Conditions for shock revival by neutrino heating in core-collapse supernovae

By Hans-Thomas Janka. 2000

253 citations recorded by the source corpus.

Energy deposition by neutrinos can rejuvenate the stalled bounce shock and can provide the energy for the supernova explosion of a massive star. This neutrino-heating mechanism, though investigated by numerical simulations and analytic studies, is not finally accepted or proven as the trigger of the explosion. Part of the problem is that different groups have obtained seemingly discrepant results, and the complexity of the hydrodynamic models often hampers a clear and simple interpretation of the results. This demands a deeper theoretical understanding of the requirements of a successful shock revival. A toy model is developed here for discussing the neutrino heating phase analytically. The neutron star atmosphere between the neutrinosphere and the supernova shock can well be considered to be in hydrostatic equilibrium, with a layer of net neutrino cooling below the gain radius and a layer of net neutrino heating above. Since the mass infall rate to the shock is in general different from the rate at which gas is advected into the neutron star, the mass in the gain layer varies with time. Moreover, the gain layer receives additional energy input by neutrinos emitted from the neutrinosphere and the cooling layer. Therefore the determination of the shock evolution requires a time-dependent treatment. To this end the hydrodynamical equations of continuity and energy are integrated over the volume of the gain layer to obtain conservation laws for the total mass and energy in this layer. The radius and velocity of the supernova shock can then be calculated from global properties of the gain layer as solutions of an initial value problem, which expresses the fact that the behavior of the shock is controlled by the cumulative effects of neutrino heating and mass accumulation in the gain layer. The described toy model produces steady-state accretion and mass outflow from the nascent neutron star as special cases. The approach is useful to illuminate the conditions that can lead to delayed explosions and in this sense supplements detailed numerical simulations. On grounds of the model developed here, a criterion is derived for the requirements of shock revival. It confirms the existence of a minimum neutrino luminosity that is needed for shock expansion, but also demonstrates the importance of a sufficiently large mass infall rate to the shock. If the neutrinospheric luminosity or accretion rate by the shock are too low, the shock is weakened because the gain layer loses more mass than is resupplied by inflow. On the other hand, very high infall rates damp the shock expansion and above some threshold, the development of positive total energy in the neutrino-heating layer is prevented. Time-dependent solutions for the evolution of the gain layer show that the total specific energy transferred to nucleons by neutrinos is limited by about 10 52 erg$ $ $M_{\odot}^{-1}$ (~5 MeV per nucleon). This excludes the possibility of very energetic explosions by the neutrino-heating mechanism, because the typical mass in the gain layer is about 0.1 $M_{\odot}$ and does not exceed a few tenths of a solar mass. The toy model also allows for a crude discussion of the global effects of convective energy transport in the neutrino-heating layer. Transfer of energy from the region of maximum heating to radii closer behind the shock mainly reduces the loss of energy by the inward flow of neutrino-heated matter through the gain radius.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a4b4bff9b05690ee10869e1337f76371b36a6a2a

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Citations in the corpus

A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Spacetime (2002, background): “The intensive neutrino emission from the cooling region undermines the pressure support below the heating region, and the material is drained from the latter onto the protoneutron star (Janka 2001).”
Non-Radial Instabilities and Progenitor Asphericities in Core-Collapse Supernovae (2014, methodology): “Most of these relations were derived in Janka (2001, 2012), but many of them are also found in other papers scattered across the literature.”
Stability of Standing Accretion Shocks, with an Eye toward Core-Collapse Supernovae (2002, background): “As pointed out by Janka (2001), it is necessary to maintain sufficient neutrino luminosity and mass in the gain region to power an explosion, and this is achieved by maintaining a sufficient level of mass accretion through the shock and onto the proto–neutron star.”
Multiple physical elements to determine the gravitational-wave signatures of core-collapse supernovae (2011, background): “ewtonian’—stands for 6This quantity represents the degree of anisotropy in neutrino emission; hµνi ∼ 0.25 near at the neutrino sphere, hµνi = 1 in the free-streaming limit (r → ∞) (e.g., Janka (2001) [69]). 4 some attempt at inclusion of general relativistic eﬀects, and “GR” denotes full relativity.”
Shock Breakout in Core-Collapse Supernovae and Its Neutrino Signature (2002, background): “…shifted focus to the “long-term” mechanism of shock revival in its various forms (Bethe & Wilson 1985; Herant et al. 1994; Burrows, Hayes, & Fryxell 1995; Fryer et al. 1999; Fryer & Heger 2000; Rampp & Janka 2000; Janka 2001; Liebendörfer et al. 2001; Liebendörfer, Mezzacappa, & Thielemann 2001).”
Viscosity and Rotation in Core-Collapse Supernovae (2004, background): “An elucidating and physical discussion of the stalled shock dynamics can be found in Janka (2001).”
Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport - I. Numerical method and results for a 15 solar mass star (2005, background): “3, middle panel), which, concerning global supernova dynamics, we consider to be the more decisive quantity (Janka 2001), the values for the two heating rates are almost indistinguishable.”
Nucleosynthesis in Massive Stars with Improved Nuclear and Stellar Physics (2001, background): “More importantly, we find 30 − 50% higher densities in the region m = 1.5 − 2M⊙ which may affect the core collapse supernova mechanism due to correspondingly higher ram-pressure of the infalling matter (cf. Janka 2001).”
NEUTRINO-DRIVEN EXPLOSION OF A 20 SOLAR-MASS STAR IN THREE DIMENSIONS ENABLED BY STRANGE-QUARK CONTRIBUTIONS TO NEUTRINO–NUCLEON SCATTERING (2015, background): “Since neutrino heating roughly neutralizes the gravitational binding energy of the matter (Janka 2001; Marek & Janka 2009), the growth of Eexp can be estimated in terms of Ṁvr>0 and an average nuclear recombination energy per nucleon, nuc, as Ėexp ≈ Ṁvr>0 nuc mB ≈ 1.2 × 1051 ( nuc 6 MeV ) erg s .”
Supernova simulations from a 3D progenitor model - Impact of perturbations and evolution of explosion properties (2017, background): “…(2015), we quantify the effect of the perturbations by considering both the critical ratio of the advection and heating time-scales τadv and τheat (Janka 1998, 2001; Thompson 2000; Buras et al. 2006b; Murphy & Burrows 2008; Fernández 2012) and the trajectories of the models in the generalised…”
REVIVAL OF THE STALLED CORE-COLLAPSE SUPERNOVA SHOCK TRIGGERED BY PRECOLLAPSE ASPHERICITY IN THE PROGENITOR STAR (2013, unknown): “3; Thompson 2000; Janka 2001; Buras et al. 2006; Fernández 2012).”
MAGNETOROTATIONALLY DRIVEN SUPERNOVAE AS THE ORIGIN OF EARLY GALAXY r-PROCESS ELEMENTS? (2012, background): “The electron fraction of the tracer is evolved using approximated rates for the neutrino emission and absorption on nucleons (see, e.g., Janka (2001)).”
THREE-DIMENSIONAL HYDRODYNAMIC CORE-COLLAPSE SUPERNOVA SIMULATIONS FOR AN 11.2 M☉ STAR WITH SPECTRAL NEUTRINO TRANSPORT (2011, background): “A Poisson equation (in Equation (5)) can be solved either by the ICCG4 method in the original ZEUSMP code or by the multi-domain spectral method developed in the Lorene code (Grandclément & Novak 2009).”
BLACK HOLE FORMATION IN FAILING CORE-COLLAPSE SUPERNOVAE (2010, methodology): “We include neutrino heating via a parameterized chargedcurrent heating scheme based on Janka (2001).”
SELF-SUSTAINED ASYMMETRY OF LEPTON-NUMBER EMISSION: A NEW PHENOMENON DURING THE SUPERNOVA SHOCK-ACCRETION PHASE IN THREE DIMENSIONS (2014, unknown): “For the dominant processes of νe absorption on free neutrons and ν̄e absorption on free protons the heating rate per nucleon can be approximated by (see Janka 2001) q̇ ∝ σ0 r2 ( Lνe 〈 2νe 〉 Yn + Lν̄e 〈 2ν̄e 〉 Yp ) , (4) where σ0 is the normalizing cross section, r−2 describes the radial flux…”
Delayed outflows from black hole accretion tori following neutron star binary coalescence (2013, unknown): “For fast computation, the absorption coefficients for this optical depth functions4 are approximated as in Janka (2001) κνe ≃ 2.2 × 10−7 ρ10T 2νe,4 √ Xp(2Xn +Xp) cm −1, (21) κν̄e ≃ 2.2 × 10−7 ρ10T 2νe,4 √ Xp(2Xp +Xn) cm −1.”
THE DEVELOPMENT OF EXPLOSIONS IN AXISYMMETRIC AB INITIO CORE-COLLAPSE SUPERNOVA SIMULATIONS OF 12–25 M ⊙ ?> STARS (2012, methodology): “…of τadv/τheat > 1 indicates that matter passing from the shock to the gain surface will undergo substantial heating while in the gain region, and conditions will therefore become favorable for a thermal runaway and the revival of the shock (Janka 2001; Thompson et al. 2005; Buras et al. 2006a).”