3. STELLAR NUCLEOSYNTHESIS

The nucleosynthesis of elements heavier than those produced in the BBN requires the extreme temperatures and pressures found within stars. Charged-particle reactions are the main source of energy generation in stars and are responsible for the creation of elements up to Fe [34]. It is beyond the scope of this review to describe the highly complex phenomena of nucleosynthesis. The interested reader is referred to [35] for a review of stellar nucleosynthesis. In this section, we will focus mostly on massive stars (> 8 M_⊙) nucleosynthesis since this is the critical mass for a star needed to start the C fusion after central He has been exhausted. After three further fusion phases, an iron core is formed and no further energy can be gained. These processes begin as H and He from the Big Bang collapsed into the first protostars at 250 million years [36]. Star formation has occurred continuously in the universe since that time. Once a critical ignition temperature of ∼ 10⁶ K is achieved, protostars begin to fuse D. The start of central H-burning is the start of the Main Sequence (MS). Then the conversion of central H into He (T ∼ 10⁷ K) occurs with energy production and with the simultaneous destruction (due to the high temperatures) of the newly synthesized LI, Be and B nuclei. Nevertheless, these atoms would be reformed, although in small quantities, in the ISM by the action of cosmic rays [37]. The release of nuclear energy by fusion prevents further contraction of the star. The needed energy is released by nuclear reactions of the carbon-nitrogen-oxygen cycles (CNO-cycles) and proton-proton chains (pp-chains). The pp-chain [38] provides a He nucleus from the synthesis of four H nuclei, while in the CNO-cycles nuclei of C, N and O do not directly participate in the reaction but serve as catalysts [39]. The central energy release establishes a temperature and pressure gradient, falling from center to surface, creating a force acting in the opposite direction to gravity and keeping the star stable. During the MS massive stars have an inner convective core and a radiative envelope, i.e., in the core the energy is mainly transported outwards by flows of matter while in the envelope by outward diffusion of photons. Stars, in general, stay about 90% of their lifetime on the MS with a rather constant surface temperature and luminosity.

The end of the MS is marked by the exhaustion of H in the stellar center. The missing energy production leads to a short contraction phase of the whole star, until the H-burning ignites in a shell around the core, leading to an expansion of the envelope, while the core still contracts until He-burning starts. The core reaches a temperature of ≈ 1.5 × 10⁸ K, and it is now that the creation of C nuclei begins. Low and intermediate mass stars (0.8-8 M_⊙) develop, after H and He core burning, an electron-degenerate C-O core which is too cool to ignite C-burning. The convective envelope moves down and penetrates in the He layer until it reaches the boundary of the core. At this point in time, a double shell structure develops: the center of the star is formed by a contracting degenerate C-O core, which is surrounded by both a He and an H-burning shell. This structure is unstable and He shell flashes develop, resulting in thermal pulses that are characteristic of Asymptotic Giant Branch (AGB) stars [40]. During this Thermally Pulsing (TP-AGB) phase, the star has a high mass loss rate, which removes the entire envelope in a short time, leaving a naked C-O core which evolves into a White Dwarf (WD) (see [41] for a review). On the contrary, as suggested by Hoyle [42], in stars that have reached core temperatures of ∼ 10⁸ K, a nucleus of ¹²C is formed through a reaction involving three ⁴He nuclei, the so-called 3-α process [43]. The process is favored by both the high temperature in the core of stars, which allows overcoming the electrostatic repulsion, and by the environment composed almost exclusively of ⁴He. The 3-α process has been revisited in many theoretical studies in recent years, due to the impossibility to measure this reaction directly. However, there are discrepancies between some works regarding the 3-α process rates (e.g., [44, 45, 46]). Furthermore, using new theoretical approaches, a very large reaction rate was obtained by Ogata et al [47] but subsequent works, with improved theory, did not find a large enhancement. More discussions on these deviations and more recent results on the 3-α reaction rates are reported in [48] and [49].

With the formation of ¹²C via the 3-α process, following α-capture reactions can occur to produce ¹⁶O. The further increase of temperature, due to the contraction and ignition of the C-O core, causes the fusion of ¹²C atoms through which the ²⁰Ne, ²³Na, and ²⁴Mg are created. Massive stars will proceed to synthesize by α-capture Ne to O and Mg during a Ne-burning phase; O and Mg to Si and S during an O-burning phase and finally in Si-burning, Si and S are built into iron-group elements like Ni, Fe, and Cr. These burning phases ignite in this order with increasing temperatures, from T ⩾ 6 × 10⁸ K for C-burning to T ⩾ 3.5 × 10⁹ K for Si-burning. With increasing ignition temperatures also the time scales of the burning phases decrease, so while C-burning is of the order of 1000 years, Si is exhausted in the center in a couple of days. The shorter time scales of the later burning phases are related to the increasing energy loss by neutrinos with increasing temperatures. Because the maximum of nuclear binding energy is around Fe, stars cannot gain energy by fusion after Si-burning. As a consequence, the iron core grows until it reaches the critical mass, the Chandrasekhar mass (M_Ch ≈ 1.38 M_⊙), and it collapses marking the death of the star. Prior to collapse, a massive star will eventually consist of concentric onion-like layers burning different elements. Lighter elements will be produced in the outer layers, moving progressively through the α-ladder towards the interior of the star, with Fe and Ni at the core. During the final moments, electron degeneracy pressure in the core will be unable to support its weight against the force of gravity. As a result, the collapse increases temperatures in the core, which releases very high-energy gamma rays. These high-energy photons break the Fe nuclei up into He nuclei through photodisintegration process. At this stage, the core has already contracted beyond the point of electron degeneracy, and as it continues contracting, protons and electrons are forced to combine to form neutrons (Proto-Neutron Star (PNS)). This process releases vast quantities of neutrinos carrying substantial amounts of energy, again causing the core to cool and contract even further. The contraction is finally halted by the repulsive component of the nuclear force once the density of the inner core is nearly twice that of the atomic nucleus. The abrupt halt of the collapse of the inner core and its rebound generates an outgoing shock wave which reverses the infalling motion of the material in the star and accelerates it outwards. Such explosions are called Core-Collapse Supernovae (ccSNe) (see Section 4.2). The result of this dramatic explosions is the birth of a Neutron Star (NS) or a Black Hole (BH) (see, for more details, [50, 51]). The products of stellar nucleosynthesis are dispersed into the ISM through mass loss episodes (planetary nebulae), stellar winds of low-mass stars and ccSNe. ccSNe not only serve as the mechanism for the creation of heavier elements, they also serve as the mechanism for their dispersal.

During the CNO-cycle the chemical abundances are not well-known since the rates by which the nuclei undergo α-capture in the stellar core are only based on uncertain theoretical extrapolations of experimental data taken at energies that are substantially higher than the ones in stellar interiors. The reaction rates define the timescale for the stellar evolution, dictate the energy production rate, and determine the abundance distribution of seed and fuel for the next burning stage. The extrapolations are based on theoretical assumptions such as the incompressibility of nuclei reducing the probability of fusion [52] and the possible impact of molecular cluster formation during the fusion process that increases the fusion probability [53]. This uncertainty range may have severe consequences for our understanding of stellar heavy ion burning associated with late stellar evolution and stellar explosions [54]. New measurements of the ¹²C+¹⁶O fusion reaction need to be performed over a wide energy range to provide a more reliable extrapolation of the fusion cross-section and to reduce substantially the uncertainty for stellar model simulations. Some other poorly known nuclear reactions that are of particular importance for stellar evolution are capture and fusion reactions (e.g., ³He(α,γ)⁷Be, ¹⁴N(p,γ)¹⁵O, ¹⁷O(p,γ)¹⁸F) and heavy-ion reactions (e.g., ¹²C+¹²C, ¹⁶O+¹⁶O) which influence the subsequent evolutionary stages of massive stars [55]. Recently, advances have been made in this context. More than a thousand stellar models aimed at exploring properties of pre-supernova massive stars and C-O WDs have been proposed by Fields et al [56, 57]. The group found that experimental uncertainties in reaction rates (e.g., 3-α, ¹⁴N(p,γ)¹⁵O, ¹²C(α,γ)¹⁶O, ¹²C(¹²C,p)²³Na, ¹⁶O(¹⁶O,n)³¹S, ¹⁶O(¹⁶O,α)²⁸Si) dominate the variations of the properties of both, the progenitor and the CO core, such as burning lifetime, composition, central density, the core mass and O-depletion. The study allowed identification of the reaction rates that have the largest impact on the variations of the properties investigated and suggests that the variation in properties of the stellar model grows with each passing phase of the evolution towards Fe core-collapse. More progress is required to significantly improve the accuracy of stellar models and to provide more reliable nucleosynthesis predictions for nuclear astrophysics. The current generation of stellar models is still affected by several, not negligible uncertainties related to our poor knowledge of some thermodynamic processes and nuclear reaction rates, as well as the efficiency of mixing processes. These drawbacks have to be properly taken into account when comparing theory with observations, to derive evolutionary properties of both resolved and unresolved stellar populations.

The synthesis of heavy elements in massive stars provides an important source for the chemical enrichment of their surrounding ISM and hence of the universe. The ejecta of stars, the stellar yield, have been calculated by various groups since the early stage of stellar evolution modelling [58]. Each stellar mass can produce and eject different chemical elements and the yields are therefore a function of the stellar mass but also of the original stellar composition. Low and intermediate mass stars produce He, N, C and heavy s-process elements (Section 4.1). Stars with M < 0.8 M_⊙ do not contribute to the galactic chemical enrichment and have lifetimes longer than the Hubble time. Massive stars (M > 8-10 M_⊙ ) produce mainly α-elements (O, Ne, Mg, S, Si, Ca), some Fe, light s-process elements and perhaps r-process elements and explode as ccSNe. Predictions from Romano et al [59] concerning several chemical elements obtained by using different sets of stellar yields and compared to observation in stars are in agreement for some chemical species whereas for others the agreement is still very poor. The reason for that resides in the uncertainties still existing in the theoretical stellar yields. Côté et al [60] have compiled several observational studies to constrain the value and uncertainty of fundamental input parameters, including the stellar initial mass function and the rate of supernova explosions. The resulting uncertainty, which is a lower limit, depends on the galactic age and on the targeted elemental ratio. Portinari et al [61] and Marigo [62] have published the most recent complete self-consistent yield set of AGB and massive stars. Drawbacks of this set are that AGB models are not based on full stellar evolution simulations (synthetic models), the explosion yields are not consistent (based on yields by Woosley and Weaver [63]) and they include only isotopes up to Fe. Because of the lack of alternatives, these yields are still in use (e.g., [64, 65]). Despite several considerable improvements in the field of stellar nucleosynthesis in recent years, no single combination of stellar yields is found which is able to reproduce at once all the available measurements of chemical pattern and abundance ratios in the Milky Way. Further efforts need to be performed to improve and expand the current existing grids of stellar yields and to better understand their dependence on the metallicity, mass, and rate of rotation. A further discussion on stellar nucleosynthesis is given in Section 4.1.

3.1. Solar neutrino physics: current status

The production of energy in the stars through nuclear reactions has been proved only in the 60s. Thanks to the predicted solar neutrino flux [66] and to the following detection [67] of these neutrinos emitted during the H-burning it was possible to confirm the presence of thermonuclear reactions in the interior of the Sun. Neutrinos created by H-burning can escape almost without interaction straight from the heart of the star. In so doing, they carry information on what is actually happening at the center. H-burning necessarily involves the emission of neutrinos. They arise when the nuclear weak interaction changes a proton to a neutron p → n + e⁺ + _e. This must occur twice during the H-burning process 4p → ⁴He + 2e⁺ + 2_e. The expected flux of neutrinos can be found by noting that the formation of each ⁴He is accompanied by the release of two neutrinos and a thermal energy Q_eff of about 26 MeV. Results obtained from the solar neutrinos detection have been explained with theoretical predictions that account for neutrino flavor oscillations. It is interesting to point out that this explanation was proposed only after more than thirty years, and the problem is discussed here from a historical perspective. The following sections outline what is left to do in solar neutrino research and solar abundances models. We also discuss the main results from recent researches.

The solar neutrino problem was definitely solved by combining the SNO and the Super-Kamiokande measurements in 2001 [73]. The SNO collaboration determined the total number of solar neutrinos of all types (electron, muon, and tau) as well as the number of just electron neutrinos. The total number of neutrinos of all types agrees with the number predicted by the solar model. Electron neutrinos constitute about a third of the total number of neutrinos. The missing neutrinos were actually present but in the form of the more difficult to detect muon and tau neutrinos. The agreement between theoretical predictions and observations was achieved thanks to a new understanding of neutrino physics, which required a modification of the Standard Model to make neutrinos oscillations permitted [74]. There are still open questions that remain to be addressed in the future including what is the total solar neutrino luminosity, what is the CNO neutrino flux of the Sun and what is the solar core metallicity.

The latest predictions of the Standard Solar Model (SSM) and the neutrino fluxes from various processes taking place inside the Sun are given in Vinyoles et al [68] and Bergström et al [69]. As expected, the neutrinos originate from the primary reaction of the proton-proton chain, the so-called pp neutrinos, and constitute nearly the entirety of the solar neutrino flux, vastly outnumbering those emitted in the reactions that follow. These neutrinos have low energy, never exceeding 0.42 MeV. The neutrinos from electron capture by ⁷Be (the reaction which initiates the ppII reaction branch) are the next most plentiful. The ³He(α,γ)⁷Be reaction is the starting point of the ppII and ppIII reaction branches in the solar H-burning, therefore its rate has a substantial impact on the solar ⁷Be and ⁸B neutrino production. Using the SSM, the flux of these neutrinos can be calculated [70]. The reaction ³He(α,γ)⁷Be is one of the most uncertain, even if many experiments have been done in the last decade clearing up some long-standing issues [71]. Most of these cross-section measurements concentrated on the low energy range and their precision mostly reached the limits. Furthermore, there is no experimental data above 3.1 MeV, and there are conflicting data sets for the ⁶Li(p,γ)⁷Be reaction having an impact on the level scheme of ⁷Be [72].

In the last years, many efforts have been conducted in the understanding of the solar neutrino physics, including nuclear physics experiments, improvements of the SSM model and extensive solar neutrino measurements at new facilities such as Super-Kamiokande [75, 76] and Borexino [77]. Plans at Borexino [78] include improvements in purity to reduce backgrounds and enable the first detection of neutrinos from the CNO cycle [79]. SNO+ [80] is nearing completion and promises detection of proton-electron-proton (pep) as well as CNO neutrinos. The pep reaction produces sharp-energy-line neutrinos of 1.44 MeV. Detection of solar neutrinos from this reaction was reported by Bellini et al [81] on behalf of the Borexino collaboration. The detection of CNO neutrinos, together with further constraints from precision measurements of the ⁸B neutrino flux, offers the most promising pathway to determine the metal content of the Sun, which is still under debate (see [82, 83, 84, 85] and references therein). Neutrinos produced by ⁸B → ⁸Be + e⁺ + _e have very small flux, about 4.9 × 10⁶ cm⁻² s⁻¹, but because of their high-energy (up to ∼ 15 MeV) the ⁸B neutrinos dominate the fluxes of many chlorine and water detectors, such as the more recent SNO and Super-Kamiokande experiments. Despite the improvements obtained in the last measurements, the flux uncertainty associated with these neutrinos (± 10%) is rather large [86]. The uncertainty for the ⁷Be neutrinos is smaller than that for ⁸B neutrinos, about ± 5% [87] and the flux of pp-neutrinos are accurately determined to the level of 1%. Another factor to be taken into account is the different temperature-dependence of each reaction. The ⁸B neutrinos depend on temperature as T_c²⁵, where T_c is the characteristic one-zone central temperature [88]. The ⁷Be neutrinos vary as T_c¹¹. The pp-neutrinos are relatively less dependent on the central temperature. It is, however, worth mentioning the efforts made to accurately determine the cross-section of the ⁷Be(p,γ)⁸B reaction. The ⁷Be(p, γ)⁸B cross-section directly affects the detected flux of ⁸B decay neutrinos from the Sun and plays a crucial role in constraining the properties of neutrino oscillations [89]. The ⁷Be(p,γ)⁸B reaction also plays an important role in the evolution of the first stars which formed at the end of the cosmic dark ages [90]. The precision of the astrophysical S-factor at solar energies (∼ 20 keV) is limited by extrapolation from laboratory energies of typically 0.1-0.5 MeV [71]. The theoretical predictions have uncertainties of the order of 20% [91], whereas recent experiments were able to determine the neutrino flux emitted from ⁸B decay with a precision of 9% [92]. Direct measurements were carried out with the radioactive ⁷Be beam on the H₂ target [93], or with the proton beam on the ⁷Be target [94]. Furthermore, indirect measurements were performed through Coulomb dissociation method [95, 96, 97] and the transfer reaction method [98, 99]. More recently the astrophysical S-factors and reaction rates of ⁷Be(p,γ)⁸B have been also investigated by Du et al [100].

In addition to advanced neutrino detection experiments, titanic efforts are being invested in studying the solar abundance problem. Recent more accurate analyses [84, 101] have indicated that the solar photospheric metallicity is significantly lower than older values [102]. This abundance problem has been the subject of a large number of investigations and reviews [103, 83, 82, 85]. Many models have been proposed to modify the solar model, including enhanced diffusion [104], the accretion model [105, 106], etc. However, none of these models has succeeded in solving the problem. At present, the main task of solar nuclear physics is to improve the precision of the underlying nuclear reaction rates that connect neutrino observations with solar and neutrino physics, and to produce more accurate and realistic stellar models.