Simulated light curves for the outbursts I (left panel) and II (right panel) of MXB 1659−29 versus observations. The light curves have been computed using the BSk24 EoS model for a neutron star with M = 1.65 M_⊙ with a partially accreted envelope under different assumptions on the envelope and crust composition. The envelope is composed either of carbon (curves 1, 2) or of helium (curves 3–5). The accreted crust is modeled according to F+18 and is assumed to extend down to ρ_acc = 10¹³ g cm⁻³. Beyond this density, the non-accreted crust is either in a ground-state (curves 1, 3) or in a frozen equilibrium state (curves 2, 4, 5). The accreted crust is either pure (curves 1–4) or not (curve 5). The errorbars show the spectral fitting results from Parikh et al. (2019) (at the 90% confidence), except for the two bars at t = 10.8 yr in the left-panel inset, which represent two alternative fits from Cackett et al. (2013). In the numerical simulations, the long-term mean accretion rate is adjusted to the equilibrium value within uncertainties and the shallow heating is adjusted so as to reproduce the first observation in quiescence after outburst I, within the uncertainties. The parameters of the simulations are listed in Table 1 (see the text for details).