Discovery of an Exceptionally Strong $\beta$-Decay Transition of $^{20}$F and Implications for the Fate of Intermediate-Mass Stars

TL;DR

This study measures an exceptionally strong beta-decay transition in $^{20}$F, significantly impacting models of stellar evolution and supernova mechanisms in intermediate-mass stars by clarifying nuclear reaction rates.

Contribution

It provides the first measurement of the transition strength, resolving a key nuclear physics uncertainty in stellar core evolution models.

Findings

The transition strength is exceptionally large.

Electron capture rate is increased by several orders of magnitude.

Implications favor thermonuclear explosion over collapse in certain stars.

Abstract

A significant fraction of stars between 7-11 solar masses are thought to become supernovae, but the explosion mechanism is unclear. The answer depends critically on the rate of electron capture on $^{20}$Ne in the degenerate oxygen-neon stellar core. However, due to the unknown strength of the transition between the ground states of $^{20}$Ne and $^{20}$F, it has not previously been possible to fully constrain the rate. By measuring the transition, we have established that its strength is exceptionally large and enhances the capture rate by several orders of magnitude. This has a decisive impact on the evolution of the core, increasing the likelihood that the star is (partially) disrupted by a thermonuclear explosion rather than collapsing to form a neutron star. Importantly, our measurement resolves the last remaining nuclear physics uncertainty in the final evolution of degenerate oxygen-neon stellar cores, allowing future studies to address the critical role of convection, which at present is poorly understood.

Full text

Stars of 7–11 solar masses (M*⊙*) are prevalent in the Galaxy, their birth and death rate comparable to that of all heavier stars combined doherty2017 . Yet, the ultimate fate of such “intermediate-mass stars” remains uncertain. According to current models poelarends2008 ; jones2013 ; takahashi2013 , a significant fraction explode, but the mechanism is a matter of ongoing debate isern1991 ; canal1992 ; gutierrez1996 ; jones2016 . The answer—gravitational collapse or thermonuclear explosion—depends critically on the rate of electron capture on 20Ne in the stellar core. However, due to the unknown strength of the transition between the ground states of 20Ne and 20F, it has not previously been possible to constrain this rate in the relevant temperature-density regime pinedo2014 . Here, we report the first measurement of this transition, provide the first accurate determination of the capture rate and explore the astrophysical implications.

Intermediate-mass stars that undergo central carbon burning become super-AGB stars doherty2017 with a degenerate oxygen-neon (ONe) core consisting mainly of 16O and 20Ne and smaller amounts of 23Na and 24,25Mg. We are interested in the scenario where the ONe core is able to increase its mass gradually and approach the Chandrasekhar limit, $M_{\mathrm{Ch}}\sim 1.37$ M⊙. This can occur if nuclear burning continues long enough outside the core or if the core, having lost its outer layers, becoming a white dwarf (WD), is able to accrete material from a binary companion star. As the core approaches $M_{\mathrm{Ch}}$, it contracts and warms up, but only gradually as the heating from compression is balanced by cooling via the emission of thermal neutrinos. The density, on the other hand, rises rapidly eventually triggering a number of electron-capture processes that greatly influence the temperature evolution of the core. First, the core is cooled by cycles of electron capture followed by $\beta$ decay on the odd-mass nuclei 25Mg and 23Na schwab2017 . At higher densities, the core is cooled by another such cycle on 25Na, and heated by double electron captures on the even-mass nuclei 24Mg and 20Ne, which produce substantial energy in the second capture. Electron capture on 24Mg occurs first at lower densities due to its smaller $Q$-value, but 24Mg is depleted before the temperature can reach the threshold for oxygen ignition ($T\sim 10^{9}$ K). Instead, oxygen is ignited by electron capture on 20Ne at somewhat higher densities. Previous studies miyaji1980 ; nomoto1982 ; nomoto1984 ; isern1991 ; canal1992 ; gutierrez1996 ; schwab2015 ; schwab2017 have considered that electron capture on 20Ne at such conditions proceeds mainly by the allowed transition from the ground state in 20Ne to the first $1^{+}$ state in 20F, which requires a central density of the stellar core of $\rho_{9,\mathrm{c}}\approx 9.8$ ($\rho_{9}\equiv\rho/{10^{9}}$ g cm*-3*), but it was recently argued pinedo2014 that electron capture on 20Ne can start at much lower densities of $\rho_{9,\mathrm{c}}\approx 6.8$ via the second-forbidden, non-unique, $0^{+}\rightarrow 2^{+}$ transition connecting the ground states of 20Ne and 20F. However, due to the transition’s unknown strength it was not possible to determine its impact schwab2015 . The onset of electron capture on 20Ne heats the central region producing a large temperature gradient, which by itself would drive convection but is counteracted by the composition gradient, which has a stabilizing effect. Stellar models are therefore sensitive to the treatment of convection isern1991 ; canal1992 ; hashimoto2013 ; tominaga2013 ; schwab2015 and electron screening gutierrez1996 ; schwab2015 , predicting central oxygen ignition densities in the range $\rho_{9,\mathrm{c}}^{\mathrm{ign}}\approx 8.9$–15.8.

The fate of the star—gravitational collapse or thermonuclear explosion—is sensitive to the competition between electron capture and nuclear energy generation. If the ignition of oxygen occurs below some critical central density $\rho_{\mathrm{c}}^{\mathrm{crit}}$, oxygen burning releases sufficient energy to reverse the collapse and completely or partially disrupt the star in a thermonuclear explosion jones2016 . If it occurs above $\rho_{\mathrm{c}}^{\mathrm{crit}}$, the deleptonization behind the burning front is so rapid that the loss in pressure cannot be recovered by nuclear burning. Therefore, the collapse continues to nuclear densities, resulting in the birth of a neutron star and the ejection of the stellar envelope kitaura2006 ; janka2008 . Stability analyses based on spherically symmetric simulations predict $\rho_{9,\mathrm{c}}^{\mathrm{crit}}=8.9$ times92 though such one-dimensional simulations are able to produce thermonuclear explosions at $\rho_{\mathrm{9,c}}\approx 10$ if the flame propagates fast enough NomoKondo91 . In fact, multi-dimensional simulations are necessary to model the flame propagation as the efficiency of the thermonuclear combustion is set by non-linear instabilities and turbulence that govern the flame propagation speed. Implementing such effects in numerical schemes is very challenging. 2D simulations predict $\rho_{9,\mathrm{c}}^{\mathrm{crit}}=7.9$–8.9 leung2019 while 3D simulations still produce thermonuclear explosions at these densities jones2016 . Due to the non-linear nature of the physical processes involved, the outcome should be highly sensitive to the initial conditions. From simulations of thermonuclear supernovae in carbon-oxygen WDs fink2013 , we expect that the geometry and the location of the ignition region have a significant impact on the evolution of the flame morphology. Indeed, 2D simulations just above the critical density no longer predict collapse if oxygen is ignited off center leung2019 .

This illustrates that precise knowledge of the ignition conditions is critical for determining the fate of these intermediate-mass stars. Therefore, the strength of the second-forbidden transition connecting the ground states of 20Ne and 20F was determined through the measurement of the transition’s branching ratio in the $\beta$ decay of 20F. Here we briefly summarize the main aspects of the measurement; details are given in an accompanying paper kirsebom2019_prc . The measurement was performed at the JYFL Accelerator Laboratory in Jyväskylä, Finland, using a low-energy radioactive 20F beam from the IGISOL-4 facility arje1985 ; moore2013 . Singly-charged 20F+ ions were produced by bombarding a BaF2 target with 6-MeV deuterons. The ions were accelerated to 30 keV, separated according to their mass-to-charge ratio, and guided to the experimental station where they were implanted in a thin carbon foil. The detection system consisted of a Siegbahn-Slätis type intermediate-image magnetic electron transporter julin1988 combined with a segmented plastic-scintillator detector. The magnetic transporter served to focus the high-energy electrons from the forbidden ground-state transition into the detector, while suppressing the intense flux of $\gamma$-rays and lower-energy electrons due to the allowed transition to the first-excited state in 20Ne, and hence eliminating $\beta\gamma$ summing and $\beta\beta$ pile-up as sources of background. Meanwhile, the segmentation of the detector allowed for highly efficient rejection (99.72%) of the cosmic-ray background, while a baffle was used to prevent positrons from reaching the detector. Finally, a LaBr3(Ce) detector was used to measure the 1.63-MeV $\gamma$ ray associated with the allowed transition, ensuring overall normalisation of the measurement.

The allowed $\beta$ spectra of 20F and 12B and monoenergetic conversion electrons from a 207Bi source were used to characterize the acceptance window of the magnetic transporter and the response of the plastic-scintillator detector for electron energies up to 8.0 MeV. This permitted the detection efficiency of the forbidden transition to be determined directly from experimental data with a precision of 16%. The response was further modelled with a GEANT4 simulation geant2003 ; geant2016 and good agreement was achieved between measured and simulated energy distributions. For the measurement of the forbidden transition, data were collected for 105 hours with the magnet tuned to focus electrons with energies of $\sim 6$–7 MeV and background data were collected for 183 hours without beam, but with the magnet still on. The $\beta$ spectra obtained in these long measurements are displayed in Fig. 1. The forbidden transition (end-point energy of 7.025 MeV) gives rise to the excess counts between 5.6–6.8 MeV, while the five orders of magnitude more intense allowed transition to the first-excited state in 20Ne (end-point energy of 5.391 MeV) dominates at lower energies.

The statistically significant detection of a signal was established through a maximum likelihood fit in which the shapes of the allowed and forbidden transitions were obtained from the GEANT4 simulation, while the shape of the cosmic-ray background was parameterized by an exponential function with two free parameters. Including the forbidden transition in the fit model, we obtained a satisfactory fit quality ($p$-value of 0.080) and constrained the magnitude of the signal with a statistical uncertainty of 19%. In contrast, fitting without the forbidden transition gives an unsatisfactory fit quality ($p$-value of 0.0003). Correcting for the $\beta$ detection efficiency, normalizing to the total number of decays inferred from the 1.63 MeV $\gamma$-ray yield, and adopting the shape factor predicted by our shell-model calculation (see below), we determine the branching ratio to be $0.41(11)\times 10^{-5}$, where systematical and statistical uncertainties have been added in quadrature. Using the known half-life for 20F of 11.0062(80) s burdette2019 , we determine the transition strength to be $\log ft=10.89(11)$. Thus, the transition is three orders of magnitude stronger than the only other known second-forbidden, non-unique transition for a nucleus with a similar mass (${}^{36}\mathrm{Cl}\rightarrow{}^{36}\mathrm{Ar}$, $\log ft=13.321(3)$ kriss2004 ) and, in fact, one of the strongest of its kind singh1998 .

The electron-capture rate on 20Ne is shown in Fig. 2 for a temperature of $T=0.4$ GK. Including the forbidden transition, the electron capture rate increases by up to eight orders of magnitude in the important density range $\rho_{9}\simeq 4.5$–9.5 ($\log_{10}[\rho Y_{e}(\mathrm{g}\;\mathrm{cm}^{-3})]\simeq 9.35$–9.68). As a result, it competes with the timescale of core contraction and affects the evolution of the core. We note that if the strength of the forbidden transition had been similar to what is observed for 36Cl, the electron-capture rate would “only” have been enhanced by five orders of magnitude. It would then have remained below the contraction rate, and the forbidden transition would not have been able to affect the evolution of the stellar core.

The electron-capture rate and $\beta$-decay rates were calculated following the approach of Ref. pinedo2014 . For forbidden transitions, the constant matrix element is replaced by an energy dependent shape factor Behrens and Bühring (1982) that is a function of the matrix elements between the initial and final nuclear states. The exact relationship depends on the type of transition. We use the formalism of Refs. Behrens and Bühring (1971, 1982) for $\beta^{-}$ and electron capture. The matrix elements are determined from shell-model calculations performed in the $sd$ shell with the USDB interaction brown2006 using harmonic oscillator single-particle wave functions and constrained by the known strength of the analog E2 transition in 20Ne together with the conserved vector current theory. Moreover, we use the bare value of the axial coupling constant since previous calculations of unique second-forbidden transitions have not found evidence of quenching of the axial coupling constant Warburton (1992); Martínez-Pinedo and Vogel (1998). Our calculations reproduce the observed half-life of the second-forbidden transition to within better than 10%. The matrix elements, rescaled to the observed half-life, are then used for the evaluation of the electron-capture rate taking into account the appropriate kinematics. In this way, we are able to constrain the electron-capture rate to within 25% at the relevant density and temperature conditions taking into account also the uncertainty on the theoretical shape factor kirsebom2019_prc .

To quantify the impact of the forbidden transition, we simulate the final evolution of an accreting ONe core using the stellar evolution code MESA paxton2018 following the procedure of Refs. schwab2015 ; schwab2017 where matter is accreted onto the core at a constant rate, $\dot{M}$. We consider the cases $\dot{M}_{-6}=0.1$, 1.0 and 10 ($\dot{M}_{-6}\equiv\dot{M}/10^{-6}\;$M${}_{\odot}\;$yr*-1*) representative of thermally stable hydrogen burning $(\dot{M}_{-6}\approx 0.4\textrm{--}0.7)$ wolf2013 and helium burning $(\dot{M}_{-6}\approx 1.5\textrm{--}4.5)$ brooks2016 . We find that the inclusion of the forbidden transition allows the electron captures on 20Ne to proceed at lower densities (see Supplemental Material). However, since the forbidden transition is more than five orders of magnitude weaker than a typical allowed transition, the captures do not produce a thermal runaway, as would be the case for an allowed transition, but rather a gradual heating of the core. As a result, the star develops an isothermal core with a radius of 10–60 km and for the $\dot{M}_{-6}=0.1$ and $1.0$ cases, this phase lasts long enough that most 20Ne within the isothermal core is converted to 20O by double electron capture. Hence, further heating occurs in the outer regions of the core triggering an off-center ignition of oxygen. For the $\dot{M}_{-6}=10$ case, the ignition occurs in a central region with $10$ km radius. Fig. 3 summarizes the results of our simulations. For all cases considered, the contribution of the forbidden transition leads to earlier heating resulting in oxygen ignition at lower densities. Changes in the chemical composition, in particular the initial amount of 24Mg and 25Mg, affect the evolution somewhat, but do not alter the picture qualitatively, unless the 24Mg fraction is made very large schwab2015 .

Determining the final outcome after oxygen ignition—gravitational collapse or thermonuclear explosion—requires multi-dimensional hydrodynamical simulations. We have performed four high-resolution 3D hydrodynamical simulations using the LEAFS code reinecke2002 ; jones2016 with different assumptions for the initial density and flame geometry motivated by the results of the MESA stellar evolution simulations. We also calculate the nucleosynthesis in the ejecta following the approach of Ref. jones2018 . None of our simulations actually result in core collapse into a neutron star; all are partial thermonuclear explosions that produce a bound remnant consisting of oxygen, neon and iron-group elements (ONeFe WD). The inclusion of the forbidden transition, which favors an off-center ignition at lower densities, has a significant impact on the explosion: The lower density slows down the conductive flame and leads to less energetic burning, which results in a more massive remnant because less material is ejected (Fig. 4, top panel). On the other hand, the off-center ignition leads to more energetic burning during the first 1 second of the explosion (see Supplemental Material), resulting in a higher fraction of iron-group elements in the remnant compared to the centrally ignited models (Fig. 4, bottom panel).

We find that the explosion mechanism has a significant impact on the nucleosynthesis yields. This is primarily due to thermonuclear explosion ejecting far more material, $M_{\mathrm{ej}}\sim 1\,$M*⊙, than the gravitational collapse, $M_{\mathrm{ej}}\sim 0.01\,$M⊙* wanajo2018 , although the isotopic distributions also exhibit some differences (Fig. 5), notably in the production factors of 50Ti and 54Cr, which are enhanced by factors of $\sim 20$ in the thermonuclear explosion. On the other hand, the changes in ignition density and geometry caused by the forbidden transition have a modest impact on nucleosynthesis, leading to changes of up to $\sim 10\%$ in the production factors of individual isotopes (see Supplemental Material). We find that the ejecta of the thermonuclear explosion are particularly rich in the neutron-rich isotopes 48Ca, 50Ti and 54Cr and the trans-iron elements Zn, Se and Kr (Fig. 5). This has important implications for our understanding of early Galactic chemical evolution jones2018 and may also explain unusual Ti and Cr isotopic ratios found in presolar grains jones2018 ; nittler2018 . The radionuclide 60Fe is also produced in large amounts ($3.63\times 10^{-3}$ M*⊙*), implying that the live 60Fe found in deep-sea sediments wallner2016 could have originated from the recent death of a nearby intermediate-mass star wanajo2013fe60 . On the other hand, the production of 26Al is rather modest, resulting in a large 60Fe$/^{26}$Al ratio jones2018 .

In summary, our work indicates that the ONe core, for realistic growth rates and composition, will not collapse to a neutron star, but rather be partially disrupted by the oxygen deflagration wave, producing a ONeFe WD and a subluminous Type Ia supernova. This is contrary to the commonly accepted view that collapse to a neutron star is more likely gutierrez1996 ; leung2019 and has the notable corollary that the Crab Nebula (SN 1054) likely was the result of a low-mass iron core-collapse supernova. Our findings suggest that intermediate-mass stars may be an important (and potentially the only) channel for making ONeFe WDs. Detection or non-detection of such objects with future missions would provide important insights into the explosion mechanism.

The present determination of the electron capture rate on 20Ne removes the last remaining nuclear physics uncertainty in the evolution of degenerate ONe cores. Not only does the new accurate capture rate result in a reduced ignition density below $\rho_{\mathrm{c}}^{\mathrm{crit}}$, it also modifies the initial conditions by causing an off center ignition. With this result, the most uncertain aspect of the progenitor evolution is whether or not the core becomes convectively unstable schwab2017 , and whether the convective energy transport is efficient enough to delay the ignition and the start of the oxygen deflagration wave to densities above the critical density for collapse. Future efforts should therefore focus on characterising convection in the progenitor evolution. However, the main result of this work will not change: The new accurate 20Ne capture rate tips the balance in favour of a thermonuclear explosion.

This is the first astrophysical case in which a second-forbidden transition has been found to play a decisive role. Our result allows advances in our understanding of the fate of intermediate-mass stars and their contribution to galactic chemical evolution, populations of compact objects in the Universe, and diversity of supernova light curves.