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Article

The RADIOSTAR Project

by
Maria Lugaro
1,2,3,*,
Benoit Côté
1,4,5,†,
Marco Pignatari
1,4,6,†,
Andrés Yagüe López
1,†,‡,
Hannah Brinkman
1,7,
Borbála Cseh
1,
Jacqueline Den Hartogh
1,
Carolyn Louise Doherty
1,
Amanda Irene Karakas
3,8,
Chiaki Kobayashi
9,
Thomas Lawson
1,6,
Mária Pető
1,
Benjámin Soós
1,2,
Thomas Trueman
1,6 and
Blanka Világos
1,2
1
Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Eötvös Loránd Research Network (ELKH), Konkoly Thege Miklós út 15-17, H-1121 Budapest, Hungary
2
ELTE Institute of Physics, Eötvös Loránd University, Pázmány Péter Sétány 1/A, 1117 Budapest, Hungary
3
School of Physics and Astronomy, Monash University, Melbourne, VIC 3800, Australia
4
Joint Institute for Nuclear Astrophysics-Center for the Evolution of the Elements (JINA-CEE), USA
5
Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada
6
E. A. Milne Centre for Astrophysics, Department of Physics and Mathematics, University of Hull, Kingston upon Hull HU6 7RX, UK
7
Graduate School of Physics, University of Szeged, Dom tér 9, 6720 Szeged, Hungary
8
ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
9
Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK
*
Author to whom correspondence should be addressed.
†
NuGrid Collaboration, http://nugridstars.org.
‡
Current address: Computer, Computational and Statistical Sciences (CCS) Division, Center for Theoretical Astrophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
Universe 2022, 8(2), 130; https://0-doi-org.brum.beds.ac.uk/10.3390/universe8020130
Submission received: 10 January 2022 / Revised: 2 February 2022 / Accepted: 7 February 2022 / Published: 17 February 2022
(This article belongs to the Special Issue AGB Stars—In Honor of Professor Maurizio Busso on the Occasion of His 70th Birthday)
Browse Figures
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Abstract

:
Radioactive nuclei are the key to understanding the circumstances of the birth of our Sun because meteoritic analysis has proven that many of them were present at that time. Their origin, however, has been so far elusive. The ERC-CoG-2016 RADIOSTAR project is dedicated to investigating the production of radioactive nuclei by nuclear reactions inside stars, their evolution in the Milky Way Galaxy, and their presence in molecular clouds. So far, we have discovered that: (i) radioactive nuclei produced by s l o w ( 107 Pd and 182 Hf) and r a p i d ( 129 I and 247 Cm) neutron captures originated from stellar sources —asymptotic giant branch (AGB) stars and compact binary mergers, respectively—within the galactic environment that predated the formation of the molecular cloud where the Sun was born; (ii) the time that elapsed from the birth of the cloud to the birth of the Sun was of the order of 10 7 years, and (iii) the abundances of the very short-lived nuclei 26 Al, 36 Cl, and 41 Ca can be explained by massive star winds in single or binary systems, if these winds directly polluted the early Solar System. Our current and future work, as required to finalise the picture of the origin of radioactive nuclei in the Solar System, involves studying the possible origin of radioactive nuclei in the early Solar System from core-collapse supernovae, investigating the production of 107 Pd in massive star winds, modelling the transport and mixing of radioactive nuclei in the galactic and molecular cloud medium, and calculating the galactic chemical evolution of 53 Mn and 60 Fe and of the p-process isotopes 92 Nb and 146 Sm.

1. Introduction

High-precision analysis of meteoric rocks and inclusions has allowed us to discover an intriguing property of our Solar System: at its birth, 4.6 billion years ago, it was rich in radioactive nuclei. Most of them were short-lived, with half-lives (T 1 / 2 ) less than 100 million years (Myr), and became extinct within the first few hundreds Myr of the Solar System evolution. We can still infer their initial abundances by analysing meteorites for excesses in the abundances of the daughter nuclei into which they decay. For example, if a mineral has a high 27 Al/ 24 Mg ratio and a 26 Mg/ 24 Mg ratio higher than solar, then the 26 Mg excess must have been originally incorporated in the mineral as 26 Al, which behaves chemically as 27 Al but is radioactive and has a half-life of 0.7 Myr. From the correlation between the 27 Al/ 24 Mg and the 26 Mg/ 24 Mg ratios, a relatively high 26 Al/ 27 Al∼ 5 × 10 − 5 is derived for the time when the Sun was born [1,2]. Therefore, the decay of 26 Al was the major source of heating in the planetesimals that accreted within the first few million years in the early Solar System (ESS). This heat led to melting and differentiation [3], as well as water circulation and loss in those planetesimals that were ice rich [4,5].
On top of 26 Al, there is convincing evidence of the presence in the ESS of another ten short-lived radioactive (SLR) nuclei produced in stars and explosive environments: 36 Cl (T 1 / 2 = 0.3 Myr), 53 Mn (T 1 / 2 = 3.7 Myr), 60 Fe (T 1 / 2 = 2.6 Myr), 92 Nb (T 1 / 2 = 34.7 Myr), 107 Pd (T 1 / 2 = 6.7 Myr), 129 I (T 1 / 2 = 15.7 Myr), 146 Sm (T 1 / 2 = 68 or 103 Myr, debated), 182 Hf (T 1 / 2 = 8.9 Myr), 244 Pu (T 1 / 2 = 80 Myr), and 247 Cm (T 1 / 2 = 15.6 Myr). These are listed in Table 2 of [6], together with their half-lives, the stable isotopes used as reference to derive their abundances, and the abundance ratios inferred for the ESS. For another six isotopes, including 41 Ca (T 1 / 2 = 0.1 Myr), weaker evidence or only upper limits exist for their ESS abundances. The physical properties of these SLR nuclei cover wide ranges: half-lives are from 0.1 to 100 Myr and masses from very light ( 26 Al) to extremely heavy ( 247 Cm). Production of these nuclei in stars is ascribed to a large variety of nuclear physics processes: from proton captures (e.g., 26 Al), to neutron captures (e.g., 129 I), disintegration of heavier nuclei (e.g., 146 Sm), and nuclear statistical equilibrium (e.g., 53 Mn). These processes occur in different stellar environments, from core-collapse and thermonuclear supernovae to giant stars. Moreover, the accuracy and precision of the SLR abundances in the ESS vary from a few percent (e.g., for 26 Al and 182 Hf) to values debated by orders of magnitudes. For example, the value of 60 Fe/ 56 Fe is most likely to be low, ∼ 10 − 8 [7,8], but higher values up to ∼ 10 − 6 have been reported too [9].
The origin of SLR nuclei in the ESS, and consequently their potential presence in extrasolar planetary systems, is still poorly understood and hotly debated. The different scenarios have implications on the circumstances and the sequence of events that led to the birth of the Sun [10,11] and on heating and ionisation in star-forming regions [12,13]. Furthermore, the decay of 26 Al, and potentially 60 Fe, was an important source of heat inside the first planetesimals. Therefore, their presence or absence determines several important properties of extrasolar planetesimals, including water circulation and loss for those planetesimals that are ice rich. This, in turn, determines not only mineral diversity and modification of organic molecules, as the presence of water drives hydro-thermal processing, but also the amount of water delivered by these planetesimals to planets in the habitable zone. If 26 Al is present, a high fraction of water is mobilised and removed from ice-rich planetesimals and mainly dry planets result in the habitable zone [14]. Without 26 Al, instead, ice-rich planetesimals keep their initial ice content and deliver more water to planets in the habitable zone [4,5]. A vast amount of literature (e.g., [15,16,17,18,19,20,21,22,23,24,25,26,27]) in the past 40 years has been devoted to try to solve the puzzle of radioactivity in the ESS, as reviewed by Lugaro, Ott, and Kereszturi [6]. A more recent review on the production specifically of 26 Al and 60 Fe and their astrophysics relevance can be found in [28].
The RADIOSTAR1 project was funded by the European Research Council (ERC-CoG-2016) starting from September 2017. Its objective is to produce the first complete, self-consistent picture of the origin of SLR nuclei in the ESS from the stars that produced them. The two main goals of RADIOSTAR are (see Figure 1): (1) To derive the time that elapsed from the formation of the molecular cloud to the formation of the Sun (the “isolation” time). The abundances of those SLR nuclei that are sensitive to galactic timescales can be used to this aim. The isolation time also represents the timescale of the potential process of self-pollution by stellar ejecta within the molecular cloud itself. (2) To consider all the SLR nuclei and analyse all the mechanisms of their stellar production in all the possible different stellar sources. The final objectives are to find global self-consistent solutions for all the SLR nuclei, derive the uncertainty space where such solutions are valid, and provide testable predictions for the abundances of those SLR nuclei whose abundances in the ESS are not yet well known.
Here, we report the progress that has been made by the project since 2017, both in the stellar yield calculations (Section 2) and in the modelling of the galactic chemical evolution of the SLR nuclei (Section 3). In Section 4, we report on current and future work to be performed within the project, as it will run to its completion at the end of August 2023.

2. Progress on Stellar Yields of Radioactive Isotopes

Massive stars and their core-collapse supernovae (CCSNe) are one of the main sources of the SLR abundances measured in the ESS. Therefore, within the RADIOSTAR project, we dedicated a special effort to the study of the nucleosynthesis within these stellar objects. Present uncertainties affecting theoretical stellar simulations of massive stars are a major challenge for our analysis. In Lawson et al. [29], we explored the production of SLR nuclei relevant for the ESS using 62 CCSN models with initial masses of 15, 20, and 25 M ⊙ . The models cover a range of explosion energies between 3.4 × 10 50 and 1.8 × 10 52 ergs and different ejecta configurations [30]. The same models were previously adopted to study the nucleosynthesis of radioactive isotopes relevant for future γ -ray astronomy observations [31] and the nucleosynthesis of 60 Fe [32]. In [29], we highlighted the diversity and the wide range of production mechanisms seen for the SLR nuclei. In some cases, such as 36 Cl and 41 Ca, isotopes can be efficiently made in different parts of the ejecta by different nucleosynthesis production paths and different nuclear reactions. In other cases, like 60 Fe, the same nuclear reactions are triggered at different temperature and density conditions in the ejecta. We also showed that we cannot neglect the impact of nucleosynthesis prior to the CCSN. Isotopic abundances produced prior to the explosion, for example, for 26 Al, 60 Fe, and 182 Hf, may also be ejected by the explosion, and the relevance of such a contribution with respect to explosive nucleosynthesis varies greatly between models.
Our set of CCSN models [29] allowed us to study the impact of both the explosion energy and the compact remnant mass, which varies between 1.5 M ⊙ and 4.9 M ⊙ in this set of models [30]. Isotopes such as 92 Nb and 97 Tc are significantly produced within the innermost ejecta, and therefore they are strongly affected by the remnant mass, which is very uncertain. In particular, for 92 Nb, we obtain yields varying by five orders of magnitude between different CCSN models of the same stellar progenitor. An extensive comparison with other models available in the literature [33,34,35,36] confirms or increases the scatter of SLR yields obtained in our study. For the yields of 60 Fe and lighter SLR nuclei, with the exception of 41 Ca, we find agreement within an order of magnitude across the published sets of models for different progenitors. Concerning heavier SLR nuclei, we obtain roughly an order of magnitude less 98 Tc compared to other models available in the literature. The same applies to 126 Sn, for the smaller stellar progenitors, the 15 M ⊙ and 20 M ⊙ stars. The source of such a discrepancy is still unclear, given the large parameter space covered in our study in terms of CCSN model setup. Our 92 Nb median yield for the 15 M ⊙ models overproduce this SLR isotope by at least three orders of magnitude compared to other mass models, due to its high production in models with small remnant mass and medium-high explosion energy. Another heavy SLR isotope, the proton-rich 146 Sm, shows the largest variation between different stellar sets, of about two orders of magnitude. The other heavy SLR isotope yields considered in our study ( 97 Tc, 107 Pd, 129 I, 135 Cs, 182 Hf, and 205 Pb) are consistent among the different masses within an order of magnitude.
The SLR signatures are not the only isotopic anomalies detected in the ESS. In fact, several stable isotope variations of nucleosynthetic origin have been identified in meteoritic samples (see review by [37]), also possibly correlated to unstable isotopic abundances (e.g., [38]). The source of such variations is generally attributed to the presence of stardust grains that predated the formation of the Solar System. Since CCSNe are among the relevant producers of stardust grains (e.g., [39]), the same models used to study the production of SLR nuclei can be compared with stardust grains abundances and meteoritic anomalies. In den Hartogh et al. (2022, ApJ accepted2), we used CCSN models to study stardust chromium-rich oxide grains recently measured by [40]. These grains are possibly responsible for the observed 54 Cr variations in materials formed in different regions of the proto-planetary solar disk (e.g., [41,42]) and their correlation with 26 Mg variations [38]. By using three different sets of CCSN models, in den Hartogh et al., we showed that CCSN ejecta can reproduce the grain anomalous 54 Cr/ 52 Cr, 53 Cr/ 52 Cr ratios observed in the chromium-rich grains. They can also match the measured 50 Cr/ 52 Cr (the C-ashes) or 50 Ti/ 48 Ti3 (the He ashes) ratios. Therefore, these grains, previously attributed to electron-capture supernovae [40,43], could have been made by CCSNe. Finally, we found that in the CCSN models, 54 Cr excesses are accompanied by excesses in the stable 26 Mg, rather than in the SLR 26 Al. The stellar winds of massive Wolf–Rayet stars may also eject a significant amount of material in the interstellar medium (ISM) and are therefore also relevant for the production of SLR nuclei. References [44,45] first provided a comprehensive analysis of the production of SLR nuclei in massive stars and their ejection by Wolf–Rayet winds, for both non-rotating and rotating stellar models. In Brinkman et al. [46,47], we presented an updated study of the production of the SLR nuclei in massive star winds, where we also considered the effect of binary interaction. Wind yields were calculated for stellar evolution models of solar metallicity in the mass range 10 M ⊙ ≤ M≤ 80 M ⊙ for non-rotating single and binary stars (for 26 Al [46]) and for non-rotating and rotating single stars (for 26 Al, 36 Cl, and 41 Ca [47]). The main results are that binary interactions increase the 26 Al wind yields in stars of masses 10–35 M ⊙ , while for the more massive Wolf–Rayet stars the impact is small [46]. Rotation does not affect significantly the 26 Al yields but increases/decreases the 36 Cl and 41 Ca yields for stars in the lower/higher mass range. From about 45 M ⊙ , the yields become again comparable between models with different initial conditions [47]. The full impact of the new models and their effect relative to the CCSN contribution in the Galaxy and specifically in star-forming regions can only be established by considering full models of population synthesis (see, e.g., [48]). Nevertheless, our two studies confirm that massive star winds are a realistic candidate for the origin of at least 26 Al, 36 Cl, and 41 Ca in the ESS, as demonstrated by the example shown in Figure 2.

3. Progress on Galactic Chemical Evolution of Radioactive Isotopes

The ESS abundances of SLR nuclei are typically given as an abundance ratio between an SLR nucleus and a stable or long-lived reference isotope. The SLR nuclei only encode the contribution of a few enrichment events, i.e., the last events that occurred prior to the formation of the Sun. Therefore, their abundances reflect the convolution between the stellar yields and the local star formation rate at the time of the ESS. Instead, because the stable reference isotopes do not decay, their abundances encode the contribution of all enrichment events that occurred prior to the formation of the Sun. Therefore, they reflect the complete chemical evolution history of the Galaxy, at least for the solar neighbourhood. To properly interpret the meteoritic abundances ratios, galactic chemical evolution (GCE) models and simulations must be employed, which incorporate nucleosynthesis and stellar evolution predictions into galactic frameworks that follow the star formation history of our Galaxy. The use of GCE not only allows us to predict the abundances of SLR nuclei in the ESS but to gain insights into their astrophysical origins and to quantify the isolation time.
Previous GCE studies developed analytical solutions for the abundances of SLR nuclei in the ISM by combining production yields ratios with parametrised star formation histories [18,20,49,50]. Building and extending upon these pioneering studies, we incorporated radioactivity in the GCE code OMEGA+ [51]. This code is part of an open-source numerical pipeline [52,53] that offers several advantages over the use of analytical solutions. First, it has strong connections with the nuclear astrophysics community. In fact, it can directly incorporate nucleosynthetic yields predictions from a wide range of astrophysical sites such as CCSNe, low- and intermediate-mass stars, neutron star mergers and black hole–neutron star mergers, as well as different channels for supernovae Type Ia (SNeIa, see also [54]). Each set of yields can be mass and metallicity dependent. Second, our framework considers delay-time distributions, representing the probability of an enrichment event (e.g., an SNIa) to occur after a given time since the formation of its progenitor (e.g., a low-mass binary system). Third, the radioactivity in OMEGA+ is connected to a decay module that can accommodate radioactive isotopes with multiple decay channels. Finally, fourth, our GCE codes include important galaxy evolution processes that were not accounted for in previous analytical solutions, such as galactic outflows driven by the energy of supernova explosions.
The first step in the development of our framework was to quantify the reliability of GCE predictions, given the uncertainties in the observational constraints that we used to calibrate our Milky Way models (see Figure 3). In particular, we generated a range of numerical predictions for the abundances ratios between SLR nuclei and their reference isotopes by varying input parameters such as the temporal profile of the star formation history of the Galaxy, the total stellar mass formed, the present star-to-gas mass ratio, and the galactic inflow and outflow rates. Accounting for all of these sources of variations, we found that our predictions were uncertain by a factor of ∼ 3.6 at the time of the ESS (see bottom-right panel of Figure 3). We also provided an analytical solution that reproduces our predicted abundances. Using constant production yields ratios for various enrichment sources, we used this framework to provide a range of isolation times for specific SLR nuclei. To do so, we compared our predicted abundances (taken at the time the Sun formed) to the ESS values and calculated how much time was needed to freely decay our predicted values down to the ESS values. For example, using 53 Mn/ 55 Mn and 60 Fe/ 56 Fe, we derived isolation times of 17–24 and 10–15 Myr, respectively. We could not derive isolation times for 26 Al/ 27 Al because our predictions fell below the ESS value, which confirms the need for local source for this isotope (for example, the massive star winds investigated in Figure 2). Furthermore, isolation times derived for 92 Nb and 146 Sm were inconsistent between each other, when using the assumption that both isotopes came from SNeIa (which confirmed the result of [55]).
Our GCE code OMEGA+ assumes homogeneous mixing and a continuous stellar enrichment process. However, when studying the chemical evolution of a given parcel of gas (i.e., the parcel of gas from which the Sun would eventually form) within the Milky Way, the stellar enrichment process should be considered as made up by discrete events. A new enrichment event (e.g., a nearby supernova explosion) will bring freshly synthesised isotopes and increase the overall abundance of SLR nuclei. Following such an enrichment event, the SLR nuclei freely decay until another enrichment event occurs nearby. To account for such an evolution, we extended our GCE codes and developed a statistical Monte Carlo framework that quantifies the confidence level of our GCE predictions given the stochastic nature of local enrichment events [57,58].
We first defined a constant time interval between the formation of enrichment progenitors. We then calculated delay times, defined as the time interval between the formation of progenitors (e.g., binary neutron star systems) and their enrichment event (e.g., neutron star merger) by randomly sampling delay-time probability distribution functions. We found that the spread (or width of our confidence levels) depends on the ratio between the mean-life ( τ ) of the considered SLR nucleus and the average time interval ( γ ) between enrichment events [57]. When τ / γ > 2 , the ejecta of new enrichment events tends to pile up on the SLR abundances synthesised by previous events. In other words, SLR nuclei do not have time to completely decay before the occurrence of a new enrichment event. In this regime, the abundance of an SLR nucleus reaches a steady-state value defined by the product of τ / γ times the nucleosynthetic yields and has a spread that can be properly quantified with statistical confidence levels (top panel of Figure 4). Overall, we found that the enrichment stochasticity adds at most an extra 60% uncertainty to the much larger GCE uncertainties (factor of ∼ 3.6 ) derived from the homogeneous framework described above. Instead, when τ / γ < 1 , SLR nuclei significantly decay before a new enrichment event occurs (bottom panel of Figure 4). In this regime, extremely low values of the abundance can be reached and the spread of an SLR abundance cannot be properly quantified.
In addition to investigating the timescales at which the ESS was enriched with SLR nuclei, our GCE framework can also be used to provide insights into the physical conditions in which these SLR nuclei were produced. In particular, we found that abundances ratios between two SLR nuclei, rather than ratios between an SLR nucleus and its stable reference isotope, are sometimes more effective in probing the astrophysical sites of SLR nuclei [58]. This is because they are less affected by the uncertainties associated with the long-term evolution of our Galaxy, which means that the predicted ratios become more sensitive to the nuclear astrophysics inputs. Nevertheless, such an abundance ratio still varies over time due to the different timescales at which the two SRLs freely decay between enrichment events [58]. However, when the half-lives of the two SLR nuclei are similar, their abundance ratio does not significantly vary with time. In that regard, using our stochastic Monte Carlo framework, we found four ratios for which our predicted uncertainties are minimal and controlled by their stellar production: 129 I/ 247 Cm, 107 Pd/ 182 Hf, 97 Tc/ 98 Tc, and 53 Mn/ 97 Tc [58].

3.1. The SLR Isotopes Produced by the r Process

We studied in more detail the case of 129 I/ 247 Cm, which involves two SLR nuclei synthesised by the r a p i d neutron-capture (r) process. We found that since 129 I and 247 Cm have almost the same half-life (15.7 and 15.6 Myr, respectively), their abundance ratio did not change significantly since the last event that enriched the pre-solar nebula [59]. In addition, given the rarity of r-process events ( τ / γ < 1 ), we found that the meteoritic 129 I/ 247 Cm ratio is likely dominated by the contribution of one event. This ratio can thus be seen as a direct window into the nucleosynthesis of the last r-process event that occurred ∼100–200 Myr4 prior to the formation of the Sun. In collaboration with an international team of experts in r-process nucleosynthesis, we found that the last wave of r-process production likely occurred in moderately neutron-rich conditions [59]. The 129 I/ 247 Cm ratio represents a unique example of how GCE uncertainties could be completely removed from the picture, following our detailed uncertainty analysis. While numerical predictions are still sensitive to the large nuclear physics and astrophysical uncertainties, the reduced layer of uncertainties brings us closer to the astrophysical origin of these SLR nuclei.

3.2. The GCE of SLR Isotopes Produced by AGB Stars

Using our updated GCE framework, we also investigated in more detail the origin of SLR nuclei synthesised by the s l o w neutron-capture (s) process in AGB stars [60]. To this aim, we incorporated two different sets of mass- and metallicity-dependent AGB yields, the Fruity [61,62] and the Monash [63] yields. Then, we followed the chemical evolution of the 107 Pd/ 108 Pd, 135 Cs/ 133 Cs, and 182 Hf/ 180 Hf ratios also accounting for GCE uncertainties (Figure 5).
The main difference between the Fruity and the Monash models is the treatment of the decay rate of 181 Hf, which is the branching point on the s-process path responsible for the production of 182 Hf. The Monash models include the terrestrial value of the decay rate. This is to follow the results of Reference [64], who showed that the previously recommended faster decay of 181 Hf at stellar temperatures was based on a wrong assignment [65]. The Fruity models include the previous faster decay of 181 Hf and, therefore, produce a much lower 182 Hf abundance than the Monash models.
When assuming τ / γ > 2 , and adding the Monte Carlo stochastic uncertainties to the values of the ratios shown in Figure 5, we found self-consistent isolation times, between 9 and 26 Myr, using all three abundance ratios and the Monash yields. The 107 Pd/ 108 Pd and 135 Cs/ 133 Cs ratios calculated using the Fruity yields are also in agreement with this range of values. From considering the 107 Pd/ 182 Hf ratio, we also identified a potential missing nucleosynthesis source of Pd in our GCE code. Recently, some of us [66] compared the abundances of a large sample of Ba stars, the binary companions of AGB stars, to predictions from Monash and Fruity models. In general, we found that many such Ba stars have excesses in the elements Nb, Mo, and Ru that are not explained by current AGB s-process models. Although it has not been possible to observe Pd yet in Ba stars, this element is located just after Ru. Therefore, it may also be present there in excess of the AGB models. This would be in qualitative agreement with the missing 107 Pd relative to 182 Hf abundance we have found in Trueman et al. [60].
When assuming τ / γ < 1 , instead, we could calculate the time that elapsed between the formation of the Solar System and the last s-process enrichment event that polluted the pre-solar nebula. In particular, we found a self-consistent elapsed time of 25.5 Myr when assuming a 2 M ⊙ AGB model with an initial composition of Z = 0.01 .

4. Ongoing and Future Work

There are several current investigations ongoing and planned within the RADIOSTAR project to move towards a complete picture of the stellar origin of SLR nuclei and their presence in the ESS. We present a brief summary of each of them below, with a prospective on the future work and impact beyond the project.
  • CCSN nucleosynthesis We are currently investigating (Lawson et al., in preparation) if our CCSN models produce a self-consistent solution for some of the SLR nuclei present in the ESS. We are also considering the effect on SLR abundances of further processes and uncertainties related to explosion and mixing in CCSNe beyond those already mentioned in Section 2. Specifically, we are looking at the effects of possible ingestions of protons in the He shell [67] and of merging of different shells [68] just prior to the explosion. Updated investigations will still be needed on the impact of nuclear reaction rate uncertainties on the production of each SLR nucleus in CCSNe, even for the best studied 26 Al and 60 Fe. For instance, new experimental constraints have allowed us to significantly reduce the impact of the uncertainty of the 59 Fe(n, γ ) 60 Fe cross section [69], one of the main nuclear inputs for the production of 60 Fe [32].
  • Massive star winds and the production of 107 Pd We are currently calculating the production and ejection of 36 Cl and 41 Ca in binary systems. At the same time, we are also extending our current nuclear network to include the production of SLR nuclei up to 107 Pd (Brinkman et al., in preparation). Within the possible scenario where 26 Al, 36 Cl, and 41 Ca in the ESS originated from massive star winds (Figure 2), 107 Pd is the only heavier isotope that can also be significantly produced. As discussed in Section 3.2, our current modelling of the s-process contribution from AGB stars to the galactic background can explain the currently recommended ESS value of the 107 Pd/ 108 Pd ratio self-consistently with that of 182 Hf/ 180 Hf. Therefore, a second contribution to 107 Pd from massive star winds may result in overproduction relative to the ESS value and create a problem for this scenario. For the first time, the RADIOSTAR project can investigate together all the potential different components of 107 Pd in the ESS. Within the topic of massive star winds, we also need to investigate if the produced SLR nuclei can be incorporated into dust. Dust is necessary to penetrate the ESS material and carry and deposit the SLR abundances within it. It is observed to form in the carbon-rich winds of massive binary star systems [70]. Finally, we note that, aside from massive star binaries and Wolf–Rayet stars, the winds of stars with mass above 100 M ⊙ can also contribute significantly to the 26 Al enrichment of the ISM. These stars are nearly homogeneous and can convert almost all 25 Mg initially present into 26 Al via proton captures5. These stars are extremely rare, however, and even a few events may have a strong impact, which should be analysed in relation to the ESS.
  • Origin of 244 Pu Among the r-process SLR nuclei, 244 Pu has also been observed to be present in the ESS, although its abundance is still relatively uncertain. New laboratory measurements within our project are aimed at better defining its ESS value and distribution (Pető et al., in preparation). We are also considering if the same models that can explain 129 I and 247 Cm can also fit 244 Pu (Lugaro et al., in preparation). The further complication of this isotope is that its half-life (of 80 Myr) is much longer than that of the other two isotopes; therefore, it is more likely that the abundance of this SLR nucleus carried the memory of several events in the galactic background.
  • Heterogeneous GCE modelling One of the main open problems to achieve an accurate description of the abundances of SLR nuclei both within GCE and in molecular clouds, is the transport in the ISM. So far, our GCE models have been simplistic in this respect because they do not included transport. By considering stellar sources that produce both the SLR and the stable reference isotope, we have exploited the fact that the dilution factor due to transport from the source to each parcel of ISM gas must be the same for both isotopes. However, reality is more complex because such dilution factor would effectively give a different weight to different sources, depending on their distance and on how far the isotopes can travel. Effectively, distance and speed control the numbers of sources that contribute material to a given parcel of gas and, therefore, when considered per unit time, the parameter γ . Furthermore, the stable isotope abundance completely loses the memory of each single production event, as material becomes well mixed in the Galaxy within its rotation period of 100 Myr. Instead, the SLR nuclei keep the memory of the events that occurred locally in time and space. For these reasons, we are now developing more complex models. We have introduced SLR nuclei into the Inhomogeneous Chemical Evolution (ICE) code [72], where mixing in the ISM is treated in three dimensions and driven by supernova explosions (Wehmeyer et al., in preparation). We have also developed a mixing code based on the scheme of Hotokezaka et al. [73] where material is transported by diffusion (Yagüe Lopéz et al., in preparation). A couple of preliminary test examples of our Hotokezaka-stlye simulations are shown in Figure 6.
  • Chemodynamical SPH simulations We are considering a higher level of complexity by introducing SLR nuclei also within sophisticated models of the Galaxy based on cosmological constraints [74]. While these models cannot zoom into each single stellar source, they account for all the dynamical features of the Milky Way and provide us a more accurate description of the distribution of SLR nuclei in the Galaxy. We have introduced a number of SLR nuclei within such models and are currently running high-resolution simulations to be compared to global galactic observables, such as the 26 Al γ -ray emission line (Wehmeyer et al., in preparation).
  • 53 Mn and the contribution of Type Ia supernovae 53 Mn is a particularly interesting well-known SLR nucleus in the ESS whose abundance still needs to be analysed in terms of stellar sources and GCE evolution. The element Mn is produced most significantly in the Galaxy by SNeIa, and particularly those that reach the Chandrasekhar mass [75,76], but also partly by CCSNe, also depending on the models considered. A full GCE model is required to follow the production of 53 Mn and 55 Mn, together with that of 56 Fe, also significantly produced by SNeIa, and 60 Fe, which is only produced by CCSNe instead. Such a model will help us to verify if the origin of both 53 Mn and 60 Fe in the ESS can be attributed to the galactic background, similarly to the longer lived s- and r-process SLR nuclei discussed in Section 3.
  • The p-process SLR nuclei Finally, 92 Nb and 146 Sm are p-process isotopes for which the ESS values are well known, while their stellar origin is still unclear. The origin of p-process nuclei in general is still strongly debated, with many potential sources related to various types of supernova explosions. Detailed GCE models of the evolution of the abundances of these two isotopes are needed and may help in understanding the origin of the p process by testing different combinations of stellar yields. Furthermore, the other two SLR nuclei synthesised by the p process, 97 Tc and 98 Tc, have very close half-lives (4.21 and 4.2 Myr, respectively) and could be the subject of a study similar to that which we performed for 129 I/ 247 Cm, once more precise meteoritic abundance determinations are available for these isotopes [58].
On top of the efforts related to the modelling of the stellar sources and galactic evolution listed above, improvements in the nuclear and meteoritic experimental data would strongly help us to constrain the problem of the origin of SLR nuclei in the ESS. In terms of nuclear physics inputs, several advances have been made, also with the contribution of the RADIOSTAR project (see [69,77] and Laird et al. 2022, submitted to J.Phys.G.). Main inputs are still required in terms of charged-particle reactions, for example, on the crucial 22 Ne( α ,n) 25 Mg reaction that produces the neutrons needed to make 182 Hf in AGB stars. Neutron-capture reactions are also to be improved, for example, those on 36 Cl and 41 Ca that control the abundance of these isotopes in massive star winds [47], as well as decay rates with their temperature and density dependence. A crucial case is that of 146 Sm, whose terrestrial decay rate is still debated between the two values of 68 [78] and of 103 Myr [79]. Furthermore, model predictions for 205 Pb (and, to a lesser extent, for 41 Ca) also present large uncertainties due to the almost unknown temperature and density dependence of its electron capture rate.
Finally, more accurate determination of the SLR ESS abundances would truly allow us to discard and/or favour different scenarios. Some crucial isotopes discussed above and to be improved are 36 Cl, 41 Ca, 107 Pd, and 244 Pu. More resonance ionisation mass spectrometry (RIMS) data on 60 Fe are also needed. The potentially correlated presence of different SLR nuclei (e.g., [80]) and even with stable isotope anomalies in the same materials would also be very useful constraints. Furthermore, ESS values, rather than upper limits, are still needed for 205 Pb (main s origin and minor massive star wind production [45]), 135 Cs (r and s origin), 97 Tc (p origin), and 98 Tc (main p origin and minor massive star wind production [45]). These would allow us to confirm the origin of the s-process SLR nuclei and to link the p process to Chandrasekhar mass SNeIa, which also produce 53 Mn, whose half-life is very similar to that of 97 Tc and 98 Tc [58]. Finally, 126 Sn is a potentially interesting very short-lived (0.23 Myr) isotope of main r origin and minor CCSN production, for which we only have an ESS upper limit. For all these isotopes, it is outstandingly difficult to derive accurate and precise ESS values for several reasons, from their very low abundance (e.g., the Tc isotopes) to their volatility (for Cs and Pb) to problems with age determinations of the meteorite (for 107 Pd). Any analytical improvement will help us to better exploit our analysis of their astrophysical origin.

Author Contributions

All the authors have contributed to the conceptualisation, methodology, software, validation, formal analysis, and investigation. The original draft was prepared by M.L., B.C. (Benoit Côté), and M.P. (Marco Pignatari), with Figure 4 contributed by A.Y.L. All the authors contributed to the review and editing of the paper. M.L. contributed to the supervision, project administration, and funding acquisition for the project. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by ERC via CoG-2016 RADIOSTAR (Grant Agreement 724560).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Acknowledgments

We would like to thank Krisztina Botos for financial management of the project and Evelin Bányai for IT management and software development. We also thank all the colleagues who have visited our team since September 2017, in order of time: Ertao Li, Ulrich Ott, Waheed Akram, Martin Bizzarro, Georges Meynet, Roland Diehl, Reto Trappitsch, Melanie Hampel, Yusuke Fujimoto, Xiaodong Tang, Kuoang Li, Kai Zuber, Etienne Kaiser, Marius Eichler, Jenny Feige, Alessandro Airo, Stein Jacobsen, Akshat Garg, Claudia Travaglio, Moritz Pleintinger, Nicole Vassh, and Andre Sieverding. We are grateful for the time they have spent with us and all their help and discussion. We are also grateful for discussions with Maria Schoenbachler and Mattias Ek. Finally, we thank Sara Palmerini for the opportunity of presenting this paper and Maurizio Busso for his life-long inspiration on the study of the topic of radioactive nuclei.

Conflicts of Interest

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Abbreviations

The following abbreviations are used in this manuscript:
AGB starasymptotic giant branch star
CCSN (CCSNe)core-collapse supernova (core-collapse supernovae)
ESSearly Solar System
GCEgalactic chemical evolution
ISMinterstellar medium
r a p i d neutron-capture processr process
s l o w neutron-capture processs process
SLRshort-lived radioactive
SNIa (SNeIa)supernova Type Ia (supernovae Type Ia)

Notes

1
“Radioactivities from Stars to Solar Systems”, https://konkoly.hu/radiostar/ (accessed on 1 January 2022)
2
https://arxiv.org/abs/2201.04692 (accessed on 1 January 2022)
3
The origin of the observed signal at mass 50 is still unknown, as it could come from Cr and Ti.
4
This time from the last r-process event is derived self-consistently using the two ratios 129 I/ 127 I and 247 Cm/ 235 U.
5
For example, the 500 M ⊙ model by [71] produces 100 more 26 Al than their 60 M ⊙ star.

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Figure 1. Flowchart of the RADIOSTAR project. From top: stellar models and nuclear physics are used as input for calculating the stellar yields of SLR nuclei. These, in turn, serve as input for investigating the evolution of the SLR abundances in the Milky Way Galaxy and in molecular clouds. In first approximation, the half-life of each SLR nucleus (third row) determines if its abundance in the ESS was predominately contributed by stars in the Galaxy (over longer timescales), in molecular cloud (over shorter timescales), or in both. The abundances of the SLR nuclei with relatively long half lives (third row, left box) have a predominant galactic contribution. They can be used to determine the initial composition of the molecular cloud where the Sun was born and the timescale of such birth. This information can be fed (green arrows) into the analysis of the cloud evolution.
Figure 1. Flowchart of the RADIOSTAR project. From top: stellar models and nuclear physics are used as input for calculating the stellar yields of SLR nuclei. These, in turn, serve as input for investigating the evolution of the SLR abundances in the Milky Way Galaxy and in molecular clouds. In first approximation, the half-life of each SLR nucleus (third row) determines if its abundance in the ESS was predominately contributed by stars in the Galaxy (over longer timescales), in molecular cloud (over shorter timescales), or in both. The abundances of the SLR nuclei with relatively long half lives (third row, left box) have a predominant galactic contribution. They can be used to determine the initial composition of the molecular cloud where the Sun was born and the timescale of such birth. This information can be fed (green arrows) into the analysis of the cloud evolution.
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Figure 2. Previously published as panel (e) of Figure 7 in [47], ©AAS, reproduced with permission. Abundance ratios (R/S) for the SLR 26 Al, 36 Cl, and 41 Ca over their stable reference isotope ( 27 Al, 35 Cl, and 40 Ca) for a dilution factor f in the range 0.16–0.5 × 10 − 4 . These values are calculated as M ESS ( 26 Al)/ M star ( 26 Al), where M ESS ( 26 Al) is the mass of 26 Al observed in the ESS and M star ( 26 Al) its stellar yield from the example stellar models of initial 80 M ⊙ and different initial velocities as indicated. The horizontal bands represent the ESS ratios, with their respective errors. The vertical lines represent the delay time, i.e., the time interval needed to match the ESS 41 Ca/ 40 Ca ratio, typically of the order of 1 Myr.
Figure 2. Previously published as panel (e) of Figure 7 in [47], ©AAS, reproduced with permission. Abundance ratios (R/S) for the SLR 26 Al, 36 Cl, and 41 Ca over their stable reference isotope ( 27 Al, 35 Cl, and 40 Ca) for a dilution factor f in the range 0.16–0.5 × 10 − 4 . These values are calculated as M ESS ( 26 Al)/ M star ( 26 Al), where M ESS ( 26 Al) is the mass of 26 Al observed in the ESS and M star ( 26 Al) its stellar yield from the example stellar models of initial 80 M ⊙ and different initial velocities as indicated. The horizontal bands represent the ESS ratios, with their respective errors. The vertical lines represent the delay time, i.e., the time interval needed to match the ESS 41 Ca/ 40 Ca ratio, typically of the order of 1 Myr.
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Figure 3. Previously published as Figure 6 in [51], ©AAS, reproduced with permission. Time-evolution predictions from our OMEGA + GCE framework for the Milky Way. Top left: the star formation rate M ˙ * . Top right: the gas inflow rate M ˙ inflow . Bottom left: the mass of gas M gas . Bottom right: the abundance ratio between an SLR nucleus and a reference stable isotope M radio / M stable . The vertical bands near 13 Gyr represent observational data taken from [56]. In this framework, solar metallicity is reached at 8.2 Gyr. Our best GCE model (solid line) represents the case where the current observational values of M ˙ * , M gas , and M ˙ inflow are all fitted. The other two lines correspond to two more GCE models we explored to cover the observational uncertainties in M gas and M ˙ inflow . These produce a minimum (dashed line) and a maximum (dotted line) value of M radio / M stable .
Figure 3. Previously published as Figure 6 in [51], ©AAS, reproduced with permission. Time-evolution predictions from our OMEGA + GCE framework for the Milky Way. Top left: the star formation rate M ˙ * . Top right: the gas inflow rate M ˙ inflow . Bottom left: the mass of gas M gas . Bottom right: the abundance ratio between an SLR nucleus and a reference stable isotope M radio / M stable . The vertical bands near 13 Gyr represent observational data taken from [56]. In this framework, solar metallicity is reached at 8.2 Gyr. Our best GCE model (solid line) represents the case where the current observational values of M ˙ * , M gas , and M ˙ inflow are all fitted. The other two lines correspond to two more GCE models we explored to cover the observational uncertainties in M gas and M ˙ inflow . These produce a minimum (dashed line) and a maximum (dotted line) value of M radio / M stable .
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Figure 4. Previously published as Figure 6 in [57], ©AAS, reproduced with permission. Statistical distribution of the mass of an SLR in the ISM ( M radio ) as a function of galactic age, assuming each enrichment event ejects 1 M ⊙ of radioactive material. Different panels show results from our stochastic Monte Carlo framework using different τ / γ values, representing ratios between the SLR mean-life and the average time interval between enrichment events.
Figure 4. Previously published as Figure 6 in [57], ©AAS, reproduced with permission. Statistical distribution of the mass of an SLR in the ISM ( M radio ) as a function of galactic age, assuming each enrichment event ejects 1 M ⊙ of radioactive material. Different panels show results from our stochastic Monte Carlo framework using different τ / γ values, representing ratios between the SLR mean-life and the average time interval between enrichment events.
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Figure 5. Previously published as Figure 3 in [60], ©AAS, reproduced with permission. Time-evolution predictions from our OMEGA+ GCE framework for the Milky Way of the SLR isotopes produced by AGB stars, relative to their stable reference isotope (the two top and the bottom left panel). These panels are the realisation of the bottom right panel of Figure 3 for the three specific isotopes, where the solid line is the best fit GCE and the colored bands represent the minimum and maximum models, derived using the Fruity (blue) and the Monash (red) yields. The bottom right panel represents the evolution of the ratio of the two SLR isotopes 107 Pd/ 182 Hf, for which we found the uncertainties from the stochastic Monte Carlo framework to be minimal. The dotted vertical line represents the time of the formation of the Sun and we decayed the values of the ratios at that time to their corresponding ESS values to calculate the isolation time.
Figure 5. Previously published as Figure 3 in [60], ©AAS, reproduced with permission. Time-evolution predictions from our OMEGA+ GCE framework for the Milky Way of the SLR isotopes produced by AGB stars, relative to their stable reference isotope (the two top and the bottom left panel). These panels are the realisation of the bottom right panel of Figure 3 for the three specific isotopes, where the solid line is the best fit GCE and the colored bands represent the minimum and maximum models, derived using the Fruity (blue) and the Monash (red) yields. The bottom right panel represents the evolution of the ratio of the two SLR isotopes 107 Pd/ 182 Hf, for which we found the uncertainties from the stochastic Monte Carlo framework to be minimal. The dotted vertical line represents the time of the formation of the Sun and we decayed the values of the ratios at that time to their corresponding ESS values to calculate the isolation time.
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Figure 6. Hotokezaka-style model example calculations showing the abundance evolution in time of an SLR nucleus in the ISM. For the 1000 runs calculated for this example, the median (yellow line), 1 σ (black region), 2 σ (dark grey), and total (light grey) distribution are shown, as well as one example case (blue line). The set-up represents the case of a stellar source with a constant total galactic rate of 15 events per Myr (compatible to the current neutron-star merger rate), ISM mixing length α = 0.1, and turbulent velocity of 7 km/s. The mass of SLR nucleus ejected by each event is the numerical value 1 (if multiplied by M ⊙ , then the y-axis can be considered in units of M ⊙ ). The left and right panels represent the case of an SLR nucleus with τ = 10 and 100 Myr, respectively, and the abundances can be compared to each other. The median for τ = 10 Myr is roughly 3 orders of magnitude lower than that for τ = 100 Myr, because the longer τ allows for the SLR nucleus to accumulate. The spread, e.g., at 68%, is 2 to 3 orders of magnitudes larger for τ = 10 Myr than for τ = 100 Myr, which reflects the impact of the faster decay. The peaks in the single case, blue lines are more spaced out in the τ = 100 Myr case because the slower decay and memory build up produces a higher median abundance; therefore, some of the events do not have a visible impact.
Figure 6. Hotokezaka-style model example calculations showing the abundance evolution in time of an SLR nucleus in the ISM. For the 1000 runs calculated for this example, the median (yellow line), 1 σ (black region), 2 σ (dark grey), and total (light grey) distribution are shown, as well as one example case (blue line). The set-up represents the case of a stellar source with a constant total galactic rate of 15 events per Myr (compatible to the current neutron-star merger rate), ISM mixing length α = 0.1, and turbulent velocity of 7 km/s. The mass of SLR nucleus ejected by each event is the numerical value 1 (if multiplied by M ⊙ , then the y-axis can be considered in units of M ⊙ ). The left and right panels represent the case of an SLR nucleus with τ = 10 and 100 Myr, respectively, and the abundances can be compared to each other. The median for τ = 10 Myr is roughly 3 orders of magnitude lower than that for τ = 100 Myr, because the longer τ allows for the SLR nucleus to accumulate. The spread, e.g., at 68%, is 2 to 3 orders of magnitudes larger for τ = 10 Myr than for τ = 100 Myr, which reflects the impact of the faster decay. The peaks in the single case, blue lines are more spaced out in the τ = 100 Myr case because the slower decay and memory build up produces a higher median abundance; therefore, some of the events do not have a visible impact.
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Lugaro, M.; Côté, B.; Pignatari, M.; Yagüe López, A.; Brinkman, H.; Cseh, B.; Den Hartogh, J.; Doherty, C.L.; Karakas, A.I.; Kobayashi, C.; et al. The RADIOSTAR Project. Universe 2022, 8, 130. https://0-doi-org.brum.beds.ac.uk/10.3390/universe8020130

AMA Style

Lugaro M, Côté B, Pignatari M, Yagüe López A, Brinkman H, Cseh B, Den Hartogh J, Doherty CL, Karakas AI, Kobayashi C, et al. The RADIOSTAR Project. Universe. 2022; 8(2):130. https://0-doi-org.brum.beds.ac.uk/10.3390/universe8020130

Chicago/Turabian Style

Lugaro, Maria, Benoit Côté, Marco Pignatari, Andrés Yagüe López, Hannah Brinkman, Borbála Cseh, Jacqueline Den Hartogh, Carolyn Louise Doherty, Amanda Irene Karakas, Chiaki Kobayashi, and et al. 2022. "The RADIOSTAR Project" Universe 8, no. 2: 130. https://0-doi-org.brum.beds.ac.uk/10.3390/universe8020130

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