TypeIa supernovae

There are strong theoretical and observational indications that SNe Ia are thermonuclear explosions of accreting white dwarfs in binary systems (Hoflich and Khokhlov 1996; Nugent etal. 1997; Nomoto etal. 2000; Livio etal. 2001; Hoflich etal. 2003; Thielemann et al. 2004; Hoflich 2006). The basic idea is simple: a white dwarf in a binary system grows towards the Chandrasekhar mass limit through accretion of material from the companion. The contraction and central carbon ignition cause thermonuclear runaway since the pressure is dominated by a degenerate electron gas and has no temperature dependence. This prevents stable and controlled burning, causing a complete explosive disruption of the white dwarf (Nomoto et al. 1984; Woosley and Weaver 1994). The mass-accretion rate determines the central ignition density in spherically symmetric models. However, the initial white dwarf mass, its C/O ratio, and its metallicity might enter as well (Umeda et al. 1999; Hoflich et al. 2000; Domínguez et al. 2001; Hoflich et al. 2003; Hoflich 2006). In addition, rotation and multi-dimensional effects complicate the situation (e.g. Travaglio et al. 2004b).

The flame front propagates initially at subsonic speed as a deflagration wave due to heat transport across the front (Hillebrandt and Niemeyer 2000; Reinecke et al. 2002; Ropke et al. 2003). The averaged spherical flame speed depends on the development of instabilities of various scales at the flame front. Multi-dimensional hydrodynamic simulations suggest a speed vdef as slow as a few percent of the sound speed vs in the central region of the white dwarf. Electron capture affects the central electron fraction Fe and depends on (i) the electron-capture rates of nuclei, (ii) vdef, influencing the duration of survival of matter at high temperatures (and with it the availability of free protons for electron captures), and (iii) the central density of the white dwarf pign (increasing the electron chemical potential, i.e. the Fermi energy) (Iwamoto etal. 1999; Brachwitz etal. 2000; Langanke and Martinez 2000). After an initial deflagration in the central layers, the deflagration might turn into a detonation (supersonic burning front) at larger radii and lower densities (Khokhlov et al. 1999; Niemeyer 1999). This is debated (Reinecke et al. 2002; Ropke et al. 2003) but leads to a picture that is more consistent with observations (Hoflich 2006). The transition from a deflagration to a detonation (the delayed-detonation model) leads to a change in the ratios of Si-burning sub-categories with varying entropies. It also leaves an imprint on the Fe-group composition.

Explosive-nucleosynthesis calculations in spherical symmetry for slow deflagrations followed by a delayed detonation or a fast deflagration are used to investigate the constraints on the parameters pign, vdef, and the transition density. Variations in the ignition density pign and the initial deflagration velocity vdef affect the Fe-group composition in the central part. The effect of the choice of model on the maximum temperature and density during Si-burning of the central layers, which occurs during the propagation of the burning front, has been discussed extensively (Iwamoto etal. 1999).

The ignition density pign dominates the amount of electron capture and thus Fe in the central layers. The deflagration speed vdef affects the duration of burning in a zone and with it the possible amount of electron captures by free protons and nuclei. It is also responsible for the time delay between the arrival of the information that a burning front is approaching (propagating with the speed of sound and causing an expansion of the outer layers) and the actual arrival of the burning front. Burning

Mass Number a Mass Number a

Mass Number a Mass Number a

Figure 37.2. Abundance ratios in comparison with Solar for a series of central ignition densities of (2-6) x 109 g cm-3 (the models B2C20-60) (Thielemann et al. 2004). While ignition densities in the range (2-3) x 109 g cm-3 lead to Solar relative abundance ratios in the Fe-group, higher ignition densities can explain overabundances of 48Ca, 50Ti, 54Cr, 58Fe, 64Ni, and 66Zn. They should happen occasionally to account for the known abundances of these isotopes.

Mass Number a Mass Number a

Figure 37.2. Abundance ratios in comparison with Solar for a series of central ignition densities of (2-6) x 109 g cm-3 (the models B2C20-60) (Thielemann et al. 2004). While ignition densities in the range (2-3) x 109 g cm-3 lead to Solar relative abundance ratios in the Fe-group, higher ignition densities can explain overabundances of 48Ca, 50Ti, 54Cr, 58Fe, 64Ni, and 66Zn. They should happen occasionally to account for the known abundances of these isotopes.

at lower densities causes less electron capture. Thus, t>def determines the resulting Ye gradient as a function of radius (Iwamoto et al. 1999; Brachwitz et al. 2000).

During the burning the central region undergoes electron captures by free protons and Fe-peak nuclei. Similar central densities with higher temperatures lead (via more-energetic Fermi distributions of electrons and hence larger abundances of free protons) to larger amounts of electron captures and therefore smaller central Ye values.

Most of the central region experiences conditions for complete Si-burning and subsequent normal (or alpha-rich) freeze-out. The main nucleosynthesis products are Fe-group nuclei. The outer part of the central region undergoes incomplete Si-burning (due to lower peak temperatures) and has therefore Ca and other alphaelements as main products. The total nucleosynthesis yields obtained in slow-deflagration models (Figure 37.2) show that the production of Fe-group nuclei is a factor of 2-3 larger than the production of intermediate nuclei from Si to Ca in comparison with their Solar values (Iwamoto et al. 1999; Brachwitz et al. 2000).

There are some Fe-group contributions from alpha-rich freeze-out and layers with incomplete Si-burning that depend on the deflagration-detonation transition. The mass of the region experiencing incomplete Si-burning (indicated by the production of 54Fe) decreases with decreasing transition density. The region experiencing alpha-rich freeze-out (indicated by the production of 58Ni) increases with decreasing transition density. The isotopes 52Fe (decaying to the dominant Cr isotope, 52Cr) and 55 Co (decaying to the only stable Mn isotope, 55 Mn) are typical products of incomplete Si-burning. Production of 59Cu (decaying to the only stable Co isotope, 59Co) is a typical feature of an alpha-rich freeze-out.

Generally speaking, to first order we do not expect these main features to change with galactic evolution or metallicity. The main Fe-group composition is determined by the Fe resulting from electron captures in the explosion. The Fe of the outer layers, which are not affected by electron captures, depends mildly on the initial CNO (i.e. metallicity). However, secondary effects such as (a) the main-sequence mass distribution of the progenitors (determining the C-O core from core He-burning and the C-O layers from burning during the accretion phase), (b) the accretion history within the progenitor binary system, and (c) the central ignition density (determined by the binary accretion history) can implicitly be affected by the metallicity (Hoflich 2006).

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