tokens: higher post-outburst luminosities lead to shorter durations (∼hours to days) when DNB contributes significantly to the total luminosity and surface temperature. The total amount of energy available from burning hydrogen is set by the initial hydrogen column, and corresponds to the integral of the elevated luminosity cooling curves, which is constant in all cases with the same initial hydrogen column. For the initial hydrogen column of y H ∼ 1.2 × 10 6 g cm −2 , the total amount of energy that is released from hydrogen burning is 10 38 erg (i.e. ∼7 MeV nucleon −1 ). Without residual accretion or a large helium buffer that may slow down the depletion of hydrogen, the times when DNB significantly increases the observed surface temperature for an H–C envelope are ∼0.1–80 d from the end of the accretion outburst, depending on the initial hydrogen column and cooling luminosity. For larger initial cooling luminosities (and thus higher surface temperatures), the initial change in surface temperatures increases, while the relevant duration decreases, as the available hydrogen is consumed more rapidly. 4.2 Effect on cooling curves due to changing composition In addition to releasing energy through nuclear reactions, DNB can alter the observed cooling after accretion outbursts by altering the light element column in the envelope over time. In Section 2.1 , we show the effect on the T s – T b temperature relations for varying hydrogen column sizes in H–C envelopes (see Fig. 1 ). The decreasing hydrogen column due to DNB will only affect the cooling curve when the hydrogen column is varied in the transition region (as shown in Fig. 2 ). At the relevant temperatures for NSs in quiescence (with initial post-outburst surface temperatures T s > 8 × 10 5 K), this means that the same boundary temperature (at the bottom of the envelope) corresponds to different surface temperatures when the hydrogen column varies in the range 10 4 ≲ y H ≲ 10 7 g cm −2 . When the initial hydrogen column after the accretion outburst is smaller than y H ∼ 10 4 g cm −2 , a further decreasing hydrogen column will not affect the cooling curve. When the initial hydrogen column is larger than y H ∼ 10 4 g cm −2 , the cooling curve transitions from relatively hydrogen-rich envelope temperature relations towards those for a hydrogen-poor envelope. We show this effect in Fig. 8 , where we ignore the effect of heat released by DNB and only show the effect of a changing envelope composition. The dashed cooling curves in Fig. 8 correspond to fixed hydrogen columns, while the solid cooling curves correspond to the scenario where the hydrogen column decreases over time due to DNB. When DNB is taken into account, all the plotted cooling curves (irrespective of initial column density) correspond to that of a hydrogen-poor envelope after ∼50 d. Note that for larger post-outburst luminosities, it can take less time (∼1 d) to decrease the hydrogen column below y H ∼ 10 4 g cm −2 (see e.g. the
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