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4. HEAVY ELEMENTS NUCLEOSYNTHESIS

Elements much heavier than Fe, such as Pb, Au, U are not produced in ordinary stellar nucleosynthesis (fusion reactions). Their formation involves different processes occurring inside stars or during explosive and catastrophic events. During these events, the capture of neutrons or protons by atoms is the main process by which heavy elements are formed.

There are three main processes by which nucleosynthesis of heavier elements happens: the s-, the r- and the p-process [107, 108, 109].

In the following sections, we will address the main aspects associated with the neutron and proton capture nucleosynthesis. This is supplemented with an overview of observations from explosive processes that characterize ccSNe.

4.1. Massive and AGB stars

4.1.1. s-, and i-processes

The weak s-process takes place at the end of the convective He-burning core and in the subsequent convective C-burning shell [120] in massive stars (e.g., 25 M), whereas the main s-process occurs in low-mass AGB stars. It is characterized by comparably low neutron densities, so that neutron capture times are much slower than most β-decay times. This implies that the reaction path of the s-process follows the stability valley. Although the available cross-sections under stellar conditions were very scarce and rather uncertain, was already inferred [7] that the product of cross-section times the resulting s-abundance represents a function of mass number A with jumps at shell closures and gaps at branchings.

The weak s-process nucleosynthesis is responsible for the production of the low-mass range of the s-process elements from iron group seed nuclei to 58Fe on up to Sr and Y (see [121] and references therein). The neutron source is provided by the reaction 22Ne(α,n)25Mg. First attempts to investigate the possible role of rotational mixing on the s-process production in massive stars have shown that this classic picture could be significantly revised. The impact of rotation on the nucleosynthesis in low-Z massive rotating stars has been explored by different groups [122, 123, 124]. At solar metallicity, rotation-induced mixing has a moderate effect on s-process production. At very low metallicities, however, rotation-induced mixing has a much stronger effect, and therefore a heavy impact on the evolution and nucleosynthesis of the first stellar generations in the universe. Indeed, rotation leads to mixing between the He-burning core and the H-burning shell. Eventually, the He-burning products 12C and 16O are mixed into the H-burning shell, which produces 14N via the CNO cycle. Later on, the 14N is mixed back into the He-burning core, at which point it immediately converts into 22Ne via 14N(α, n)18 F(e+, nue) 18O(α, γ)22Ne. At the end of He-burning core, 22Ne(α, n)25Mg releases large amounts of neutrons and drastically changes the s-process production [125]. Due to a high neutron number density, the weak s-process possibly produces heavy nuclei up to A ∼ 200. Recent observations [126, 127] have confirmed that s-abundance in globular clusters in the bulge of our Galaxy is compatible with the s-process production in fast-rotating massive stars at low metallicity, supporting the view that massive stars could indeed be also important sources for these elements. However, there are studies about the uncertainty of nuclear physics on the s-process [128, 129, 130], and production of heavy s-process nuclei in massive low-Z stars strongly depends on rotation. The abundance is also influenced by the uncertainty of neutron source or neutron poison reactions (see [131] and references therein). The production of Sr and Ba in metal-poor stars has been investigated because of the observational importance [132]. In their work, Cescutti et al [133] presented galactic chemical evolution models using the larger grid of models and showed that rotation-induced mixing is able to explain the large scatter for [Sr/Ba] observed in extremely metal-poor stars. Since there still remain a number of stars at the lowest metallicities with only upper limits on Sr and/or Ba, increasing the sample sizes and the quality of the available high-resolution spectroscopy for stars at these metallicities is an essential step toward understanding nucleosynthesis at the earliest epochs and ultimately to characterize environmental influence of the astrophysical sites of heavy elements production [134].

As already mentioned before, the AGB phase represents the last stage of nuclear burning of small and intermediate mass stars. The AGB phase is short if compared to the MS stage, but is very important because it is a rich site of nucleosynthesis. These stars, once the supply of He for fusion in their core is exhausted, draw energy from fusion of the H and He shells around the degenerate C-O core. In this phase, the stars increase their brightness and their size, losing material from the outer layers due to strong stellar winds. One of the characteristics of the AGB phase is the intermittent thermal instability of the He-burning shells. These energy bursts manifest themselves as thermal pulses and hence this phase is known as the TP-AGB phase. These pulses typically happen every 104 - 105 years (see, for more details, [40]). The s-process nucleosynthesis in AGB stars occurs in relatively low neutron density conditions (∼ 107 neutrons/cm3) during the late stages of the stellar evolution when the star has a thin radiative layer (intershell region) and an expanded convective envelope (Fig. 4). The main neutron enrichment sources are the 13C(α, n)16O reaction, which releases neutrons radiatively during interpulse periods, and the 22Ne(α, n)25Mg reaction, partially activated during the convective thermal pulses. The production of neutrons through the channel 22Ne(α, n)25Mg is really efficient only in high-mass AGB stars (M ≥ 4 M), due to the high temperature required for this reaction to occur. Such temperatures can also be reached during the TP-AGB phase of less massive stars, but in this case, the produced neutrons only marginally affect the final distribution of the s-process abundances. This reaction takes place in a convection environment. The 13C(α, n)16O reaction requires at the same time proton and α-capture reactions to occur in the He shell. One of the problems related to the modelling of this channel of neutrons production is due to the low abundance of 13C. This element is produced during the phases following the development of the intermediate convective layer where some penetration of protons creates a reservoir of H in the He-rich layers. When the outer parts of the star re-contract and heat, H-burning is ignited again and the trapped protons are captured by the abundant 12C, inducing the chain 12C(p, γ) 13N(β+ nu)13C. However, the 13C produced is not sufficient to explain the neutron production needed for the s-process nucleosynthesis. The reaction occurs in a radiative environment and leads to the formation of the so-called 13C pocket (see [135] and references therein). The mass occupied by the 13C pocket is ΔM ≃ 7 × 10−4 M [110], and the temperature required for this reaction is of the order of T ≈ 9 × 107 K. Recently, new calculations aiming at clarifying the 13C issue have been carried out [136, 137, 138]. The models are based on the development of toroidal magnetic fields, induced by stellar dynamos, in the radiative He-rich layers below the convective envelope, and help to constrain the nucleosynthesis results obtained with the 13C pocket extension with observations from the solar composition.

Figure 4

Figure 4. Schematic structure of a TP-AGB star. The degenerate C-O core is surrounded by the H and He-burning shells. The C-O core is very compact and it is surrounded by a first shell in which the He combustion takes place. Over this layer, there is a region, called the intershell, rich in He produced from the second shell, the one where the H fusion takes place. Other elements present in non-negligible quantities are C, Ne, and O. As can be seen in the figure, the two shells are very close each other and this is precisely one of the characteristics that induce the thermal pulse and the consequent instability.

Recent advances in s-process nucleosynthesis are related to the determination of the neutron density in massive AGB stars [139, 140]. In particular, compared to solar abundances, the spectra of massive AGB stars of our Galaxy and the Magellanic Clouds, reveal a strong overabundance of Rubidium [141, 142] and high [Rb/Zr] ratios [143]. Rb is an example of element produced not only by the s-process but also by the r-process. The exact contribution of the two processes depends on the s-process model used to estimate the abundance, which is directly linked to the neutron enrichment process and, consequently, to the local neutron density. AGB stars nucleosynthesis models [110] are far from matching the extremely Rb and [Rb/Zr] values, and the explanation of Rb overabundance would eventually lead to a better understanding of the 22Ne(α,n)25Mg reaction. Within the framework of the s-procees, it is difficult to explain the lack of co-production of Zr, which is part of the same production peak of Rb and should be produced in similar quantities. Some solutions have been discussed in the literature to account for the Rb overabundance. Karakas et al [112] demonstrated that for solar-metallicity stars, [Rb/Fe] ∼ 1.4 could be reached if the final stage of mass loss was delayed, resulting in a larger number of thermal pulses and increased Rb production. However, the observed [Zr/Fe] ratios are roughly solar (within 0.5 dex [144]), suggesting no production of this element in intermediate mass AGB stars. A different explanation has been proposed, such as the possibility that the gaseous Zr, having a condensation temperature (1741 K) [145] greater than that of Rb (800 K), condenses in dust grains, producing an apparent lack of Zr, when measured from the molecular bands of ZrO [146, 143]. Others possible solutions to the problem include the fact that the Magellanic Cloud observations are very uncertain, an incomplete understanding of the atmospheres of luminous AGB stars [142] and a different AGB mass-loss rate [147, 148]. Clearly, the future resolution of the Rubidium problem promises to be an exciting challenge.

The nucleosynthetic model for the lighter s-process elements between Sr and Ba is not well understood yet. Travaglio et al [153] studied these elements and by summing up all contributions from their model the authors found that 8%, 18% and 18% of Sr, Y, and Zr were missing. This missing fraction is assumed to come from primary origin from massive stars at low [Fe/H]. Because the process mainly affects the lighter peak elements this additional (unknown) nucleosynthetic contribution is called Lighter Element Primary Process (LEPP), or weak r-process [154], and could explain some differences between these elements. Recently, the LEPP abundances have been further investigated by many authors [155, 156, 157] confirming the need for an additional process to account for the missing component of the light s-process isotopes. Most of the elements are produced through a mixture of s- and r-process [158]. This makes it harder to determine which of the processes are involved when creating the elements. The main component of the s-process is produced at metallicities starting at [Fe/H] ∼ -0.66 [159], which corresponds to the time interval t > 2.6 Gyr. Going to even lower metallicities or further back in time, gives insight into an undiluted view on other processes. At lower metallicities, from [Fe/H] ∼ -1.16 to [Fe/H] ∼ -0.66 [159], the site for the strong component of the s-process was identified. At even lower metallicities, before the s-process sets in, the LEPP is believed to occur somewhere in stars. According to Cristallo et al [160] a variation of the standard paradigm of AGB nucleosynthesis would make it possible to reconcile models predictions with solar system s-only abundances. However, the LEPP cannot be definitely ruled out, because of the uncertainties still affecting stellar and galactic chemical evolution models. Several scenarios have been recently explored, both involving the primary r-process during the advanced phases of explosive nucleosynthesis (see [161] for a review) or secondary s-process in massive stars (e.g., cs-component [162]). Therefore, even if promising theoretical improvements related to the explosive phases of massive stars and ccSNe, as well as recent spectroscopic investigations [163, 164] have been made, a full understanding about the origin of the neutron capture elements from Sr up to Ba is still lacking.

New models and observations have suggested that in addition to the well-known slow- and rapid neutron capture processes, there may be an intermediate mode of neutron capture nucleosynthesis, the so-called i-process. This process is defined by a neutron flux larger than those found in the well-established s-process, yet smaller than the extreme conditions of the r-process. A possible signature of the i-process [149] could be the simultaneous enhancement of Eu, usually considered an r-process element, and La, usually considered an s-process element, in some carbon enhanced metal-poor stars that have been classified as CEMP-r/s stars [150]. Post-AGB stars have been discussed earlier as possible nucleosynthesis sites for the i-process, yet there are still discrepancies and open questions to be addressed. In a new study by Jones et al [151], super-AGB stars are identified as another possible astrophysical site for the i-process. In their new computational models of these very heavy AGB stars, mixing at convective boundaries are taken into account according to a parameterized model. These new stellar evolution models suggest that proton-rich material could be convectively mixed into He-burning shell, leading to conditions suitable for the i-process. Interestingly, it could be shown that i-process conditions are more prominently found in models with lower metal content, indicating that the i-process could have been more important in the early universe. 1-D stellar evolution models can only identify possible sites for i-process nucleosynthesis [151] but the H-ingestion ashes are likely associated with substantial nuclear energy release, reaching maybe the level of the local binding energy of the He-burning shell. Such enormous energy input is coupled with a multi-scale turbulent mixing which cannot be realistically described with 1-D simulations [152]. 3D stellar hydrodynamics simulations are mandatory to understand these nuclear astrophysics events fully and provide the appropriate context for further nuclear astrophysics investigations.

A recent discussion has proposed the possibility of neutrons catalyzing the formation of heavier nuclei, for example, the formation of the Rydberg nuclear molecule 16O (10Be + n + n + 10Be), which might exist in rich neutron environments within AGB stars [165]. In this mechanism of formation, neutrons mediate the Efimov long-range interaction of the Be nuclei, and could eventually be used to form other nuclear molecules with heavier nuclei facilitating the nuclear reaction and eventually nucleosynthesis. Calculations show that one cannot confirm, but it is also difficult to rule out the existence of such molecules based on what is known about nuclear interactions.

4.2. Supernovae

Supernovae can be distinguished into two kinds: Type Ia (SNIa) which are thought to be the explosion of a WD in a binary system that accretes sufficient mass from its companion, and all the rest (Type II, Ib, Ic), which are generated within several possible scenarios (for a review of all scenarios see, [166, 167, 168]). Observationally they can be classified according to the absence (Type I) or presence (Type II) of H lines in their spectra. Type II (SNII), Ib and Ic, are produced from massive stars ≈ 10 M and are observed in the spiral and irregular galaxies. SNIa happens in all types of galaxies with no preference for star-forming regions, consistent with their origin from an old or intermediate age stellar population. Within the framework of SNIa the general scenario is that a C-O WD accretes mass from a companion star in a binary system until it ignites near to the Chandrasekhar mass [169]. The companion star of the C-O WD is usually a He-burning star or a He-rich WD [170, 171, 172, 173, 174]. It has been proposed that the detonation of the He-rich shell is triggered via thermal instability if the companion of the C-O WD is a He star (e.g., [175]), whereas the detonation of the He-rich envelope is ignited dynamically if the companion is a He-rich WD (e.g., [171]). For more discussions on the progenitors of SNIa see, [176, 177, 178, 179]. WD instabilities are relevant for SNIa since are related not only to strong magnetic fields in the star interior [180] but also to neutronization due to electron capture reactions. Because of this reaction, atomic nuclei become more neutron-rich and the energy density of the matter is reduced, at a given pressure, leading to a softer Equation of State. Other nuclear reactions that turn very massive WDs unstable are the pycnonuclear fusion reactions in the cores of these compact stars [181, 182]. These reactions among heavy atomic nuclei, schematically expressed as ZAY + ZAY2Z2AY, are possible due to the high density matter of WDs; an important reaction is carbon on carbon, 12C + 12C. Pycnonuclear reactions have been found to occur over a significant range of stellar densities (see, for instance, [183]), including the density range found in the interiors of WDs [184, 185]. Recently, WD calculations in general relativity also showed that central energy densities are limited by nuclear fusion reactions and inverse β-decay [184, 181]. The nuclear fusion rates at which very low energy pycnonuclear reactions proceed, however, are highly uncertain because of some poorly constrained parameters [186]. Finally, it should be mentioned that very recently it has been suggested that pycnonuclear reactions could be able to drive powerful detonations in single C-O WDs [187].

4.2.1. Explosive nuclear burning: observations

The explosive nucleosynthesis is associated with the passage of the ccSN shock wave through the layers above the PNS (see [188] for a review). The shock heats the matter it traverses, inducing an explosive nuclear burning characterized by short times which lead to large deviations from equilibrium and hydrostatic nuclear burning patterns. This explosive nucleosynthesis can alter the elemental abundance distributions in the inner (Si, O) shells. The properties of the process are tied to those of the explosion. The details of the nucleosynthesis, which produces radioactive nuclei such as 26Al, 28Si, 44Ti, 56Ni and 56Co during the explosions, are not yet fully understood. In order to shed light on the mechanism which drives the explosive nucleosynthesis, one can have some hints from the observations of the energy and material which are injected into the interstellar medium from ccNS explosions. Some of this material, which is the result of nucleosynthesis processes occurring during the explosion, is made of radioactive isotopes, and therefore allow us to infer the ccSN nucleosynthesis conditions which are needed in order to produce them. For instance, the observations of gamma-rays from 44Ti and 56Ni in ccSN events represents a valuable tool to penetrate deep into the interiors of these explosions, which are otherwise only accessible through neutrinos [189]. In this section, we outline the results of the comparison of explosive nucleosynthesis models with observations from ccSNe. Since the launch of the INTEGRAL observatory has been possible to accurately determine the gamma-ray flux associated to heavy elements produced by the astrophysical sources. The main site of production of the radioisotope 44Ti is thought to be the innermost ejected layers of ccSN explosions, and the study of its abundance has been the focus of several works [190, 191, 192]. The 44Ti yield of ccSNe is notoriously difficult to calculate because it depends on the explosion energy and on the symmetry of the explosion [193]. 44Ti is believed to be produced in the deepest layers of the exploding star from which it may be ejected, and theoretical calculations indicate that both increased explosion energy and increased asymmetry result in an increased 44Ti yield. Observationally, the presence of the radioisotope 44Ti is revealed to the gamma-ray astronomer through the emission of three gamma-ray lines. The decay 44Ti → 44Sc gives rise to gamma rays at 67.9 keV and 78.4 keV. The subsequent decay 44Sc → 44Ca gives rise to a line at 1157.0 keV. The amount and the velocity of 44Ti is a powerful probe of the explosion mechanism and dynamics of ccSNe, and in addition, the 44Ti gamma-ray line emission is an ideal indicator of young supernovae remnants. Up to now, 44Ti has not yet been directly detected in SN 1987A. From modelling of the Ultraviolet Optical Infrared (UVOIR) light curves, which are usually modeled by the radioactive decay, different values of the amount of produced 44Ti have been predicted, which do not always agree with each other, neither within the respective uncertainties. For example, from analysis of X-ray data taken from INTEGRAL, Grebenev et al [194] suggested a value of (3.1 ± 0.8) × 10−4 M, while UVOIR bolometric light curves analysis of Seitenzahl et al [195] indicate a value (0.55 ± 0.17) × 10−4 M. Observations of the supernova remnant Cas A by the Nuclear Spectroscopic Telescope ARray (NuSTAR) suggested for the produced amount of 44Ti a value of (1.25-0.3) × 10−4 M, by measuring the flux of decay lines of 44Ti at about 78 and 68 keV [196]. Furthermore, there is a lack of consistency between the theoretical predictions and observations. Spherically symmetric (1D) models of SN 1987A produce, in general, a few 10−5 M 44Ti [195]. For instance, Perego et al [197] using the method PUSH to produce a 1D supernova explosion, which better fits to the produced amounts of 56Ni in SN 1987A, predict an amount of 3.99 × 10−4 M for 44Ti. Magkotsios et al [190] investigated the 44Ti abundance produced from ccSNe by studying the impact on the 44Ti abundance evolution of variation of the nuclear reactions, including (α,γ), (α,p), (p,α), and (α,n) in light and intermediate mass targets. It was found that the variation in the 17F(α,p)20Ne reaction rate causes a primary impact on the 44Ti abundance. The 17F(α,p)20Ne reaction rate, however, has never been measured. Because the reaction rate may be dominated by the properties of energy levels of 21Na above the α-threshold at 6.561 MeV, searching for energy levels of 21Na and studying their properties may impact our understanding of the abundance evolution of 44Ti. In this context, the reaction 24Mg(p,α)21Na plays a central role and knowledge of its rate is of key importance. The 24Mg(p,α)21Na reaction was recently measured by Cha et al [198] in order to make a spectroscopic study of the energy levels in the 21Na for the 17F(α,p)20Ne reaction rate at stellar temperatures. Further comparisons between observations and models are clearly demanded in the future, and more precise nuclear physics inputs are required.

The short-lived radioisotope 56Ni is also synthesized in the deep interiors of ccSN explosions. CcSN light is understood as being powered mainly by 56Ni radioactive decay, as demonstrated by the characteristic light curve and spectral-evolution data [199]. These radioactive isotopes carry the information about the environment of the explosion formation, unaffected by the violent expansion of the ccSN [200]. One of the key issues from observations is the broad range of inferred amounts of 56Ni. The proximity of SN 1987A allowed the very first detection of gamma-ray lines from the radioactive process 56Ni → 56Co → 56Fe [201]. By estimates of the extinction towards Cas A and the Fe mass from X-ray observations, Eriksen et al [202] predict the mass of 56Ni to be in the range (0.58-0.16) M. The standard value is 56Ni ∼ 0.07 M [195]. Different theoretical predictions have been carried out for the amount of 56Ni. Concerning Cas A, Magkotsios et al [190] post-processed the trajectories of a 1D ccSN model from Young et al [203], whose progenitor was designed to match Cas A, and obtained a value of 2.46 × 10−1 M for 56Ni. While using a two-dimensional rotating 15 M model of Fryer and Heger [204], they obtain a higher value of 3.89 × 10−1 M for 56Ni. However, it must be emphasized, that all the above models do not follow the ccSN shock wave long enough, and therefore hydrodynamic trajectories have to be extrapolated in order to be able to perform nucleosynthesis calculations.

Another important element which is synthesized during the final burning stage is the gamma-ray emitter 26Al, which has been detected in the interstellar medium of our Galaxy [205, 206]. 26Al is produced mainly in massive star winds and during ccSN explosions. 26Al production for different candidate sources has been estimated by various groups [207, 208, 209]. Chieffi and Limongi [210] include stellar rotation and its effect upon the computed yields compared to non-rotational models. The galactic mass yields of 26Al is ∼ 1.7-2.0 ± 0.2 M [211]. Voss et al [212] studied the variations between different models of massive stars, in particular, the effects of rotation and the strength of wind mass-loss on the radio-active tracers and the energetics of star-forming regions. The individual nearby star-forming regions Sco-Cen [213], Orion [212], and Cygnus [214] have been studied in detail and good agreement has been found between theory and the observations. Theoretical ccSN models, however, suffer from considerable uncertainties in 26Al production because of a lack of experimental knowledge of the reactions that create and destroy 26Al under ccSN conditions [63, 208]. For instance, the uncertainties in the nuclear reaction rates responsible for the formation of 26Al ejected in the supernova explosions lead to uncertainties of a factor ∼ 3 [215]. Classical novae [216] are one potential source of 26Al and it has been shown that up to 0.4 M of the galactic abundance could have been produced in these sites [217]. In particular, the 26Al(p,γ)27Si [218] reaction strongly affects the abundance of 26Al in nova ejecta. The short-lived isomer, 26mAl in the destruction of 26Al in novae plays a special role since 26mAl and 26Al are in quasi-equilibrium in these conditions, and thus knowledge of both, the destruction of the ground state and isomer, is needed to determine the effective 26Al half-life and ejected abundance. Therefore indirect studies are required to determine the 26mAl(p,γ)27Si reaction rate. Moreover, 26Al nucleosynthesis in novae is also contributed by the 23Mg(p,γ)24Al reaction. The 23Mg(p,γ)24Al reaction was measured directly for the first time at the DRAGON facility to a precision sufficient for novae yield purposes [219]. Measurements led to a reduction in the uncertainties of ejected 26Al in the types of nova model seen in, e.g., [220]. Nevertheless, at temperatures lower than those reached in O-Ne classical novae, the rate is still dominated by direct capture and uncertainties will be related to this component.

4.2.2. r-process

Neutrinos play a crucial role in our understanding of SNII (see, for example, [221]). According to the currently most widely accepted theory for the explosion of a massive star, the explosion energy is provided by the neutrinos that are abundantly emitted from the nascent PNS and interact with the material of the progenitor star (Fig. 5). This energy deposition is not only supposed to power the propagation of the supernova shock into the stellar mantle and envelope regions as well as to cause the violent disruption of the star but also drives a mass outflow from the surface of the PNS. This continues for more than 10 seconds and might be a suitable site for r-process nucleosynthesis. The baryonic outflow that expands with supersonic velocities is known as the neutrino-driven wind [222]. The PNS cools by emitting neutrinos, i.e., nue, bar{nu}e. As these neutrinos pass through the hot material predominantly consisting of free nucleons immediately outside the PNS, a fraction of the nue and bar{nu}e can be absorbed through nue + np + e and bar{nu}e + pn + e+. On average, a nucleon obtains ∼ 20 MeV from each interaction with nue or bar{nu}e. In order to escape from the PNS gravitational potential of GMNS mu / RNS ∼ 200 MeV, a nucleon in the wind must interact with nue and bar{nu}e for ∼ 10 times. Eventually, the neutrino-driven wind collides with the slow, early ccSN ejecta resulting in a wind termination shock or reverse shock [223]. The above reactions also interconvert neutrons and protons, thereby determining the electron fraction Ye in the wind [224]. The neutrino-driven wind has attracted vast attention over the last 20 years as it was suggested to be a candidate for the astrophysics site where half of the heavy elements are produced via the r-process [222]. The general conditions required for the r-process were investigated both via analytical [225] and via steady-state [226] models of neutrino-driven winds.

Figure 5

Figure 5. Schematic representation of the neutrino-driven wind from the surface of the recently born PNS. The horizontal axis gives mass information whereas the vertical axis shows corresponding radii, with Rns and Rnu being the NS and neutrinosphere, respectively. The supersonic neutrino-driven wind, which forms after the onset of the explosion, provides favorable conditions for the r-process – a high neutron abundance, short dynamical time scales, and high entropies. In this high-entropy environment, it is possible that most nucleons are in the form of free neutrons or bound into α particles. Thus, there can be many neutrons per seed nucleus even though the material is not particularly neutron-rich. The predicted amount of r-process material ejected per event from this environment agrees well with that required by simple galactic evolution arguments. For more details, the reader is referred to [227].

In order to account for the solar r-process abundances associated with the peaks at A ∼ 130 and 195, each supernova must eject ∼ 10−6 – 10−5 M of r-process material. Although the current neutrino-driven wind models have difficulty in providing the heavy r-process conditions [237], the wind naturally ejects ∼ 10−6 – 10−5 M of material over a period of ∼ 1 s [228]. This is because the small heating rate due to the weakness of neutrino interaction permits material to escape from the deep gravitational potential of the PNS star at a typical rate of ∼ 10−6 – 10−5 M s−1 [226]. Indeed, the ability to eject a tiny but interesting amount of material was recognized as an attractive feature of the neutrino-driven wind model of the r-process (e.g., [229]). However, current models fail to provide the conditions for an r-process to occur in the wind. For instance, the production of heavy r-process elements (A > 130), requires a high neutron-to-seed ratio. This can be achieved by the following conditions: high entropy, fast expansions or low electron fraction [230, 226]. As Arcones et al [231] remark, these conditions are not yet realized in hydrodynamical simulations that follow the outflow evolution during the first seconds of the wind phase after the explosion [232]. Contrarily, the weak r-process, which accounts for the lighter neutron-capture elements (A ∼ 80 peak), is strongly believed to take place in neutrino-driven winds that could occur in ccSNe or collapsar accretion disks [233]. The astrophysical conditions required to produce the peak region through weak r-process can be found in the recent study by Surman et al [234]. Once the wind has cooled down after a few seconds, charged particle reactions are key in the production of the heavy elements. For a typical wind evolution, the (α,n) is faster than all other charged particle reactions, thus driving the nucleosynthesis evolution in neutron-rich winds. None of the most relevant (α,n) reactions had been measured in the energy range relevant for weak r-process astrophysical conditions. So far modelers have to rely on theoretical predictions of those rates. Furthermore, the theoretical uncertainties of the calculated reaction rates can be as high as 2 orders of magnitude and abundance network calculations are highly sensitive within the expected theoretical uncertainties of these rates [235]. A recent systematic study searching for the critical reaction rates that influence the most of the final abundances in weak r-process scenarios has allowed identifying the most impactful reaction rates, which can then be pinned down experimentally by measurements in radioactive beam facilities [236]. Most of the reaction rates responsible for the production of elements (A ∼ 80) in neutrino-driven winds are either viable with current beam intensities in existing nuclear physics facilities or will be in the near future. Nuclei that participate in the r-process typically have half-lives that are too short to allow them to be made into a target. As neutron targets are not available, neutron capture experiments performed on these nuclei represent a big challenge. Improvements in theoretical reaction rates are needed, along with the advances in experiments, to reduce these fundamental nuclear physics uncertainties. Another possible scenario could be the r-process nucleosynthesis in the neutrino-driven outflows from the thick accretion disk (or "torus") around a BH, as recently investigated by Wanajo et al [238]. BHs accretion torus is expected as remnants of binary NS or NS-BH mergers. The computed mass-integrated nucleosynthetic abundances are in good agreement with the solar system r-process abundance distribution, suggesting that BH torus winds from compact binary mergers have the potential to be a major, and in some cases dominant, production site of r-process elements [239].

There is direct evidence that ccSNe also produce Magnetohydrodynamic (MHD) jets with a power comparable to the explosion itself [240, 241, 242]. Expected speeds are ∼ 0.25-0.5c (the escape speed from the new PNS). While NSs are expected to be left after ccSN explosions, it has been suggested that a star of more than 25 M may collapse to a BH [243]; an accretion disk is formed around the BH if the star has enough angular momentum before the collapse. This system could produce a relativistic jet of gamma-ray (GRBs, see Section 4.3.3) due to MHD effects, whose system is called a Collapsar model [244]. Magnetically driven jets of collapsar models have been extensively investigated as a site of the r-process [245, 246]. Strong magneto-rotational driven jets of the collapsar model can produce heavy r-process nuclei with a very simple treatment of BH formation [247]. Estimations of the compositions of jets ejected by a collapsar have shown that the synthesis of heavy elements can occur also in the ejection phase during the core-collapse of the star [115]. It was found found that elements like U and Th are synthesized through the r-process when the source has a large magnetic field (1012 G). In addition, many p-nuclei are produced in the jets. The material far from the axis does not fall straight in but forms an accretion disk first if the angular momentum of the star is high enough. For high accretion rates, the accretion disk is so dense and hot that nuclear burning is expected to proceed efficiently, and the innermost region of the disk becomes neutron-rich through electron captures on nuclei. This region is an efficient r-process site, and about 0.01 M of massive neutron-rich nuclei can be ejected from the collapsar being U and Th the most abundantly synthesized elements [248]. Recent nucleosynthesis calculations in a three-dimensional MHD supernova model have suggested that such supernova could be the sources of the r-process elements in the early Galaxy [249]. However, in those calculations, the produced nuclei are limited to primary synthesized ones inside the jets and comparisons with the solar system abundances have been focused on elements heavier than iron-group nuclei. Ono et al [250, 247] performed explosive nucleosynthesis calculations inside the jetlike explosions for the collapsar of a massive He core star of 32 M. These calculations include hydrostatic nucleosynthesis using a nuclear reaction network, which has 1714 nuclei (up to 241U). The jet model cannot considerably produce both the elements around the third peak of the solar r-elements and intermediate p-elements when compared with the previous study [115, 251] of r-process nucleosynthesis calculations in a collapsar model of 40 M. This may be attributed to the differences in the progenitor and the specified initial angular momentum and magnetic field distributions. A study by Banerjee et al [252] has shown that the synthesis of rare elements, such as 31P, 39K, 43Sc, and 35Cl and other uncommon isotopes is also possible. These elements, which are produced in the simulations at outer parts of low Ṁ accretion disks (i.e., 0.001-0.01 M s−1), have been discovered in the emission lines of some long GRBs afterglows. However, they are yet to be confirmed by future observations. More different models have been proposed. The list includes calculations based upon a model for a MHD+neutrino-heated collapsar jet [253], prompt-magnetic-jet and delayed-magnetic-jet explosion models [254] and rapidly rotating strongly magnetized core-collapse models [242, 255, 256]. For additional information on topics related to the r-process in ccSNe, see [257].

4.2.3. p-process

In this section, we will outline the latest progress associated with the production of p-nuclei during supernovae explosions. The number of proton-rich isotopes cannot be synthesized through sequences of only neutron captures and β-decays, therefore the postulation of a third process is required (see, for example, [258] and references therein). There are several possibilities to get to the proton-rich side. As discussed above, p-nuclei are synthesized by successively adding protons to a nuclide or by removing neutrons from pre-existing s- or r-nuclides through sequences of photodisintegrations. Under conditions encountered in astrophysical environments, it is difficult to obtain p-nuclei through proton captures because the Coulomb barrier of a nucleus increases with increasing proton number. Furthermore, at high temperature (γ,p) reactions become faster than proton captures and prevent the build-up of proton-rich nuclides. Photodisintegrations are an alternative way to make up p-nuclei, either by destroying their neutron-richer neighbour isotopes through sequences of (γ,n) reactions or by flows from heavier and unstable nuclides via (γ,p) or (γ,α) reactions and subsequent β-decays. It is clear that the term p-process is used for any process synthesizing p-nuclei, even when no proton captures are involved. Indeed, so far it seems to be impossible to reproduce the solar abundances of the p-isotopes by one single process. In our current understanding, there is evidence that more than one process in more than one astrophysical scenario is relevant for the production of p-nuclei [233, 118, 259, 260, 261]. Arnould [109] proposed the p-process in presupernova phases, and Woosley and Howard [262] proposed the γ-process in supernovae. This so-called γ-process requires high stellar plasma temperatures and occurs mainly in explosive O/Ne-burning during a ccSN (see, for example, [263, 260, 264]). The γ-process during a ccSN explosion is the most well-established astrophysical scenario for the nucleosynthesis of the p-nuclei [262]. Since earlier works [265, 266] the O/Ne-rich layers of massive stars were considered to host the γ-process. The γ-process is activated with typical timescales of less than a second when the shock front passes through the O/Ne-burning zone. Historically there are 35 p-nuclides identified, with 74Se being the lightest and 196Hg the heaviest. The isotopic abundances of p-nuclei are 1-2 orders of magnitude lower than for the respective r- and s-nuclei in the same mass region. The nuclear reactions occurring in the γ-process are mainly induced by photons in the MeV-energy range, being the reaction rate determined by the Planck distribution. Temperatures of the order of several 109 K are required to provide a sufficient energy. Such temperatures are realized within ccSN explosions. Explosive events also provide the correct timescale of several seconds – if the photon intensity would last for longer times the seed distribution would completely convert to light isotopes without leaving p-nuclei behind. In the early work of Woosley and Howard [262], it was discovered that different conditions are required to produce the complete range of p-nuclei from 74Se up to 196Hg. Therefore, different density and temperature profiles were dedicated to different layers of material of ccSNe. A typical range of peak temperatures is 2 to 3 × 109 K while maximum densities vary between 2 × 105 g cm−3 and 6 × 105 g cm−3. A combination of a density profile and a temperature profile is often referred to as trajectory. These trajectories vary significantly for different astrophysical sites fulfilling the general conditions.

It has been shown that the γ-process scenario suffers from a strong underproduction of the most abundant p-isotopes, 92,94Mo (see, for example, [268]) and 96,98Ru. In contrast to the r- and s-process, the abundances produced in the γ-process vary significantly with the composition of the seed distribution. Detailed studies performed by Costa et al [269] showed that an enrichment of weak s-process material allows for a sufficient production of the Mo and Ru p-nuclei. At the same time, the overproduction factors of the lighter p-nuclei are further increased. Therefore, a variation of the seed distribution alone cannot solve the overabundance of the Mo-Ru isotopes. CcSN models cannot reproduce the relatively large abundances of 92,94Mo and 96,98Ru, even taking into account nuclear uncertainties [263, 270], except for a possible increase of the 12C + 12C fusion reaction rate [162]. Based on the observations from metal-poor stars of the galactic halo, these elements can be considered as highly mixed elements, where contributions from s-process of stellar nucleosynthesis and main and weak r-processes are all mixed with smaller contributions from the main p-process. Alternatively, other processes in massive stars different from the classical p-process have been proposed to contribute to the missing Mo-Ru p-abundances, e.g., the nup-process in proton-rich neutrino wind conditions [271]. Mo and Ru are promising elements for studying the extent of planetary scale nucleosynthetic isotopic heterogeneity in the inner solar system. Both the elements have seven isotopes of roughly equal abundance that were produced by distinct nucleosynthetic processes. Furthermore, they occur in measurable quantities in almost all meteorite groups, permitting a comprehensive assessment of the extent of any isotopic heterogeneity in the inner solar system. Identifying isotope anomalies at the bulk meteorite scale provides important information regarding the extent and efficiency of mixing processes since the isotope variations are most readily accounted for by variable abundances of p-, s- and r-process in these samples. Isotopic heterogeneity in iron meteorites and bulk chondrites has been observed for a number of elements, including Mo [272] and Ru [273]. These results contrast with evidence for isotopic homogeneity [274, 275]. Mo isotopic anomalies in the bulk meteorites correlate with those in Ru exactly as predicted from nucleosynthetic theory, providing strong evidence that the correlated Ru and Mo anomalies are caused by a heterogeneous distribution of one or more s-process carriers [276, 273, 277]. However, the extent of the isotope anomalies in meteorites is poorly constrained because previous studies obtained different results regarding the presence of Mo isotopic anomalies in meteorites [274, 272, 278]. The origin and extent of nucleosynthetic Mo-Ru isotope variations in meteorites and their components need to be further investigated and more detailed neutron capture process yields are required to determine their contribution to the abundance of the elements. Typical theoretical overproduction factors are shown in Figure 6 for all p-nuclei. If the lightest p-nuclei 74Se and 80Kr are ignored, on average, a monotonic increase is observed with increasing mass number. This trend cannot be corrected by nuclear physics uncertainties as shown in [267] but is based on the model, e.g., the heaviest p-nuclei only survive in the outermost layers with the lowest peak temperatures, an effect which might be overestimated in the current models. Usually, the seed composition is a mixture of r- and s-process nucleosynthesis as found in the solar abundance distribution. There are many excellent papers on the Mo-Ru problem, and the interested reader will find more information in [279, 280, 281].

Figure 6

Figure 6. Overproduction factors <F> of p-nuclei in SNII of 25 M stars. Top: The light p-nuclei 92,94Mo and 96Ru are most strongly underproduced. Data taken from [263]. Bottom: Displayed for each nuclide are the maximum and minimum abundances predicted from the p-process calculations. Nuclear uncertainties indicated by the vertical bars are not the only source of the observed trends. Adapted from [267]. For details, see text.

Another process in ccSNe that can produce the light p-process nuclei up to Pd-Ag, including 92Nb, is the combination of α, proton, neutron captures, and their reverse reactions in α-rich freezeout conditions [282]. Neutrino winds from the forming NS are also a possible site for the production of the light p-process nuclei [283, 284], although one of its possible components, the nup-process [118], cannot produce 92Nb because it is shielded by 92Mo [271]. The same occurs in the case of the rp-process in X-ray bursts [285] (see Section 4.3.2). Moreover, the total amount of p-nuclei produced in one event and the expected rate of SNII explosions do not match the absolute observed abundances. Therefore, SNIa were investigated as an additional site [286]. In total, the same trend was observed as shown in Figure 6 for SNII. The underproduction of the Mo-Ru p-nuclei was less pronounced maybe due to the slightly higher temperatures. Despite the total amount of p-nuclei produced in one event is higher than for SNII the less frequent occurrence of SNIa reduces their contribution to the observed abundances [287]. Two recent studies [261, 288] confirm these findings, although the estimated underproduction of 92,94Mo and 96,98Ru is further decreased by an additional contribution to their abundances stemming from proton capture reactions. Thus, a combination of both SNIa and SNII is mandatory to match the absolute observed abundances. There might be additional but small contributions from events occurring less frequently like, e.g., sub-Chandrasekar mass supernovae [289] or pair-creation supernovae [290]. As for SNIa, processes besides the γ-process also contribute at these more exotic sites.

It is also worth mentioning the nucleosynthesis of Ta, which has remained a puzzle over the years. An accurate determination of the isotopic composition of Ta would enable p-process nucleosynthetic calculations to be evaluated in terms of an accurate isotope abundance for 180Ta. This nuclide is produced by both the p- and s-process and has the remarkable property of being the rarest isotope in the solar system, which exist in a long-lived isomeric state at Ex = 77 keV (t1/2,iso > 1015 yr) with an isotopic abundance of about 0.012%, so that in reality one is measuring the isotope abundance of 180mTa, which is a unique situation in nature. In its ground state, 180Ta decays to 180Hf and 180W with a half-life of only 8 hours. 180mTa is the rarest isotope in nature and is, therefore, an important isotope in deciphering the origin of the p-process. Over the years many processes, such as slow- and rapid neutron capture reactions in stars and ccSN explosions, photon- and neutrino-induced reactions in ccSNe, have been proposed to be the production mechanism of 180Ta. However, no consensus exists and it has been theoretically shown that 180Ta could be exclusively explained with the γ-process (γ, n) [266]. The s-process alone can exclusively explain the production of 180Ta, as well, mostly via branching in 179Hf through the reactions 179Hf(β) 179Ta(n, γ) 180Ta and/or 179Hf(n, γ) 180mHf(β) 180Ta [291]. Furthermore, more exotic reactions such as neutrino processes, which include 180Hf(nue, e)180Ta, have been proposed to partly explain its synthesis [292, 293]. Nevertheless, the significance of individual processes cannot be clearly determined as a result of the uncertainties on the reaction rates for 180Ta due to unavailability of experimental data, such as the γ-ray strength function [294]. An accurate determination is required to provide a better basis for p-process production calculations [295]. Recently, a high-precision method has been developed to measure the isotope ratios from extraterrestrial samples with low concentrations of Ta, but the extreme difference in isotope abundances of a factor of more than 8000 makes the precise and accurate determination of Ta isotope ratios by mass spectrometry very challenging (see, for more details, [296]).

4.3. Neutron star and neutron star-black hole mergers

4.3.1. r-process

The original site for the production of r-process nuclei was proposed by Tsuruta et al [297] early in the development of the theory of nucleosynthesis. It relies on the fact that at high densities (typically ρ > 1010 g cm−3) matter tends to be composed of nuclei lying on the neutron-rich-side of the valley of nuclear stability as a result of endothermic free-electron captures [298]. Such conditions are found in the compression of the matter when the NS forms and in the merger of two NSs, making these systems promising sites of heavy r-process elements [299, 300, 301]. It was estimated that 5% of the original NS mass may be ejected during tidal disruption of the NS in a NS-BH merger [302, 303]. Recent estimates for the amount of cold NS matter ejected during a NS merger range from ∼ 10−4 M to ∼ 10−2 M [304], with velocities 0.1-0.3c. For NS-BH mergers, the ejecta can be up to ∼ 0.1 M, with similar velocities [305]. Most of the dynamical ejecta originate from the contact interface between the colliding binary components, which get deformed into drop-like shapes prior to the merging, as seen in Figure 7. Subsequently, the shock-heated matter is expelled by quasi-radial pulsations of the remnant in a broad range of angular directions. For the 1.35-1.35 M binary the ejecta in the shear interface between the stars are separated into two components, each being fed (nearly) symmetrically by material from both colliding stars. The mass ratio also influences the ejected mass, with very asymmetric binaries generating up to about twice the material as a symmetric binary of the same total mass [306]. Recent works have used detailed hydrodynamic simulations of mergers of two NSs to find a robust production of r-process nuclei with A ≳ 130 (e.g., [307, 306]). Based on these studies, the extremely neutron-rich ejecta is heated by β-decay during its decompression and can also be shocked to high temperatures during its dynamic ejection. Due to the very high initial density of the dynamical ejecta, heavy nuclei are already present during the nuclear statistical equilibrium phase of the expansion. The subsequent hot r-process undergoes fission cycling, thereby producing a stable abundance pattern for A ≳ 130. Important results have been obtained from recent research (e.g., [308, 309, 310, 311, 312, 239]) including simulations that consider both the composition of the dynamical ejecta and the neutrino wind (along the poles), where matter is ejected from the hot NS up to the point of BH formation, followed by the ejection of matter from (viscous) BH accretion disks. The main aspects of these studies can be summarized as follows: the dynamical ejecta mass depends weakly on the mass ratio and significantly on the binary asymmetry degree; outflows from BH accretion discs formed in NS mergers provide an important contribution to the r-process yields of compact binary mergers; the time and angle dependency of the composition in the neutrino wind nucleosynthesis; eccentric binaries can eject orders of magnitude more mass than binaries in quasi-circular orbits and only slightly less than NS-BH mergers. In NS-BH mergers [313, 314, 315, 305, 316] the primary mechanism of mass ejection is the tidal force that disrupts the NS on the equatorial plane via angular momentum redistribution [304]. The geometry of the ejecta is thus fundamentally different from that of NS mergers, as Figure 8 illustrates. Also, the ejecta from NS-BH mergers often covers only part of the azimuthal range [305].

Figure 7

Figure 7. Merger and mass ejection dynamics of the 1.35-1.35 M binary neutron-star with the nuclear equation of state DD2, visualized by the color-coded conserved rest-mass density (logarithmically plotted in g/cm3) in the equatorial plane. The dots mark particles which represent ultimately gravitationally unbound matter. Credit: [306], reproduced with permission.

One interesting aspect to be discussed relates to the ejected nucleosynthesis composition from compact object mergers. The nucleosynthesis is constrained by solar r-process abundances and by observations of low-metallicity stars. NS and NS-BH mergers seem to significantly contribute to the galactic r-process abundance pattern. However, the results obtained by different studies are conflicting or inconclusive. For instance, the overall amount of heavy r-process material in the Milky Way is consistent with the expectations of mass ejection in numerical merger simulations [312] with their expected rates as estimated from galactic NS mergers (e.g., [317]). Furthermore, recent studies obtained by Matteucci et al [319] point out how r-process elements originating in NS binary mergers seems to represent the most promising channel for r-process element production these days. In contrast, estimates of the impact of such double NS mergers on the galactic nucleosynthesis was questioned by detailed inhomogeneous chemical evolution studies [318] which are not consistent with observations at very low metallicities. The reason for the reported differences is probably due to the fact that the model proposed by Argast et al [318] does not assume instantaneous mixing in the early galactic evolutionary phases. In the study reported by Vangioni et al [320], the r-process evolution using the NS scenario as the main astrophysical site is in good agreement with observations, assuming that the early evolution is dominated by mergers of binary systems with a coalescence timescale of the order of ∼ 100 Myr. Such mergers represent a significant fraction of all mergers according to recent estimations obtained with detailed population synthesis codes. Furthermore, following the last developments, several recent works [321, 322] have confirmed that the enrichment history and distribution of various r-process elements in galaxies can be accounted by NS mergers.

Figure 8

Figure 8. Density rendering from a NS-BH merger with mass ratio 1.2/7 M (from [314]). The ejecta is confined to the equatorial plane because it is generated primarily by tidal forces.

A new theoretical model has been proposed such that ccSNe first contribute to the enrichment of heavy elements in the early Galaxy, then the NS mergers follow gradually towards the solar system [323]. The model predicts several specific observational evidence for the time evolution of isotopic abundance pattern. It also satisfies the universality of the observed abundance pattern between the solar system and extremely metal-poor stars in the Milky Way halo or recently discovered ultra-faint dwarf galaxies [324]. Models based on particle hydrodynamics codes [325] and detailed abundance analysis of dwarf galaxies [326] strongly support the argument that NS mergers are the major astrophysical site of the r-process. However, recently Bramante et al [327] have claimed that NS mergers are unlikely to produce the r-process overabundance observed in the Reticulum II dwarf Galaxy, since the total production rate of NS mergers is low, and supernova natal kicks efficiently remove binary stellar systems from the shallow gravitational well of the Galaxy. A second problem that arises is that dwarf galaxies are composed of a very old stellar population [328], suggesting that the chemical abundances have been frozen since ≈ 13 Gyr ago. This requires that the r-process formation should take place relatively soon after the formation of the first stars. This raises the question whether mergers could take place sufficiently rapidly so that their r-process material would be able to enrich the old stellar population. Despite this, the first direct detection of gravitational waves from a binary NS merger (GW170817) marked the true beginning of the joint gravitational wave-electromagnetic multi-messenger astronomy [330] and placed stronger constraints on r-process enrichment from NS mergers. The masses ejected are broadly consistent with the estimated r-process production rate required to explain the Milky Way r-process abundances, providing the first evidence that binary NS mergers are the dominant source of heavy r-process nuclei in the Galaxy [331, 332]. Finally according to Foucart et al [314] also NS-BH mergers may contribute to the enrichment of r-process elements in galaxies. According to this study, a large amount of neutron-rich, low entropy material is ejected (0.04 M - 0.2 M), which will undergo robust r-process nucleosynthesis although the ejecta is more proton-rich than the material ejected during NS binary mergers.

A reliable estimate of the NS merger rate in the Galaxy is crucial in order to predict their contribution to the r-process elements enrichment. Estimates of this rate are rather low because we only know few of such systems with merger times less than the age of the universe. Two of the observed binary NS systems in our Galaxy, the PSR J0737-3039 [333], and the PSR 2127+11C [334], will merge in less than a few hundred Myr due to orbital decay caused by gravitational radiation emission. The total time from birth to merger is ≈ 8 × 107 yr for PSR J0737-3039 and ≈ 3 × 108 yr for PSR 2127+11C. Estimates for the rate of NS mergers in the Galaxy range from ∼ 10−6 to ∼ 3 × 10−4 yr−1 with the best guess being ∼ 10−5 yr−1 (e.g., [335, 336]). The birth rates of NS-BH and NS binaries are comparable. Nevertheless, the fraction of NS-BH binaries having the appropriate orbital periods for merging within the age of the universe (∼ 1010 yr) is uncertain due to their complicated evolution involving mass exchange [337]. In any case, the total rate of NS (including NS-BH) mergers in the Galaxy is perhaps ∼ 10−5 yr−1, which is ∼ 103 times smaller than the galactic rate of SNII [338]. This means that each merger must eject ≳ 10−3 M of r-process material if NS mergers were solely responsible for the solar r-process abundances associated with the peaks at A = 130 and 195 (∼ 10−6 – 10−5 M of r-process material is required from each event in the case of ccSNe) [228]. Alternative scenarios based on strange star - strange star mergers have also been proposed to account for the nucleosynthesis following the merger of compact objects [339]. In particular, the most prominent feature would be the total absence of lanthanides with a mass buildup populating the low-mass (A < 70) region. The exact composition of NSs is still under debate and quark matter represent one of the most considered possibilities [340]. New tools and developments in this field are needed since the nucleosynthesis output from NS mergers is still uncertain and the existence of multiple r-process sites cannot yet be ruled out. For a deeper study of strange quark stars, see [341].

4.3.2. rp-process

Nuclei close to the proton drip-line are crucial in both quiescent and explosive astrophysical scenarios. Conditions suited for the synthesis of nuclides in the range of the p-nuclei are also established by explosive scenarios such as, X-Ray Bursts (XRBs) and X-ray pulsars, which represent possible sites for the astrophysical rp-process [342]. The rp-process consists of a series of rapid proton and α-capture reactions, interspersed with β+ decays, that drives the reaction path close to the proton drip-line. Nuclear properties such as masses, lifetimes, level densities and spin-parities of states for many nuclei close to the proton drip-line must be known to fully understand the rp-process. The rp-process is inhibited by α-decay, which puts an upper limit on the endpoint at 105Te [343]. XRBs occur in binary stellar systems where a compact NS accretes H- or He-rich material from a companion star [344]. Type I XRBs occur when accretion rates are less than 10−9 M per year [342] and are characterized by extremely energetic (∼ 1039 ergs) bursts of X-ray radiation that appear in a very regular fashion on a timescale of hours-days. The bursts themselves last for tens to hundreds of seconds and are the result of the accumulation of material on the NS surface. After few hours a thermonuclear runaway under the extreme temperature (≥ 109 K) and density (ρ ∼ 106 g cm−3) conditions triggers an explosion that gives rise to a bright X-ray burst [345]. A great difficulty in the modelling of XRBs comes from the lack of clear observational nucleosynthesis constraints. A recent review of type I XRBs can be found in [346]. Although the large gravitational potential generated by NSs is thought to prevent the rp-process from contributing to the chemical composition of the universe, knowledge regarding the rp-process is, however, crucial in understanding energy generation in XRB scenarios. Additionally, the chemical composition of the ashes that remain on the surface of the NS as a consequence of the rp-process is critically affected by the precise path and rate of progression of the thermonuclear reactions that constitute the rp-process [342]. It is thought that proton-rich Tz = -1 nuclei (where Tz = 1/2(N - Z)) in particular play a critical role in XRB scenarios [347]. For instance, a recent theoretical study by Parikh et al [348] highlighted the radiative proton capture reactions 61Ga(p,γ)62Ge and 65As(p,γ)66Se as reactions that critically affect the chemical yields generated in XRBs [345]. As such, detailed structure information for states above the proton threshold in the Tz = -1 nuclei 62Ge and 66Se is required. Consideration of mirror nuclei indicates that level densities in the astrophysically relevant energy regions are very low, rendering statistical methods, such as Hauser-Feshbach calculations, inappropriate in these cases [349]. Indeed, the proton capture reaction rates may be dominated by a single resonance.

A major puzzle to be solved in rp-process studies comes from the reaction flow through the long-lived waiting points 64Ge, 68Se, and 72Kr which are largely responsible for shaping the tail of XRBs [350]. Of critical importance are the proton capture Q-values of these waiting points which strongly determine to which degree proton captures can bypass the slow β-decays of these waiting points. Waiting point nuclides slow down the rp-process and strongly affect burst observables. They are characterized by long β-decay half-lives of the order of the burst duration, and low or negative proton capture Q-values may hinder further proton capture because of strong (γ,p) photodisintegration. Significant progress has been made recently about the proton capture Q-value of the 68Se [351]. The slow β-decay of the 68Se waiting point in the astrophysical rp-process can in principle be bypassed by a sequential two proton capture. The authors concluded that 68Se(2p, γ) reaction has at best a very small effect and 68Se is a strong waiting point in the rp-process in XRBs. This provides a robust explanation of occasionally observed long burst durations of the order of minutes. Important experimental results of rp-process reaction rates have also been made recently with the GRETINA array at NSCL [352]. The measurements essentially remove the uncertainty contribution of the 57Cu(p, γ)58Zn reaction in XRB models and also determine the effective lifetime of 56Ni, an important waiting point in the rp-process. When the NS accretes H and He from the outer layers of its companion star, thermonuclear burning processes enable the αp-process (a sequence of (α, p) and (p, γ) reactions) as a break out mechanism from the hot CNO-cycle. XRB models predict (α, p) reaction rates to significantly affect light curves of XRBs and elemental abundances in the burst ashes [353]. Theoretical reaction rates used in the modelling of the αp-process need to be verified experimentally. An important case in the αp-process is the 34Ar(α, p)37K reaction which has been identified in sensitivity studies [345] as an important nuclear uncertainty. Indeed, recent R-matrix calculations [354] for several (α,p) reactions, including 34Ar(α,p)37K, indicate a lower than predicted cross-section. The Jet Experiments in Nuclear Structure and Astrophysics (JENSA) gas jet target [355] enables the direct measurement of previously inaccessible (α,p) reactions with radioactive beams provided by the rare isotope re-accelerator ReA3. Preliminary results have been presented of the first direct cross-section measurement of the 34Ar(α, p)37K reaction [356].

Tremendous advancements have been obtained in mass measurements of nuclei involved in the rp-process [357], allowing more accurate calculations of XRBs light curves and burst ashes. Most recently, the mass of 31Cl has been measured with the JYFLTRAP [358]. The precision of the mass-excess value of 31Cl was improved from 50 keV to 3.4 keV. The mass of 31Cl is relevant for estimating the waiting point conditions for 30S as the 31Cl(γ, p) 30S - 30S(p, γ)31Cl equilibrium ratio which depends exponentially on the Q value i.e., on the masses of 31Cl and 30S. It has been suggested that the 30S waiting point could be a possible explanation for the double-peaked type I XRBs curves observed from several sources [359]. With the new Q value, photodisintegration takes over at lower temperatures than previously, and the uncertainties related to the reaction Q value have been significantly reduced.

4.3.3. Gamma-ray bursts: r-process

GRBs are flashes of gamma rays associated with extremely energetic explosions that are observed in distant galaxies (as their origin is extragalactic, they are isotropically distributed in the sky). They are the brightest electromagnetic events known to occur in the universe, and they last from milliseconds to several minutes. GRBs come in two varieties - long and short - depending on how long the flash of gamma rays lasts (from milliseconds to several minutes). The energy released in each explosion varies between 1050 and 1054 erg. In general, about one burst per day is detected. A characterizing feature of GRBs is the observation of an X-ray glow (afterglow) which is created when the high-speed jet of particles interact with the surrounding environment and persists for days at the GRB location. Short GRBs result from the collision of two NSs or a NS and a BH, whilst long GRBs are linked to ccSNe. As discussed before, cataclysmic events like GRBs are strongly thought to be sites of heavy elements production. More details on GRBs can be found in [360, 361].

In a recent work, Berger et al [362] have estimated that the amount of Au produced and ejected during an optical/near-infrared (NIR) transient known as a Kilonova (KN), may be as large as 10 moon masses. A KN is thought to be the NIR counterpart of the merging of two compact objects in a binary system and its emission is approximately isotropic. It is 1,000 times brighter than a nova, but it is only 1/10th to 1/100th the brightness of an average supernova. The basic properties of KNe can be found in [363]. The group studied the fading fireball from the first clear detection of a KN, which was in association with the short GRB 130603B. GRB 130603B, detected by the Swift satellite, lasted for less than two-tenths of a second. Although the gamma rays disappeared quickly, GRB 130603B also displayed an afterglow dominated by NIR light whose brightness and behavior did not match a typical afterglow. Instead, the glow behaved like it came from exotic radioactive elements. The neutron-rich material synthesized in dynamical and accretion-disk-wind ejecta during the merger can generate such heavy elements, through r-process, which then undergo radioactive decay emitting a glow that is dominated by NIR light. Calculations say that ∼ 10−2 M of material was ejected by the GRB, some of which was Au and Pt. By combining the estimated Au produced by a single short GRB with the number of such explosions that have occurred over the age of the universe, all the Au in the universe might have come from GRBs. In figure 9 is shown the interpolation of optical and NIR emissions of GRB 130603B to the F606W and F160W filters. The optical afterglow decays steeply after the first ∼ 0.3 days and is modeled here as a smoothly broken power law (dashed blue line). The key conclusion from this plot is that the source seen in the NIR requires an additional component above the extrapolation of the afterglow (red dashed line) [364]. This excess NIR flux corresponds to a source with absolute magnitude of ∼ -15.35 at ∼ 7 days after the burst in the rest frame. The re-brightening in the NIR afterglow is the kind one would expect from a KN [365]. Further observational evidence of the GRB-KN scenario is given in [366, 367].

Figure 9

Figure 9. Light curves of the KN seen in GRB 130603B [364]. The points represent the X-ray (black) optical (blue) and IR (red) photometry of the afterglow, along with their expected decay. The excess near-IR flux can be explained by emission powered by r-process radioactive elements produced by the ejection of neutron-rich matter during the merger of the compact objects.

Numerical simulations show that KN scenarios can eject a small part of the original system into the interstellar medium [298] and also form a centrifugally supported disk that is quickly dispersed in space with a neutron-rich wind [368]. These two different ejection mechanisms are characterized by a material of differing composition. The outflows from the disk are likely lanthanide-free since the synthesis of heavier elements is suppressed by the high temperature [365], while the surface material is the site of an intense r-process nucleosynthesis, producing heavy elements. According to Kasen et al [368], the intimate relationship between KNe and the production of r-process elements makes the transient a powerful diagnostic of the physical conditions in the merger. This feature arises from the sensitivity of the optical opacity to the type of r-process composition of the ejecta: even a small fraction of lanthanides or actinides (A > 140) can increase the optical opacity by orders of magnitude relative to iron-group-like composition. The KN transient produces optical emission for the first day after the merger, then evolves to the NIR. The peak optical and infrared luminosities, as well as the transient duration, are increasing functions of the total ejected mass. A substantial amount of blue optical emission is generated by the lanthanide -rich ejecta at early times when the temperatures are high. The duration of this signal is < 1 day [369]. Further calculations and atomic structure models are needed to fully establish the early time KN colors since the reliability of the predicted optical emission is affected by the uncertainties in the lanthanide atomic data.

The fresh and revolutionary joint detection of gravitational and electromagnetic radiation from a single source, GW170817 produced by the merger of two NSs, is strongly supporting the connection between short GRBs and the following KNe powered by the radioactive decay of r-process species synthesized in the ejecta [370, 371, 372, 373]. The thermal spectrum of the optical counterpart of GW170817 (e.g. [374]) is in agreement with the KN model, as compared to the power-law spectrum expected for non-thermal GRB afterglow emission. The shape of the bolometric light curve following peak is broadly consistent with the ∝ t−1.3 radioactive heating rate from freshly synthesized r-process nuclei [363, 332]. The light curves exhibit a rapid decline in the bluest bands, an intermediate decline rate in the red optical bands, and a shallow decline in the NIR. The total mass of the red (lanthanide-bearing) ejecta was estimated to be ≈ 4 × 10−2 M with a somewhat lower expansion velocity, v ≈ 0.1c, than the blue ejecta. The red KN emitting ejecta component dominates the total ejecta mass and thus likely also dominates the yield of both light and heavy r-process nuclei. Assuming an r-process abundance pattern matching the solar one, one infers that ∼ 100-200 M in Au and ∼ 30-60 M in U were created within a few seconds following GW170817 [375]. Future developments in this field at the intersection of nucleosynthesis, GW astronomy, and galactic chemical evolution promise to be exciting.

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