... below

According to Imshennik & Khokhlov (1984), at densities lower than about $10^7~\ensuremath{{\rm g}~{\rm cm}^{-3}}$ the timescale for NSE formation becomes so large that the flame width would be bigger than the extent of the whole core. Since it can be assumed that NSE is no longer reached even before the flame width gets close to the extension of the core, 3 $\times$ $10^7~\ensuremath{{\rm g}~{\rm cm}^{-3}}$ instead of $10^7~\ensuremath{{\rm g}~{\rm cm}^{-3}}$ is used as the transition density.

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... e.g.

Here and in the following indices 1 and 2 refer to quantities on the unburnt and the burnt side of the front, respectively.

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... products

Correctly, one would have to use burning and flow velocities on either the burnt or the unburnt side of the flame to update G due to burning and advection.

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...

We neglect here that over-driven detonations powered by shock waves entering the core due to the He shell detonation could also play a role.

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... linear

With respect to inner mass.

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... mass

In Table 1 only the results for a mixture of equal mass fractions of C and O are shown. In their work Niemeyer & Woosley (1997) additionally investigated the dependence on the mass fraction.

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... model "B''

Geometrical amplification effects do not play a role at such big radii.

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...##)

For an ultra-relativistic degenerate gas like in a WD's center $\gamma = \frac{4}{3}$ holds in good approximation and thus $\left(\frac{\gamma + 1}{\gamma - 1}\right)^3 = 7^3 = 343$.

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... resolution

Note that in this case the minimum detonator volume may be the limiting constraint.

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