Self-consistent three-dimensional modeling of the Cassiopeia A supernova: explosion energy, $^{44}$Ti production and distribution, jet origin, and the connection to the remnant

The concluding discussion of Wongwathanarat et al. (2017), whose three-dimensional model driven by a parametrized neutrino engine reproduced the gross ejecta morphology of the Cassiopeia A (Cas A) remnant, posed a coherent set of open questions about the neutrino-driven explosion mechanism: whether energy-dependent, multi-dimensional neutrino transport can predict the electron fraction $Y_e$ precisely enough to fix the $^{44}$Ti yield; whether the mechanism can reach Cas A's ~2.3 B explosion energy for progenitors of ~18-22 $M_\odot$ while leaving a neutron star; what creates the wide, high-velocity Si-rich jets; whether the model can be extended through radioactive decay heating and circumstellar interaction to the remnant stage for quantitative comparison with the observed chemical and velocity structure; and whether SN 1987A shares the same one-sided ejecta/kick geometry. Later literature resolves parts of the question - self-consistent three-dimensional simulations now reproduce Cas A-level $^{44}$Ti masses and ratios, remnant-stage pipelines exist but only with parametrized neutrino heating, and SN 1987A modeling supports a neutron-star kick directed toward the observer - yet no end-to-end self-consistent simulation of a Cas A-like progenitor reproduces the full diagnostic set, the jet origin remains actively debated, and different codes still disagree on achievable explosion energies. The problem is open with a precise surviving core.

Background

Core-collapse supernovae (SNe) end the lives of massive stars: the unstable iron core collapses to a proto-neutron star, and the stalled bounce shock must be revived to eject the stellar mantle. In the standard theory revival is driven by neutrino heating - the deposition of a small fraction of the enormous neutrino flux emitted by the cooling proto-neutron star - assisted by turbulent convective overturn and by the standing accretion shock instability (SASI), a global sloshing or spiraling oscillation of the stalled shock. Cassiopeia A (Cas A) is the youngest known Galactic core-collapse remnant, the outcome of a Type IIb explosion (hydrogen envelope mostly stripped before collapse) whose light reached Earth around 1680. It contains a fast-moving neutron star (NS), and gamma-ray observations with NuSTAR (the Nuclear Spectroscopic Telescope Array) have mapped the radioactive isotope $^{44}$Ti (half-life about 60 yr, produced only in the innermost, hottest ejecta): roughly $(1.0-1.7)\times10^{-4}\,M_\odot$ was synthesized, about three times more than spherically symmetric models predict, concentrated in one hemisphere opposite the direction of the NS recoil - the pattern expected from the gravitational tugboat mechanism, in which asymmetric mass ejection kicks the NS opposite the stronger explosion. Wongwathanarat et al. (2017) simulated such an explosion in three dimensions by driving a 15 $M_\odot$ progenitor (hydrogen envelope removed to mimic the IIb channel) with a parametrized neutrino engine - prescribed, time-dependent neutrino luminosities at the inner grid boundary coupled to a gray, energy-integrated transport approximation - which permits tuning the explosion energy to a chosen value (~1.5 B; 1 B = 1 Bethe = $10^{51}$ erg). Stochastic convective and SASI asymmetries grew into a one-sided $^{44}$Ti distribution and an NS kick compatible with the observations, showing in principle that neither rapid rotation nor a jet-driven explosion is needed for Cas A's basic morphology. The paper's conclusions, however, list what remains unexplained, and every item stems from the same gap between such parametrized models and a physics-complete treatment. First, the electron fraction $Y_e$ (protons per baryon) in neutrino-processed ejecta is set by the competition between $\nu_e$ and $\bar{\nu}_e$ captures, and gray transport determines it only to within a few percent around 0.5 - yet this uncertainty swings the predicted $^{44}$Ti mass by an order of magnitude ($1.6\times10^{-5}$ to $1.6\times10^{-4}\,M_\odot$ in the same model), because $^{44}$Ti is made by $\alpha$-rich freeze-out (recombination of alpha-rich, high-entropy matter at silicon-burning temperatures) only in a narrow $Y_e$ window near 0.5; effects missing from all global models, such as collective neutrino flavor oscillations (flavor transformations induced by neutrino-neutrino refraction) and the lepton-emission self-sustained asymmetry (LESA, a spontaneously developing dipole of $\nu_e$-$\bar{\nu}_e$ emission found in 3D simulations), could shift $Y_e$ at exactly this level. Second, the explosion energy inferred for Cas A (~2.3 B) had not been reached by any modern self-consistent multi-dimensional simulation, whereas one-dimensional calibrated models reach such energies only for the most extreme cases, with (hydrogen-rich) progenitors of ~18-22 $M_\odot$, around the suspected mass of the Cas A progenitor; the paper elsewhere attributes Cas A to a hydrogen-stripped (Type IIb) star in the ~15-20 $M_\odot$ range (possibly 18-20 $M_\odot$) and quotes $E_{\rm exp}\approx2.3$ B and $M_{\rm ej}\approx4\,M_\odot$ as its likely values. Third, the origin of Cas A's wide, high-velocity, Si-rich jets was unexplained, candidate explanations being low-mode convective asymmetries in the pre-collapse silicon/oxygen burning shells, late bipolar (magnetar-like) spin-down activity of the new NS, or direction-dependent interaction of the asymmetrically expelled inner ejecta with the reverse shock (the shock driven back into the decelerating ejecta by the circumstellar environment). Fourth, the simulation stopped about one day after core bounce, without radioactive decay heating or long-term circumstellar interaction, so no quantitative comparison with the remnant's observed chemical and velocity structure was possible. Fifth, as a speculation, the model suggested that SN 1987A shares the same one-sided geometry with its NS kick directed nearly toward the observer, which would explain the redshifted $^{44}$Ti lines and the nickel/iron infrared emission of that event, pending dedicated multi-dimensional modeling and spectral synthesis. These five items are facets of one scientific objective: a self-consistent, physics-complete account of the Cas A explosion and of its connection to the observed remnant.

Problem Statement

Can the neutrino-driven mechanism quantitatively account for the Cassiopeia A supernova? The problem, as posed by the concluding discussion of Wongwathanarat et al. (2017), is to construct a self-consistent three-dimensional simulation of the core collapse of a hydrogen-stripped (Type IIb) progenitor compatible with the suspected Cas A progenitor - the source attributes Cas A to a star in the ~15-20 $M_\odot$ range (possibly 18-20 $M_\odot$) and quotes $E_{\rm exp}\approx2.3$ B and $M_{\rm ej}\approx4\,M_\odot$ as its likely values, while the 18-22 $M_\odot$ window quoted in the paper is the mass range of the hydrogen-rich progenitors for which one-dimensional parametrically calibrated models reach ~2.3 B and motivates the energy target rather than restricting admissible models, the true progenitor mass remaining observationally uncertain - that uses energy-dependent, multi-dimensional neutrino transport with no parametrized neutrino engine or tuned luminosities, leaves a neutron star, and: (i) attains an explosion energy of order Cas A's ~2.3 B; (ii) synthesizes $M(^{44}\mathrm{Ti})\approx(1.0-1.7)\times10^{-4}\,M_\odot$ with the observed one-sided spatial and velocity distribution opposite the neutron-star kick, with the electron fraction $Y_e$ of the neutrino-processed ejecta predicted by the transport rather than assumed; collective neutrino flavor transformations and LESA-type $\nu_e$/$\bar{\nu}_e$ emission asymmetries are recognized residual uncertainties that can shift $Y_e$ by a few percent around 0.5, and their consequences for the predicted yields are to be assessed or bounded (for example through sensitivity or imposed-asymmetry studies) rather than included self-consistently in the global simulation; (iii) either reproduces the wide, high-velocity Si-rich jets of Cas A or determines which mechanism creates them (low-mode convective asymmetries in the pre-collapse silicon/oxygen burning shells, late bipolar spin-down activity of the young neutron star, or direction-dependent interaction of the asymmetric inner ejecta with the reverse shock); and (iv) is extended through radioactive decay heating and interaction with the circumstellar medium to the remnant stage, and the chemical and velocity structure it produces is compared quantitatively with the observations of Cas A. The related hypothesis that SN 1987A shares the same one-sided ejecta/kick geometry, with its neutron star moving nearly toward the observer, is an explicitly labeled speculation and separate future-research topic in the source, not a required component of a complete answer here. The common objective is a physics-complete, end-to-end account of Cas A: a complete answer must address all four components within the same self-consistent model, or within a single consistently coupled model chain for the same explosion, whereas resolving a component in isolation (for example the yield alone, or the remnant morphology with a parametrized engine) resolves only part of the problem. Since the headline question also admits a negative answer, a demonstrated failure of the neutrino-driven mechanism must be established by controlled evidence - an independent multi-code comparison over a stated set of neutron-star-forming, hydrogen-stripped progenitors spanning the relevant mass range and computed with explicit transport treatments, whose collective failure to simultaneously meet targets (i)-(iv) is treated as establishing the negative answer - and not by the failure of any single chosen run.

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