Systematic study of the composition of Type I X-ray burst ashes: Neutron star structure v.s. Reaction rate uncertainties

In this study, we calculate for the first time the impacts of neutron star(NS) structure on the type I X-ray burst ashes using the \texttt{MESA} code. We find an increased mass fraction of the heavier elements with increasing surface gravity (increase mass or decrease radius), resulting in a higher average mass number ($A_{\rm ash}$) of burst ashes (except for higher mass NS due to the competition between the envelope temperature and the recurrence time). The burst strength ($\alpha$) increases as surface gravity increases, which indicates the positive correlation between $A_{\rm ash}$ and $\alpha$ with changes in surface gravity. If the $\alpha$ value is higher, heavier $p$-nuclei should be produced by the type I X-ray burst nucleosynthesis. Besides, the effects of various burst input parameters, e.g. base heating ($Q_{\rm b}$), metallicity ($Z$) and some new reaction rates are calculated for comparison. We find that the heavier nuclei synthesis is inversely correlated to the base heating/metallicity, the smaller the base heating/metallicity, the greater the mass fraction of the heavier elements. The $\alpha$ value decreases as $Q_{\rm b}$ or $Z$ decreases, which also indicates the positive correlation between $A_{\rm ash}$ and $\alpha$ with variation in $Q_{\rm b}$ or $Z$. The new reaction rates from the $(p,\gamma)$ reactions on $^{17}\rm{F}$, $^{19}\rm{F}$, $^{26}\rm{P}$, $^{56}\rm{Cu}$, $^{65}\rm{As}$, and $(\alpha,p)$ reaction on $^{22}\rm{Mg}$ have only minimal effects on burst ashes. In hydrogen-rich X-ray binary systems, nuclei heavier than $^{64}\rm{Ge}$ are fertile produced with larger NS mass, smaller NS radius, smaller base heating and smaller metallicity.