Comparative roles of $pp$ chain reactions as a trigger for suprathermal processes in the solar core

Continuing the study of suprathermal effects in the solar core [Phys. Rev. C 91, 028801 (2015); J. Phys. G 44, 045202 (2017)], we examine the roles of different $pp$ chain processes generating fast $\alpha$ particles as trigger for suprathermal $\mathrm{B}(\alpha ,p)\mathrm{A}$ reactions neglected in standard solar model simulations. The suprathermal impact on the balance of the $p{+}^{17}\mathrm{O}\rightleftarrows \alpha {+}^{14}\mathrm{N}$ reactions involved in the solar CNO cycle is determined. It is obtained that MeV $\alpha$ particles born in the ${}^7\mathrm{Li}(p,\alpha )\alpha$ and ${}^3\mathrm{He}{(}^3\mathrm{He},2p)\alpha$ reactions are the main agents that are able to crucially change the reaction balance through an appreciable enhancement of the reverse $(\alpha ,p)$ reaction. The comparative role of the $p{+}^7\mathrm{Li}$ and ${}^3\mathrm{He}{+}^3\mathrm{He}\alpha$ particles is clarified. It is found that the former particles control the reverse ${}^{14}\mathrm{N}{(\alpha ,p)}^{17}\mathrm{O}$ reaction in the inner core, while the latter ones play a dominant role in the outer core, additionally increasing the $(\alpha ,p)$ reaction rate by several times and providing favorable conditions for synthesis of some elements. In particular, we show that the total suprathermal enhancement of ${}^{17}\mathrm{O}$ and ${}^{18}\mathrm{O}$ mass fractions in the outer core can reach $\sim 80$ or 50, depending on a model for $\alpha$-particle energy loss used in the simulation. In this context, we note that the $p{+}^7\mathrm{Li}\alpha$ particles alone provide the mass fraction enhancement by a factor of 20 or less.

Figure 1

The three principal branches of the solar $pp$ chain.

Figure 2

The emission rates of fast $\alpha$ particles in the $pp$ chain processes. An explanation for the ${}^3\mathrm{He}{+}^3\mathrm{He}$ rate denoted by open squares is given in Sec. 3.

Figure 3

The solar CNO cycle. Shown are the three branches I, II, and III.

Figure 4

The ratio $\delta$ of the energy loss rate ${(d{E}_{\alpha }/dt)}_{\text{Coul}}$ predicted by the SKUP77 model to that obtained for the KAM86 model. Three different regions of the solar core are shown: the inner core ($R={10}^{-3}{R}_{\odot }$), the middle core ($R=0.1R_{\odot }$), and the outer core ($R=0.2R_{\odot }$).

Figure 5

The probability of the in-flight ${}^{14}\mathrm{N}{(\alpha ,p)}^{17}\mathrm{O}$ reaction in the solar core induced by fast $\alpha$ particles from different $pp$ chain processes. The solid and dashed curves show the results found for the KAM86 and SKUP77 models for the $\alpha$-particle energy loss, respectively.

Figure 6

The solid curve and the curves marked with symbols present the suprathermal ${}^{14}\mathrm{N}{(\alpha ,p)}^{17}\mathrm{O}$ rate in the solar core. Shown are the total as well as partial rates provided by fast $\alpha$ particles from the different $pp$ chain processes. The KAM86 model for the $\alpha$-particle energy loss rate was used in the calculations.

Figure 7

The contribution of the $p{+}^7\mathrm{Li}$ and ${}^3\mathrm{He}{+}^3\mathrm{He}\alpha$ particles to the suprathermal ${}^{14}\mathrm{N}{(\alpha ,p)}^{17}\mathrm{O}$ rate obtained for the KAM86 model. Shown are the ratios of the partial rates provided by these $\alpha$ particles to the total rate $R_{{\alpha }^{14}\mathrm{N},\text{sprth}}$.

Figure 8

A comparison of the forward ${}^{17}\mathrm{O}{(p,\alpha )}^{14}\mathrm{N}$ and reverse ${}^{14}\mathrm{N}{(\alpha ,p)}^{17}\mathrm{O}$ reaction rates in the solar core. The partial reverse rate shown here is provided by the $p{+}^7\mathrm{Li}\alpha$ particles.

Figure 9

The mass fraction enhancement $\delta X=X^{\prime }/X$ for ${}^{17}\mathrm{O}$ and ${}^{18}\mathrm{O}$ isotopes caused by the suprathermal ${}^{14}\mathrm{N}{(\alpha ,p)}^{17}\mathrm{O}$ reaction. The KAM86 and SKUP77 models for the $\alpha$-particle energy loss rate were used in the calculations.