solutionmentioning

confidence: 99%

“…16 in [42]). As discussed in [42,44], if we remove the box, the halo should be expelled at large distances in a process reminiscent of a supernova explosion [96][97][98]. This is because the collapse of the core heats the halo which those that are thermodynamically unstable.…”

Section: Small Dm Halos Withmentioning

confidence: 99%

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Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

Chavanis

2019

Phys. Rev. D

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121

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We develop a model of Bose-Einstein condensate dark matter halos with a solitonic core and an isothermal atmosphere based on a generalized Gross-Pitaevskii-Poisson equation [P.H. Chavanis, Eur. Phys. J. Plus 132, 248 (2017)]. This equation provides a heuristic coarse-grained parametrization of the ordinary Gross-Pitaevskii-Poisson equation accounting for violent relaxation and gravitational cooling. It involves a cubic nonlinearity taking into account the self-interaction of the bosons, a logarithmic nonlinearity associated with an effective temperature, and a source of dissipation. It leads to superfluid dark matter halos with a core-halo structure. The quantum potential or the self-interaction of the bosons generates a solitonic core that solves the cusp problem of the cold dark matter model. The logarithmic nonlinearity generates an isothermal atmosphere accounting for the flat rotation curves of the galaxies. The dissipation ensures that the system relaxes towards an equilibrium configuration. In the Thomas-Fermi approximation, the dark matter halo is equivalent to a barotropic gas with an equation of state P = 2πas 2 ρ 2 /m 3 + ρkBT /m, where as is the scattering length of the bosons and m is their individual mass. We numerically solve the equation of hydrostatic equilibrium and determine the corresponding density profiles and rotation curves. We impose that the surface density of the halos has the universal value Σ0 = ρ0r h = 141 M /pc 2 obtained from the observations. For a boson with ratio as/m 3 = 3.28 × 10 3 fm/(eV/c 2 ) 3 , we find a minimum halo mass (M h )min = 1.86 × 10 8 M and a minimum halo radius (r h )min = 788 pc. This ultracompact halo corresponds to a pure soliton which is the ground state of the Gross-Pitaevskii-Poisson equation. For (M h )min < M h < (M h ) * = 3.30 × 10 9 M the soliton is surrounded by a tenuous isothermal atmosphere without plateau. For M h > (M h ) * we find two branches of solutions corresponding to (i) pure isothermal halos without soliton and (ii) isothermal halos harboring a central soliton and presenting a plateau. The purely isothermal halos (gaseous phase) are stable. For M h > (M h )c = 6.86 × 10 10 M , they are indistinguishable from the observational Burkert profile. For (M h ) * < M h < (M h )c, the deviation from the isothermal law (most probable state) may be explained by incomplete violent relaxation, tidal effects, or stochastic forcing. The isothermal halos harboring a central soliton (core-halo phase) are canonically unstable (having a negative specific heat) but they are microcanonically stable so they are long-lived. By extremizing the free energy (or entropy) with respect to the core mass, we find that the core mass scales as Mc/(M h )min = 0.626 (M h /(M h )min) 1/2 ln(M h /(M h )min). For a halo of mass M h = 10 12 M , similar to the mass of the halo that surrounds our Galaxy, the solitonic core has a mass Mc = 6.39×10 10 M and a radius Rc = 1 kpc. The solitonic core cannot mimic by itself a supermassive black hole at the center of the Galaxy but i...

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Section: B Methodologymentioning

confidence: 99%

“…Together with the relation (98) between µ and M h , Eq. ( 108) determines the core mass-halo mass relation M c (M h ).…”

Section: The MC − M H Relation For the Ch Solutionmentioning

confidence: 99%

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Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

Chavanis

2019

Phys. Rev. D

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121

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“…This is because they work in the canonical ensemble and consider relatively small systems while the phase transition leading to an implosionexplosion phenomenon, associated with a core-halo structure, occurs in the microcanonical ensemble for larger systems (see Ref. [38] and Sec. XIII).…”

Section: Introductionmentioning

confidence: 99%

Caloric curves of self-gravitating fermions in general relativity

Alberti,

Chavanis

2018

Preprint

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We study the nature of phase transitions between gaseous and condensed states in the selfgravitating Fermi gas at nonzero temperature in general relativity. The condensed states can represent compact objects such as white dwarfs, neutron stars, or dark matter fermion balls. The caloric curves depend on two parameters: the system size R and the particle number N . When N < NOV, where NOV is the Oppenheimer-Volkoff limit, there exists an equilibrium state for any value of the temperature T and of the energy E as in the nonrelativistic case [P.H. Chavanis, Int. J. Mod. Phys. B 20, 3113 (2006)]. Gravitational collapse is prevented by quantum mechanics (Pauli's exclusion principle). When N > NOV, there is no equilibrium state below a critical energy and below a critical temperature. In that case, the system is expected to collapse towards a black hole. We plot the caloric curves of the general relativistic Fermi gas, study the different types of phase transitions that occur in the system, and determine the phase diagram in the (R, N ) plane. The nonrelativistic results are recovered for N NOV and R ROV with N R 3 fixed. The classical results are recovered for N NOV and R ROV with N/R fixed. We discuss the commutation of the limits c → +∞ and → 0. We study the relativistic corrections to the nonrelativistic caloric curves and the quantum corrections to the classical caloric curves. We highlight a situation of physical interest where a gaseous Fermi gas, by cooling, first undergoes a phase transition towards a compact object (white dwarf, neutron star, dark matter fermion ball), then collapses into a black hole. This situation occurs in the microcanonical ensemble when NOV < N < 3.73 NOV. We also relate the phase transitions from a gaseous state to a core-halo state in the microcanonical ensemble to the onset of red-giant structure and to the supernova phenomenon.

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“…Alberti and Chavanis 2 emphasized the core-halo structure of the equilibrium states in the microcanonical ensemble and mentioned the relation to red-giants (leading to white dwarfs) and supernovae (leading to neutron stars and black holes) suggested in Refs. [64][65][66][67] . They also provided the complete phase diagram of the general relativistic Fermi gas.…”

Section: General Relativistic Fermions At T >mentioning

confidence: 99%

The self-gravitating Fermi gas in Newtonian gravity and general relativity

Chavanis¹

2021

Preprint

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We review the history of the self-gravitating Fermi gas in Newtonian gravity and general relativity. We mention applications to white dwarfs, neutron stars and dark matter halos. We describe the nature of instabilities and phase transitions in the self-gravitating Fermi gas as energy (microcanonical ensemble) or temperature (canonical ensemble) is reduced. When N < N OV , where N OV is the Oppenheimer-Volkoff critical particle number, the self-gravitating Fermi gas experiences a gravothermal catastrophe at Ec stopped by quantum mechanics (Pauli's exclusion principle). The equilibrium state has a core-halo structure made of a quantum core (degenerate fermion ball) surrounded by a classical isothermal halo. When N > N OV , a new turning point appears at an energy E c below which the system experiences a gravitational collapse towards a black hole [P.H. Chavanis, G. Alberti, Phys. Lett. B 801, 135155 (2020)]. When N OV < N < N * , the self-gravitating Fermi gas experiences a gravothermal catastrophe at Ec leading to a fermion ball, then a gravitational collapse at E c leading to a black hole. When N > N * , the condensed branch disappears and the instability at Ec directly leads to a black hole. We discuss implications of these results for dark matter halos made of massive neutrinos.

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Implosion-explosion in supernovae

Cited by 13 publications

References 14 publications

Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

Caloric curves of self-gravitating fermions in general relativity

The self-gravitating Fermi gas in Newtonian gravity and general relativity

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