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Last updated: April 28, 2022.
Element synthesis in a wide variety of astrophysical scenarios, ranging from the Sun to stellar explosions, usually involve a large number of nuclear processes. The corresponding reaction rates often rely on theory (i.e., statistical models, such as the Hauser-Feshbach theory), particularly when involving short-lived, radioactive isotopes. One particular site, however, classical nova outbursts, constitutes a noticeable exception, since their somewhat limited nuclear activity and range of energies of interest allow modelers to rely primarily on experimental inputs.
1. What to measure (or not to measure)
Currently existing nuclide charts contain data on about 4000 experimentally observed isotopes (in ground and isomeric states). Accordingly, the list of possible nuclear interactions (e.g., proton and alpha captures, neutron captures, beta-decays and electron captures, photodisintegrations, and additional, more complex forms of interactions) is really huge, probably approaching 100000. Obviously, an experimentalist may decide to perform a measurement related to any specific nuclear interaction. However, while any interaction would be probably of interest for nuclear structure or to determine specific properties of the nuclei involved, its interest for nuclear astrophysics needs to be duly justified. In essence, only a subset of all possible nuclear interactions are really relevant for nuclear astrophysics.
Moreover, the theoretical and experimental efforts aimed at providing accurate reaction rates to stellar modelers are hampered sometimes by significant nuclear uncertainties. Such uncertainties originate either from partial knowledge of spins, parities, and energies of the nuclear levels of interest, interferences, or from difficulties in the assignment of analog states between mirror nuclei. These uncertainties may have a notorious influence on the predicted nucleosynthesis (but that’s not always the case!). In that sense, it is crucial to know which is the required level of precision in the determination of the reaction rates of interest for an specific astrophysical site.
All uncertain reactions of interest for a particular astrophysical site need to be conveniently identified and compiled, and after assessing the impact of their associated uncertainties (in one or more astrophysical sites), need to be improved. Such lists of key uncertain reactions,often flagged by means of sensitivity studies, constitute a first guide for future, priority measurements at stable and/or radioactive ion-beam facilities.
2. A sample of sensitivity studies
Several sensitivity studies of the impact of nuclear uncertainties on the yields produced in different astrophysical scenarios have been published, adopting somewhat complementary approaches. Ideally, such uncertain reactions are identified in a series of hydrodynamic or hydrostatic tests, in which each reaction rate is individually varied within uncertainty limits (provided that upper and lower limit to the rates are available). This approach, which requires the use of a stellar code coupled to a detailed nuclear reaction network, often becomes computationally intensive and therefore has only been applied to a reduced number of cases (see below).
Alternatively, a simpler, more feasible approach relies on post-processing calculations that rely on temperature and density versus time profiles extracted from state-of-the-art, stellar evolution simulations (or from semi-analytical models). This approach allows a huge number of tests, provided that the uncertainties affecting a particular nuclear reaction will not have an impact on the energetics of the star (in which case, the adopted temperature and density profiles would not be valid anymore; see, e.g., Section 2.2). It is also worth noting that such post-processing calculations can be conducted for one or multiple shells.
Other studies, performed in the framework of post-processing calculations, adopted somewhat different strategies, including Monte Carlo simulations in which all nuclear reactions are simultaneously varied with randomly sampled factors. The goal is to properly account for possible correlations between input rates and model predictions, since several reactions, not just one, participate in the synthesis and destruction of each element.
2.1 Classical Novae
A number of sensitivity studies of the effect of thermonuclear reaction-rate variations on nova nucleosynthesis have been performed in the last two decades (see Iliadis et al. 2002, for examples of one-zone, post-processing calculations with T(t)-ρ(t) profiles extracted from hydrodynamic models; Hix et al. 2001 and Smith et al. 2002, for Monte Carlo-based, postprocessing simulations, and José, Coc & Hernanz 1999, 2001, Coc et al. 2000, Fox et al. 2004, and Rowland et al. 2004, for limited studies based entirely on hydrodynamic models).
It is worth noting that most (but not all) post-processing calculations ignore the critical impact that convection has on the final nova yields (Parete-Koon et al. 2002), and, hence, they are not suitable for defining absolute final abundances. Moreover, one-zone post-processing studies tend to overestimate the impact of the nuclear uncertainty that affects a specific rate. In fact, hydrodynamic simulations significantly smooth the results obtained through one-zone approaches because of the role of convective mixing between adjacent shells.
One of the most important results obtained from these sensitivity studies is that nova yields are influenced by variations of a very limited number of key reaction rates. Furthermore, they have also revealed that an uncertainty of about 30% in the reaction rates of interest is enough for quantitative nova nucleosynthesis studies. Finally, it is worth mentioning that most of the uncertain reaction rates identified by Iliadis et al. (2002) have been the focus of a huge experimental effort worldwide. In fact, current uncertainties affecting nova nucleosynthesis are mostly limited to a handful of nuclear reaction rates1, particularly 18F(p,α), 25Al(p,γ), and 30P(p,γ).
2.2 Type I X-Ray Bursts
A number of sensitivity studies have also analyzed the influence of the size of the adopted nuclear reaction network, the use of different reaction-rate and mass compilations, and the impact of varying reaction rates within uncertainty limits for type I X-ray bursts (see, e.g., Amthor et al. 2006, Brown et al. 2002, Cooper & Narayan 2006, Cyburt et al. 2010, Davids et al. 2011, Fisker et al. 2004, 2006, 2007, Iliadis et al. 1999, Koike et al. 1999, 2004, Schatz et al. 1998, Tan et al. 2007, Thielemann et al. 2001, Wallace & Woosley 1981, Woosley et al. 2004). The most extensive work to date has been performed by Parikh et al. (2008, 2009), which included a twofold approach. First, the effect of individual reaction-rate variations was quantified in the framework of post-processing calculations for different temperature and
density versus time profiles. To that end, a large nuclear network with 606 isotopes (from H to 113Xe), linked through 3551 nuclear processes, was used. Each reaction was randomly and individually varied, to account for its associated uncertainty. The study revealed that only a handful of reactions, out of the 3551 nuclear processes considered, had an impact on the yields larger than a factor of 2, and on, at least, 3 isotopes of the network, in any of the models computed, when their nominal rates were varied by a factor of 10, up and down. The list includes2 mostly proton-capture reactions, such as 65As(p,γ)66Se, 61Ga(p, γ)62Ge, 96Ag(p,γ)97Cd, 59Cu(p, γ)60Zn, 86Mo(p,γ)87Tc, 92Ru(p,γ)93Rh, or 102,103In(p,γ)103,104Sn, and a handful of α-capture reactions3, like 12C(α,γ)16O, 30S(α,p)33Cl, or 56Ni(α,p)59Cu. Parikh et al. also identified 17 reactions affecting energy production by more than 5% (as well as the yield of at least one isotope), when individually varied within a factor of 10, up and down.
In a second, complementary approach to the individual-reaction rate variation study, all reaction rates were simultaneous varied through a Monte Carlo approach, aiming at mimicking the complex interplay between multiple nuclear processes in the highly coupled environment of an X-ray burst. In this second approach, all rates were multiplied by a random factor that followed a Log-Normal distribution, with an expected value of 1, and a probability of 95.5% to range between 0.1 and 10 (the same uncertainty limits adopted in the first approach). Here, the most influential reactions are flagged on the basis of correlation coefficients between each isotope and all reaction rates: the larger the correlation coefficient, the more influential the reaction is. Like in the individual reaction-rate variation study, only a small subset of the
thousands of reactions considered had an impact on the final yields. And more important, all reactions identified in the Monte Carlo simulations were previously flagged in the individual reaction-rate variation study. When not too restrictive conditions were applied to the Monte Carlo study, a total agreement on the results obtained with both techniques was achieved. However, the individual reaction-rate variation study turned out to be better suited for flagging reactions that affect the overall energy output or for handling specific reactions whose rates are known with better precision.
The impact of uncertainties in reaction Q-values on the nucleosynthesis accompanying type I X-ray bursts has also been explored by Parikh et al. (2009). Only the reactions 26P(p,γ)27S, 45,46Cr(p,γ)46,47Mn, 55Ni(p,γ)56Cu, 60Zn(p,γ)61Ga, and 64Ge(p,γ)65As showed an effect on the final yields when their corresponding Q-values were varied within 1σ bounds. In fact, 64Ge(p,γ)65As, whose influence extends between 64Zn and 104Ag, displayed the largest effect, and has motivated a number of direct mass measurements on 65As and other species (Tu et al. 2011, Walker 2011).
2.3 Type Ia Supernovae
Nucleosynthesis in type Ia supernovae depends critically on the peak temperature achieved and the density at which the explosion occurs. Nevertheless, the composition of the white dwarf hosting the explosion (in particular, the amount and distribution of 12C and 22Ne) plays also a key role as it affects the ignition density, the overall energy released, the flame speed, or the specific density at which the deflagration-to-detonation transition occurs [309, 310, 1816].
First attempts to address the impact of uncertainties in the nuclear processes involved in type Ia supernova nucleosynthesis mostly focused on 12 C+ 12 C [248, 315, 868, 1684], since this reaction triggers the explosion when the temperature exceeds ∼7×108 K. Recently, Anuj Parikh and collaborators  have investigated the sensitivity of the predicted nucleosynthesis to variations of both thermonuclear reaction and weak interaction rates involved in the explosion, in the framework of two representative models: the C-deflagration W7 model , decades, and a 2D delayed-detonation model (see Figure 5.30). Postprocessing calculations with a network containing 443 species, ranging from n to 86Kr, were performed with temperature and density versus time profiles extracted from a representative number of shells of the C-deflagration model and trace particles of the delayed detonation 2D simulations . All thermonuclear reaction and weak interaction rates were individually varied by a factor of ten, up and down. Several million, postprocessing calculations were performed to recalculate the yields accordingly, which were subsequently compared with those obtained with standard, recommended rates. The study revealed that out of the 2305 thermonuclear reactions included in the network, only the uncertainties in 53 reactions affect the yield of any species with an abundance ≥ 10−8 M⊙ , by a factor ≥ 2. A subset of these reactions, whose variation by a factor of ten affects the yields of three or more species by a factor ≥ 2 in any of the models, is listed, for illustrative purposes, in Table 5.1. The study revealed that variation of the rates of the 12C(α,γ), 12C+12C, 20Ne(α,p), 20Ne(α,γ), and 30Si(p,γ) reactions have the largest impact on the yields. Furthermore, the individual variation of 658 weak interaction rates by a factor of ten, underlined that only variations of the stellar 28Si(β+)28Al, 32S(β+)32P, and 36Ar(β+)36Cl rates have a significant effect on the yields in any of the models considered.
According to this study, nucleosynthesis in the two adopted models turns out to be relatively robust to variations in individual nuclear reaction and weak interaction rates. Laboratory experiments aimed at reducing the nuclear uncertainties of the subset of reactions identified (particularly at T ≥ 1.5×109 K) are, however, needed for a better account of the nucleosynthesis expected in type Ia supernovae and for further constraining model predictions. In addition, a detailed, consistent treatment of all relevant stellar weak interaction rates is clearly needed, since simultaneous variation of all these rates (as opposed to individual variations) turns out to have a significant effect on the yields.
[This section will be expanded in the next revision.]
3. Types of experiments
4. On formats and availability of the new rates in public websites
5. Assessing the astrophysical impact of the new rate
1 In sharp contrast, β-decay half-lives of interest for nova nucleosynthesis are experimentally well known and do not suffer significant uncertainties.
2 The single, most influential nuclear process turned out to be the triple-α reaction. However, when more realistic uncertainty limits were adopted (±12%; Tur et al. 2006), no effect, neither on the final yields nor on the overall energy output, was found. The same applies to individual variations of the β-decay rates included in the network.
3 Note, however, that the 12C(α,γ) rate is constrained to better than a factor of ∼10 for X-ray burst conditions. Note also that variations of these reaction rates within uncertainty limits mostly affect isotopes with masses and atomic numbers similar to those of the projectile plus target system.