Free Access
Issue
A&A
Volume 653, September 2021
Article Number A64
Number of page(s) 10
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/202140339
Published online 08 September 2021

© ESO 2021

1. Introduction

Classical novae are thermonuclear explosions that take place in the envelopes of accreting white dwarfs in stellar, short orbital period, binary systems (see Starrfield et al. 2008; José et al. 2008, and José 2016 for reviews). They have been systematically observed in all wavelengths, ranging from radio to γ rays. However, while novae have been predicted to emit γ rays of specific energies around 1 MeV, associated with electron-positron annihilation (e.g., from 18F(β+ν)) and with nuclear decay (e.g., 22Na at 1.275 MeV and 26Al at 1.809 MeV), they have only been detected in γ rays for energies exceeding 100 MeV. In symbiotic binary systems, such as V407 Cyg, this high-energy emission has been attributed to shock acceleration in the ejected shells after interaction with the dense wind of the red giant companion. The emission reported from several classical novae involving less evolved stellar companions (e.g., V1324 Sco, V959 Mon, V339 Del, and V1369 Cen; Ackermann et al. 2014) has been attributed to internal shocks in the ejecta. In this scenario, γ rays are produced either through a hadronic process, in which accelerated protons collide with matter to create neutral pions that decay into γ-ray photons, or through a leptonic process, in which visible or infrared photons reach high energies in the interaction with high-energy electrons. While the hadronic process seems to be favored, the exact nature of the mechanism responsible for γ-ray production remains unknown.

The most intense γ-ray signal predicted for classical novae corresponds to the 511-keV line that is due to electron-positron annihilation in the expanding ejecta, together with a lower-energy continuum (powered both by positronium decay and by Comptonization of 511-keV photons) with a cutoff at ∼20–30 keV due to photoelectric absorption (Clayton & Hoyle 1974; Leising & Clayton 1987; Gomez-Gomar et al. 1998; Hernanz et al. 1999). As the expanding envelope begins to become transparent to γ radiation after around ∼2 hr, the main contributor to the bulk of positrons is 18F, which decays with a characteristic half-life, t1/2, of about 110 min. Therefore, all nuclear processes involved in the synthesis and destruction of 18F are of paramount importance for predicting the expected amount of 18F that survives the explosion and powers the predicted prompt 511-keV line and the lower-energy continuum. Synthesis of 18F in novae is driven by the CNO-cycle reaction 16O(p, γ)17F, which is either followed by 17F(p, γ)18Ne(β+)18F or by 17F(β+)17O(p, γ)18F. Because of the relatively long half-life of 18F, its dominant destruction channel is mainly 18F(p, α)15O, with a minor contribution from 18F(p, γ)19Ne. The most uncertain nuclear process involved in the creation and destruction of 18F for nova conditions is 18F(p, α)15O (José et al. 2006; José 2016, and references therein).

We begin in Sect. 2 with a review and analysis of the present nuclear physics uncertainties affecting the 18F(p, α) reaction, including the latest experimental results. Using these evaluated experimental nuclear uncertainties, in Sect. 3 we calculate a range of reaction rates and vary these within new hydrodynamic nova simulations. Subsequently, in Sect. 4 we discuss and interpret all observed differences in our model outputs. In Sect. 5 we conclude by providing a road map to guide future nuclear experiments.

2. Nuclear physics uncertainties

The 18F(p, α)15O reaction plays a critical role in nova explosions, yet insufficient experimental information is available to calculate a reliable, precise rate for this reaction. A quarter of a century ago, the first pioneering direct measurements were performed using 18F radioactive beams (Coszach et al. 1995; Rehm et al. 1995). However, the cross section at the lowest temperatures achieved in novae (T8≈ 1, where T8 is in units of 108 K) remains highly uncertain because it is too small for direct measurement, even with presently available radioactive beam intensities. Consequently, the structure of the 19Ne compound nucleus has also been extensively studied in order to indirectly estimate the 18F(p, α) stellar reaction rate (for previous evaluations of the 18F(p, α) rate, see, e.g., Nesaraja et al. 2007; Iliadis et al. 2010b; La Cognata et al. 2017; Kahl et al. 2019; Hall et al. 2019, 2020). As our understanding of excited states near the proton threshold in 19Ne continues to progress, it is necessary to address the latest findings and any discrepancies. Several new experimental works have recently been published (Kahl et al. 2019; Hall et al. 2019; La Cognata et al. 2019), and it is timely to review the status of nuclear physics uncertainties to examine which ones most strongly influence the 18F(p, α) rate in classical novae. Here we provide the first self-consistent evaluation of the 18F(p, α) reaction rate, combining all these latest results in a hydrodynamic nova model.

The 18F(p, α) reaction rate at the highest nova temperatures (T8 ≈ 4) is dominated by a Jπ = 3/2 (orbital angular momentum  = 1) state at a resonance energy Er = 332 keV and a broad 3/2+ ( = 0) resonance at 665 keV (Bardayan et al. 2002, 2001); we adopt the precisely measured properties of these states in the present work. At lower nova temperatures (T8 ≲ 3), 1/2+ and 3/2+ ( = 0) states predicted near the proton threshold in 19Ne, including subthreshold resonances, can significantly influence the reaction rate by interfering with higher-lying, broad 1/2+ and 3/2+ states (Dalouzy et al. 2009; Chae et al. 2006). A broad 1/2+ state has been reported, but not resolved, near Er ≈ 1.5 MeV in several works (Dalouzy et al. 2009; Adekola et al. 2012; Mountford et al. 2012). Most recently, an  = 0 state with a total width of Γ = 130(10) keV was firmly observed at 1.38(3) MeV by Kahl et al. (2019).

To explore the magnitude of quantum interference effects on the 18F(p, α) cross section, we carefully evaluated uncertainties in our knowledge of s-wave states in 19Ne close to the proton separation energy Sp = 6.4100(5) MeV (Wang et al. 2017). Because 19F (the mirror nucleus of 19Ne) is stable, its excitation structure has been comparatively well understood (see, e.g., Tilley et al. 1995), and a comprehensive, high-resolution experimental and theoretical investigation of electron inelastic scattering has been conducted (Brown et al. 1985). Near the proton threshold energy in 19Ne, there is one 1/2+ state and two 3/2+ states known in 19F, located at 6.255, 6.497, and 6.528 MeV, respectively. We therefore focus our attention on the location and properties of three such s-wave states in 19Ne. The values adopted in the present work are shown in Fig. 1 and Table 1 and discussed presently.

thumbnail Fig. 1.

Partial level scheme of 19Ne, with an emphasis on s-wave states affecting the 18F(p, α) reaction rate. See Table 1 for details.

Table 1.

Resonance parameters and uncertainties used in the 18F(p, α) reaction rate calculations.

Most recently, Hall et al. (2019, 2020) considered the astrophysical impact of uncertainties in the resonance properties on the 18F(p, α) reaction rate by deriving attributes of multiple resonances in 19Ne from the same analog state in 19F. Unfortunately, such an approach can lead to unphysical results. In the present work, all calculations are self-consistent, that is, they are in agreement with the overall known structure and properties of 19F. For example, we only pair the properties of the known 6.528 MeV state in 19F with just one candidate analog state in 19Ne for each calculation, whereas these properties are applied simultaneously to four resonances in 19Ne by Hall et al. (2020). This, for example, impacts the potential importance of the recently observed  = 0 subthreshold resonance at 6.13 MeV in 19Ne by Kahl et al. (2019).

Despite tabulated mirror pairings1, Hall et al. (2020) clearly obtained the alpha partial width, Γα, for both their suggested (3/2+) states in 19Ne from the broader 6.528 MeV state in 19F. They further adopted a (5/2) resonance with Γα and the proton partial width, Γp, derived from the same 6.528 MeV state in 19F (see Appendix A and Laird et al. 2013). Hall et al. (2020) then evaluated that the subsequent “inclusion” of the 6.13 MeV state in 19Ne (with its properties derived from the same 6.528-MeV state in 19F) has a less than ±7.5% influence on their reaction rate limits over nova temperatures. Those authors justified not “including” this  = 0 state because γ-ray transitions have not been observed for this unbound state, and no significant strength was seen in a measurement of the 18F(d, n) reaction (Adekola et al. 2011a), yet they adopted other states that do not satisfy the same criteria. We demonstrate in Fig. A.1 that the sum of four  > 0 resonances included by Hall et al. (2019, 2020) exhibits an influence smaller than 7.5% near peak nova temperatures, resulting in an inconsistent methodology.

In the present work, for the neighboring 3/2+ states at 6.497 and 6.528 MeV in 19F, one of which has a measured alpha strength and one just an upper limit from experiments, we only allow one of these values per candidate analog state in 19Ne. For near-threshold and subthreshold resonances in the 18F(p, α) reaction, Γ is dominated by Γα. We find that the values of Γα chosen for a given state strongly affect the magnitude of interference with higher-lying, broad resonances and thus can significantly influence the 18F(p, α) reaction rate. In contrast, Hall et al. (2019, 2020) find Γα to be negligible by application of the isolated, narrow-resonance condition for the reaction A(i,j)B as

(1)

where γ is the reduced width (Rolfs & Rodney 1988). However, the simplification of Eq. (1) is inapplicable to the case of interference with a broad resonance of the same Jπ.

Kahl et al. (2019) unambiguously identified an  = 0 state at 6.130(5) MeV in 19Ne using a model-independent approach and, based on the systematics of Coulomb energy differences, strongly favored pairing this state with the 1/2+ 6.255-MeV state in 19F. This conclusion is supported by the significant strength from a 1/2+ resonance in 19Ne observed near ∼6.1 MeV (Laird 2000; Laird et al. 2002) with a magnitude comparable to the population of the 1/2+ 6.225-MeV state in analogous studies of 19F (Green et al. 1970; Schmidt & Duhm 1970). Torresi et al. (2017) observed the signature of a 1/2 state of ambiguous parity in 19Ne at 6.197(8)(50) [statistical and systematic uncertainties] with a large Γα of 16 keV. In the present work, we adopted the excitation energy of 6.132(5) MeV from the highest-resolution studies to observe this low-spin state (Laird et al. 2013; Parikh et al. 2015). As a possible 3/2+ assignment for this state cannot be definitively ruled out, we compared and contrasted the implications of the J assignment of the 6.132-MeV state. Table 1 shows that the resulting uncertainty in Γα of the 6.132-MeV state spans considerably different ranges depending upon the assumed J.

A strong  = 0 component was observed by Adekola et al. (2011a,b) at 6.289 MeV, but subsequent studies led to the conflicting conclusions that the state was not low spin (Laird et al. 2013) and that it was 1/2+ (Bardayan et al. 2015). There is now compelling evidence of a doublet in this region. Parikh et al. (2015) observed a structure broader than their experimental resolution (Γ ≈ 16 keV) and identified the possibility of a doublet with peaks at 6.282 and 6.294 MeV. Subsequently, Kahl et al. (2019) demonstrated that the structure at 6.288(5) MeV cannot be attributed to a single, pure  = 0 resonance. Finally, Hall et al. (2019) observed a state at 6291.6(9) keV that they suggested to be (11/2+). Although such a high-spin subthreshold state would not contribute to the astrophysical reaction rate, its presence near a subthreshold  = 0 state continues to be challenging to simultaneously and unambiguously resolve experimentally.

The mirror partner of the remaining  = 0 state in 19F is likely located above the proton threshold in 19Ne, but the situation is complicated as half a dozen states may exist within just 50 keV (see, e.g., Nesaraja et al. 2007 and Laird et al. 2013). Hall et al. (2019) tentatively suggest (3/2+) assignments for two states above the proton threshold: a newly proposed state at 6.423(3) MeV and a previously identified state at 6.441(3) MeV. Clearly, three  = 0 states in 19F cannot be paired with four states in 19Ne, and one of these tentative (3/2+) pairings should be rejected. Kahl et al. (2019) observed a peak at 6.421(10) MeV, which could include an  = 0 component near the centroid, but an  = 0 state at higher excitations is incompatible with that study and Laird et al. (2013). The 3/2+ state at 6.528 MeV in 19F has the larger Γα, with values of 4, 1.2, and 13.9 keV reported (Smotrich et al. 1961; Bardayan et al. 2005; La Cognata et al. 2019); its mirror partner in 19Ne is thus unlikely to be observed in the low-statistics γ-ray spectroscopy experiment of Hall et al. (2019). We therefore assumed the mirror partner of the 3/2+ state at 6.497 MeV in 19F to be near 6.42 MeV in 19Ne, which is supported by perfect consistency in the observed γ transitions (Tilley et al. 1995; Hall et al. 2019).

As for the possible contribution of  > 0 resonances near the proton threshold, none have firm values for all their properties – besides many Jπ ambiguities, at least one of the partial widths for each resonance is an experimental upper limit (see, e.g., Nesaraja et al. 2007 and Laird et al. 2013). Nonetheless, we consider the possible impact of such  > 0 states on the 18F(p, α) reaction rate in novae (see Table A.2).

3. Reaction rate and stellar model

We calculated a wide range of 18F(p, α) stellar reaction rates with the R-Matrix code AZURE2 (Azuma et al. 2010; Mountford et al. 2014) based on the nuclear physics uncertainties presented in Table 1. Our goal was to assess which specific nuclear quantities have the largest impact on nova observables in our model to guide future experimental measurements. Based on our evaluation in Sect. 2, we focused on, but did not limit ourselves to, variation in the following ten parameters within their uncertainties: (i) the interference sign between the two 1/2+ states; (ii) interference signs between up to three 3/2+ states; (iii) the J of the  = 0 state at 6.13 MeV; (iv) the unknown proton asymptotic normalization coefficient (ANC) of the 6.13 MeV state; (v) the J and Eex of the  = 0 state near 6.29 MeV; (vi) the Γα for the mirror of the 3/2+, 6.528-MeV state in 19F; (vii) the Γα of the 1/2+ subthreshold state; (viii) the Eex of a narrow (3/2+) state just above Sp; (ix) the influence of  > 0 states near Sp; and (x) the Γ as well as the Γpα ratio of the 1/2+ state near 7.8 MeV.

We found variation in other properties to be implausible or inconsequential. Further details of the R-Matrix calculations are provided in Appendix A.

Considering this large set of codependent parameters, a Monte Carlo approach, such as that employed in RatesMC (Longland et al. 2010; Iliadis et al. 2010b,a), is quite attractive. However, the case of 18F(p, α) presents a particular challenge owing to the possible influence of the interference between up to three resonances of the same Jπ, namely the 3/2+ states. For this reason, the previous evaluation of Iliadis et al. (2010b) considered only the interference between a pair of 3/2+ states, and RatesMC uses the simple Lane and Thomas analytic formula (Longland, priv. comm., Lane & Thomas 1958, and Longland et al. 2010). Here we aim to improve upon the previous works by fully considering the latest experimental results using an R-matrix approach to handle multiple interference effects over a large and internally consistent parameter space. A comparison of the range of the present rates against those of Iliadis et al. (2010b) is shown in Fig. 2; the corresponding rates from the present work are listed in Table B.1. We recommend the median rates (Sets XIII and IX) obtained in the present work (see Fig. A.2). After a careful evaluation of the impact of each noted uncertainty on the stellar reaction rate, we selected a representative sample of 16 possible rates over the full range for a further analysis.

thumbnail Fig. 2.

Range of reaction rates explored in the present work (see Tables 1 and B.1) normalized to the median rate of Iliadis et al. (2010b); the low and high rates of Iliadis et al. (2010b) are also shown. The recommended (median) rates from the present work are shown in magenta for Sets VIII and IX, where the subthreshold spin ordering is 3/2+, 1/2+ and 1/2+, 3/2+, respectively. The highest rate (Set XVI) represents a case of maximally constructive interference, while the lowest rates (Sets I and II) are obtained via maximally destructive interference.

We assessed the astrophysical impact of these new 18F(p, α) rates through a series of 16 new hydrodynamic models of nova explosions. The simulations were performed with the hydrodynamic, Lagrangian, finite-difference, time-implicit code SHIVA (José & Hernanz 1998; José 2016). SHIVA relies on the standard set of differential equations of stellar evolution and has been extensively used in the characterization of nova outbursts, Type-I X-ray bursts, and sub-Chandrasekhar supernova explosions for more than 20 years. SHIVA uses a general equation of state that includes contributions from the degenerate electron gas, the ion plasma, and radiation. Coulomb corrections to the electron pressure are taken into account, and both radiative and conductive opacities are considered in the energy transport. Nuclear energy generation is obtained by means of a reaction network that contains 120 species (from 1H to 48Ti), linked through 630 nuclear processes, with updated rates from the STARLIB database (Sallaska et al. 2013 and Iliadis, priv. comm.). The accreted matter from the stellar companion, at a typical rate of 2 × 10−10M yr−1, is assumed to mix with material from the outer layers of the underlying white dwarf to a characteristic level of 50%. In all the hydrodynamic simulations performed in this work, the mass of the (ONe) white dwarf hosting the explosion was assumed to be 1.25 solar masses (and its initial luminosity 10−2 solar luminosities); all these simulations were identical, differing only in the specific prescription adopted for the 18F(p, α) rate.

4. Results

The main difference in our output nova model parameters is centered, as expected, around 18F. As the energetics of the explosion are not affected by variations in the 18F(p, α) reaction rate within current uncertainties, the results for other model quantities are identical, such as the total ejected mass, the peak temperature, Tpeak, achieved, etc. The values shown in Table 2 correspond to mass-averaged (mean value) abundances of 18, 19F in mass fractions, X, in the ejecta and representative temperature samples of the employed reaction rate. The ejected abundances of all the other isotopes examined varied between the models by at most a relative shift of ±1%, which we adopted as the precision of sensitivity achieved in the present work. While classical novae are thought to be a major source of 15N, 17O, and, to some, extent 13C (José et al. 2006 and José 2016, and references therein), we observed no significant variation in the abundances of any of these isotopes in the present study. For example, the contribution of radiogenic 15N from the 18F(p, α)15O reaction is negligible as our model consistently ejected 15N with an abundance of 3.39 × 10−2, about four orders of magnitude larger than our predicted ±5 × 10−6 abundance shift in 18F. It can be seen in Table 2 that the ejected abundances of 18F (1 hour after Tpeak) and 19F covary by about an order of magnitude and are inversely correlated with the respective 18F(p, α) reaction rate. Since the observational detectability distance is taken as the square root of the ejected mass fraction, our results indicate a factor of ∼3 uncertainty in the detectability distance of γ rays from 18F decay in classical novae from the 18F(p α) reaction rate alone.

Table 2.

Mean, mass-averaged abundances of 18, 19F in the nova ejecta.

The strong correlation of 18F and 19F abundances over a wide range of 18F(p, α) reaction rates is consistent with this reaction’s predominance over the 18F(p, γ)19Ne reaction in novae. 19Ne is very short lived (t1/2 ≈ 18 s) and decays to the only stable isotope of fluorine, 19F, which was indeed identified in the spectra of Nova Mon 2012 (Shore et al. 2013). The abundance shifts in 19F are understandable since the 18F(p, α) rate limits the available 18F by flushing away material faster than the 18F(p, γ)19Ne(β+)19F sequence can occur. We emphasize that the true 18F(p, α) rate remains quite uncertain.

Snapshots of the evolution of a number of representative isotopes of the O-Ne group, relevant in the synthesis and destruction of 18F (i.e., 16, 17, 18O, 17, 18, 19F, and 18, 19Ne) are depicted in Fig. 3. The initial mass fractions of these species throughout the envelope at the onset of the accretion stage are as follows: X(16O) = 0.13, X(17O) = 2.1 × 10−6, X(18O) = 1.2 × 10−5, and X(19F) = 3.1 × 10−7. As matter transferred from the secondary star piles up on the surface of the white dwarf star, compressional heating and nuclear reactions increase the temperature (and pressure) of the accreted envelope. When the temperature at the base of the envelope achieves Tbase ∼ 5 × 107 K (Fig. 3, panel 1), the main nuclear activity in the O-Ne mass region is dominated by the chain 16O(p, γ)17F(β+)17O(p, α)14N. The main effect, at this stage, is the increase in 17O, whose abundance rises by two orders of magnitude at the base of the envelope with respect to its initial value. However, since the temperature achieved is not high enough to fuse a significant fraction of 16O, changes on most of the species are moderate. This mostly affects the buildup of 17, 18F, whose mass fractions reach ∼10−7. Proton capture reactions onto 17, 18F also result in a very modest increase in both 18, 19Ne (< 10−10, by mass). Convective transport is scarcely present at this stage, which explains the inhomogeneous chemical abundance pattern of the envelope (see, for instance, the larger abundance of 18F near the core-envelope interface in panel 1).

thumbnail Fig. 3.

Mass fractions of selected isotopes within the expanding envelope at various stages of the explosion using our newly recommended 18F(p, α) reaction rate, Set IX. The horizontal axes correspond to a relative mass coordinate where the origin is set at the surface of the envelope and where the arrows show the limit of the ejected material. The different panels correspond to temperatures at the base of the accreted envelope of approximately 5 × 107 (panel 1), 7 × 107 (panel 2), 1 × 108 (panel 3), 2 × 108 (panel 4), and Tmax = 2.4 × 108 K (panel 5) and to the last phases of the evolution, when the nova envelope has already expanded to a size of Rwd ∼ 109 (panel 6), 1010 (panel 7), and 1012 cm (panel 8). We plot our results in a manner almost identical to Fig. 2 in Coc et al. (2000) to facilitate comparison.

A similar behavior is observed when Tbase  ∼  7  ×  107 K (Fig. 3, panel 2), with the same chain of reactions as described in panel 1 still dominating the nuclear activity in the envelope. Convection has already extended throughout larger areas of the envelope, which translates into smoother chemical profiles across the envelope for species such as 18F, which is synthesized close to the base of the envelope and is efficiently carried away to the outer, cooler layers of the envelope. At this stage, 18F ∼10−6 (17F ∼10−5) at the base of the envelope. After 16O, the second most abundant isotope of the O-Ne group at this stage is still 17O.

When Tbase reaches 108 K (Fig. 3, panel 3), most of the accreted envelope becomes convective. This tends to homogenize the envelope, as shown by the nearly flat profiles of most species, particularly 16, 17O and 17, 18, 19F. The abundance of 16O is being reduced by (p, γ) reactions. An increase in 17O is seen, with a mass fraction ranging from 6.3 × 10−4 (inner envelope) to 8.7 × 10−4 (outer envelope). Here, the chain 16O(p, γ)17F(β+)17O dominates the destruction channel 17O(p, α)14N. Both 17, 18F have notoriously increased with respect to the previous panel, through 16, 17O(p, γ)17, 18F reactions, while 19F has been severely depleted, mostly through 19F(p, α)16O. The mean, mass-averaged abundances of the isotopes of 18, 19Ne continue to rise in the innermost layers of the envelope by means of proton captures onto 17, 18F.

When Tbase reaches 2 × 108 K (Fig. 3, panel 4), 16O experiences a significant decrease via proton-capture reactions, which reduce its abundance by nearly a factor of two in the innermost layers of the envelope. This, in turn, induces a reduction in 17O (with 17O(p, α)14N reactions dominating over 17F(β+)17O). With regard to 18F, its abundance is mostly dominated by the destruction channel 18F(p, α)15O at the hotter, inner regions of the envelope, while 17O(p, γ)18F and 18Ne(β+)18F contribute to raising its mass fraction in the outer, cooler regions. As a result, 18F begins to show a steeper profile, which, except for the outermost layers of the envelope, increases outward. At this stage, 18O and 19F have been severely reduced by proton captures, while a remarkable increase in 18, 19Ne by several orders of magnitude is mainly driven by proton-capture reactions onto 17, 18F, which, at these temperatures, become faster than the corresponding β+ decays.

Shortly thereafter, the base of the envelope achieves a maximum temperature of 2.38 × 108 K (Fig. 3, panel 5). At this stage, the entire envelope has become fully convective. The 16O abundance continues to decrease via proton captures, and, for the first time, a different species, 17F, becomes the most abundant O-Ne group element in most of the envelope. The nuclear path is still dominated by the 16O(p, γ)17F(β+)17O(p, α)14N chain. At this stage, the abundances of the different species reflect a competition between different destruction and creation modes, which are mostly governed by (p, γ) and (p, α) reactions in the inner regions of the envelope and by β+ decays in the outer regions. With the exception of 16O, the O-Ne group isotopes shown in panel 5 experience a net increase.

A few minutes after the envelope attains peak temperature, the sudden release of energy from the very abundant, short-lived species 13N, 14, 15O, and 17F forces the envelope to expand. Hereafter, proton-capture reactions become confined to the innermost regions of the envelope following a dramatic temperature decrease in the outer layers (Fig. 3, panels 6 and 7). Simultaneously, convection begins to recede from the outer envelope shells.

The final stages of the outburst (Fig. 3, panel 8), when a significant fraction of the envelope has already achieved escape velocity, are dominated by the release of nuclear energy by the β+-decay processes 17, 18F(β+)17, 18O. The mean 18F abundance in the ejecta for this model (Set IX), one hour after peak temperature, is X(18F) = 2.6 × 10−6. The most abundant isotopes of the O-Ne group in the ejecta are, however, X(16O) = 9.2 × 10−3 and X(17O) = 7.9 × 10−3. In addition, some amounts of 18O (1.1 × 10−6, by mass) and 19F (3.1 × 10−8, by mass), have been found for this model (Set IX), assuming that all radioactive isotopes have already decayed into the corresponding daughter nuclei.

We confirmed that the largest variation among the 18F(p, α) reaction rates, and thus the ejected 18F, arises from the unknown interference signs between the  = 0 resonances. As for directly measurable quantum properties, we found that the Γα of a broad 3/2+ subthreshold state has the most profound influence on both the maximum and minimum reaction rates. In the case of maximally destructive interferences, the lowest rates are always obtained when the 6.13 MeV state is assumed to be 1/2+. Conversely, the maximum rates are similar for either spin ordering for the  = 0 subthreshold states, depending on the other assumptions. Our minimum rate is sensitive to the proton ANC of the 6.13 MeV state when it is 1/2+; here, a lower (but nonzero) value of 4 fm−1/2 compared with the presumed experimental upper limit of 8 fm−1/2 surprisingly leads to the largest effects, by shifting the dip of the destructive interference into the center of the astrophysical energy region. Although the broad 1/2+ state near 7.8 MeV is found to strongly affect the reaction rate by interference, we found that the rate is not sensitive to the adopted Γpα ratio nor to the uncertainty in Eex for this state. Finally, a 3/2+ state above the proton threshold can have a modest impact on the rate, depending on its exact energy and if Γα, Γp, and Eex are simultaneously taken to be near the maximal values consistent with experimental measurements, although we consider such a scenario to be unlikely.

We found that the possible impact of  > 0 states (e.g., the ones assumed in Hall et al. 2019) near Sp to the maximum 18F(p, α) rate is in general trivial in relation to other nuclear uncertainties, the magnitude of their effect on the reaction rate being comparable to the least influential uncertainties of  = 0 resonances we considered (see Appendix A). For the minimum rate, setting a given partial width with only an upper limit to an arbitrarily small value is compatible with experimental results.

5. Conclusions

We performed a thorough analysis of the impact of the presumed 18F(p, α) reaction rate on the predicted abundance of the astronomical observable 18F produced in classical novae. The reaction rates were obtained using the R-Matrix method, where the uncertainties in the nuclear input parameters were derived from a self-consistent evaluation of all available nuclear physics data, including the latest experimental results. An advantage of our approach is the ability to include all quantum interference effects on the reaction rate. The range of reaction rates we explored turned out to be quite large, and we selected 16 evenly spaced rates over our full range for further analysis. Using these new rates, we performed 16 (otherwise identical) hydrodynamic nova simulations, and we have presented and analyzed the only differences in model results we observed. The uncertainty in the observational distance arising from the decay of ejected 18F from novae is about a factor of three. We conclude by emphasizing the extant nuclear physics quantities that need to be known more precisely to significantly reduce this astronomical uncertainty:

  • interference effects between  = 0 states;

  • precise knowledge of the properties of the  = 0 states near 6.13 and 6.29, the lack of which dominates the uncertainties;

  • the proton ANC of the 6.13 MeV state;

  • more definitive spin assignments on the  = 0 states near 6.13 and 6.29 MeV, ideally with < 5 keV resolution;

  • a stronger upper limit on the Γα, and thus on the Γ, of the putative 3/2+ state near 6.42 MeV.

In the future, it will be interesting to investigate the uncertainties in other nuclear reactions that affect 19F abundances in novae to determine if 19F can be used as an observational tracer for the 18F(p, α) reaction.


1

Hall et al. (2020) show a firm value for Γα of the 19F state at 6.497 MeV in their Table 1, where there is only an upper limit (see Nesaraja et al. 2007, cited therein). They also did not consider the recent value of Γα = 13.9 keV for the 6.528-MeV state in 19F (La Cognata et al. 2019).

Acknowledgments

D.K. and P.J.W. are appreciative of funding from the UK STFC. D.K. acknowledges the support of the Romanian Ministry of Research and Innovation under research contract 10N/PN 19 06 01 05. J.J. acknowledges partial support through the Spanish MINECO grant AYA2017-86274-P, E.U. FEDER funds, and through the AGAUR/Generalitat de Catalunya grant SGR-661/2017. This article benefited also from discussions within the “ChETEC” COST Action (CA16117).

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Appendix A: Details of R-Matrix calculations

We calculated the 18F(p, α) stellar reaction rate using the R-Matrix formalism with AZURE2 (Azuma et al. 2010; Mountford et al. 2014). We fixed the channel radius a = 5.25 fm, similar to the values adopted in previous works of 5.5, 5.0, and 5.2 fm (in de Séréville et al. 2009, Beer et al. 2011, and Hall et al. 2019, respectively). The sensitivity of the R-Matrix calculations on the assumed channel radius was previously explored over the range 4.5–6.5 fm (see Fig. 6 of de Séréville et al. 2009), where a larger channel radius was seen to push a destructive interference dip to lower energies, and vice versa, all other parameters being equal. We separate our employed 19Ne resonance parameters into the following three categories: (i) strongly influential resonances used in all calculations where variation in their properties within experimental uncertainties has a negligible influence on the reaction rate (shown in Table A.1); (ii)  > 0 resonances with poorly known properties that nevertheless exhibit a minimal influence on the present uncertainty in the reaction rate (shown in Table A.2); and (iii)  = 0 resonances that dominate the present uncertainty in the reaction rate (shown in Table A.3).

Table A.1.

Resonance parameters used in all of the 18F(p, α) astrophysical calculations.

Table A.2.

Resonance parameters added to the maximum rate (Set XVI) that exhibits minimal influence.

Table A.3.

Resonance parameters varied in the calculation of the 18F(p, α) reaction rate and S(E).

The possible contribution of the  > 0 resonances in Table A.2 is shown in Fig. A.1. We compare the sum of these four resonances against the maximum rate (Set XVI), as well as the case when the 6.13 MeV state is 1/2+ and has Γα = 16 keV (Torresi et al. 2017) rather than 8.6 keV (as assumed in Set XVI). Our analysis showed that the largest resonant contribution in Table A.2 is from the 6.459 MeV state in 19Ne; this was tentatively assigned as (5/2) by Laird et al. (2013), who did not observe any 3/2+ states in 19Ne in this region. As there seemed to be no corresponding 5/2 state in 19F near this energy, Laird et al. (2013) scaled the properties of the 6.528 MeV 3/2+ state in 19F given by Nesaraja et al. (2007). As our calculations already assign a mirror partner to the 6.528 MeV state in 19F, we infer that the maximum contribution of the 6.459 MeV state in 19Ne is significantly less than what Fig. A.1 suggests.

thumbnail Fig. A.1.

Comparison of the potential contribution of  > 0 resonances in Table A.2 to the 18F(p, α) rates utilized in the astrophysical calculations in the present work (normalized to our Set IX). We demonstrate that the potential influence of the sum of those four resonances is not much more than, e.g., the uncertainty in Γα of the 6.13 MeV state observed by Kahl et al. (2019).

For the (3/2) state at 6.416 MeV, Hall et al. (2019) have the value of Γp shown in Table A.2, while Hall et al. (2020) claim Γp = 2.8 × 10−27 keV for a 1 keV resonance energy shift (inconsistent with Bardayan et al. 2015). We instead found Γp = 2.3 × 10−45 keV for such a (3/2) resonance at Ec.m. = 6 keV. We tested all of these values for Γp, and, even with an erroneous increase of 1018 in Γp, the contribution of this state to the maximum reaction rate of Set XVI remains negligible. We explore the energies near 6.416 versus 6.423 MeV for a (3/2+) state in Table A.3, with appropriate shifts in Γp and consistent use of Γα so that readers can evaluate the impact of the state newly suggested by Hall et al. (2019); this is not the same as considering a 6.416-MeV, negative parity state to be the same as the mirror pair of a 3/2+ state, but rather as a previously unresolved doublet.

The astrophysical S factor, S(E), is shown and compared with experimental results in Fig. A.2. We show the exact S(E) without taking into account the individual experimental target thicknesses, which differ from one another by more than a factor of two. Considering the scatter in the experimental data, the agreement is reasonably good, except at 250 keV, where only two events (and no background) were observed by Beer et al. (2011), allowing for the possibility that the true S(E) could be significantly smaller, as explored in the present work.

thumbnail Fig. A.2.

Astrophysical S(E) for the 18F(p, α) reaction. See Tables 1, A.1, and A.3 for details. Experimental works are from Bardayan et al. (2001, 2002); de Séréville et al. (2009), and Beer et al. (2011).

Appendix B: Reaction rate table

Table B.1.

Thermonuclear reaction rates for the 18F(p, α) sets shown in Fig. 2.

All Tables

Table 1.

Resonance parameters and uncertainties used in the 18F(p, α) reaction rate calculations.

Table 2.

Mean, mass-averaged abundances of 18, 19F in the nova ejecta.

Table A.1.

Resonance parameters used in all of the 18F(p, α) astrophysical calculations.

Table A.2.

Resonance parameters added to the maximum rate (Set XVI) that exhibits minimal influence.

Table A.3.

Resonance parameters varied in the calculation of the 18F(p, α) reaction rate and S(E).

Table B.1.

Thermonuclear reaction rates for the 18F(p, α) sets shown in Fig. 2.

All Figures

thumbnail Fig. 1.

Partial level scheme of 19Ne, with an emphasis on s-wave states affecting the 18F(p, α) reaction rate. See Table 1 for details.

In the text
thumbnail Fig. 2.

Range of reaction rates explored in the present work (see Tables 1 and B.1) normalized to the median rate of Iliadis et al. (2010b); the low and high rates of Iliadis et al. (2010b) are also shown. The recommended (median) rates from the present work are shown in magenta for Sets VIII and IX, where the subthreshold spin ordering is 3/2+, 1/2+ and 1/2+, 3/2+, respectively. The highest rate (Set XVI) represents a case of maximally constructive interference, while the lowest rates (Sets I and II) are obtained via maximally destructive interference.

In the text
thumbnail Fig. 3.

Mass fractions of selected isotopes within the expanding envelope at various stages of the explosion using our newly recommended 18F(p, α) reaction rate, Set IX. The horizontal axes correspond to a relative mass coordinate where the origin is set at the surface of the envelope and where the arrows show the limit of the ejected material. The different panels correspond to temperatures at the base of the accreted envelope of approximately 5 × 107 (panel 1), 7 × 107 (panel 2), 1 × 108 (panel 3), 2 × 108 (panel 4), and Tmax = 2.4 × 108 K (panel 5) and to the last phases of the evolution, when the nova envelope has already expanded to a size of Rwd ∼ 109 (panel 6), 1010 (panel 7), and 1012 cm (panel 8). We plot our results in a manner almost identical to Fig. 2 in Coc et al. (2000) to facilitate comparison.

In the text
thumbnail Fig. A.1.

Comparison of the potential contribution of  > 0 resonances in Table A.2 to the 18F(p, α) rates utilized in the astrophysical calculations in the present work (normalized to our Set IX). We demonstrate that the potential influence of the sum of those four resonances is not much more than, e.g., the uncertainty in Γα of the 6.13 MeV state observed by Kahl et al. (2019).

In the text
thumbnail Fig. A.2.

Astrophysical S(E) for the 18F(p, α) reaction. See Tables 1, A.1, and A.3 for details. Experimental works are from Bardayan et al. (2001, 2002); de Séréville et al. (2009), and Beer et al. (2011).

In the text

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