S-curves during a TI-induced accretion event for the MREF model with (panel a) and without (panel b) the effect of irradiation heating, calculated at the respective radii at which the reflares are ignited. These radii are 0.091 AU and 0.087 AU for panel a and panel b, respectively. The data points with red, yellow, green, blue and pink colours were taken during the first, second, third, fourth and fifth reflare, respectively. With irradiation heating, the later reflares are ignited at smaller surface densities than the first three. The different critical surface density values are marked with ${\mathrm{\Sigma }}_{\text{crit,1}}^{\max },{\mathrm{\Sigma }}_{\text{crit,2\hspace{0.17em}}}^{\max }$ and ${\mathrm{\Sigma }}_{\text{crit,3\hspace{0.17em}}}^{\max }$. In the case without irradiation heating, all reflares are ignited at the same critical surface density value.