Mass measurement of ${}^{27}\mathrm{P}$ to constrain type-I x-ray burst models and validate the isobaric multiplet mass equation for the $A=27, T=\frac{3}{2}$ isospin quartet

Background: Light curves are the primary observable of type-I x-ray bursts. Computational x-ray burst models must match simulations to observed light curves. Most of the error in simulated curves comes from uncertainties in $rp$ process reaction rates, which can be reduced via precision mass measurements of neutron-deficient isotopes in the $rp$ process path.

Purpose: Perform a precise atomic mass measurement of ${}^{27}\mathrm{P}$. Use this new measurement to calculate $rp$ process reaction rates and input these rates into an x-ray burst model to reduce simulated light curve uncertainty. Use the mass measurement of ${}^{27}\mathrm{P}$ to validate the isobaric multiplet mass equation (IMME) for the $A=27 T=\frac{3}{2}$ isospin quartet which ${}^{27}\mathrm{P}$ belongs to.

Method: High-precision Penning trap mass spectrometry utilizing the time-of-flight ion cyclotron resonance technique was used to determine the atomic mass of ${}^{27}\mathrm{P}$. The mesa code (Modules for Experiments in Stellar Astrophysics) was then used to simulate x-ray bursts using a one-dimensional multizone model to produce updated light curves.

Results: The mass excess of ${}^{27}\mathrm{P}$ was measured to be $-670.7\left(6\right)$ keV, a 14-fold precision increase over the mass reported in the 2020 Atomic Mass Evaluation (AME2020). The ${}^{26}\mathrm{Si}(p,\gamma ){}^{27}\mathrm{P}-{}^{27}\mathrm{P}(\gamma ,p){}^{26}\mathrm{Si}$ rate equilibrium has been determined to a higher precision based on the precision mass measurement of ${}^{27}\mathrm{P}$. x-ray burst light curves were produced with the mesa code using the new reaction rates. Changes in the mass of ${}^{27}\mathrm{P}$ seem to have minimal effect on light curves, even in burster systems tailored to maximize impact.

Conclusion: The mass of ${}^{27}\mathrm{P}$ does not play a significant role in x-ray burst light curves. It is important to understand that more advanced models do not just provide more precise results, but often qualitatively different ones. This result brings us a step closer to being able to extract stellar parameters from individual x-ray burst observations. In addition, the IMME has been validated for the $A=27,T=3/2$ quartet. The normal quadratic form of the IMME using the latest data yields a reduced ${\chi }^2$ of 2.9. The cubic term required to generate an exact fit to the latest data matches theoretical attempts to predict this term.

Figure 1

A sample 250 ms total excitation time ${}^{27}\mathrm{PO}^{+}$ time-of-flight ion cyclotron Ramsey resonance measurement. The central dip in the interference pattern corresponds to the resonant cyclotron frequency. The red curve is a fit to the theoretical profile [23].

Figure 2

Measured cyclotron frequency ratios $R=\frac{f_{\text{ref}}^{\text{int}}\left({\text{HCNO}}^{+}\right)}{f_{\text{c}}{(}^{27}{\text{PO}}^{+})}$ relative to the average value $\overline{R}=1.000270250\left(16\right)$. The gray bar represents $\pm 1\sigma$ uncertainty in $\overline{R}$ and has been scaled by the Birge ratio [26].

Figure 3

Mass excess of ${}^{27}\mathrm{P}$ as measured by LEBIT (dotted lines) compared with recommended values from AME2012/16 [6, 31] and AME2020 [32] and values measured by Benenson et al. [27], Janiak et al. [28], Fu et al. [29], and Sun et al. [30] as well as the value predicted by an IMME calculation [5].

Figure 4

Photodisintegration rate ${\lambda }_{(\gamma ,p)}$ for the reaction ${}^{27}\mathrm{P}(\gamma ,p){}^{26}\mathrm{Si}$ using the mass of ${}^{27}\mathrm{P}$ from LEBIT (black), AME2016 [6] (orange), and AME2020 [32] (blue), each varied $\pm 3\sigma$ (LEBIT: 1.9 keV, AME2016: 72 keV, AME2020: 27 keV). AME2016 is included to compare to Schatz and Ong's sensitivity study [5]. A zoomed inset is included to clarify the ${\lambda }_{(\gamma ,p)}$ precision improvement due to the LEBIT measurement.

Figure 5

mesa multizone XRB light curve generated using the mass of ${}^{27}\mathrm{P}$ from LEBIT (blue) and AME2016 [6] (orange), each varied $\pm 3\sigma$ (1.9 keV for LEBIT, 72 keV for AME2016). Their overlap is a dull pink. Single-zone model results from [5] (gray) are included to show the qualitative difference in light curve tail shape. Burster is “GS 1826-24”-like, with accretion rate decreased from $2.98\times {10}^{-9}$ to $1.23\times {10}^{-9}{\mathrm{M}}_{\odot }/\mathrm{yr}$ to enhance the impact of ${}^{27}\mathrm{P}$ mass. AME2020 [32] excluded as it would produce a third curve with near-perfect overlap.

Figure 6

Contour plots of the fraction of escape from the ${}^{26}\mathrm{Si}$ waiting point via alpha capture—$(\alpha ,p)/\left(\right(p,\gamma )+(\alpha ,p\left)\right)$—during a type-I XRB. Contours generated using a ${}^{27}\mathrm{P}$ mass value of AME2016 $\pm 3\sigma$ (left: $+3\sigma$, right : $-3\sigma$). This range is fully inclusive of the LEBIT and AME2020 mass values. $T_9$ is the temperature in GK, $\rho {\mathrm{Y}}_p$ is the proton density. Arrows show the temperature-density profile of the single-zone model over the course of an XRB and are identical in each plot. The horizontal line shows the maximum temperature reached ($T\approx 1.1$ GK) in any multizone mesa XRB simulation using a ${}^{27}\mathrm{P}$ mass from AME2016/20, or LEBIT.