Neutrino Emission from Supernovae

TL;DR

This paper reviews the role of neutrinos in supernovae, covering their production, transport, and impact on explosion mechanisms and nucleosynthesis, highlighting the importance of neutrino physics in understanding supernova evolution.

Contribution

It provides a comprehensive overview of neutrino processes in supernova cores, including emission phases and implications for future neutrino detection from galactic supernovae.

Findings

Neutrino emission phases have characteristic signal features.

Neutrino interactions influence supernova explosion dynamics.

Neutrino detection can reveal supernova core processes.

Abstract

Supernovae are the most powerful cosmic sources of MeV neutrinos. These elementary particles play a crucial role when the evolution of a massive star is terminated by the collapse of its core to a neutron star or a black hole and the star explodes as supernova. The release of electron neutrinos, which are abundantly produced by electron captures, accelerates the catastrophic infall and causes a gradual neutronization of the stellar plasma by converting protons to neutrons as dominant constituents of neutron star matter. The emission of neutrinos and antineutrinos of all flavors carries away the gravitational binding energy of the compact remnant and drives its evolution from the hot initial to the cold final state. The absorption of electron neutrinos and antineutrinos in the surroundings of the newly formed neutron star can power the supernova explosion and determines the conditions in the innermost supernova ejecta, making them an interesting site for the nucleosynthesis of iron-group elements and trans-iron nuclei. In this Chapter the basic neutrino physics in supernova cores and nascent neutron stars will be discussed. This includes the most relevant neutrino production, absorption, and scattering processes, elementary aspects of neutrino transport in dense environments, the characteristic neutrino emission phases with their typical signal features, and the perspectives connected to a measurement of the neutrino signal from a future galactic supernova.

Tables

Table 1. Table 1: Most important neutrino processes in supernova and proto-neutron star matter.

Process	Reactiona
\svhline Beta-processes (direct URCA processes)
electron and ${\nu }_e$ absorption by nuclei	$e^{-}+(A,Z)⟷(A,Z-1)+{\nu }_e$
electron and ${\nu }_e$ captures by nucleons	$e^{-}+p⟷n+{\nu }_e$
positron and ${\overline{\nu }}_e$ captures by nucleons	$e^{+}+n⟷p+{\overline{\nu }}_e$
“Thermal” pair production and annihilation processes
Nucleon-nucleon bremsstrahlung	$N+N⟷N+N+\nu +\overline{\nu }$
Electron-position pair process	$e^{-}+e^{+}⟷\nu +\overline{\nu }$
Plasmon pair-neutrino process	$\tilde{\gamma }⟷\nu +\overline{\nu }$
Reactions between neutrinos
Neutrino-pair annihilation	${\nu }_e+{\overline{\nu }}_e⟷{\nu }_x+{\overline{\nu }}_x$
Neutrino scattering	${\nu }_x+\{{\nu }_e,{\overline{\nu }}_e\}⟷{\nu }_x+\{{\nu }_e,{\overline{\nu }}_e\}$
Scattering processes with medium particles
Neutrino scattering with nuclei	$\nu +(A,Z)⟷\nu +(A,Z)$
Neutrino scattering with nucleons	$\nu +N⟷\nu +N$
Neutrino scattering with electrons and positrons	$\nu +e^{\pm }⟷\nu +e^{\pm }$

Equations

$$E_{\mathrm{b}}\sim E_{\mathrm{g}}\approx \frac{3}{5}\frac{G{M}_{\mathrm{ns}}^2}{R_{\mathrm{ns}}}\approx 3.6\times 10^{53}{\left(\frac{M_{\mathrm{ns}}}{1.5M_{\odot }}\right)}^2{\left(\frac{R_{\mathrm{ns}}}{10\mathrm{km}}\right)}^{-1}\mathrm{erg}.$$

$${\mathcal{H}}_{\mathrm{weak}}=\frac{G_{\mathrm{F}}}{\sqrt{2}}{J}_{\mu }^{†}{J}^{\mu },$$

$$\mathcal{M}(f+\nu \to f^{\prime }+{\nu }^{\prime })=\frac{G_{\mathrm{F}}}{\sqrt{2}}{\overline{\psi }}_{f^{\prime }}{\gamma }_{\mu }(C_V-C_A{\gamma }_5){\psi }_f{\overline{\psi }}_{{\nu }^{\prime }}{\gamma }^{\mu }(1-{\gamma }_5){\psi }_{\nu }.$$

$${\sigma }_{A,\mathrm{coh}}\approx \frac{1}{16}{\sigma }_0{\left(\frac{E}{m_e{c}^2}\right)}^2{N}^2.$$

$$M_{\mathrm{hc}}\text{vbox}\text{offinterlineskip}<\sim M_{\mathrm{Ch}}=1.457(2Y_e{)}^2{M}_{\odot },$$

$$t_{\mathrm{ff}}\sim \frac{1}{\sqrt{G\rho }}\sim \frac{0.004}{\sqrt{{\rho }_{12}}}\mathrm{s}$$

$${\nu }_e+n$$

$${\bar{\nu }}_e+p$$

$$t_{\mathrm{L}}$$

$$t_{\mathrm{E}}$$

$${\lambda }_0=\frac{1}{n_b⟨{\sigma }_{\nu }⟩}\sim 10\mathrm{cm}{\left(\frac{E}{100\mathrm{MeV}}\right)}^{-2}{\left(\frac{M_{\mathrm{ns}}}{1.5M_{\odot }}\right)}^{-1}{\left(\frac{R_{\mathrm{ns}}}{10\mathrm{km}}\right)}^3$$

$$L_{{\nu }_x}=4\pi \varphi s_{\nu }{R}_{\mathrm{ns}}^2{T}_{\nu }^4,$$

$$L_{{\nu }_e}+L_{{\bar{\nu }}_e}=2{\beta }_1{L}_{{\nu }_x}+{\beta }_2\frac{G{M}_{\mathrm{ns}}\dot{M}}{R_{\mathrm{ns}}}.$$

$$L_{\nu }^{\mathrm{tot}}\equiv \sum _{i=e,\mu ,\tau }{L}_{{\nu }_i}+L_{{\bar{\nu }}_i}\sim \frac{E_{\mathrm{b}}}{t_{\mathrm{E}}}\sim \mathrm{several}10^{52}{\mathrm{erg}\mathrm{s}}^{-1}.$$

$$f_{\alpha }(E)\propto {\left(\frac{E}{⟨E⟩}\right)}^{\alpha }{e}^{-(\alpha +1)E/⟨E⟩},$$

$$⟨E⟩=\frac{{\int }_0^{\infty }\mathrm{d}EE{f}_{\alpha }(E)}{{\int }_0^{\infty }\mathrm{d}E{f}_{\alpha }(E)}$$

$$\frac{⟨E^2⟩}{⟨E{⟩}^2}=\frac{2+\alpha }{1+\alpha }.$$

$$\frac{\mathrm{d}{L}_{\nu }(E)}{\mathrm{d}E}\approx \frac{1}{4}c(4\pi R_{\nu }^2(E))B_{\nu }(E)\equiv \pi c{R}_{\nu }^2(E)\frac{4\pi }{(hc{)}^3}\frac{E^3}{1+\exp [(E-{\mu }_{\nu })/T]},$$

Full text

In this Chapter the basic neutrino physics in supernova cores and nascent neutron stars will be discussed. This includes the most relevant neutrino production, absorption, and scattering processes, elementary aspects of neutrino transport in dense environments, the characteristic neutrino emission phases with their typical signal features, and the perspectives connected to a measurement of the neutrino signal from a future galactic supernova.

1 Introduction

The paramount importance of neutrinos in the context of stellar core collapse and the question how massive stars achieve to produce supernova (SN) explosions was first pointed out in seminal papers by Colgate and White (1966) and Arnett (1966). They recognized that the huge gravitational binding energy of a neutron star is carried away by neutrinos, which are therefore a copious reservoir of energy for the explosion. Approximating the neutron star of mass $M_{\mathrm{ns}}$ and radius $R_{\mathrm{ns}}$ by a homogeneous sphere with Newtonian gravity, its binding energy, which roughly equals its gravitational energy, can be estimated as

[TABLE]

If only a fraction of this energy can be transferred to the gas surrounding the newly formed neutron star, the overlying stellar layers could be accelerated and expelled in a violent blast wave. A major revision of the theoretical picture of neutrino effects in collapsing stars became necessary after weak neutral currents, which had been predicted in theoretical work by Weinberg and Salam, were experimentally confirmed in the early 1970’s (Freedman et al, 1977). With neutral-current scatterings of neutrinos off nuclei and free nucleons being possible, it was recognized that the electron neutrinos, $\nu_{e}$, produced by electron captures can escape freely only at the beginning of stellar core collapse (which starts out at a density around $10^{10}$ g cm*-3*), but get trapped to be carried inward with the infalling stellar plasma when the density exceeds a few times $10^{11}$ g cm*-3*. At this time the implosion has accelerated so much that the remaining collapse time scale becomes shorter than the outward diffusion time scale of the neutrinos, which increases when scatterings become more and more frequent with growing density. Shortly afterwards, typically around $10^{12}$ g cm*-3*, the electron neutrinos equilibrate with the stellar plasma and fill up their phase space to form a degenerate Fermi gas. During the remaining collapse until nuclear saturation density (about $2.7\times 10^{14}$ g cm*-3*) is reached, and the incompressibility of the nucleonic matter due to the repulsive part of the nuclear force enables the formation of a neutron star, the entropy and the lepton number (electrons plus electron neutrinos) of the infalling gas (stellar plasma plus trapped neutrinos) remain essentially constant. Since the change of the entropy by electron captures and $\nu_{e}$ escape until trapping is modest, it became clear that the collapse of a stellar core proceeds nearly adiabatically (for a review, see Bethe, 1990).

The proto-neutron star, i.e., the hot, mass-accreting, still proton- and lepton-rich predecessor object of the final neutron star, with its super-nuclear densities and extreme temperatures of up to several $10^{11}$ K (corresponding to several 10 MeV) is highly opaque to all kinds of (active) neutrinos and antineutrinos. Neutrinos, once generated in this extreme environment, are frequently re-absorbed, re-emitted, and scattered before they can reach semi-transparent layers near the “surface” of the proto-neutron star, which is marked by an essentially exponential decline of the density over several orders of magnitude. Before they finally decouple from the stellar medium closely above this region and escape, neutrinos have experienced billions of interactions on average. The period of time over which the nascent neutron star is able to release neutrinos with high luminosities until its gravitational binding energy (Eq. 1) is radiated away therefore lasts many seconds (Burrows and Lattimer, 1986; Burrows, 1990a).

This expectation was splendidly confirmed by the first and so far only detection of neutrinos from a stellar collapse on February 23, 1987, in the case of SN 1987A in the Large Magellanic Cloud at a distance of roughly 50 kpc (Raffelt, 1996). The two dozen neutrino events in the three underground experiments of Kamiokande II (Hirata et al, 1987), Irvine-Michigan-Brookhaven (IMB; Bionta et al, 1987), and Baksan (Alexeyev et al, 1988) were recorded over a time interval of about 12 seconds (Fig. 1). Also their individual energies (up to 40 MeV) and the associated integrated energy of the neutrino signal (some $10^{53}$ erg) were in the ballpark of model predictions and evidenced the birth of a neutron star in this supernova. Figure 2 displays a schematic representation of the neutrino emission that drives the evolution from the onset of stellar core collapse to the cooling of the nascent neutron star, finally leading to a neutrino-transparent neutron star with central temperature below about 1 MeV (roughly $10^{10}$ K) within some tens of seconds.

The neutrino-interaction processes and basic physics of neutrino transport in supernova matter will be described in Sect. 2, the neutrino-emission phases and corresponding neutrino effects in Sect. 3, and the neutrino-emission properties during the different phases in Sect. 4. Conclusions and an outlook will follow in Sect. 5.