Colloquium: Perspectives on core-collapse supernova theory

Core-collapse theory brings together many facets of high-energy and nuclear astrophysics and the numerical arts to present theorists with one of the most important, yet frustrating, astronomical questions: “What is the mechanism of core-collapse supernova explosions?” A review of all the physics and the 50-year history involved would soon bury the reader in minutiae that could easily obscure the essential elements of the phenomenon, as we understand it today. Moreover, much remains to be discovered and explained, and a complicated review of an unresolved subject in flux could grow stale fast. Therefore, this paper describes various important facts and perspectives that may have escaped the attention of those interested in this puzzle. Furthermore, an attempt to describe the modern theory’s physical underpinnings and a brief summary of the current state of play are given. In the process, a few myths that have crept into modern discourse are identified. However, there is much more to do and humility in the face of this age-old challenge is clearly the most prudent stance as its eventual resolution is sought.

Figure 1

The electron fraction $Y_e$ vs enclosed mass for a suite of massive-star progenitor models. The numbers given (the “X”s in this caption) denote either the ZAMS masses or the helium-core masses. The dots indicate $Y_e$ discontinuities and the three-pointed markers indicate the boundaries of fossil burning shells. The outer edges of the iron cores are well marked by the large circular colored dots. Note that they are positioned from $\sim 1.25M_{\odot }$ to $\sim 2.0M_{\odot }$ and are roughly in order of progenitor mass. See text for discussion. Models from 139 (“sXXs” model), and 104 (“heliumX” model)

Figure 2

Similar to Fig. 1, but depicting the logarithm of the mass density ($\rho$, in $\mathrm{g}{\mathrm{cm}}^{-3}$) vs interior mass (in solar masses) for various initial progenitor masses. Note that the lower-mass progenitors have steeper slopes, and that these profiles translate into more quickly dropping mass accretion rates ($\overline{M}$) through the stalled shock after bounce.

Figure 3

The velocity (in ${10}^9\mathrm{cm}{\mathrm{s}}^{-1}$) vs interior mass (in solar masses) at various prebounce and postbounce times. The shock wave, when present, is clearly indicated by the vertical drop, and is seen only for the postbounce times. Within $\sim 20\mathrm{ms}$ of bounce, the shock wave has stalled into accretion and postshock speeds go negative. Reviving this structure is the goal of modern core-collapse supernova theory. Note the line without the shock that changes slope in the middle. This transition in slope near $\sim 0.6M_{\odot }$ marks the edge of the homologous core a few milliseconds before bounce. Exterior to this minimum is the supersonic mantle whose maximum infall speed can reach $\sim 80000\mathrm{km}{\mathrm{s}}^{-1}$. The $11M_{\odot }$ progenitor model was taken from 139 as well as for Figs. 4, 6, 8, 9. Numerical data from 125.

Figure 4

The luminosity (in units of ${10}^{53}\mathrm{ergs}{\mathrm{s}}^{-1}$) at infinity of the ${\nu }_e$, ${\overline{\nu }}_e$, and, collectively, the ${\nu }_{\mu }$, ${\overline{\nu }}_{\mu }$, ${\nu }_{\tau }$, and ${\overline{\nu }}_{\tau }$ neutrinos, vs time (in seconds) around bounce. The ${\nu }_e$ breakout burst is clearly seen. After shock breakout, the temperatures are sufficient to generate the other species in quantity. Generally, the nonelectron types carry away $\sim 50\%$ of the total, with the ${\nu }_e\mathrm{s}$ and ${\overline{\nu }}_e\mathrm{s}$ sharing the rest. The $11M_{\odot }$ progenitor model was taken from 139. From 125.

Figure 5

The logarithm base 10 of the gravitational binding energy (in ergs, including the thermal energy) of the shells in various progenitor stars (see Fig. 1) exterior to the interior mass coordinate (in $M_{\odot }$) shown on the abscissa. These are the approximate energies that the supernova blast must overcome to eject the stellar shells exterior to a given residual neutron star or black hole mass. Note that the more massive the progenitor the greater the binding energy cost for a given baryon mass left behind.

Figure 6

Snapshots of $Y_e$ vs interior mass (in solar masses) profiles before and just after bounce. Capture decreases $Y_e$ on infall, but lepton number is soon trapped in the interior. After bounce, the outward progress of the shock wave liberates ${\nu }_e$ neutrinos, creating a trough in $Y_e$ interior to the shock, but exterior to the opaque core. The shock wave resides just rightward of the steep drop in $Y_e$ on the right. The numerical data for this $11M_{\odot }$ progenitor model run were from 125.

Figure 7

A storyboard of the evolution of the core of the onion-skin structure into the radiating protoneutron star. See text for a discussion.

Figure 8

Temperature (in MeV) vs interior mass (in solar masses) at various times before and just after bounce. The shock is depicted by the vertical drop in temperature and propagates out in mass as (and after) it stalls into accretion. Initial postbounce central temperatures are $\sim 10\mathrm{MeV}$ and the peak temperature just before shock breakout can exceed 20 MeV, but soon falls. The various neutrinopheres after $\sim 20–100\mathrm{ms}$ after bounce are at $\sim (1.0–1.1)M_{\odot }$. Numerical data from 125.

Figure 9

Similar to Fig. 8, but for entropy (in $k_B$ per baryon) vs interior mass (in solar masses). The black curves depict the evolution of profiles using realistic neutrino transport and stopping $\sim 10\mathrm{ms}$ after bounce, while the colored curves depict the corresponding developments when neutrino physics is turned off. Note that the colored curves extend further in mass and reach much higher early mantle entropies. See text for discussion. Numerical data from 125.

Figure 10

An early snapshot during the bipolar explosion of the mantle of a rapidly rotating core. Depicted are representative magnetic field lines. The scale is 2000 km from top to bottom. The extremely twisted lines are just interior to the shock wave being driven out by magnetic pressure generated within 200 ms of bounce in a “2.5”-dimensional magneto-radiation-hydrodynamic calculation conducted by 22. The progenitor employed for this calculation was from the $15M_{\odot }$ model of 54.

Figure 11

The debris field generated in a 3D neutrino-driven explosion approximately 200 ms after its onset. The scale from top to bottom is 1000 km. The blue colored exterior is a rendering of the shock wave, the colored interior is a volume rendering of the entropy of the ejecta, and the sphere in the center is the newly born neutron star. Numerical data from 106 and the $15M_{\odot }$ progenitor from 139.

Figure 12

A different rendering of the 3D neutrino-driven explosion shown in Fig. 11, but approximately 25 ms after its onset. The scale from top to bottom is $\sim 500\mathrm{km}$. The prominent bubble structures in magenta are isoentropy surfaces and are provided to highlight the neutrino-heated bubbles that seem to be generic in current 3D simulations. The bounding shock is not shown. The red colored interior (between the bubbles) is an experimental (only partially successful) volume-rendering of the density. Numerical data from 106 and the $15M_{\odot }$ progenitor from 139.