Explosion Mechanism

Today, over 50 000 supernovae or supernova candidates have been detected and detailed lightcurves and spectra are available for several thousand of them according to the Open Supernova Catalog [111, 112]. Furthermore, these numbers are expected to grow rapidly in the near future, with the Large Synoptic Survey Telescope alone expected to observe 3×¹⁰⁵core-collapse supernovae per year when it starts opera-tions in the early 2020s [113, 114]. However, measurements in the electromagnetic spectrum only allow observations of the surface layers of the supernova. While these give detailed information on the composition of these outer layers and thus the properties of the progenitor, they give little information about the mechanism underlying the actual explosion, which takes place at the centre of the star several minutes to hours before the resulting shock wave reaches the stellar surface and the supernova becomes visible to telescopes.

Unlike electromagnetic radiation, neutrinos only interact weakly and are therefore unlikely to experience scattering or be absorbed in outer layers of star. Neutrinos are thus the only known channel that allows us to directly observe the processes occurring near the centre of a star in the moment of explosion. On the other hand, the small cross sections of weak interactions mean that most neutrinos pass through any detector unnoticed and only very large neutrino fluxes can be observed. This limits the reach of current neutrino detectors to supernovae within the Milky Way or its immediate cosmic neighbourhood, where the rate of core-collapse supernovae is estimated to be about 2–3 per century [115].

Due to this severe scarcity of observational data, progress in understanding the core-collapse explosion mechanism has come mostly from computer simulations.

Pioneering contributions to numerical models of supernovae were made by Colgate, Grasberger & White [116, 117], Arnett [118] and Wilson [119, 120]. These early simulations often imposed spherical symmetry to reduce the required computing power, making them effectively one-dimensional. Optical observations of SN1987A made it obvious that this assumption does not generally hold true in nature [121], which increased the effort put into more complex simulations that only imposed rotational symmetry around one axis. Today, these two-dimensional simulations are very common, while one-dimensional simulations are still used for parametric studies that compare a wide range of models. Only in recent years has it become computationally feasible to simulate three-dimensional models that include detailed treatment of neutrino production and transport processes [122, 123].

22

1.2 Supernovae

The difficulty in simulating supernova explosions stems both from the huge computing power required and the inherent complexity of the phenomenon itself:

Supernovae stand out from most other physical phenomena in that they involve all known fundamental forces—gravity as well as the strong and electroweak force—

and operate at extreme conditions, which often cannot be reproduced in laboratory experiments. Simulating them also requires solving difficult and non-linear hy-drodynamical equations and taking into account relativistic effects. The latter are currently often treated as a modified potential in Newtonian gravity to simplify cal-culations, which might cause an error of tens of percent in some physical quantities and lead to qualitatively different outcomes [124].

Computer simulations of supernovae have made remarkable progress in the last decades, in part due to a dramatic increase in available computing resources and in part due to an improved understanding of the neutrino physics and nuclear cross sections involved in the explosion of a core-collapse supernova. Thus, while current simulations disagree on many points and “are still too far apart to lend ultimate credibility to any one of them” [6], they have reached widespread agreement on the basic explosion mechanism.

After Burbidge and others highlighted the gravitational instability of old massive stars [125], Colgate and others proposed a solely hydrodynamical “bounce and shock” explosion mechanisms for core-collapse supernovae in 1961 [116], where the equation of state of the collapsing core stiffens after it reaches nuclear density and infalling matter bounces off the now incompressible core resulting in an outgoing shock wave. Several years later, they studied the role of the high neutrinos fluxes inside a supernova [117].

In the early 1980s, Wilson and Bethe [120, 126] described the delayed neutrino-driven explosion mechanism generally accepted today. This mechanism consists of six steps which are sketched in figure 1.7.

1. Initial phase: The progenitor of a core-collapse supernova is a star with a mass of more than about 8 M, whose central region is sufficiently hot and dense to produce iron through nuclear fusion. Since the iron cannot produce energy through further nuclear fusion steps it forms an inner core, which is held up by electron degeneracy pressure whose density dependence is initially P ∝ ρ⁵³. At the same time, hydrostatic equilibrium requires P∝ GMρR⁻¹, which leads to a mass-radius relationship for the iron core of R∝ M⁻¹³. As silicon burning continues to produce iron that accretes onto the core, the core shrinks due to the increase in mass. Electrons occupy increasingly higher energy states until they become relativistic and their equation of state changes to P∝ ρ⁴³.¹²

12Analogous to the mass limit for white dwarf stars, this happens when the iron core reaches the Chandrasekhar mass of about 1.4 M.

Chapter 1 Introduction

Shock Stagnation and Heating,

,µ,τ

Shock Propagation and Burst

R ~ 100 km_s

Figure 1.7: Sketch of the six phases of the delayed explosion mechanism as described in the text. In each panel, the upper section shows the dynamical processes, with arrows representing velocity vectors, while the lower section shows the nuclear composition of the star. Figure from reference [127].

24

1.2 Supernovae

During this transition to the relativistic regime, the mass-radius relationship becomes steeper and the shrinking of the core accelerates until the mass-radius relationship of the iron core breaks down, indicating that there is no stable configuration. The core collapses. During this phase, some electrons get captured by nuclei and the resulting neutrinos transport energy away from the core, thus reducing the degeneracy pressure which counteracts the collapse.

2. ν trapping: After about 100 ms, the inner core reaches a density of about 10¹²g/cm³. At this density, the mean free path of neutrinos becomes smaller than the radius of the inner core and they become trapped inside it.

3. Bounce and shock formation: After about 110 ms, the core has collapsed from a radius of about 3000 km to just tens of kilometres, with infalling matter reaching about 10 % of the speed of light. At this point, the density of the inner core surpasses nuclear density, reaching about 3×^{1014g/cm3, and its} equation of state stiffens. Infalling matter now hits a “wall” and is reflected, resulting in an outgoing shock wave. Meanwhile, neutrinos are still trapped in the inner core due to its high density.

4. Shock propagation: After about 120 ms, the outgoing shock wave reaches the surface of the iron core at a radius of about 100 km, dissociating the iron nuclei into free nucleons along the way. Since the electron capture cross section on free protons (e⁻+p→ⁿ+ν_e) is much higher than on the larger, neutron-rich nuclei, this leads to a sudden increase in the electron capture rate. The matter density in the outer parts of the core is too low to trap the neutrinos, so a brief ν_eburst is released.

5. Shock stagnation and ν heating: After about 200 ms, the shock wave stagnates at a radius of about 100 km to 200 km, having used up most of its energy to dissociate heavy nuclei into their constituent nucleons. Matter from outer layers infalling onto the almost stationary shock front creates an accretion shock, which powers neutrino emission. At this phase, convection sets in at the accretion shock layer.

Meanwhile, the neutrinos that were trapped inside the inner core are starting to diffuse out. While some escape the supernova immediately, others deposit energy in the accretion shock layer mainly by neutrino capture on free nuc-leons, i. e. ¯ν_e+p → ⁿ+e⁺and ν_e+n → ^p+e⁻. This heating increases the pressure in the region behind the shock front and reignites the shock wave.

6. ν cooling: During the following tens of seconds, the remnant of the core, a proto-neutron star (PNS), cools by diffusive neutrino transport. The outgoing shock wave takes several minutes or hours to reach the surface of the star, where it will expel the matter in its outer shells and produce a signal that is visible in the electromagnetic spectrum.

Chapter 1 Introduction

Figure 1.8: Luminosity (top) and mean energy (bottom) of νe(dashed blue line), ¯νe

(solid black) and ν_x(dotted red) for a 20 Mmodel [128]. The left panels show the prompt νeburst and the following phase of shock stagnation, while the right panels show the neutrino cooling phase.

Throughout this process, neutrino emission occurs in three distinct steps, which are displayed in figure 1.8.

The first step is a prompt νeburst from electron capture during phase 4 above.

With a duration of roughly 10 ms, this is expected to give a very sharp and unmis-takeable feature that consists of almost pure νe. Since this signal originates in the iron core, which collapses at a well-defined set of physical conditions, independent of the properties of the outer shells of the star, it is very similar across a wide range of simulations with different progenitors [129].

The second step has a duration of several 100 ms and corresponds to the shock stagnation in phase 5 above. Neutrino emission during this phase is powered by matter from outer layers accreting onto the shock front. Radial movement of the shock front therefore leads to changes in the accretion rate, such that hydrodynamical

26

1.2 Supernovae

features like the standing accretion shock instability could be observed as striking sinusoidal features in the neutrino event rate [130, 131, 132, 133]. In this phase, the luminosities Lνe and L¯νe are roughly equal (and higher than Lνx) while the average energies are unequal (h^Eνei < h^E¯νei ≈ h^Eνxi), which contributes to the de-leptonization of the core. This energy difference is caused by the higher cross section for νein electron-rich matter, which means that νeleaving the star are, on average, emitted at larger radii and thus lower temperatures.

The final step of neutrino emission corresponds to the ν cooling (phase 6) and has a duration of some tens of seconds. During this time, the supernova remnant cools through diffusive emission of neutrinos that became trapped in its core during the earlier phases of the explosion. The composition of the neutrino flux at this stage is governed by a number of different physical processes, including nucleon-nucleon bremsstrahlung and neutrino-antineutrino pair annihilation [134, 135, 136, 137], which lead to roughly equal luminosities of all neutrino species that fall off exponentially with time, while the average energies remain unequal.