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Nucleosynthesis in thermonuclear supernovae with tracers: convergence and variable mass particles

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.