  Nucleosynthetic yield predictions for multi-dimensional simulations of
thermonuclear supernovae generally rely on the tracer particle method to obtain
isotopic information of the ejected material for a given supernova simulation.
We investigate how many tracer particles are required to determine converged
integrated total nucleosynthetic yields. For this purpose, we conduct a
resolution study in the number of tracer particles for different hydrodynamical
explosion models at fixed spatial resolution. We perform hydrodynamic
simulations on a co-expanding Eulerian grid in two dimensions assuming
rotational symmetry for both pure deflagration and delayed detonation Type Ia
supernova explosions. Within a given explosion model, we vary the number of
tracer particles to determine the minimum needed for the method to give a
robust prediction of the integrated yields of the most abundant nuclides. For
the first time, we relax the usual assumption of constant tracer particle mass
and introduce a radially vary- ing distribution of tracer particle masses. We
find that the nucleosynthetic yields of the most abundant species (mass
fraction > 10E-5) are reasonably well predicted for a tracer number as small as
32 per axis and direction - more or less independent of the explosion model. We
conclude that the number of tracer particles that were used in extant published
works appear to have been sufficient as far as integrated yields are concerned
for the most copiously produced nuclides. Additionally we find that a suitably
chosen tracer mass distribution can improve convergence for nuclei produced in
the outer layer of the supernova where the constant tracer mass prescription
suffers from poor spatial resolution.
