Impact of an accurate modeling of primordial chemistry in high
  resolution studies
  The formation of the first stars in the Universe is regulated by a sensitive
interplay of chemistry and cooling with the dynamics of a self-gravitating
system. As the outcome of the collapse and the final stellar masses depend
sensitively on the thermal evolution, it is necessary to accurately model the
thermal evolution in high resolution simulations. As previous investigations
raised doubts regarding the convergence of the temperature at high resolution,
we investigate the role of the numerical method employed to model the chemistry
and the thermodynamics. Here we compare the standard implementation in the
adaptive-mesh refinement code \verb|ENZO|, employing a first order backward
differentiation formula (BDF), with the 5th order accurate BDF solver
\verb|DLSODES|. While the standard implementation in \verb|ENZO| shows a strong
dependence on the employed resolution, the results obtained with \verb|DLSODES|
are considerably more robust, both with respect to the chemistry and
thermodynamics, but also for dynamical quantities such as density, total energy
or the accretion rate. We conclude that an accurate modeling of the chemistry
and thermodynamics is central for primordial star formation.
