The double-peaked type I X-ray bursts with different mass accretion rate and fuel composition

Using the MESA code, we have carried out a detailed survey of the available parameter space for the double-peaked type I X-ray bursts. We find that the double-peaked structure appears at mass accretion rate $\dot{M}$ in the range of $\sim(4-8)\times10^{-10}\,M_{\odot}/{\rm yr}$ when metallicity $Z=0.01$, while in the range of $\sim(4-8)\times10^{-9}\,M_{\odot}/\rm{yr}$ when $Z=0.05$. Calculations of the metallicity impact suggest that the double peaks will disappear when $Z\lesssim0.005$ for $\dot{M}=5\times10^{-10}\,M_{\odot}/\rm{yr}$ and $Z\lesssim0.04$ for $\dot{M}=5\times10^{-9}\,M_{\odot}/\rm{yr}$. Besides, the impacts of base heating $Q_{\rm b}$, as well as nuclear reaction waiting points: $^{22}\rm{Mg}$, $^{26}\rm{Si}$, $^{30}\rm{S}$, $^{34}\rm{Ar}$, $^{56}{\rm Ni}$, $^{60}\rm Zn$, $^{64}\rm{Ge}$, $^{68}\rm{Se}$, $^{72}\rm{Kr}$ have been explored. The luminosity of the two peaks decreases as $Q_{\rm b}$ increases. $^{68}{\rm Se}(p,\gamma){^{69}{\rm Br}}$ is the most sensitive reaction, the double peaks disappear assuming that $^{56}{\rm Ni}(p,\gamma)^{57}{\rm Cu}$ and $^{64}{\rm Ge}(p,\gamma)^{65}{\rm As}$ reaction rates have been underestimated by a factor of 100 and the $^{22}{\rm Mg}(\alpha,p)^{25}{\rm Al}$ reaction rate has been overestimated by a factor of 100, which indicates that $^{22}{\rm Mg}$, $^{56}{\rm Ni}$, $^{64}{\rm Ge}$, $^{68}{\rm Se}$ are possibly the most important nuclear waiting points impedance. Comparisons to the double-peaked bursts from 4U 1636-53 and 4U 1730-22 suggest that the nuclear origins of double-peaked type I X-ray bursts are difficult to explain the observed larger peak times ($t_{\rm p,1}\gtrsim4\,{\rm s}$, $t_{\rm p,2}\gtrsim8\,{\rm s}$) and smaller peak ratio($r_{1,2}\lesssim0.5$). The composition of ashes from double-peaked bursts is very different from the single-peaked bursts especially for the heavier p-nuclei.