tokens: final abundances at some specific values of A that differ by up to two orders of magnitude from the other networks. This shows the importance of using detailed balance to compute inverse rates. We again see good agreement in Figure 9 between the three networks in the proton and helium abundance evolution (left panel of Figure 9 ). But there are a handful of mass numbers at which SkyNet with detailed balance produces final abundances that deviate from the other networks by up to two orders of magnitude (right panel of Figure 9 ). This indicates that it is vital to compute the inverse reaction rates correctly with detailed balance in this scenario. However, the average fractional abundance errors shown in Table 1 are still at the few percent level, and the differences between SkyNet and WinNet or XNet are comparable to the differences between WinNet and XNet. We note that the errors between SkyNet without detailed balance and WinNet or XNet are smaller if screening is turned off. This indicates that screening is somewhat important in this case and we expect the discrepancy between the different codes to increase if screening is turned on due to the different screening implementations. The effect is especially noticeable when comparing SkyNet to XNet with self-heating turned on, because in this case XNet uses the temperature computed from SkyNet, but if screening is switched off, the error between the two codes decreases from 1.1% to 0.086%. SkyNet’s screening implementation is presented in Section 4 . WinNet uses a single fit of the two-body screening factor by Chugunov et al. ( 2007 ) across all screening regimes. XNet computes the two-body screening function provided by Graboske et al. ( 1973 ) for weak and intermediate screening and the one provided by Dewitt Slattery ( 1999 ) for strong screening. XNet then uses a selection rule to select one of the three screening regimes without interpolating between them. 6.2.3. Hydrostatic Carbon–Oxygen Burning In order to compare the self-heating methods implemented in the three networks, we perform a hydrostatic burn at constant density. We keep fixed and start with T = 3 GK and the initial composition consists of half and half (by mass). As a baseline comparison, we also perform non-self-heating runs, where we keep the temperature fixed at 3 GK. The increase in the errors between the networks with self-heating enabled compared to with it disabled must then be due to the difference in the self-heating implementations in the codes. We use a mid-size network containing all nuclides from the full network (Section 6.2.1 ) with . This results in a network with 1530 species and 20,000 reactions. Figure 10 shows the results of this test case with self-heating and screening turned on. We find good qualitative agreement between the three networks, but quantitatively, the differences between XNet and the other two codes are much larger than in the previous test cases. These discrepancies come from the different
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