  It is widely accepted that the onset of the explosive carbon burning in the
core of a CO WD triggers the ignition of a SN Ia. The features of the ignition
are among the few free parameters of the SN Ia explosion theory. We explore the
role for the ignition process of two different issues: firstly, the ignition is
studied in WD models coming from different accretion histories. Secondly, we
estimate how a different reaction rate for C-burning can affect the ignition.
Two-dimensional hydrodynamical simulations of temperature perturbations in the
WD core ("bubbles") are performed with the FLASH code. In order to evaluate the
impact of the C-burning reaction rate on the WD model, the evolution code
FLASH_THE_TORTOISE from Lesaffre et al. (2006) is used. In different WD models
a key role is played by the different gravitational acceleration in the
progenitor's core. As a consequence, the ignition is disfavored at a large
distance from the WD center in models with a larger central density, resulting
from the evolution of initially more massive progenitors. Changes in the C
reaction rate at T < 5e8 K slightly influence the ignition density in the WD
core, while the ignition temperature is almost unaffected. Recent measurements
of new resonances in the C-burning reaction rate (Spillane et al. 2007) do not
affect the core conditions of the WD significantly. This simple analysis,
performed on the features of the temperature perturbations in the WD core,
should be extended in the framework of the state-of-the-art numerical tools for
studying the turbulent convection and ignition in the WD core. Future
measurements of the C-burning reactions cross section at low energy, though
certainly useful, are not expected to affect dramatically our current
understanding of the ignition process.
