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Presupernova models and supernovae

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Abstract

Present status of the theories for presupernova evolution and triggering mechanisms of supernova explosions are summarized and discussed from the standpoint of the theory of stellar structure and evolution. It is not intended to collect every detail of numerical results thus far obtained, but to extract physically clear-cut understanding from complexities of the numerical stellar models. For this purpose the evolution of stellar cores is discussed in a generalized fashion. The following types of the supernova explosions are discussed. The carbon deflagration supernova of intermediate mass star which results in the total disruption of the star. Massive star evolves into a supernova triggered by photo-dissociation of iron nuclei which results in a formation of a neutron star or a black hole depending on its mass. These two are typical types of the sueprnovae. Between them there remains a range of mass for which collapse of the stellar core is triggered by electron captures, which has been recently shown to leave a neutron star despite oxygen deflagration competing with the electron captures. Also discussed are combustion and detonation of helium or carbon which take place in accreting white dwarfs, and the collapse which is triggered by electron-pair creation in very massive stars.

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Abbreviations

A :

mass number of atomic nucleus

B v(a, b):

incomplete beta function

c p :

specific heat at constant pressure

c p :

sound velocity

c(sub):

center of the star

〈E e 〉:

mean energy of an electron captured by nucleus

E n :

nuclear energy release from unit mass of the nuclear fuel specified by n

E thr :

threshold energy (9.3)

E thr,0 :

energy difference between the ground states of daughter nucleus and parent nucleus (9.1)

E γ :

energy of gamma ray emitted from daughter nucleus (9.1)

〈E v 〉:

mean energy of a neutrino emitted by electron capture (9.1)

f :

flatness parameter (2.17)

g :

local gravitational acceleration (2.16)

H :

atomic mass unit

H p :

scale height of pressure (2.22)

H (sub):

hydrogen-burning shell

k :

Boltzmann constant

l :

mixing length of convection

L cr(M r ):

local Eddington's critical luminosity (4.3)

L n :

integrated nuclear energy generation rate by nuclear fuel specified by n

L v :

neutrino luminosity

L v, cr(M r ):

local Eddington's critical neutrino luminosity (11.2)

M :

(current) mass of a star

m M :

core mass contained interior to the carbon-burning shell

M Ch :

Chandrasekhar's limiting mass (9.6)

M H :

core mass contained interior to the hydrogen-burning shell

M He :

core mass contained interior to the helium-burning shell

M ms :

mass of a star at its zero-age min-sequence

M O :

core mass contained interior to the oxygen-burning shell

M r :

mass contained interior to a shell at r

M Si :

core mass contained interior to the silicon-burning shell

M WD :

mass of white dwarf (7.1)

M 0 :

normalization factor to the non-dimensional mass (3.3)

M 1 :

core mass (3.6)

N :

polytropic index between pressure and density (2.3)

n :

polytropic index between pressure and temperature (10.1)

N A :

Avogadro number

N ad :

adiabatic polytropic index

N e :

number of electrons in unit mass of matter

NSE:

nuclear statistical equilibrium

P :

pressure

ph (sub):

photosphere

Q e :

mass fraction of the envelope exterior of the shell e (2.14)

R :

stellar radius

r :

radial distance of a shell

r 0 :

normalization factor to the non-dimensional radius (3.2)

s :

specific entropy

S i :

specific entropy of ions

T :

temperature

U :

homology invariant defined by (2.1)

u gas :

specific internal energy of gas

u rad :

energy of the radiation field per volume in which unit mass of gas is contained (6.4)

V :

homology invariant defined by (2.2)

υdef :

velocity of deflagration front (6.10)

X :

concentration by weight of hydrogen

Y :

concentration by weight of helium

Y e :

mole number of electrons in one gram of matter (9.7)

Y v :

mole number of neutrinos in one gram of matter

Z :

concentration by weight of the elements other than hydrogen and helium

z :

shock strength (6.6)

1 (sub):

usually denotes the core edge (2.13)

α:

ratio of the mixing length to the scale height of pressure (l/H p )

β:

ratio of gas pressure to the total pressure

γ:

ratio of the specific heats

gD :

locus of singularity in U-V plane (2.5)

ΔM(H p ):

mass contained within unit scale height of pressure (4.4)

ɛec :

energy rate by electron captures (9.5)

ɛ n :

nuclear energy generation rate by the nuclear fuel specified by n

ɛ v :

neutrino loss rate

L (D) v :

neutrino loss rate excluding the neutrinos from the electron captures (9.4)

η:

non-dimensional density (3.1)

θ:

P/ϱ, not the non-dimensional temperature (2.7)

θW :

Weinberg's angle (5.8)

κ:

opacity

κ v :

neutrino opacity (11.2)

Λ:

describes the effect of electron degeneracy in equation of state (2.19)

λec :

rate of electron capture

μ:

mean molecular weight

μ e :

mean molecular weight of electrons

μ e :

chemical potential of an electron excluding the rest mass (8.1)

μ i :

mean molecular weight of ions

ξ:

non-dimensional radius (3.1)

ω:

non-dimensional pressure (3.1)

ϱ:

matter density

ϱ GR cr :

critical density above which the general relativistic instability sets in

ϱ β cr :

critical density for reimplosion of the core by beta processes (Section 5)

ϱign :

density at the ignition

ϱnse :

density above which the deflagrated matter results in NSE composition

σ e :

non-dimensional entropy of electron-per one electron in units of k(9.2)

τ ff :

timescale of free fall (6.2)

τ h (H p ):

timescale of heat transport over unit scale height of pressure (4.4)

τ n :

nuclear timescale for a change in temperature (6.1)

φ:

non-dimensional mass (3.1)

ψ e :

chemical potential of an electron in units of kT (8.1)

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Author notes

  1. Ken'ichi Nomoto

    Present address: NASA, Goddard Space Flight Center, 20771, Greenbelt, MD, USA

Authors and Affiliations

  1. Department of Earth Science and Astronomy, College of General Education, University of Tokyo, Meguro-ku, 153, Tokyo, Japan

    Daiichiro Sugimoto

  2. Department of Physics, Ibaraki University, 310, Mito, Japan

    Ken'ichi Nomoto

Authors
  1. Daiichiro Sugimoto
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  2. Ken'ichi Nomoto
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Sugimoto, D., Nomoto, K. Presupernova models and supernovae. Space Sci Rev 25, 155–227 (1980). https://doi.org/10.1007/BF00212318

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  • DOI: https://doi.org/10.1007/BF00212318

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