Study of the $in ^{34}$Ar($α,p$)$^{37}$K reaction rate via proton scattering on $^{37}$K, and its impact on properties of modeled X-Ray bursts

Abstract

Background: Type I X-Ray bursts (XRBs) are energetic stellar explosions that occur on the surface of a neutron star in an accreting binary system with a low-mass H/He-rich companion. The rate of the $^{34}$Ar($α,p$)$^{37}$K reaction may influence features of the light curve that results from the underlying thermonuclear runaway, as shown in recent XRB stellar modelling studies. Purpose: In order to reduce the uncertainty of the rate of this reaction, properties of resonances in the compound nucleus $^{38}$Ca, such as resonance energies, spins, and particle widths, must be well constrained. Method: This work discusses a study of resonances in the $^{38}$Ca compound nucleus produced in the $^{34}$Ar($α,p$) reaction. The experiment was performed at the National Superconducting Cyclotron Laboratory, with the ReA3 facility by measuring proton scattering using an unstable $^{37}$K beam. The kinematics were designed specifically to identify and characterize resonances in the Gamow energy window for the temperature regime relevant to XRBs. Results: The spins and proton widths of newly identified and previously known states in $^{38}$Ca in the energy region of interest for the $^{34}$Ar($α,p$)$^{37}$K reaction have been constrained through an R-Matrix analysis of the scattering data. Conclusions: Using these constraints, a newly estimated rate is applied to an XRB model built using Modules for Experiments in Stellar Astrophysics (MESA), to examine its impact on observables, including the light curve. It is found that the newly determined reaction rate does not substantially affect the features of the light curve.

Figures (6)

• Figure 1: Schematic design of the experimental setup. The $^{37}$K beam impinges on the polypropylene target, with the lighter product, the protons, emitted at larger angles and entering the silicon telescope. The heavier products and the unreacted beam are forward focused into the ionization chamber (IC). The green wire grids in the IC are printed circuit boards that provide position sensitivity, while signals from the gray grids are combined in sequence in adjustable groups to measure energy loss and total energy of the particles.
• Figure 2: Average differential cross section as a function of excitation energy measured for proton scattering on $^{37}$K in this work. Also pictured is a representative R-matrix fit calculated at the average angle ($\theta_{cm}=36^{\circ}$) from the process described in Sec. \ref{['Analysis']} with the corresponding goodness-of-fit statistic, $\chi^2/N=1.1508$.
• Figure 3: (TOP) The mean astrophysical reaction rate calculated from Monte Carlo sampling is depicted here along with the 68% and 95% quantiles. The REACLIB rate is also shown, as well as the rate calculated in Long et al.long_indirect_2017. (BOTTOM) The ratio of the rates depicted above normalized to REACLIB (i.e. NON-SMOKER). The gray band represents the range of values resulting from the Monte Carlo sampling.
• Figure 4: (TOP) The full series of bursts for the "clocked burster" scenario and accompanying rate variations. (BOTTOM) The luminosity results of each model are averaged and "folded", such that their peaks are aligned. The resulting plot demonstrates that the variation in burst frequency for the folded light curve caused by changes in reaction rate is not significant enough to be detected on visual inspection. However, variations in the magnitude of the luminosity may explain integrated luminosity variations. Numerical values describing these results are available in Table \ref{['tab:model_res']}. Note "factor" refers to the 0.022 factor described in the text.
• Figure 5: (TOP) The full series of bursts for the slow accretion scenario and accompanying rate variations. (BOTTOM) The same set of models "folded" such that they are averaged for a given model and their peaks aligned.