The Regulated GeAs Cycles with the New $^{63}$Ga(p,$γ$)$^{64}$Ge and $^{64}$Ge(p,$γ$)$^{65}$As Reaction Rates and Their Impact on the GS 1826$-$24 Clocked Bursts and SAX J1808.4$-$3658 Photospheric Radius Expansion Bursts

TL;DR

This work tests the impact of newly determined $^{63}$Ga(p,$\gamma$)$^{64}$Ge and $^{64}$Ge(p,$\gamma$)$^{65}$As rates, derived with nuclear-structure input, on Type I X-ray burst models using self-consistent Kepler 1D multizone hydrodynamics. By comparing baseline REACLIB v2.2 runs with Present$^\mathrm{dag}$ (group (i)) and Present$^\mathrm{ddag}$ (group (ii)) variants for GS 1826$-$24 and SAX J1808.4$-$3658, the study finds that the GS 1826$-$24 clocked bursts are largely insensitive to the updated GeAs-cycle rates when all observables are fitted, while the SAX J1808.4$-$3658 PRE bursts show clear sensitivity, particularly to group (ii) updates. The results emphasize that self-consistent, multi-epoch modeling is essential to draw reliable conclusions about the effect of nuclear uncertainties on burst observables and neutron-star properties, and they highlight the need for direct measurements of reactions like $^{22}$Mg($\alpha$,p)$^{25}$Al at XRB Gamow energies. Overall, the work challenges previous claims of large GS 1826$-$24 sensitivity and confirms stronger PRE-burst sensitivity, guiding future experimental and theoretical efforts toward constraining key reaction rates and stellar parameters.

Abstract

The $^{63}$Ga(p,$γ$)$^{64}$Ge and $^{64}$Ge(p,$γ$)$^{65}$As thermonuclear reactions connect the ZnGa and GeAs cycles by diverting the flow of the rapid proton capture process from $^{63}$Ga to $^{65}$As. Changes in these two reaction rates regulate the ZnGa and GeAs cycles and may affect the modeled properties matching with the observed counterparts of a type I X-ray burster. We implement the latest $^{63}$Ga(p,$γ$)$^{64}$Ge and $^{64}$Ge(p,$γ$)$^{65}$As reaction rates to the state-of-the-art self-consistent one-dimensional multi-zone thermo-hydrodynamic code, KEPLER, to study the influence of these new reaction rates on the models of the GS 1826$-$24 clocked burster and SAX J1808.4$-$3658 photospheric radius expansion burster. Both new reaction rates obtained by Lu et al. [Phys. Rev. C 110, 065804 (2024)] are determined from complementing the experimental input with the nuclear spectroscopic information deduced from the full pf-shell space configuration-interaction shell-model calculations. By constraining the models on reproducing the observed burst peak, light-curve profile, fluence, and recurrence time, we find that the impact of the newly measured proton thresholds and respective proton-capture reactions on the burst light-curve profile of the GS 1826$-$24 clocked burster is, in fact, not as significant as claimed by Zhou et al. [Nat. Phys. 19, 1091 (2023)]. With or without the inclusion of the newly determined reaction rate of the highly influential $^{22}$Mg($α$,p)$^{25}$Al reaction, the impact of the new $^{63}$Ga(p,$γ$)$^{64}$Ge and $^{64}$Ge(p,$γ$)$^{65}$As reaction rates on SAX J1808.4$-$3658 photospheric radius expansion bursts is evident. Our finding indicates that the models reproducing the 2002 October epoch of SAX J1808.4$-$3658 photospheric radius expansion burster is more sensitive to the uncertainties of thermonuclear reaction rates.

Figures (6)

• Figure 1: The breakout of the ZnGa cycles via the $^{63}$Ga(p,$\gamma$)$^{64}$Ge(p,$\gamma$)$^{65}$As reaction. The arrows depicting the reaction flow are scaled to the logarithmic strength of the respective reaction rates at $T\!=\!1$ GK. The ZnGa cycles are displayed as red arrows. Stable nuclei are represented by thick black squares, and the historical $^{60}$Zn and $^{64}$Ge waiting points are shown in red text. Both $^{63}$Ga(p,$\gamma$)$^{64}$Ge and $^{63}$Ga(p,$\alpha$)$^{60}$Zn reactions compete at $^{63}$Ga. The reaction flow mainly diverges out to $^{64}$Ge via $^{63}$Ga(p,$\gamma$)$^{64}$Ge as the $^{63}$Ga(p,$\gamma$)$^{64}$Ge reaction rate is up to 4 orders of magnitude higher than the $^{63}$Ga(p,$\alpha$)$^{60}$Zn reaction rate at temperature $T\!=\!0.5$-$1.6$ GK (top panel of Fig. \ref{['fig:rp_63Ga_64Ge_60Zn_contri']}). Both $^{64}$Ga(p,$\gamma$)$^{65}$Ge and $^{65}$Ga(p,$\gamma$)$^{66}$Ge reactions could be the alternative paths for the reaction flow to reach the weak GeAs cycles. The strengths of these alternative paths are up to a factor of $\sim$13 higher than $^{63}$Ga(p,$\gamma$)$^{64}$Ge at $T\!=\!0.5$-$1.6$ GK (middle and bottom panels of Fig. \ref{['fig:rp_63Ga_64Ge_60Zn_contri']}). These alternative paths depend on the strengths of the $\beta$-decay of $^{64}$Ge and of the forward and reverse $^{64}$Ge(p,$\gamma$)$^{65}$As reactions during the onset of XRBs. See the detailed study of the weak GeAs cycles performed by Lam2022a.
• Figure 2: The comparisons of thermonuclear reaction rates connecting the ZnGa and GeAs cycles based on the available reaction rates compiled in JINA REACLIB v2.2 Cyburt2010. The temperature range, $0.1\!\leq\!T(\mathrm{GK})\!\leq\!2.0$, is in the region of XRB interest. Top panel: $^{63}$Ga(p,$\gamma$)$^{64}$Ge and $^{63}$Ga(p,$\alpha$)$^{60}$Zn. Middle panel: $^{63}$Ga(p,$\gamma$)$^{64}$Ge, $^{64}$Ga(p,$\gamma$)$^{65}$Ge, and $^{65}$Ga(p,$\gamma$)$^{66}$Ge. Bottom panel: $^{64}$Ge(p,$\gamma$)$^{65}$As, $^{65}$Ge(p,$\gamma$)$^{66}$As, and $^{66}$Ge(p,$\gamma$)$^{67}$As.
• Figure 3: The observed and modeled burst light-curve profiles of the GS 1826$-$24 clocked burster (epoch Mar 2007). The observed burst light-curve profile (black dots) is plotted against the respective modeled counterparts. Modeled light-curve profiles from Zhou2023: baseline (dashed gray line) and updated (dashed cyan line). The light-curve profiles of the upper and lower limit of group (i) reaction rates are indiscernible from the respective centroid light curve (Present$^\dag$; blue line). The burst peaks of the upper limit (dashed red line) and lower limit (dash-dotted red line) of group (ii) reaction rates enclose the burst peak of the respective centroid light-curve profile (Present$^\ddag$; solid red line). The burst peak of Present$^\dag$ is merely $\approx\!0.4$ % different from the burst peak of baseline of this work (yellow line).
• Figure 4: The observed and modeled burst recurrence times, fluences, and peaks of the GS 1826$-$24 clocked burster (epoch 2007 March). The observed burst properties (black diamonds) are plotted against the respective modeled counterparts, i.e., the baseline of this work (yellow diamonds), Present$^\dag$ (blue crosses), and Present$^\ddag$ (red dots). The burst fluences and peaks from Zhou2023, baseline (gray squares) and updated (cyan crosses), are calculated in this work.
• Figure 5: The observed and modeled PRE burst light curves of SAX J1808.4$-$3658 (epoch 2002 October). Each observed burst light curve of the epoch (black lines) is plotted against the respective modeled counterparts. The modeled fluxes are transformed from the modeled luminosities using the factor $4\pi d^2\xi_b\!\approx\!0.9\!\times\!10^{45}$ cm$^2$ as previously implemented Hu2021. Left column: modeled light curves are constructed from the J01 PRE model using the centroid, upper, and lower limits of the reaction rates of group (i). Middle column: modeled light curves yielded from the J01 PRE model using the centroid, upper, and lower limits of the reaction rates of group (ii). Right column: modeled light curves generated from the restored PRE burst model Hu2021 using the centroid, upper, and lower limits of the reaction rates of group (ii). See text.