## 2. Type I X-ray burst modelAs a type I X-ray burst model for the rp-process, we adopt a plane parallel approximation by Fujimoto et al. (1981). This model is reasonable enough to investigate the nuclear process during the shell flash if we assume that physical quantities are averaged over the accumulated layers, hydrostatic equilibrium is maintained, and the configuration is spherically symmetric. In fact, Hashimoto et al. 1983, and HSH have performed the calculation of the nucleosynthesis under these assumptions. Let us summarize the formulation of the model for the following discussion. A hydrostatic equilibrium equation to determine the structure of the accreting neutron star is written as follows: Here, where is the general relativistic correction factor of Schwarzschild metric. We have = 1.3 and log = 14.4 for a model with and km. The amount of accreted matter can be estimated from to (Fujimoto et al. 1987). Eq. (1) is integrated and reduced to be a constant pressure if we adopt a plane parallel approximation: where cm s The energy equation is written as where where K, The nuclear reaction network has been coupled to the thermodynamical equations through . The rate equations of abundance are written as follows: Here the first and second terms account for the destruction and production, respectively, of the 0-th abundance and expresses the rate of reaction or decay , where denote the species of particles concerned: nucleus, neutron, proton, electron, positron, neutrino, antineutrino, and photon. Once a set of parameters or
is specified, using the initial
values of temperature and abundances, we can get density and other
thermodynamical quantities for the next time step from the equation of
state. Here the total pressure We note that in the calculation of
, we have taken into account the
effects of non-ideal gas as Here, the region is assumed to be radiation dominated around the
peak of the flash. HSH have examined the shell flashes for
and
; During the shell flash, the peak
temperature in units of K ranges from
and the corresponding density ranges
from g cm © European Southern Observatory (ESO) 1999 Online publication: February 22, 1999 |