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Register a new userA Comparison of Explosion Energies for Simulated and Observed Core-Collapse Supernovae
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There are now $sim$20 multi-dimensional core-collapse supernova (CCSN) simulations that explode. However, these simulations have explosion energies that are a few times $10^{50}$ erg, not $10^{51}$ erg. In this manuscript, we compare the inferred explosion energies of these simulations and observations of 38 SN~IIP. Assuming a log-normal distribution, the mean explosion energy for the observations is $mu_{rm obs} = -0.13pm 0.05$ ($log_{10}(E/10^{51}, {rm erg})$) and the width is $sigma_{rm obs} = 0.21^{+0.05}_{-0.04}$. Only three CCSN codes have sufficient simulations to compare with observations: CHIMERA, CoCoNuT-FMT, and FORNAX. Currently, FORNAX has the largest sample of simulations. The two-dimensional FORNAX simulations show a correlation between explosion energy and progenitor mass, ranging from linear to quadratic, $E_{rm sim} propto M^{1-2}$; this correlation is consistent with inferences from observations. In addition, we infer the ratio of the observed-to-simulated explosion energies, $Delta=log_{10}(E_{rm obs}/E_{rm sim})$. For the CHIMERA set, $Delta=0.33pm0.06$; for CoCoNuT-FMT, $Delta=0.62pm0.05$; for FORNAX2D, $Delta=0.73pm0.05$, and for FORNAX3D, $Delta=0.95pm0.06$. On average, the simulations are less energetic than inferred energies from observations ($Delta approx 0.7$), but we also note that the variation among the simulations (max($Delta$)-min($Delta$) $approx 0.6$) is as large as this average offset. This suggests that further improvements to the simulations could resolve the discrepancy. Furthermore, both the simulations and the observations are heavily biased. In this preliminary comparison, we model these biases, but to more reliably compare the explosion energies, we recommend strategies to un-bias both the simulations and observations.
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Recent multi-dimensional simulations of core-collapse supernovae are producing successful explosions and explosion-energy predictions. In general, the explosion-energy evolution is monotonic and relatively smooth, suggesting a possible analytic solution. We derive analytic solutions for the expansion of the gain region under the following assumptions: spherical symmetry, one-zone shell, and powered by neutrinos and $alpha$ particle recombination. We consider two hypotheses: I) explosion energy is powered by neutrinos and $alpha$ recombination, II) explosion energy is powered by neutrinos alone. Under these assumptions, we derive the fundamental dimensionless parameters and analytic scalings. For the neutrino-only hypothesis (II), the asymptotic explosion energy scales as $E_{infty} approx 1.5 M_g v_0^2 eta^{2/3}$, where $M_g$ is the gain mass, $v_0$ is the free-fall velocity at the shock, and $eta$ is a ratio of the heating and dynamical time scales. Including both neutrinos and recombination (hypothesis I), the asymptotic explosion energy is $E_{infty} approx M_g v_0^2 (1.5eta^{2/3} + beta f(rho_0))$, where $beta$ is the dimensionless recombination parameter. We use Bayesian inference to fit these analytic models to simulations. Both hypotheses fit the simulations of the lowest progenitor masses that tend to explode spherically. The fits do not prefer hypothesis I or II; however, prior investigations suggest that $alpha$ recombination is important. As expected, neither hypothesis fits the higher-mass simulations that exhibit aspherical explosions. In summary, this explosion-energy theory is consistent with the spherical explosions of low progenitor masses; the inconsistency with higher progenitor-mass simulations suggests that a theory for them must include aspherical dynamics.
Most supernova explosions accompany the death of a massive star. These explosions give birth to neutron stars and black holes and eject solar masses of heavy elements. However, determining the mechanism of explosion has been a half-century journey of great complexity. In this paper, we present our perspective of the status of this theoretical quest and the physics and astrophysics upon which its resolution seems to depend. The delayed neutrino-heating mechanism is emerging as a robust solution, but there remain many issues to address, not the least of which involves the chaos of the dynamics, before victory can unambiguously be declared. It is impossible to review in detail all aspects of this multi-faceted, more-than-half-century-long theoretical quest. Rather, we here map out the major ingredients of explosion and the emerging systematics of the observables with progenitor mass, as we currently see them. Our discussion will of necessity be speculative in parts, and many of the ideas may not survive future scrutiny. Some statements may be viewed as informed predictions concerning the numerous observables that rightly exercise astronomers witnessing and diagnosing the supernova Universe. Importantly, the same explosion in the inside, by the same mechanism, can look very different in photons, depending upon the mass and radius of the star upon explosion. A 10$^{51}$-erg (one Bethe) explosion of a red supergiant with a massive hydrogen-rich envelope, a diminished hydrogen envelope, no hydrogen envelope, and, perhaps, no hydrogen envelope or helium shell all look very different, yet might have the same core and explosion evolution.
We investigate the post-explosion phase in core-collapse supernovae with 2D hydrodynamical simulations and a simple neutrino treatment. The latter allows us to perform 46 simulations and follow the evolution of the 32 successful explosions during several seconds. We present a broad study based on three progenitors (11.2 $M_odot$, 15 $M_odot$, and 27 $M_odot$), different neutrino-heating efficiencies, and various rotation rates. We show that the first seconds after shock revival determine the final explosion energy, remnant mass, and properties of ejected matter. Our results suggest that a continued mass accretion increases the explosion energy even at late times. We link the late-time mass accretion to initial conditions such as rotation strength and shock deformation at explosion time. Only some of our simulations develop a neutrino-driven wind that survives for several seconds. This indicates that neutrino-driven winds are not a standard feature expected after every successful explosion. Even if our neutrino treatment is simple, we estimate the nucleosynthesis of the exploding models for the 15 $M_odot$ progenitor after correcting the neutrino energies and luminosities to get a more realistic electron fraction.
We present self-consistent, axisymmetric core-collapse supernova simulations performed with the Prometheus-Vertex code for 18 pre-supernova models in the range of 11-28 solar masses, including progenitors recently investigated by other groups. All models develop explosions, but depending on the progenitor structure, they can be divided into two classes. With a steep density decline at the Si/Si-O interface, the arrival of this interface at the shock front leads to a sudden drop of the mass-accretion rate, triggering a rapid approach to explosion. With a more gradually decreasing accretion rate, it takes longer for the neutrino heating to overcome the accretion ram pressure and explosions set in later. Early explosions are facilitated by high mass-accretion rates after bounce and correspondingly high neutrino luminosities combined with a pronounced drop of the accretion rate and ram pressure at the Si/Si-O interface. Because of rapidly shrinking neutron star radii and receding shock fronts after the passage through their maxima, our models exhibit short advection time scales, which favor the efficient growth of the standing accretion-shock instability. The latter plays a supportive role at least for the initiation of the re-expansion of the stalled shock before runaway. Taking into account the effects of turbulent pressure in the gain layer, we derive a generalized condition for the critical neutrino luminosity that captures the explosion behavior of all models very well. We validate the robustness of our findings by testing the influence of stochasticity, numerical resolution, and approximations in some aspects of the microphysics.
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the CoCoNuT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the spacetime metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 solar mass progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared to Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong non-radial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.
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