Presupernova models and supernovae

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.Appendix: Notations 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 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) - _def 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) - ratio of the mixing length to the scale height of pressure (l/H _p ) - ratio of gas pressure to the total pressure - ratio of the specific heats - gD locus of singularity in U-V plane (2.5) - M(H _p ) mass contained within unit scale height of pressure (4.4) - _ec energy rate by electron captures (9.5) - _n nuclear energy generation rate by the nuclear fuel specified by n - _v neutrino loss rate - L _v ^(D) neutrino loss rate excluding the neutrinos from the electron captures (9.4) - non-dimensional density (3.1) - P/, not the non-dimensional temperature (2.7) - _W Weinberg's angle (5.8) - opacity - _v neutrino opacity (11.2) - describes the effect of electron degeneracy in equation of state (2.19) - _ec rate of electron capture - mean molecular weight - _e mean molecular weight of electrons - _e chemical potential of an electron excluding the rest mass (8.1) - _i mean molecular weight of ions - non-dimensional radius (3.1) - non-dimensional pressure (3.1) - matter density - _cr ^GR critical density above which the general relativistic instability sets in - _cr critical density for reimplosion of the core by beta processes (Section 5) - _ign density at the ignition - _nse density above which the deflagrated matter results in NSE composition - _e non-dimensional entropy of electron-per one electron in units of k(9.2) - _ff timescale of free fall (6.2) - _h (H _p ) timescale of heat transport over unit scale height of pressure (4.4) - _n nuclear timescale for a change in temperature (6.1) - non-dimensional mass (3.1) - _e chemical potential of an electron in units of kT (8.1)     

Cooling of neutron stars and X-ray observations

Cooling of neutron stars is calculated using an exact stellar evolution code. The full general relativistic version of the stellar structure equations are solved, with the best physical input currently available. For neutron stars with a stiff equation of state, we find that the deviation from the isothermality in the interior is significant and that it takes at least a few thousand years to reach the isothermal state. By comparing the most recent theoretical and observational results, we conclude that for Cas A, SN1006, and probably Tycho, standard cooling is inconsistent with the results from the Einstein Observatory, if neutron stars are assumed to be present in these objects. On the other hand, the detection points for RCW103 and the Crab are consistent with these theoretical results.On leave from Department of Physics, Ibaraki University, Japan     

White dwarf models for type I supernovae and quiet supernovae,and presupernova evolution

Supernova mechanisms in accreting white dwarfs (WDs) are presented, i.e., the carbon deflagration as a plausible mechanism for producing Type I supernovae and electron captures to form quiet supernovae leaving neutron stars. These outcomes depend on accretion rate of helium, initial mass and composition of the WD. The various types of hydrogen shell-burning in the presupernova stage are also discussed.on leave from Department of Physics, Ibaraki University, Japan.     

Single Degenerate Models for Type Ia Supernovae: Progenitor’s Evolution and Nucleosynthesis Yields

We review how the single degenerate models for Type Ia supernovae (SNe Ia) works. In the binary star system of a white dwarf (WD) and its non-degenerate companion star, the WD accretes either hydrogen-rich matter or helium and undergoes hydrogen and helium shell-burning. We summarize how the stability and non-linear behavior of such shell-burning depend on the accretion rate and the WD mass and how the WD blows strong wind. We identify the following evolutionary routes for the accreting WD to trigger a thermonuclear explosion. Typically, the accretion rate is quite high in the early stage and gradually decreases as a result of mass transfer. With decreasing rate, the WD evolves as follows: (1) At a rapid accretion phase, the WD increase its mass by stable H burning and blows a strong wind to keep its moderate radius. The wind is strong enough to strip a part of the companion star’s envelope to control the accretion rate and forms circumstellar matter (CSM). If the WD explodes within CSM, it is observed as an “SN Ia-CSM”. (X-rays emitted by the WD are absorbed by CSM.) (2) If the WD continues to accrete at a lower rate, the wind stops and an SN Ia is triggered under steady-stable H shell-burning, which is observed as a super-soft X-ray source: “SN Ia-SSXS”. (3) If the accretion continues at a still lower rate, H shell-burning becomes unstable and many flashes recur. The WD undergoes recurrent nova (RN) whose mass ejection is smaller than the accreted matter. Then the WD evolves to an “SN Ia-RN”. (4) If the companion is a He star (or a He WD), the accretion of He can trigger He and C double detonations at the sub-Chandrasekhar mass or the WD grows to the Chandrasekhar mass while producing a He-wind: “SN Ia-He CSM”. (5) If the accreting WD rotates quite rapidly, the WD mass can exceed the Chandrasekhar mass of the spherical WD, which delays the trigger of an SN Ia. After angular momentum is lost from the WD, the (super-Chandra) WD contracts to become a delayed SN Ia. The companion star has become a He WD and CSM has disappeared: “SN Ia-He WD”. We update nucleosynthesis yields of the carbon deflagration model W7, delayed detonation model WDD2, and the sub-Chandrasekhar mass model to provide some constraints on the yields (such as Mn) from the comparison with the observations. We note the important metallicity effects on ⁵⁸Ni and ⁵⁵Mn.