Radioactive nuclei from cosmochronology to habitability

Radioactive nuclei from cosmochronology to habitability

M. Lugaro, U. Ott, Á. Kereszturi

Konkoly Observatory, Research Centre for Astronomy and Earth Sciences,
Hungarian Academy of Sciences, H-1121 Budapest, Hungary
Monash Centre for Astrophysics, Monash University, VIC3800, Australia
Atomki Institute for Nuclear Research,
Hungarian Academy of Sciences, H-4026, Debrecen, Hungary
Max-Planck Institute for Chemistry, D-55128 Mainz, Germany
Abstract

In addition to long-lived radioactive nuclei like U and Th isotopes, which have been used to measure the age of the Galaxy, also radioactive nuclei with half-lives between 0.1 and 100 million years (short-lived radionuclides, SLRs) were present in the early Solar System (ESS), as indicated by high-precision meteoritic analysis. We review the most recent meteoritic data and describe the nuclear reaction processes responsible for the creation of SLRs in different types of stars and supernovae. We show how the evolution of radionuclide abundances in the Milky Way Galaxy can be calculated based on their stellar production. By comparing predictions for the evolution of galactic abundances to the meteoritic data we can build up a time line for the nucleosynthetic events that predated the birth of the Sun, and investigate the lifetime of the stellar nursery where the Sun was born. We then review the scenarios for the circumstances and the environment of the birth of the Sun within such a stellar nursery that have been invoked to explain the abundances in the ESS of the SLRs with the shortest lives – of the order of million years or less. Finally, we describe how the heat generated by radioactive decay and in particular by the abundant Al in the ESS had important consequences for the thermo-mechanical and chemical evolution of planetesimals, and discuss possible implications on the habitability of terrestrial-like planets. We conclude with a set of open questions and future directions related to our understanding of the nucleosynthetic processes responsible for the production of SLRs in stars, their evolution in the Galaxy, the birth of the Sun, and the connection with the habitability of extra-solar planets.

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©2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
http://creativecommons.org/licenses/by-nc-nd/4.0/

This paper is dedicated to the memory of Gerald J.  Wasserburg, who pioneered, built up, and inspired the science presented here.

1 Introduction

More than a century has passed since Marie Skłodowska Curie111The 150 anniversary of her birthday was recently celebrated on the 7 of November 2017. coined the term Radioactivity to indicate the emission of radiation and particles from peculiar nuclei. Since then, the role and applications of radioactivity have had a profound impact in many fields of science and technology. The role of radioactive nuclei in the field of astrophysics has been long recognised and described. For example, radioactive nuclei power the light of supernovae and the radiation they emit can be mapped throughout the Galaxy by satellite observatories [radiobook]. Here we focus on the most recent advances in the research directions that relate the process of short-lived (half-lives222See Table 1 for a list of all the symbols and the acronyms used throughout the paper. T 0.1 to 100 million years, Myr) radioactivity to the concept of cosmochronology, and on the relatively more recent link between short-lived radioactivity and habitability. We consider in particular the applications of radioactivity in the field of cosmochemistry, i.e., the study of the composition of meteorites and other solid Solar System samples aimed at explaining the origin of chemical matter in the Solar System and in the Universe. Due to extensive technological advances in the laboratory analysis of the isotopic composition of terrestrial and extraterrestrial materials, the amount of information and constraints that can be derived from such studies are expanding at a very fast rate. Much effort on the theoretical interpretation is needed to keep up with the experimental data. In this landscape, the connections between radioactivity, cosmochronology, and habitability are becoming more relevant than ever, and the implications of these connections are quickly becoming far reaching. The aim of this paper is to illustrate and discuss these connections and their implications.

Cosmochronology is intrinsically linked to radioactivity, being defined as the use of the abundances of radioactive nuclei to compute either the age of the elements themselves, or the age of astronomical objects and events. The first aim typically relies on very long-lived radionuclides with half-lives T of the order of billions of years (Gyr), such as U, Th, Os, Rb; an introduction to this topic can be found, for example, in Chapter 1 of [radiobook]. Here we address the second aim: to use radioactive nuclei to calculate the age of astronomical objects and events, specifically in relation to the birth of our Sun and Solar System, with the ultimate aim to compare the birth of our Sun to the birth of other stars and their extra-solar planetary systems. To such aim we use short-lived radionuclides (SLRs, T 0.1 to 100 Myr), which provide us with a range of chronometers of the required sensitivity.

It is well known that radioactive decay can be used as an accurate clock because the rate at which the abundance by number of a radioactive nucleus decreases in time due to its radioactive decay is a simple linear function of the abundance itself, where is the time-independent constant of proportionality referred to as the decay rate:

(1)

A quick integration between two set times and delivers:

(2)

which can also be written as

(3)

where is the mean-life, i.e., the time interval required to decrease by a factor (instead of a factor , as for the half-life).

Figure 1: Photomicrograph produced in 1977 [clayton77] of the CAI named Al3S4 from the Allende meteorite. The field of view is 22 mm 17 mm. In 2014, the initial Sm/Sm ratio in the ESS was derived from analysis of this CAI [marks14] (bottom left panel of Fig. 2).

Radioactive clocks have been used extensively to measure a large variety of time intervals. The decay of C, a nuclide with a half-life of 5730 yr, allows us to measure timescales related to human history; and the age of our Milky Way Galaxy of approximately 13 Gyr has been estimated also based on the ages of some of the oldest observed stars inferred from their U and Th abundances [cayrel01, frebel07]. Thanks to the SLRs considered here, it has become possible to investigate in detail the early history of the Solar System and build a chronology of planetary growth from micrometer-sized dust to terrestrial planets [dauphas11]. For example, the solidification of the lunar magma ocean has been dated to about 200 Myr after the birth of the Sun also thanks to the radioactive decay of Sm into Nd, respectively [borg11]. The age of the oldest solids in the Solar System, the calcium-aluminium-rich inclusions (CAIs) found in primitive meteorites (Fig. 1), is 4567-4568 Myr (see Table 3 of [tissot17]) as measured from the radioactive decay chain starting at the U isotopes and ending into the Pb isotopes. CAIs are believed to be among the first solids to have formed in the protosolar nebula, thus, their age is taken also as indicative for the age of the Sun.

Unlike cosmochronology, habitability has been linked to short-lived radioactivity only recently. Here we use the concept of habitability in the following sense: whether or not an astronomical object can support the formation or the maintenance of life forms partly similar to those we have on Earth [Gargaud2011]. Formation and maintenance, however, are two different processes, both related to habitability. It should be kept in mind that life forms elsewhere in the Universe could be fundamentally different from those we know from Earth. However, the definition of life as a system based on chemicals, built on organic material, and supported by liquid water as a solvent is generally accepted by the astrobiological community and thus is also used here.

The paper is structured as follows. Section 2 introduces some basic methodology and considerations and is separated into four sections: Sec. 2.1 presents the methods by which the initial SLR abundances in the early Solar System are inferred from meteoritic analysis. Section 2.2 presents a broad overview of stellar evolution and nucleosynthetic processes in stars. Section 2.3 describes the processes that have built up the Solar System chemical matter, from galactic chemical evolution to the formation of the Sun itself. Section 2.4 presents how, in general, radioactivity may influence habitability in several direct and indirect ways. Section 3 discusses in more detail each SLR, from its meteoritic abundance to the nuclear path of its stellar production. The 19 SLRs considered here are grouped into 9 subsections, according to their nucleosynthetic production processes. In Sec. 4 we deal with Galactic evolution: Sec. 4.1 presents the simple analytical models used so far to describe the evolution of SLRs in the Galaxy, and Sec. 4.2 shows how the SLR galactic abundances can be used to establish the timing of specific events related to the birth of our Sun. In Sec. 5 we discuss inferences derived from the presence of SLRs in the ESS concerning the circumstances of the Sun’s birth. For sake of clarity, we distinguish three different questions related to the general problem: the stellar sources, the injection mechanism, and the plausibility and probability of the possible scenarios (covered in Sec. 5.1, 5.2, and 5.3, respectively). In Sec. 6 we describe the potential sources of radioactive heat in the ESS and the implications on planet formation and habitability: first, we analyse all the possible radioactive heat sources (Sec. 6.1), then we consider carrier minerals (Sec. 6.2), and finally the specific, important case of Al (Sec. 6.3). Section 7 summarises the main points of the paper and presents a final set of open questions and future research directions.

The topic of the present paper covers a range of research fields, from nuclear physics, via astronomy and astrophysics, to planetary sciences, from both the experimental and the theoretical perspective. We focus here on the interdisciplinary connections between these topics. As such the paper has been written keeping in mind different audiences and with the broad aim to foster and enhance the efficiency of the knowledge transfer required to answer the currently open questions.

2 Background information

General
Myr Millions of years
SLR Short-lived radionuclide
Abundance by number of a SLR
Abundance by number of a stable reference isotope
Decay rate
Mean-life
T Half-life
ESS Early Solar System
CAI Calcium-aluminium rich inclusion
Per mil/per ten thousands variation of the abundance ratio
Stars and supernovae
M Solar mass
Stellar metallicity
AGB star Asymptotic giant branch star
CCSN Core-collapse supernova
SNIa Type Ia supernova
WD White dwarf
NSM Neutron star merger
WR star Wolf-Rayet star
(G)MC (Giant) molecular cloud
CRs Cosmic rays
Galaxy
GCE Galactic chemical evolution
ISM Interstellar medium
Infall parameter in GCE analytical models
GCE parameter in analytical granularity equation
Recurrence time between stellar additions from the same source
Age of the Galaxy up to the formation of the Sun
Isolation time of the (G)MC where the Sun was born
Time of a last nucleosynthetic event
Nucleosynthesis processes
NSE Nuclear statistical equilibrium process
process neutron-capture process
process neutron-capture process
process Process responsible for the production of p-rich isotopes heavier than Fe
process Photodisintegration process
process Neutrino process
Table 1: List of acronyms and symbols used throughout the paper.

2.1 The derivation of the SLR abundances in the ESS

Figure 2: Four typical examples of derivation of the ratio of a SLR relative to its stable (or long-lived) reference isotope from excesses in the daughter nucleus of the SLR. The excess with respect to one of the most abundant isotopes of the same element is plotted on the y-axis, both as ratio and as -value or -value, i.e., per mil or per ten thousand, respectively, variation with respect to the laboratory standard (see Eq. 4). The x-axis reports the isotopic ratio of two isotopes taken to represent the relative abundances of the two elements involved, which is controlled by the chemistry and mineralogy of the sample. Top left: Measurements of different minerals with varying Al/Mg ratios in the inclusion WA from the Allende meteorite from Lee et al. “Aluminum-26 in the early solar system - Fossil or fuel” [lee77] ©AAS. Reproduced with permission. The linear correlation between the Mg excess and the elemental ratio represented the first clear evidence that Al was incorporated live in these solids. If Al was incorporated extinct instead, i.e., already fully decayed into Mg, the Mg excess would be constant as function of Al/Mg. Top right: Inferred Ca/Ca ratio in CAI E44 from the Efremovka meteorite from Liu et al. “A Lower Initial Abundance of Short-lived Ca in the Early Solar System and Its Implications for Solar System Formation”( https://doi.org/10.1088/0004-637X/761/2/137)[liu12] ©AAS. Reproduced with permission. This is an example of a case of a weaker evidence (see Table 2) due to the large error bars. Bottom left: Derivation of the initial Sm/Sm ratio in CAI Al3S4 (Fig. 1) from very high-precision data [marks14]. Bottom right: Derivation of the ESS Cm/U ratio based on analysis of the peculiar U-depleted CAI Curious Marie also from the Allende meteorite [tissot16]. In this case Nd is used as chemical proxy for Cm, since Cm does not have stable isotopes. The blue line represents the isochrone obtained from the data, the red line represents the isochrone shifted an assumed age of 5 Myr. However, [tang17] reported a much shorter age, and the ESS ratio reported in Table 2 is essentially the same as the blue line. Reprinted from Tissot et al. (2016) Science Advances, 2, e1501400 © The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution Non Commercial License 4.0 (CC BY-NC) http://creativecommons.org/licenses/by-nc/4.0/.

Analysis of meteoritic whole rocks and separate inclusions is applied to derive the abundances of the SLRs as close as possible to the time when the Sun was born, i.e., in the early Solar System (ESS). The CAIs (FIG. 1) are one of the major components (amounting up to several %) of the most primitive meteorites, the carbonaceous (CC) and unequilibrated ordinary (UOC) chondrites, and consist of high-temperature (refractory) solids. The other components of chondrites are chondrules – solidified melt droplets that gave these meteorites their name – and matrix, both of which consist largely of silicate minerals. These meteorites are “undifferentiated”, i.e., they were not affected by major planetary/asteroidal processes like magmatism and formation of a metallic core. “Differentiated” meteorites, in contrast, suffered from such processes and include the rarer (by number) “achondrites”, and the iron and stony-iron meteorites. Important among the achondrites in the context of establishing ESS abundances of SLRs (e.g., Pu) are the angrites, named after the type specimen Angra dos Reis. Achondrites include also eucrites (magmatic rocks likely from the asteroid Vesta) as well as meteorites from the Moon and from Mars.

Since the birth of the Sun was a process that lasted a few Myr, rather than a specific point in time, the definition of the time when the Sun was born is ambiguous. As usual in cosmochemistry we define this as the time when the first solids formed, in other words, as the age of the oldest solids found in meteorites, the CAIs. As mentioned above, the age of CAIs is very well determined using U to Pb radioactive dating. Furthermore, it appears that CAIs, unlike chondrules, formed over a very short timescale of the order of 0.1 Myr [connelly12], similar to the median lifetimes of proto-stars hydrostatic cores surrounded by a dense accretion disk333These are referred to as proto-stars of Class 0. In the Class I objects more than 50% of the envelope has fallen onto the central protostar, Class II objects have circumstellar disks, while Class III proto-stars have lost their disks.. In the following we will refer to the ESS as the time when the CAIs formed.

Given that the Sun is almost 4.6 Gyr old and the SLRs we consider here live less than 100 Myr, even if they were abundantly present when the Sun was born, today they are completely extinct and their abundances in the ESS cannot be not measured directly. They are rather inferred from analysis of meteoritic samples via the identification of an in the daughter nucleus into which each SLR decays. For example, excesses in Mg or Ni, with respect to their normal abundance ratios relative to isotopes without a possible radiogenic component such as Mg or Ni, can be the product of the radioactive decay of Al or Fe, respectively. This is conceptually very different from observing, as done recently, live Fe in the Earth’s deep sea crust [wallner16] (as well as Pu [wallner15]), in fossilised bacteria [ludwig16], and on the Moon [fimiani16]. This live Fe is the fingerprint of a recent injection, roughly 2 Myr ago, from one or more supernova(e) resulting from the core-collapse of massive stars (core-collapse supernovae, CCSNe) [breitschwerdt16]. On the other hand, an excess in Ni relative to Ni measured in meteorites represents extinct Fe and potentially the fingerprint of one or more CCSNe that occurred more than 4.6 Gyr ago. Also, fifteen atoms of live Fe have been counted in accelerated particles (cosmic rays, CRs) that reach the Earth [binns16]. These live Fe atoms are the fingerprint of recent production events from CCSNe in the groups of massive stars (OB associations) from where the CRs are believed to originate.

In the case of the ESS abundances, to make more evident the radiogenic origin of the observed excesses, it is necessary to analyse materials with variable amounts of the element to which the SLR isotope belongs, relative to the element to which the daughter isotope belongs, e.g., the Al/Mg and the Fe/Ni ratios in the case of Al and Fe, respectively. True radiogenic excesses should be more evident in materials with the higher elemental ratios. These materials are advantageous in disentangling the true radiogenic excesses from other effects that may cause unusual isotopic ratios, such as statistical flukes as well as instrumental and natural mass fractionation effects. Excesses in the daughter nuclei are usually measured relative to the most abundant isotope of the same element, and to better highlight their nature as excesses, they are reported in the form of -values or -values, i.e., per mil or per ten thousand, respectively, variations with respect to a corresponding “normal” isotopic ratio, as defined by a laboratory standard. For example, in the case of the Mg/Mg ratio the -value is:

(4)

The -value is defined in the same way, except that the variation is multiplied by 10,000 instead of 1,000. A linear correlation between the excess and the elemental ratio (e.g., versus Al/Mg) proves that the SLR was incorporated in the samples while still alive ([lee77], Fig. 2). The slope of the line gives the abundance ratio of the SLR to the stable reference isotope at the time of closure of the system, i.e., the time after which the system was not disturbed anymore by any redistribution of isotopes or elements, the only compositional change coming from radiogenic decay. Any alteration event after formation of a solid can be responsible for “resetting” the chronometers. The line defined by the data points is referred to as an , since data points located on a given line have by definition the same ratio of the SLR to its reference isotope, i.e., their closure time is the same. Any younger sample, i.e., one that closed after some time, would lie on a line with a shallower slope, since it would contain a lower initial abundance of the SLR due to its decay during the given time interval. Using this method, SLRs can be used to derive relative ages for Solar System samples, from which we can infer the history of the formation of planetesimals and planets [dauphas11].

The intercept at x=0 represents the composition of a virtual sample that did not include any abundance of the SLR. As such it provides the initial ratio of the daughter nucleus to the reference isotope of the same element at the time of closure, relative to the laboratory standard. Samples that formed later from a same reservoir, as explained above, would present a shallower slope, at the same time, they would also have a higher intercept, since the SLR would have decayed further within the reservoir itself. However, different -values at x=0 for different samples could also indicate non-radiogenic (i.e., not dependent on the decay time) heterogeneities in the initial abundance of the daughter nucleus and/or the SLR itself. For example, discussion is on-going on whether Al itself was distributed heterogeneously or homogeneously in the ESS (Sec. 3.2). It is crucial to determine the presence of SLR heterogeneities also because these would disturb the derivation of the isochrone-based ages for Solar System samples.

Time differences between different samples can contribute to the uncertainties in our knowledge of the ESS abundances of the SLRs. Clearly, the best samples for this purpose are the oldest possible materials, the CAIs. In some cases analysis of a given element in CAIs is not easily possible, and other materials younger than CAIs need to be used. This is the case, for example, for Fe, due to the fact that not much Fe is present in CAIs. The age difference between the analysed sample and the CAIs can be measured using other radioactive systems and then be used to extrapolate back from the abundance measured in the sample to the ESS value (see, e.g., the case of Cm/U in the bottom right panel of Fig. 2).

Two more issues should be mentioned. The first is the case where excesses in the daughter nucleus may be present, which are not related to the radiogenic decay of the SLR. Potential intrinsic heterogeneities could be produced both by natural and artificial effects. Natural effects include nucleosynthetic signatures, i.e., anomalies in the stable isotopes due to the original presence of presolar stardust, as well as mass fractionation, both mass-dependent and non mass-dependent [dauphas16]. Artificial effects can occur during the laboratory chemical procedures and the measurement itself and are mostly of the mass-dependent fractionation type. These effects can be prominent relative to the true radiogenic effect, which is usually quite small (in fact, as explained above, it is measured in per mil or per ten thousand variations). The mass-depended artificial effects can be corrected by analysing at least three isotopes, and normalising the system to a chosen set of “normal” non-radiogenic ratios. A typical example where these issues are particularly relevant is the hotly debated case of Fe (Sec. 3.5).

The second issue is related to the derivation of useful SLR to stable isotope ratios in the ESS for the few SLRs heavier than Fe produced by the proton-capture process (the process; see Sec. 2.2), and potentially for Pu (Sec. 3.6). In these cases, to obtain a ratio that is possible to interpret within the framework of stellar nucleosynthesis it is necessary to re-normalise the measured ratio to a different stable isotope than that used for the measurement. This involves the use of the Solar System abundances of stable isotopes and their associated uncertainties, which can be relatively large when different elements are involved. A main example is Nb, whose ESS abundance is measured relative to Nb, which is the only stable isotope of Nb and is produced by neutron-capture processes. The abundance of Nb needs to be re-normalised instead to Mo, a neighbouring nucleus that is produced by the process like Nb (see Sec. 3.8).

In Table 2 we present an update of Table 1 of Dauphas & Chaussidon (2011) [dauphas11] for 19 SLRs. The half-lives are taken from the National Nuclear Data Center website (www.nndc.bnl.gov, including errors in brackets), except for Be and Sm, for which references are given in the table footnotes. Roughly a dozen new measurements and estimates have become available since 2011, improving the accuracy and precision of our knowledge of the initial ESS abundances of roughly half of the listed nuclei. The number of nuclei with three stars in the quality ranking (last column of Table 2) has increased by one since 2011 because of the more precise determination of the Pd/Pd ratio [brennecka16]. Further, the Cm/U ratio is now much more solidly determined, thanks to the discovery of the peculiar U-depleted CAI Curious Marie named after Marie Skłodowska Curie ([tissot16], bottom right panel of Fig. 2). On the other hand, we have downgraded the estimate of the Pu/U ratio from three- to two-star quality due to the fact that two different values are reported from two different types of experiments. The value given by [lugmair77] is roughly half of that listed in the table from [hudson89] (see discussion in Sec. 3.6). The number of ratios with one-star quality has decreased from five to three with respect to Table 1 of [dauphas11] due to the upgrade of the Cm/U ratio, as well as the recently improved upper limit of the Cs/Cs ratio [brennecka17a]. This is now more than two orders of magnitude lower than the previous estimate, providing a more significant constraint. For three of the SLRs produced by the process (Nb and Tc) we provide both the experimental ratio and the ratio re-normalised to a different stable isotope using the most recent Solar System abundances of the stable isotopes [lodders09, burkhardt11].

Most of the uncertainties listed in Table 2 are statistical only and given at 2, however, several exceptions are present, which are discussed in detail within the subsections of Sec. 3 dedicated to the different isotopes. Systematic uncertainties, on the other hand, are not included since they derive from specific suppositions and cannot be evaluated quantitatively. An indication of the magnitude of such uncertainties can only be derived by comparing the results from different experiments, approaches, and assumptions. For example, in the case of the ESS abundance of Pd, the main current uncertainty is related to a potential systematic error related to the age of the considered sample [matthes18].

Three more SLRs exists with half-lives in the range of interest here: Kr (0.23 Myr), Zr (1.5 Myr), and Tc (0.21 Myr). They are not included in Table 2, however, for various reasons: Kr is a noble gas isotope, and as such was virtually absent from the solid materials with which we deal here. Even if it was introduced therein by ion implantation, as in the case of noble gas trapped in meteoritic components such as stardust nanodiamond and SiC, as well as Phase Q [ott14], its abundance would still be very low compared to the neighbouring less volatile elements and not reflect the abundance produced in a stellar source. In addition, its daughter nucleus Br is also volatile and thus prone to secondary loss, complicating matters further. The daughter of Zr is Nb; for this nucleus it is not possible to observe an excess relative to other isotopes of Nb since it is the only stable isotope of Nb. Finally, Tc decays into Ru. Only upper limits are available for the similar case of Tc decaying into Ru, but Tc is even more challenging [becker03] due to the 20 times shorter half-life of Tc with respect to Tc, and the 7 times higher natural abundance of Ru with respect to Ru.

SLR Daughter Reference T(Myr) (Myr) ESS ratio Ref. Quality
Al Mg Al 0.717(24) 1.035 [jacobsen08]
Be B Be 1.388(18) 2.003 [tatischeff14]
Mn Cr Mn 3.74(4) 5.40 [tissot17]
Pd Ag Pd 6.5(3) 9.4 [matthes18]
Hf W Hf 8.90(9) 12.8 [kruijer14]
Cm U U 15.6(5) 22.5 [tang17]
I Xe I 15.7(4) 22.6 [ott16]
Nb Zr Nb 34.7(2.4) 50.1 [haba17]
Mo
Sm Nd Sm 68/103 98/149 [marks14]
Cl S, Ar Cl 0.301(2) 0.434 [tang17]
Fe Ni Fe 2.62(4) 3.78 [tang15]
Pu U 80.0(9) 115 [hudson89]
Be Li Be 53.22(6) days 76.80 days [chaussidon06]
Ca K Ca 0.0994(15) 0.1434 [liu17]
Pb Tl Pb 17.3(7) 25.0 [palk18]
Sn Te Sn 0.230(14) 0.33 [brennecka17b]
Cs Ba Cs 2.3(3) 3.3 [brennecka17a]
Tc Mo Mo 4.21(16) 5.94 [burkhardt11]
Ru
Tc Ru Ru 4.2(3) 6.1 [becker03]
Ru

According to [chmeleff10]. and references therein. A single CAI with a very high value of also exists [gounelle13]. The value needs to be confirmed by Pb-Pb dating using the U isotope composition determined for the same sample, it could be lowered down to [matthes18]. Renormalised using Solar System abundances [lodders09, burkhardt11]. According to [kinoshita12]. According to [marks14]. We calculated the error bar translating the age of less than 50 kyr [tang17] into an age of kyr. Values from to are also reported [mishra14, telus18]. The main (99.88%) decay mode of Pu is by emission. The ensuing decay chain proceeds through the very long lived Th (T=14 Gyr). The spontaneous fission of Pu, which results in measurable excesses of some Xe isotopes used to derive the ESS abundance of Pu, represents only 0.12% of the decay process. Renormalised using Solar System abundances [lodders09].

Table 2: For the 19 SLRs we list their daughter nuclei, stable or long-lived reference isotopes, T (and ) from the National Nuclear Data Center website (www.nndc.bnl.gov, including errors on the last digits in brackets), and ESS ratios. In the last column, following Dauphas & Chaussidon [dauphas11] a quality ranking is given: three stars indicate those SLRs whose ESS abundance is well determined; two stars indicate those SLRs for which there is convincing evidence for their presence in the ESS, but the initial abundance is less certain; one star indicates those SLRs for which there are reports, but the evidence is weak and awaits confirmation; means that only an upper limit on the initial abundance exists.

2.2 Stellar evolution and nucleosynthesis

Figure 3: Schematic illustration of stellar evolutionary phases with time (increasing on the x-axis), according to their initial mass (increasing on the y-axis). Image credit: NASA/CXC/M.Weiss/Public domain.

The cosmic abundances of the vast majority of the nuclei of the elements heavier than H and He are produced by processes occurring during the various hydrostatic and explosive evolutionary phases of single stars, as well as during the interaction of two or more stars in multiple stellar systems. This applies to the abundances of both stable and radioactive nuclei, the only difference being, of course, that the latter, following production, decay according to their half-lives. In fact, it was thanks to the discovery of the signature of the short-lived element Tc in the spectra of red giant stars that it was possible to definitely prove that nucleosynthesis occurs in situ inside stars [merrill52]. Any Tc originally present would have been completely decayed – its isotopes have half-lives of a few million years at most – by the time of the order of billions of years that the observed low-mass stars take to reach the red giant phase. Here below we provide a brief summary of the processes of stellar evolution and nucleosynthesis. For more detailed reviews see [woosley02, langer12, karakas14, demarco17].

In the interiors of stars matter can reach extremely high temperatures, for example, 10 million K (MK) in the core of the Sun and up to billions of K in supernovae. Under the force of gravity, high density conditions are also maintained, for example, roughly 100 gr/cm in the core of the Sun and up to 10 gr/cm in supernovae. Such conditions force nuclei to keep in a confined volume and to react via a huge variety of nuclear interaction channels. This complexity and diversity created all the variety of atomic nuclei from carbon up in the Universe. It is, however, not enough to produce nuclei in the hot and dense interiors of stars and supernovae. Mechanisms must also exist such that these nuclei are expelled into the surrounding medium and recycled into newly forming stars and planets. In stars born with mass similar to the Sun (solar mass, hereafter M) and up to roughly ten times this value, these mechanisms are identified as the combination of the mixing of matter from the deep layers of the star to the stellar surface and the stellar winds that peel off the external layers of the star. These processes are active most efficiently during the final phases of the lives of these stars, the so-called asymptotic giant branch (AGB) phase. During the AGB, efficient dredge-up episodes of matter from the hot core of the star occur together with strong stellar winds, driving mass-loss rates up to M/yr. The winds are powered by variations in the stellar radius, and thus the luminosity and the surface temperature, as well as by the presence of large amounts of dust that form in the cool (2000 K) external layers of the star. When most of the original stellar mass is lost, the matter expelled by the wind can be illuminated by UV photons coming from the central star, producing what we observe as a colourful planetary nebula. Eventually the core of the star, rich in C and O produced by previous He burning, is left as a white dwarf (WD, Fig. 3). The evolutionary timescales of such low-mass stars are relatively long, from 1,000 Myr for stars of mass around that of the Sun, down to several tens of Myr for stars of mass around 7 times larger.

More massive stars live much shorter lives, from a few Myr to a few tens of Myr, and end their lives due to the final collapse of their core (Fig. 3). Once nuclear fusion processes have turned all the material in the core into Fe, neither fusion nor fission processes can release enough energy anymore to prevent the core collapse. As the core collapses, matter starts falling onto it, which results in a bounce shock and a final CCSN explosion. The exact mechanism of the explosion is not well known although remarkable progress has been made in the past decade [janka12]. The supernova ejecta are responsible for carrying out into the interstellar medium the fraction of synthesised nuclei that does not fall back into the neutron star or black hole remnant. In the earlier phases of the evolution of these massive stars, also stellar winds can play the important role of shedding freshly synthesised material into the stellar surroundings. In fact, in some cases, the winds can be so strong that layers previously affected by nuclear burning are exposed, and the ashes of the burning of H and He in the stellar core can be observed directly at the stellar surface. These rare, peculiar stars are known as Wolf-Rayet (WR) stars [langer12] and the strong winds that characterised them are driven by radiation, when the mass of the star is so high (roughly 40 M) that its luminosity can push matter away. Binary interaction can also result in significant loss of matter from stars, if the presence of a companion results in gravitational pull, enhanced mass loss, and non-conservative mass transfer when mass is lost from the system. Another interesting consequence of binary interaction is when accretion of mass from a stellar companion onto a WD is followed by explosive thermo-nuclear burning on the surface of the WD, which results in what we observe as nova explosions. These explosion events also shed matter into their surroundings. An even more extreme case of thermo-nuclear explosions are the supernovae classified as Type Ia (SNIa). In contrast to supernovae classified as SNII, which are rich in H and originate from CCSNe, SNIa are characterised by the absence of H in their spectra. In this case C-burning initiated within a WD made mostly of C and O produces a detonation or a deflagration that tears the whole WD apart (Fig. 3). Even though the light from these events is used as a standard candle to measure the expansion of the Universe (e.g., [riess98]), their origin is still mysterious. Two major binary channels are currently proposed: a WD accreting matter from a stellar companion, and the collision of two WDs.

Stellar nucleosynthesis was first systematically organised by Cameron [cameron57] and Burbidge et al. [burbidge57] – of which an update can be found in Wallerstein et al. [wallerstein97]. Hydrogen burning is mostly responsible for the production of N by conversion of C and O into it, as well as a large variety of minor isotopes: from C produced via proton captures on C, to the only stable isotope of Na (Na) produced by proton captures on Ne, and the SLR Al, produced by proton captures on Mg. Typical temperatures are from 10 to 100 MK, depending on the stellar site. Helium burning is mostly identified with the triple- (He particle) reaction producing C, and the C(,)O reaction, producing O. Many other secondary channels of burning open as the temperature increases above 100 MK, for example, conversion of already present N nuclei into Ne via double -captures. Also reactions that produce free neutrons are typically associated with He-burning, the most famous being C(,n)O and Ne(,n)Mg. In stars with mass below roughly 10 M, nuclear burning processes do not typically proceed past He burning. When He is exhausted in the core these stars enter the AGB phase with a degenerate, inert C-O core. In more massive stars, instead, the temperature in the core increases further. A large variety of reactions can occur. These processes involve C, Ne, and O burning, and include many channels of interactions, with free protons and neutrons driving a large number of possible nucleosynthetic paths. The cosmic abundances of the “intermediate-mass” elements, roughly from Ne to Cr, are mainly the result of this burning. Once the temperature reaches billions of degrees, the probabilities of fusion and photodisintegration reactions become comparable and the result is nuclear statistical equilibrium (NSE). This process favours the production of nuclei with the highest binding energy per nucleon, resulting in a final composition predominantly characterised by high abundances of the nuclei around the Fe peak in the Solar System abundance distribution.

Beyond the Fe peak, charged-particle reactions are not efficient anymore due to the large Coulomb barrier around these heavy nuclei (with number of protons greater than 26). Neutron captures, in the form of slow neutron captures, the process (see [kaeppeler11] for a review), and rapid neutron captures, the process (see [thielemann11] for a review), are instead the main channels for the production of the atomic nuclei up to the actinides. Traditionally, these two neutron capture processes stand as the two extreme cases: during the process, neutron captures are always slower than decays, during the process, neutron captures are always faster than decays. However, intermediate cases do also occur in nature, ranging from the mild case of the operation of branching points on the -process path (as discussed below in relation to a variety of SLRs, such as Fe), to the neutron burst in CCSNe (again, possibly affecting the abundances of many SLRs), to the neutron-capture process, the process, identified so far mostly in low-metallicity environments and post-AGB stars [herwig11, hampel16].

The process requires relatively low neutron densities ( cm) and is at work during He and C burning in low-mass AGB stars (producing most of the -process elements, from Sr to Pb) and the hydrostatic burning phases of massive stars (producing the -process abundances from Fe to Sr). The neutrons are provided by the neutron source reactions on C and Ne mentioned above [kaeppeler11]. The process requires much higher neutron densities ( cm) and is at work in explosive neutron-rich environments. The stellar site of the process has been one of the most uncertain and highly debated topic in astrophysics. Currently, neutron star mergers (NSMs) are being favoured due to new constraints from the discovery of the gravitational wave source GW170817 and its counterparts in -rays (NSMs are believed to be the origin of short -ray bursts) and in the optical and infrared, where the source is a kilonova resulting from the radioactive decay of heavy -process nuclei [kilpatrick17, cote18]. Measurements of Pu in the Earth’s crust as compared to its ESS abundance also support rare events such as NSM as the site of the process [hotokezaka15]. Peculiar flavours of CCSNe (with strong magnetic fields, jets, as well as accretion disks around black holes) could also contribute to -process production in the Galaxy [thielemann11]. Another problem with the modelling of the process is the fact that the nuclei involved are extremely unstable and it is difficult to experimentally determine their properties, even their mass. The coming up large Facility for Antiproton and Ion Research (FAIR) at GSI (Germany) is one of the facilities promising future improvements on this problem, together with the Facility for Rare Isotope Beams (FRIB) at MSU (USA) and the RI Beam Factory at RIKEN (Japan).

A few tens of nuclei heavier than Fe are located on the proton-rich side of the valley of -stability and cannot be produced via neutron captures. These nuclei have typically very low abundances, i.e., they represent at the very most a few percent of the total Solar System abundance of the element they belong to. To account for their production a so-called process is invoked, whose mechanism and astrophysical site is still debated. One popular flavour of the process is the process [pignatari16], where heavier, abundant nuclei are photodisintegrated in an explosive environment to produce lighter -process nuclei. Other possibilities are related to the inverse case, where lighter nuclei capture charged particles to reach some heavier -process nuclei, typically the lightest, and most abundant up to Mo and Ru at atomic mass around 90-100. There are several proposed options for this modality, from the process (rapid process), for example, occurring in X-ray bursts from explosive burning due to accretion of matter from a stellar companion onto a neutron star, to explosive nucleosynthesis during CCSNe, in particular when matter cools down from NSE and particles becomes available (-rich freeze out), as well as the neutrino winds from a nascent neutron star (the process).

Finally, the bulk of the production of B, Be, and Li444For Li a contribution from Big Bang and stellar nucleosynthesis is also present [travaglio01]. does not occur in stars. The abundances of these nuclei are produced via spallation reactions in the interstellar medium (ISM). Spallation reactions occur when material is hit by accelerated particles, i.e., cosmic rays (CRs). This process can be also referred to as non-thermal nucleosynthesis, given that it does not occur within a Maxwellian plasma as nucleosynthetic processes in stars.

The list of SLRs present in the ESS (Table 2) cover almost the whole range of atomic masses, from approximately 10 to 250. As such, their production mechanisms cover the whole range of nucleosynthetic processes that occur in stellar production sites, as will be discussed in detail in Sec. 3.

2.3 Galactic chemical evolution and the build-up of Solar System matter

As stars end their life polluting their environment via winds or explosions with atomic nuclei freshly synthesised in their interiors, new stars are born in the ISM, collecting the gas and dust expelled by the dying stars. In this way, the chemical composition of the Galaxy evolves with time and results in stars of different ages located in different regions of the Galaxy to present different chemical compositions [tinsley80, matteucci12]. This process is referred to as galactic chemical evolution (GCE) and is specifically responsible for the fact that stars have different metallicities (), i.e., amounts of “metals”. Traditionally, in astronomy refers to all the elements heavier than H and He; the Fe abundance is often used as a proxy for it. For the Sun [asplund09], but we also find stars in our Galaxy with varying from six orders of magnitude lower than for the Sun to more than a factor of two higher, depending on both the time and place where they were born. A simple GCE model predicts that metallicity increases as the Galaxy evolves with time. The consequence is that younger (relative to present day) stars should show higher metallicity than older stars, since the younger stars would have formed later during the evolution of the Galaxy and collected material from more previous generations of stars. However, the most recent observations of large stellar galactic populations show that for each stellar age there is a large spread of metallicity [casagrande11, bensby14]. This is interpreted as the result of stellar migration from different regions of the Galaxy [spitoni15], where different star formation rates produce different numbers of stellar generations and in turn different metallicities. In this respect the field of GCE is now moving towards a more complete picture of galactic “chemo-dynamical” evolution.

Figure 4: The scales of star formation, as illustrated by [williams10]. The upper panel shows a composite view of the Rosette nebula and accompanying GMC. The nebula (in green) is powered by a collection of massive stars at the centre of a large cluster. The red is emission from the CO molecule, indicating the GMC. The lower panels zoom in on the star formation process: the left panel shows contours of emission from a cold dusty envelope around a deeply embedded stellar cluster; the right panel shows contours from embedded protostars. Figure reproduced with permission from J. Williams, Contemporary Physics 2010, 51, 381–396 Taylor & Francis Ltd www.tandfonline.com.

Within the ISM, star formation occurs within hierarchical structures (see [williams10] for an accessible review). Stellar nurseries are the coldest and denser regions of the ISM and are referred to as molecular clouds (MCs, named molecular because of the presence of molecules, in particular hydrogen molecules) or giant molecular clouds (GMCs), depending on their size, which is of the order of 50 parsec (pc) for GMCs (top panel of Fig. 4). Molecular clouds in the solar neighbourhood appear to be relatively short-lived, of the order of a few Myr [hartmann01], instead, molecular clouds further away have been observed to have lifetimes in the range 20 to 40 Myr [murray11]. Such differences have been attributed to their larger masses. It is now well established that the vast majority of stars are born in MCs large enough to produce at least a group of stars, referred to as a stellar cluster. GMCs potentially host a number of stellar clusters. The clusters have sizes on the order 0.5 pc (left bottom panel of Fig. 4) and the number of stars can vary largely, from a few tens to tens of thousands. Within clusters, the star formation process is relatively fast, on the order of a few Myr at most (see [dib13] and references therein). Within the 0.05 pc scale, a dense core (the protosolar nebula in the case of the Sun) collapses to form a single star or a multiple stellar system of typically two or three stars. The star itself is first observed as embedded within a thick envelope from which it accretes matter. Since the nebula rotates, a protoplanetary disk forms (the protosolar disk in the case of the Sun). Within a few Myr, possibly up to 10 Myr based on statistical observations [haisch01, williams11], only solids are left in the disk as all the gas is dispersed. This complex, hierarchical structure of star formation results in the possibility of stars within a given stellar cluster or GMC to evolve and pollute the gas from which new stars are born or the already formed protoplanetary disks, with some SLRs, as will be discussed in relation to the Sun in Sec. 5.3.

Figure 5: Schematic illustration of the presolar history of the Solar System matter.

Within this global picture we can identify two phases for the presolar history of Solar System matter (Fig. 5). The first phase is related to the evolution of the Galaxy on the relatively long time interval from the formation of the Milky Way Galaxy to the birth of the Sun of 9 Gyr (equal to the age of the Milky Way of 13 Gyr minus the age of the Sun of 4.6 Gyr). The bulk of the composition of our Sun and its planets was constructed by generations of hundreds to thousands of stars in the Galaxy, each contributing their parcel of atomic nuclei to the build-up of the matter that ended up in the Solar System. The elemental and isotopic composition of the Sun has been used as one of the fundamental benchmarks for GCE models because it is very well known, thanks both to spectroscopic observations interpreted using sophisticated models of the atmosphere of the Sun [asplund09], and to laboratory analyses of pristine meteorites [lodders09, lodders10]. Specifically, GCE models are required to match the Sun’s composition for stars born at the time (4.6 Gyr ago) and place (roughly 8 kpc from the galactic centre, under the assumption that the Sun did not migrate from its birth place) when and where the Sun was born.

The end of the GCE contribution is marked by the incorporation of such presolar matter into a (G)MC. At this point in time the second phase of the presolar history of Solar System matter begins: its residence time in the stellar nursery where it was born. This phase lasted of the order of few to tens of Myr, i.e., roughly three to four orders of magnitude less than the GCE timescale. In relation to the investigation of SLRs in the ESS, the time when such an incorporation occurred has been referred to as the isolation time (). The reason is that the mixing between material in the hotter ISM and in the colder (G)MC is relatively slow, i.e., the time scale to achieve complete mixing is long (100 Myr [deavillez02]), thus, during the isolation time the presolar matter was isolated from stellar contributions in the GCE regime. In other words, is the time the ESS matter spent inside a (G)MC before the formation of the Sun, isolated from the evolution of the ISM matter driven by GCE. It can also be described as the time interval between the birth of the parent (G)MC and the birth of the Sun itself, and called an “incubation” time. During a number of SLRs were only affected by radioactive decay, which thus can be used as a clock to measure (as will be presented in detail in Sec. 4.2). This method gives us the most accurate way to investigate the lifetime of the specific (G)MC where the Sun was born. As mentioned above, molecular clouds are observed to live between a few to a few tens of Myr, probably depending on their size and mass, however, we do not know which side of this range is applicable to the particular case of the Sun.

It is important to highlight here the difference between stable nuclei and SLRs in the context of the build-up of Solar System matter. In relation to stable nuclei, GCE is the most significant process and the contributions from all previous generations of stars count, given that the abundances of these nuclei continue to increase as the Galaxy evolves. Furthermore, for stable nuclei potential additions from one or a few more short-lived, massive stars within the (G)MC or the stellar cluster where the Sun was born would not have made a noticeable difference since their abundances produced by the GCE in the ISM at the time and place of the birth of the Sun were already relatively high555Some care is still needed in specific cases, e.g., if the ESS was polluted by a nearby star or supernova, this could have affected the O isotopic ratios to the level of per mil variations, which is within the resolution of measurements of meteoritic samples [gounelle07, lugaro12a].. Long-lived radioactive nuclei such as Th and U behave in this respect in a very similar way to stable nuclei, while the situation for SLRs is highly dependent on their specific half-lives. The longer the half-life, the more the abundance of the nucleus in the ESS carries the imprint of its production by GCE, as in the case of stable nuclei. The shorter the half-life, the more the abundance of the SLR nucleus in the ESS carries the imprint of its production within the (G)MC or stellar cluster where the Sun was born, simply because the isolation time is more likely to have erased its GCE contribution. In this case the SLR cannot be used as a clock to measure the isolation time, but acts instead as an indicator for the circumstances of the birth of the Sun within its stellar nursery, i.e., it indicates that the Sun was born close enough in time and space to a production event. The SRLs are thus the fingerprint of the stellar objects that populated the environment where the Sun’s birth happened. There are many different scenarios and hypotheses on the circumstances and the environment of the birth of the Sun based on such shortest-lived SLR fingerprints, particularly Al; they are discussed in more detail in Sec. 5.

2.4 Radioactivity and habitability

Figure 6: Possible connections between radioactivity and various factors that influence habitability of solid planetary bodies. Notes according to numbers: 1. Ancient melting was also supported by other processes, including exothermic heat generated by serpentinization, i.e, the addition of water into the crystal structure of minerals. 2. A very early differentiated iron core is expected to have been present in many planetesimals, based on the paleomagnetic signature of internal magnetic dynamos even in carbonaceous chondrites, where the primitive chondritic material accumulated on the surface of an already differentiated core. 3. Magmatic activity and internal liquid water generation were supported by the SLRs only in the first periods. Later on, long-lived radionuclides became the more important to enable continued activity.

Here, we briefly list connections and interactions related to how radioactivity may influence habitability. It does so in complex ways, with many lines of often intricate interaction between different factors. These factors can be grouped into two classes. Direct influences of radioactivity include internal heat generation of planetary bodies. Beside the radioactive sources, the relict heat from the accretion process contributes significantly to the temperature of the mantle and the core. There is an ongoing debate on which factor dominates among these two on the Earth today [herzberg10]. Some researchers consider them equally important [jaupart15, andrault16], however, in the longer term radioactive heat may dominate over accretionary heat. Measurements of geologically produced antineutrinos may help to settle this question, however, current uncertainties are very large [araki05]. Volcanism is a possible consequence of internal heat generation, which may then be responsible for melting of ice, additions to the atmosphere (which in turn may lead to protection of the planetary surface from UV irradiation), increasing chemical heterogeneity, and generation of additional chemical energy sources from heat driven chemical reactions. Plate tectonics is also driven by internal heat and supports planetary scale chemical circulation, while increasing geochemical diversity by producing granitic crust and continents (on the Earth). Weathering then produces an even wider variety of materials that differ from those that would have been present if the whole surface were covered by water. Sufficient rates of internal heat production can also lead to the formation of a (partially) molten iron core, which can generate a global magnetic field on a rotating planet, which in turn protects the atmosphere against erosion by stellar wind and the surface against ionising charged particle bombardment.

Indirect influences are related to the formation of molecules essential for life. Radioactivity affects the characteristics of the environment, which in turn determines whether such molecules could form or not (because of temperature, volcanic activity, and presence or absence of liquid water). Not only the organic materials produced by chemical reactions matter here, but more indirect effects are also important, like the generation of phyllosilicate minerals by the action of water. Phyllosilicates help in molecular polymerisation and increase the stability of organic molecules. Such molecules might then support prebiotic processes, and the origin of life as well. They could also support the maintenance of life after its origin by serving as nutrients and building blocks for the already emerged life.

The effects listed above and their consequences are linked to each other, creating a complex system, which influences habitability in a variety of ways. The possible connections between radioactivity and various factors that influence habitability of solid planetary bodies are shown in Fig. 6. Note that the figure is applicable only to bodies with a solid surface (including rocky planets, icy moons or asteroids, comets), while gaseous planets and brown dwarfs are different cases. Radioactive heat sources are considered, but other heat sources could be also present or even dominate over radioactivity, and may produce similar consequences as those that are listed here. Two main causal branches are visible: the heat production from radioactivity that has far reaching consequences, and the radiation itself that has a smaller number of consequences with less complexity. For example, radioactive heat driven melting causes differentiation of a planetary body, which in turn affects volcanic activity, material circulation, as well as chemical and atmospheric characteristics. In this respect it is relevant to note that the duration of radioactivity as well as its level differ between shorter- and longer-lived radionuclides. While short decay times lead to early activity on a planetary body, the presence of radionuclides with longer decay time may be essential in supporting long duration habitability – however, here the thermal budget of the body also matters: losing the continuously generated heat too efficiently may keep the given body in a frozen state.

Without the heat generated by radioactivity the conditions for habitability would be quite different and often much less favourable. In the cases where heating leads to internal melting, differentiation of the planetary body interior could contribute to liquid water and magnetic field generation, volcanic activity, as well as contribute to the generation of an atmosphere, and in general result in mineral diversity, where the latter may have a complex but poorly known connection with habitability [Hazen2008b]. Without such radioactive heat-generated differentiation and melting, liquid iron cores may be much less abundant among terrestrial planets, allowing - due to lack of a magnetic field - cosmic radiation to bombard the surface [Lazio2016]. The bombardment by cosmic ray particles probably reduces the chance of the origin of life on the surface and also the survival of organisms there. While in the subsurface region both origin and survival of life is possible even in such a case [Fisk1999], subsurface niches seem unlikely to be sufficient for supporting the emergence of more advanced life, and radiation in such cases does not allow surface organisms to exploit stellar irradiation – which is a much larger energy source than subsurface chemical sources, therefore opening the way for faster evolution [Trevors2002]. In the case of a missing magnetic field, habitability may still be possible but in restricted and limited form.

Within the context of this paper we will mostly discuss the effects on habitability of the specific case of SLRs as heat sources in the ESS (Sec. 6.3). We will see that the most interesting case is that of Al (=0.7 Myr), simply because this SLR was so abundant. Potentially, also Fe and Cl can be of interest as heat sources in the ESS, depending on their initial abundances, which for the ESS are still debated (see Secs. 3.3 and 3.5). In relation to the case of longer-lived radionuclides as long-term sources of heating, Th (T=14 Gyr), U (T=0.703 Gyr), U (T=4.5 Gyr), and K (T=1.2 Gyr) are still alive today in the Solar System and are of paramount importance in relation to the internal energy budget of the Earth. As mentioned above, their decay currently provides possibly half of the total heat budget of the solid Earth (the other half being the primordial heat left over from its formation [turcotte02]), with implications on its surface habitability. Th and U are actinides produced by the process, while K is produced together with the two stable isotopes of K (at masses 39 and 41) in CCSNe via O burning. Interestingly, from stellar observations and GCE models it is possible to determine the abundances of some of these isotopes in extra-solar planets.

Since U and Th are refractory, we can assume that their abundances, relatively to Si, observed or predicted in stars should be close to the abundances present in rocky planets around the stars. Recent observations of solar twins, with and without planets, have shown that most of these stars have larger Th abundances than the Sun [unterborn15], with a spread of almost a factor of 3. This difference probably has important implications on the habitability of extra-solar terrestrial-like planets. Galactic chemical evolution modelling of the elements produced by the process are needed to establish the reason for the spread in the abundance of Th. Because of its long half-life, Th can almost be treated as a stable isotope with respect to GCE and as such its abundance should be intrinsically less prone to inhomogeneities in the ISM as opposed to the SLRs (Sec. 4). However, since it is likely that the creation of the -process elements occurs in rare nucleosynthetic events associated with NSMs [cote18], it seems qualitatively feasible that the abundances of -process elements may show a relatively large spread, even for stars very similar in age and metal content (i.e., the recurrence time of the additions to a particular parcel of the ISM may be actually comparable with the half-life, see Sec. 4). This was already demonstrated using models of inhomogeneous GCE for the typical -process element Eu [wehmeyer15]. More observations of Th and U in stars with planets should be feasible in the future and will provide more information on the internal heat budget from long-lived radioactivity in extra-solar terrestrial planets.

The abundance of K, on the other hand, cannot be disentangled from stellar spectra from that of the much more abundant K. In this case, we will need to rely on GCE models to predict its abundance in stars. We may expect a smaller spread than in the case of Th and U since its CCSNe sources are much more common than NSMs in the Galaxy. A further problem, however, is that K is moderately volatile (with a 50% condensation temperature in the ESS of 1006 K as compared to 1610 for U [lodders03]), and presents abundance variations in the Solar System, for example, between the Earth, Mars, and chondrites. In this case, model predictions for stars cannot be directly translated into predictions for the planets around them.

Figure 7: Sections of the nuclide chart (modified from those obtained from the National Nuclear Data Center web site, www.nndc.bnl.gov) illustrating the nuclear-reaction paths favouring (green arrows) or inhibiting (red arrows) the production in stellar objects of four SLRs lighter and up to Fe: Al, Cl, Ca, and Fe. The remaining three SLR lighter than Fe are not plotted because Be and Be are not produced in stars, while Mn is produced by NSE, rather than by a defined nuclear reaction pathway. White arrows represent the radiogenic decay of each SLR, except for Al, where the decay to Mg is not overlaid onto the nuclide chart to avoid the plot being too busy.
Figure 8: Sections of the nuclide chart (modified from those obtained from the National Nuclear Data Center web site, www.nndc.bnl.gov) illustrating the nuclear-reaction paths favouring (green arrows) or inhibiting (red arrows) the production of the SLRs heavier than iron whose cosmic abundances are attributed to neutron-capture processes (in order of increasing mass: Pd, Sn, I, Cs, Hf, and Pb). The actinides Pu and Cm are not plotted, since their production is solely due to the process. Solid green arrows represent major production paths, while the dotted green arrows represent minor production paths. White arrows represent the radiogenic decay of each SLR.

3 The SLR variety: ESS abundances and stellar origins

Stellar site Process Products Relevance Ref.
Low-mass AGBs process Pd, Pd M [wasserburg06, lugaro14]
Cs, Cs M
Hf, Hf M
Pb, Pb M
Massive and p captures Al [trigo09, lugaro12a, lugaro14, wasserburg17]
Super-AGBs n captures Ca, Cl, Fe
process Pd, Cs, Hf
WR stars p captures Al M [arnould97, arnould06]
n captures Ca, Cl
n captures Tc, Pd, Cs, Pb
CCSNs p captures+explosive Al, Al M [limongi06]
n captures Fe M [limongi06]
n captures Cl, Ca M [takigawa08, lugaro14]
C/Ne/O burning Cl, Ca M [rauscher02]
NSE Mn, Mn, Fe M/ [rauscher02]
n captures Pd, Sn, Cs [meyer00]
I, Hf, Pb
-rich freezeout Nb, Mo, Tc, Tc M/ [lugaro16]
process Sm, Sm M/ [rauscher13, lugaro16]
process Be, Nb [banerjee16, hayakawa13]
SNIa NSE Mn, Mn, Fe M [travaglio04]
process Nb, Nb, Sm, Sm M/ [travaglio14]
Tc, Tc, Ru M/
NSM/special CCSN process Pd, Pd, Sn, Sn M [bisterzo11]
Cs, Cs, I, I M
Hf, Hf M
Cm, U, Pu, U M [goriely01, goriely16]
novae ejecta p captures Al [jose07]
CRs non-thermal Be, Be, Be M [tatischeff14]
Al, Ca, Cl, Mn [gounelle06]

The current understanding is that roughly 1/3 of the abundances of the Fe-peak elements in the Galaxy are produced by CCSNe, with the rest coming at later times from SNIa. Abundances to be derived using the -process predictions provided in the reference via the -residual method, where the -process abundance is given by the Solar System abundance minus the -process abundance.

Table 3: List of stellar nucleosynthesis sites and the nucleosynthetic processes occurring within them that are responsible for the production of the SLRs and stable reference isotopes listed in Column 3. Column 4 indicates if the site of production is important in terms of GCE (M=Major) or not (=minor); M/ indicates that it is still debated whether the site is major or minor. Indicative references are listed in Column 5.

The possible nucleosynthetic production sites for the SLRs and their stable reference isotopes are summarised in Table 3. All the processes listed in the table occur in stars, except for non-thermal nucleosynthesis. As mentioned above, spallation typically occurs in the ISM, however, it could also have had an important role in the ESS, with CRs coming from the Galactic background [desch04], the young, active Sun [gounelle06], or resulting from the interaction of one or more nearby CCSN remnant(s) with the ISM [tatischeff10]. A number of SLRs can be produced by this process, clearly Be and Be, but also Al, Cl, Ca, and Mn. However, there are several arguments against a major contribution the ESS as models have difficulties in providing a self-consistent solution that matches the abundances of all these isotopes [desch10]. Another difficulty is that a homogeneous distribution of the SLRs is not expected in this method of production, given the variability of the CR flux, but it is observed for Al and Mn. Furthermore, for the widely discussed model of irradiation by cosmic rays from the young Sun, it appears that not enough energy was available to produce all the Al if this SLR was homogeneously distributed throughout the ESS at the abundance level listed in Table 2 [duprat07]. Experimental data for the relevant nuclear reaction rates involved are scarce, but we note that there are recent new data on the S(,p)Cl [anderson17] and Mg(He,p)Al reactions [fitoussi08], which are important in the context of solar cosmic ray irradiation. The latter further disfavours this production channel for Al.

Column 4 of Table 3 clarifies if the listed site is a major (M) or a minor (m) site of production of the cosmic abundances of the listed isotopes. If the site is major, it means that not only the ratio of the SLR to the stable isotope of reference is significant, but also that the absolute abundance produced is large enough to impact the evolution of the SLR abundance in the Galaxy. To measure this, one can compare the mass fraction of the stable isotope in the stellar ejecta (i.e., the mass expelled in form of the given isotope divided by the total mass lost) to its mass fraction in the Solar System abundance distribution. The ratios of these two numbers can be referred to as “production factors”, and values roughly above 10 are needed to make the site under consideration a potentially important site. With respect to the presence of SLRs on the ESS, the distinction between major versus minor site is crucial. Major sites of production must be included in the analysis of the evolution of SLRs in the Galaxy described in Sec. 4 and they affect the use of SLRs as clocks to measure the isolation time. Minor sites of production are irrelevant in this context. On the other hand, if we consider the environment of the birth of the Sun, and a potential nearby stellar source of SLRs, then also minor production sites could have played a role in polluting the ESS with SLRs. In this case the stellar yields are diluted according to the distance from the star to the Sun, and given that such local sources are supposed to have been relatively close to the early Sun ( 0.5 - 5 pc, see Sec. 5), pollution even from a source that provides a relatively low absolute abundance can result in noticeable variations.

In Column 2 we also list a process referred to as “n captures”, which was not included in the list of the traditional nucleosynthesis processes described in Sec. 2.2. We use this label when we are in the context of neutron capture reactions, but the - or the -process labels do not apply. There are two possibilities for this: first, in relation to the SLRs up to Fe, Cl, Ca, and Fe. The traditional or the processes were introduced specifically for the production of the elements heavier than Fe, hence, it is not strictly appropriate to use these terms for neutron-capture reaction that produce nuclei up to Fe. The second instance involves the production of SLRs heavier than Fe, however, the neutron-capture process does not produce a significant abundance of the elements heavier than iron. Only a small number of neutrons are released in these cases, and the production of SLRs relies on the original presence of stable nuclei belonging to the same element. In line with this, the n-capture process in the case of SLRs heavier then Fe is always indicated as a minor (m) site of production in the table.

Expanding on the information given in Tables 2 and 3, in the following subsections we group the SLRs according to their nucleosynthetic production processes and for each of them we discuss in more detail their ESS abundances and nucleosynthetic origins.

3.1 Be and Be

As shown in Table 2, there is a large range of values observed for the abundance of Be in the ESS, and no compelling evidence exists for choosing one specific value over the others [chaussidon06]. The different values probably do not indicate time differences, but are the result of an inhomogeneous distribution. This in line with production by CR irradiation, since the particle flux driving the spallation reactions is likely to vary with time and location within the disk. Furthermore, the Be abundance does not correlate with that of Al. This is expected if they were produced by different processes: Be via CR irradiation and Al via stellar nucleosynthesis.

Data reported for FUN-CAIs show Be/Be in the range 3-4 [wielandt12]. FUN-CAIs show large mass-dependent fractionation effects and have much larger anomalies in stable isotopes than other CAIs (hence the name FUN, which stands for Fractionated and Unknown Nuclear anomalies). FUN-CAIs also show much lower abundances of Al than the value given in Table 2. Due to these properties, they are believed to be among the oldest CAIs, formed before Al was injected or homogenised in the disk, and before the dust carriers of the stable isotope anomalies were efficiently homogenised. Hence, the Be variations shown by the FUN-CAIs may be taken as the range of values produced by CRs that did not originate from the Sun, but from the galactic background or from the interaction with one or more nearby CCSN remnants [tatischeff14]. An alternative explanation for this baseline value was proposed by considering a model of a CCSN with low mass and explosion energy, which predicts production of Be via neutrino interactions [banerjee16]. This CCSN on the other hand does not produce enough Al to explain the ESS data, so a different source must be invoked for this SLR. The highest value of 104 for Be/Be was observed in one specific CAI only [gounelle13]. This value must clearly be due to irradiation within the ESS. All the other CAIs are only moderately higher than the baseline value.

The case of Be, which stands out from all the other SLRs for having an extremely short half-life of 53 days, is controversial: only one measurement (given at 2 in Table 2) is available and awaits confirmation. While Be can be made in some stars on the pathway to Li production [cameron71], given its short half-life the only possible origin for a potential presence of Be in the ESS is that of solar CR irradiation.

3.2 Al

Aluminium-26 is probably the most famous SLR. Not only was it one of the first discovered to have been present with a high abundance in the ESS [lee77], but its presence was predicted more than two decades before its discovery on the basis of the need for a heat source in the early Solar System [urey55]. The first hypothesis on the circumstances of the birth of the Sun, the collapse of the protosolar cloud triggered by a nearby CCSN, was also based on the discovery of Al [cameron77]. Furthermore, for Al there is some consensus that its abundance in the ESS was homogeneously distributed [villeneuve09], and thus the value reported in Table 2 is defined as a “canonical” value for the ESS [jacobsen08]. This allows us to use the decay of Al as a sensitive chronometer for the very early history of the Solar System [dauphas11].

However, some inhomogeneities exist also in case of this SLR. As mentioned above, FUN-CAIs are well known to contain Al in variable amounts (e.g., [park17]). Another case are micro-corundum (AlO) grains extracted from meteorites, which represent very early Solar nebula condensates since corundum is one of the first minerals predicted to condense in a cooling gas of solar composition. These grains show a bimodal distribution in Al: half of the grains belong to a Al-rich population, with Al/Al close to the canonical value, and the other half belong to a population of Al-poor grains with more than 20 times lower ratios [makide11]. Corundum-bearing CAIs also show large variations [makide13]. Interestingly, the Al-rich and Al-poor grains show the same O isotopic composition, close to that of the Sun666The O isotopic composition of the Solar System is not uniform, with the Sun being more rich in O by 6% with respect to planets and bulk meteoritic rocks. This difference is typically interpreted as the effect of self-shielding of CO molecules from UV radiation in the ESS, but the exact mechanism is a matter of debate, see [ireland12] for an accessible review., and typical of CAIs. This observation poses strong constraints on the origin of Al, since a successful pollution model should avoid predicting a correlation between the presence of Al and modification of the O isotopes [gounelle07].

Furthermore, it has also been pointed out that the Al/Al ratio may have been heterogeneous not only in relation to micro-corundum and special CAIs, but also at large scale in the protoplanetary disk. For example, Larsen et al. [larsen11] conclude that the canonical value is representative only of the CAI forming region, while the rest of the disk was characterised by Al/Al roughly half of the canonical value. This is based on high-precision determination of the initial Mg/Mg ratio (i.e., at the Al/Mg=0 intercept, see Sec. 2.1) and the fact that the decay of a canonical abundance of Al should have modified the global abundance of Mg by a larger amount than observed. Other interpretations are also possible, however. For example, heterogeneities in the Mg isotopes themselves, unrelated to the decay of Al. A similar conclusion of a lower ESS Al abundance was reached on the basis of comparing ages based on the Pb-Pb system and the Al-Mg system [schiller15a]. On the other hand, recently derived concordant Hf-W and Al-Mg ages for angrites and CV chondrules provide evidence for an homogeneous distribution of Al in the ESS [budde18]. In case the finding of a lower canonical value for Al will be confirmed and consensus achieved, the discussion on the origin of Al in the ESS will need to be revised, as well as its implications as a heat source [schiller15a, larsen16].

The production of Al in stars and supernovae is due to proton captures on the stable Mg (see top left panel of Fig. 7) occurring in various kinds of environments. The crucial reaction is Mg(p,)Al, which has been recently measured in the Laboratory for Underground Nuclear Astrophysics (LUNA, at the Italian National Laboratories of the Gran Sasso, LNGS). Thanks to the background suppression provided by the km-thick rock of the Gran Sasso mountain, the reaction is now known to high accuracy and better precision than before [straniero13]. However, a major problem is the fact that the reaction can feed both the ground state of Al and its isomeric state, which immediately decays into Mg with a half-life of just 6 seconds. The feeding factor to the ground state is not very well known, with large error bars and inconsistent data from different experiments (see discussion in [straniero13]). This still hampers a precise knowledge of the rate of the reaction channel leading to the ground state of Al.

In massive and Super-AGB stars777Super-AGB stars differ from AGB stars in that they experience C burning in their core, which result in a degenerate, inert core made mostly of O and Ne. They derive from the highest values of the AGB initial mass range, roughly 7-8 M. (of initial mass 5 M), H burning can occur at the base of the convective envelope, when the temperature reaches of the order of 60-100 MK. At such temperatures, the Mg-Al chain of proton captures is established, which results in the production of Al [trigo09, lugaro12a, wasserburg17]. In this environment, the main destruction channel for Al is also proton captures, via the Al(p,)Si reaction. The rate of this reaction is not very well determined because it is controlled by the strength of low-energy resonances at 68, 94, 127, and 189 keV, which are difficult to measure. Indirect methods have been used to gather more information, but have not been applied yet to a revision of the rate and its uncertainties. As for Al, relatively little production occurs in AGB and Super-AGB stars, with production factors barely above unity.

In low-mass AGB stars (of initial mass 5 M) the base of the convective envelope is too cold to allow production of Al. Extra-mixing mechanisms have been invoked to drive material from the base of the convective envelope into the hotter region lying below it, and boost the production of Al [wasserburg06]. The idea of extra-mixing in low-mass AGB stars was proposed on the basis of observations of stardust oxide grains, and specifically those classified as Group II [nittler97] showing the signature of H-burning via the CNO cycle and at the same time excesses in Al higher than the other oxide grain populations [palmerini11]. However, a new measurement of the rate of the O(p,)N reaction performed by LUNA [bruno16] resulted in a rate more than twice the one previously recommended [iliadis10]. This has allowed to attribute the origin of Group II grains to massive AGB stars instead, whose base of the convective envelope is hot enough to drive H burning [lugaro17]. Furthermore, the existence of extra-mixing during the AGB phase of low-mass stars is currently not supported by the direct observations of these stars [abia17].

In massive stars (of initial mass 10 M), large amounts of both Al and Al are produced particularly during the CCSN phase. The mechanisms at play have been previously analysed and described in detail [timmes95a, limongi06]. In brief, during the pre-CCSN phases, WR stars can be strong producers of Al due to peeling of the H-burning ashes from the convective envelope by strong winds. The same reaction chain as in AGB and Super-AGB stars applies under these circumstances, albeit activated at slightly lower temperatures (30-50 MK) and higher densities. During the CCSN explosion, further production of Al and Al occurs in the O/Ne shells, where destruction is mainly wrought by neutron captures, in particular the Al(n,)Na and Al(n,p)Mg reactions. These have relatively large cross sections, of the order of 100 mbarn [desmet07al, oginni11], whereas the (n,) channel cross section has a cross section of approximately 4 mbarn888Neutron-capture cross sections are quoted from the KADoNiS database kadonis.org [dillmann06], unless indicated otherwise.. Studies on the impact of nuclear uncertainties on the production of Al in massive stars have indicated its sensitivity not only to reactions directly related to its path of production and destruction but also indirectly to a number of other reactions (see [iliadis11] for details).

Aluminium-26 is of high interest also in the field of -ray spectroscopic observations performed, e.g., by the COMPTEL and INTEGRAL satellites, because the -ray photon at 1.8 MeV produced by its decay can be detected [diehl13]. This has allowed to establish that roughly 2 to 3 M of Al are currently present in the Galaxy. Also, it has been possible to spatially map the emission line from the Al decay, which has allowed us to identify its main production regions as being in the mid-plane of the Galaxy, where we expect more massive stars to be present. Furthermore, regions of higher Al abundance correlate with associations of massive stars (OB associations, see below). These observations provide important constraints in relation to the origin of Al in the Galaxy, and also in relation to its ESS abundance via comparison to meteoritic data. To translate the total mass of Al in the Milky Way ISM given from the -ray observation of 1.5 to 3.6 M [diehl13] into a Al/Al ratio, it is necessary to normalise it to the total mass of gas and dust in the Milky Way, of 8.1 4.5 M[kubryk15a]. This results in approximately - of Al in the Galaxy by mass fraction. To calculate the Al/Al ratio the abundance of Al is also required. This may differ from the solar value because -ray observations sample the ISM today, while the Solar System abundances sample the ISM 4.6 Gyr ago. However, as mentioned in Sec. 2.3 in recent years it has become clear that the evolution of the ISM is dominated by the effect of stellar migration [spitoni15, kubryk15a], which results in a large spread of metallicity, as traced by the abundance of Fe, for any given stellar age [casagrande11, bensby14]. For example, the increase in the abundance of Fe in the past 4.6 Gyr is predicted to be less than 25%, while the observed spread for stars in this age range is roughly a factor of 4. The evolution of Al in the Galaxy for the metallicity around solar of interest here approximately follows that of Fe [bensby14]. This is because Al is a secondary element produced more efficiently in stars of higher metallicities, and much of the production of Fe is also delayed in the Galaxy as it occurs in SNIa from WD, the product of long-living low-mass stars. Using the Solar System abundance of Al to normalise the current day -ray data, a Al/Al ratio in the ISM between and is derived. This is 3 to 25 times lower than the canonical ESS value. Taking into account an isolation time would further decreases the ISM ratio that might be inherited by the ESS. Even an isolation time of only 1 Myr would increase the lower bound of the discrepancy from 3 to 8 times lower. Thus it appears difficult to reconcile the high abundance of Al in the ESS with its current ISM abundance, and an extra source has been invoked, as will be discussed in detail in Sec. 5. In this context it should be noted that the large-scale emission observed from galactic Al is quite irregular [wang09], indicating clumpy distribution of massive stars. Localised Al emission has been reported for regions of OB associations of massive stars, such as Cygnus [martin09] and Scorpius-Centaurus [diehl10]. This suggests that (G)MCs in the neighbourhood of OB associations may in fact be more enriched in Al than the average ISM. Whether and how this enriched, hot material can find its way into cold clumps of star formation, however, still needs to be determined (see Sec. 5).

Finally, the initial abundance of Al in meteoric stardust grains recovered from meteorites [zinner14] at the time of their formation in stellar outflows can also be inferred using excess Mg. The presence of Al has been reported both for C-rich grains (silicon carbide SiC and graphite) and for O-rich grains (in particular, corundum AlO stardust). The derivation of the initial Al/Al for stardust grains is not based on an isochrone, as done for Solar System materials (Sec. 2.1) because carbonaceous and corundum grains contain much larger amounts of Al than Mg, hence, it can be assumed that all the measured Mg excess results from the original presence of Al999Magnesium is not a main component of SiC, corundum (AlO), and hibonite (CaAlO) grains, however, it is a main component of spinel (MgAlO). Stoichiometric spinel would contain two atoms of Al per each atom of Mg, which corresponds roughly to 25 times a higher ratio than in the average Solar System material. However, in single stardust spinel grains this proportion may vary.. The grains believed to be originating from CCSNe show very high abundances of Al, with inferred Al/Al ratios in the range 0.1 to 1 [groopman15], and higher than theoretical predictions. They need to be used to further constrain the nucleosynthesis models [pignatari13c]. The grains that originated in AGB stars show somewhat lower abundances, with Al/Al in the range to , which can also be used for comparison and constraints to the nucleosynthesis models [vanraai08, palmerini11, lugaro17].

3.3 Cl and Ca

These two SLRs are among the shortest lived in Table 2, with half-lives of the order of a few 10 yr. As such they can help disentangle the events that occurred closest to the birth of the Sun. The issue of the ESS abundance of Cl has been debated for some time. Potentially, this SLR can have both an initial ESS contribution resulting from stellar pollution, and a late contribution from irradiation by solar CRs in the disk. A difficulty arises from the fact that the main (98%) decay channel of Cl is via decay to Ar, a noble gas that easily escapes from solid material. Instead, estimates of the ESS value of Cl rely on measurements of excesses in S, the daughter of the electron capture channel. In support of the case for a potential stellar source of Cl in the ESS, recent analysis of the Curious Marie CAI has revealed the presence of this SLR together with Al in sodalite (a mineral that contains Cl) probably produced by the aqueous alteration event that depleted the CAI in U (see also Fig. 2 and Sec. 3.6 in relation to Cm in Curious Marie). An estimate of the time of occurrence of this event, after which the CAI can be considered as a closed system, is less 50 kyr, as inferred from the Al-Mg system [tang17]. Other studies have found very high levels of Cl in some refractory inclusions, which were not correlated to the presence of Al [hsu06], as well as large heterogeneities [nakashima08], providing a case for also a late irradiation contribution, as for Be.

The case of Ca poses a difficult measurement because of its very low abundance. The latest data on a handful of CAIs [liu12, liu17] demonstrate the presence of this very short-lived isotope in the ESS, with a relatively low inferred ESS value. However, also heterogenities appear to be present in its distribution since one CAI (out of four analysed) did not show a resolvable excess in the daughter K. Also in this case irradiation in the ESS can be responsible for the observed variations, although more data is needed to ascertain values and distributions.

The nucleosynthetic paths for the production of Cl and Ca are similar (see Fig. 7, top right panel and bottom left panel, respectively). Both SLRs are produced by neutron capture on an abundant stable isotope (Cl and Ca, respectively). Cl has a neutron-capture cross section roughly twice as large as that of Ca, however, it is roughly 15 times less abundant. The major destruction channels of Cl and Ca in the presence of neutrons are the (n,) and (n,p) reactions [desmet07cl], whose cross sections are not very well determined. Overall, it appears plausible to produce the two SLRs in stellar sources to the level required by their ESS ratios (see, e.g., Sec. 5.1 and Fig. 13). However, the large uncertainties both in their ESS abundances and distributions as well in the nuclear paths of production and destruction prevent us from drawing strong conclusions on their sources at this time.

3.4 Mn

The value of the Mn/Mn ratio in the ESS is considered very well known since several estimates are available and in good agreement with each other (e.g., [trinquier08, gopel15], see Table 9 of [tissot17]). The number reported in Table 2 is the value recommended by [tissot17] on the basis of all the available data. The half-life of Mn, on the other hand, is still a topic of debate [dressler12]. The currently recommended value of 3.7 Myr is based on three different, concordant experiments from the early 1970s, however, a higher value of 4.8 Myr has been proposed in order to explain apparent discrepancies with Al and Pb-Pb ages that exist for some (however not all) meteoritic samples [nyquist09].

The bulk of the abundance of Mn in the Galaxy, both the stable Mn and the SLR Mn, is the result of the decay of Fe and Fe produced by explosive Si burning and standard NSE. The following decay of Mn provides much of the cosmic abundance of Cr. The astrophysical site where the majority of such production occurs are probably SNIa that reach the Chandrasekhar mass. Actually, the existence of such a SNIa channel appears to be required by the need to provide a significant galactic source of Mn and the other iron peak elements at late times [seitenzahl13, hitomi17]. The production of Mn is only very marginally affected by nuclear reaction uncertainties given the nature of the NSE process, which depends more on the stability of the nuclei themselves, rather than presenting a path of production and destruction reactions, although some abundances can be affected by the properties of the freeze-out phase after the NSE. According to [parikh13] the Mn/Mn production ratio in SNIa could increase by up to a factor of two due to nuclear uncertainties. Model uncertainties are of the same order, e.g., the multi-D simulations of Chandrasekhar mass SNIa by [travaglio04] produce Mn/Mn ratios in the range 0.09 to 0.13 and the most recent results from [seitenzahl13b] range from 0.06 to 0.13. The Mn/Mn ratio produced in CCSNe is higher, up to 0.2 [lugaro14, lugaro16], however, CCSNe produce a less significant absolute amount of Mn, due to the type of freeze-out that follows the NSE process. As such they are listed as a minor site in terms of cosmic abundances in Table 3 (see Fig. 1 of [lugaro16]).

3.5 Fe

Among the inferred abundances of the SLRs in the ESS, that of Fe is the most controversial. This is not only because it represents an analytical challenge, but also because a high Fe/Fe would represent a smoking gun for stellar nucleosynthesis and specifically for a potential contribution of CCSNe to the ESS (Sec. 5.1). An extensive review of the data up to 2012 can be found in [mishra12]. Since then, the situation has not been clarified: the most recent estimates of the initial Fe/Fe ratio range from from measurements of bulk meteorites and bulk chondrules using inductively coupled plasma mass spectrometry (ICP-MS) [tang15, tang12], to - from in-situ measurements of high Fe/Ni phases using secondary-ion mass spectrometry (SIMS) [mishra14, telus18]. Crucially, while the former value rules out a CCSN source, the latter range requires it. There is the possibility that the SIMS analyses are compromised by stable isotope anomalies in Ni and/or unrecognised mass fractionation effects [boehnke17], hence, while the debate is ongoing, in Table 2 we have recommended the lower value. On the other hand, the debate related to the half-life of Fe can be now considered resolved, with two recent experiments [wallner15a, ostdiek17] confirming within uncertainties the half-life of 2.62 Myr presented by [rugel09] and roughly 75% longer than the previous estimate.

The reason why Fe is a clear signature of stellar nucleosynthesis is the fact that its production requires a chain of double neutron captures (see bottom right panel of Fig. 7). When neutrons are available, the stable Fe suffers a (n,) reaction, which produces Fe. This isotope is unstable, with a half-life of 44.5 days. The fact that Fe can either decay or capture another neutron to produce Fe results in the possibility of a splitting along the path of neutron captures, i.e., a branching point. To calculate the fraction of the neutron-capture flux that branches off the main -decay path at any given branching point, a branching factor is used and defined as:

(5)

where and are the probabilities per unit time associated with the nuclear reactions suffered by the branching point nucleus and leading onto the branch or onto the main path, respectively. The case of the Fe branching point is quite typical, i.e., corresponds to the decay rate, and corresponds to , i.e., the probability per unit time of Fe to capture a neutron, so that Eq. 5 becomes:

(6)

where is the neutron density in n/cm, is the thermal velocity ( is Boltzmann constant, the temperature and, the mass), and is the Maxwellian-averaged neutron-capture cross section. This is is typically inversely proportional to the velocity, so that is relatively constant. The values of Fe and Fe have been determined to be 6 mbarn via indirect experiments [uberseder14] and 24 mbarn via direct experiments [uberseder09], respectively, both with only a mild temperature dependence of the . For the probability of producing Fe to be above a few percent, neutron densities above n/cm are required. These are produced via the Ne(,n)Mg reaction in the He-shell burning regions of relatively massive AGB stars, Super-AGB stars, and during the pre-CCSN phase (here including also C-shell burning) of massive stars. During the CCSN blast wave Fe is further produced in the same region where Al is produced [timmes95a, limongi06]. In these conditions of very high temperature (above 500 MK), the half-lives of both Fe and Fe can decrease significantly [li16], affecting the calculation of the branching point and the survival of Fe itself. In the case of AGB stars, Fe can be expelled into the surrounding medium by the stellar winds if it was previously mixed to the stellar surface by dredge-up episodes. Other proposed sites of neutron-rich nucleosynthesis leading to the production of Fe are electron-capture supernovae [wanajo13] and carbon deflagration SNIa [woosley97]. Overall, while some of the nuclear inputs related to the activation of the Fe branching point are still uncertain, it would be difficult to radically change this current production picture for Fe.

As for Al, galactic -rays indicate significant levels of global Fe production in the Galaxy, with a ratio of the flux originating from Fe to that originating from Al of 0.15 0.05 [diehl13], and thus an abundance ratio of 0.55 0.18. Using the Al abundance for the ISM derived in Sec. 3.2 and the Solar System abundance of Fe, a Fe/Fe ratio in the ISM from 0.8 to 13 is derived. This is 8 to 130 times higher than the value of reported for the ESS in Table 2, which allows for an isolation time of at least 8 Myr, and would not require an extra source for the ESS abundance of this SLR [tang12]. If the highest value reported for the ESS of approximately [mishra14] is considered instead, no isolation time would be allowed, and a local source would need to be invoked.

It is useful also to consider the Fe abundance relative to the Al abundance because the flux ratio Fe/Al is directly determined from -rays and thus the Fe/Al abundance ratio in the Galaxy of approximately 0.55 is better determined than the absolute abundances. In the ESS, the Fe/Al ratio corresponds to 0.00178 and 0.178, when using Fe/Fe= and , respectively, i.e., it is roughly 300 to 3 times lower than the -ray ratio. This shows that whichever ESS Fe abundance is considered, the source of Al in the ESS, under-produced Fe, mildly or strongly, relatively to the Galactic average. A strong under-production would require complete decoupling of the origin Al and of Fe in the ESS, likely excluding CCSNe as potential sources of Al in the ESS. A mild under-production could represent the detailed, specific signature of the particular CCSN sources present at the birth of the Sun.

Finally, we note that on top of the -rays, the other independent constraints from Earth, Moon and CR samples already mentioned in Sec. 2.1 also indicate that significant levels of Fe are required to be produced by CCSNe in the Galaxy. For these cases the Al abundance is not available for comparison of the relative abundances, but may become possible to consider in the future.

3.6 The -process SLRs: I, Pu, and Cm

The presence of I was the first among all SLRs to be revealed in the ESS by excesses in Xe [reynolds60] given the relatively easy opportunity to analyse samples poor in the noble gas Xe. The value in the ESS presented in Table 2 is based on the estimate by [ott16] given with an uncertainty of 1. It is derived by combining the experimental value from analysis of the Shallowater meteorite given by [gilmour06] at 1, with the age of that meteorite (also given at 1), compared to the age of CAIs given at 2 by [connelly12].

The difficulty of determining the initial ESS abundances of Pu and Cm is that for these nuclei there are no stable isotopes of the same element. Therefore, Pu and Cm have to be referenced to other elements with similar nucleosynthetic and chemical properties. Conventionally, Pu is referenced to U and Cm to U. However, Pu and Cm are chemically more analogous to the light rare earth elements than to U.

For Pu there exist contradictory data based on two different approaches. The value reported in Table 2 (given at 1 as usual in work related to noble gas experiments) is the result of the analysis of the Xe composition samples of the St Severin ordinary chondrite irradiated with neutrons to induce the fission of U [hudson89]. After this treatment, the composition of Xe in the sample is a mixture of the Xe produced by the fission of the Pu present at its formation, and the fission induced on U, together with a small amount from the spontaneous fission of U and some “trapped” xenon. The relative abundance of the fission components is a function of Pu/U. However, the chemistry of St Severin may not be representative of the bulk ESS as pieces of this meteorite show highly variable U contents and Th/U ratios. Results from the analysis of Xe in ancient terrestrial zircons from Western Australia [turner07] yields data in agreement with this value, but the authors could not rule out fractionation between Pu and U during magmatic/mineral formation processes. In a different approach, mineral separates were analysed from the Angra dos Reis angrite meteorite, and Nd, an r-process-only isotope of Nd (a light rare earth element) was used as the reference isotope [lugmair77]. In order to obtain the abundance of Pu with reference to U, which is closer in mass to Pu thus providing a ratio better predictable by -process models, this must be converted using the Solar System Nd/U ratio 4.57 Ga ago [lodders09]. This results in a value101010The error here would a combination of statistical and systematic errors from the measurements [lugmair77], as well as from the renormalisation from Nd to U [hagee90]. of [peto08, hagee90], significantly lower than the value given in Table 2. However, the absolute abundance of Nd was measured separately from the noble gases, and since angrites are differentiated meteorites the original Pu/U and Pu/Nd ratios may have been modified during melting. New efforts are ongoing to derive a better estimate of the ESS Pu/U ratio on a variety of materials [peto17].

For Cm the situation is more favourable than for Pu thanks to the discovery of the peculiar Curious Marie CAI [tissot16]. This CAI is extremely depleted in U, providing an extreme data point in terms of the Nd/U ratio (see Fig. 2). With this new data [tissot16] it has been possible to derive a clear isochrone and hence a precise Cm/U ratio. In the original work, the absolute time of the latest alteration event that depleted the U was unknown, and an age of 10 Myr was applied to derive the ESS Cm/U ratio. The latest work on Curious Marie [tang17], however, implies that the alteration occurred at most 50,000 yr after the formation of the CAI, which we have taken into account in our recommended ESS Cm/U ratio listed in Table 2, where the error bar is 2 when assuming that Cm behaved chemically exactly like Nd.

The half-life of I has been relatively well known since experiments in the 1970s, and the recommended value of 15.7 Myr is in agreement with the I-Xe systematics of chondrules from primitive meteorites [pravdivtseva16, pravdivtseva17]. The half-lives of Pu and Cm are well known given that these isotopes are involved in nuclear reactor technology.

From the point of view of nucleosynthesis, the three isotopes considered here are almost exclusively produced by the process. The two heaviest belong to the actinide group of elements, with nuclear charges from 89 to 103 and chemical properties as rare earth elements. The -process production chain ends at Pb and Bi (with nuclear charges 82 and 83, respectively), where most of the reaction flow is trapped at Pb and Bi because of the small neutron-capture cross sections of these neutron magic nuclei (approximately 0.3 and 2.6 mbarn, respectively, at 30 keV). The following element on the chain of neutron captures is Po, with the isotopes Po and Po unstable against decay toward Pb and Pb [ratzel04]. This results in the impossibility of building elements beyond Bi with the process and the necessity for these elements to come from the process. The -process production of actinides has been studied in detail [goriely01, goriely16], also considering nuclear uncertainties. Since there are no solar abundances for these elements to compare to, the best strategy is to derive the actinide abundances from model predictions that match the Solar System -process abundances. The uncertainties in the yields are large, around one order of magnitude [goriely16], however, the relative isotopic ratios that are useful to compare to ESS data are somewhat less uncertain. For example, of the 20 models presented by [goriely16], 18 models present Pu/U ratios between 0.3 and 0.5 and Cm/U ratios in the range 0.2 and 0.4. Only two models have significantly different ratios around 1.3. This indicates that the absolute production of the actinides are typically correlated to each other when changing the model parameters.

The case of I is different: the reason why the process cannot produce it is the very short half-life of I. As shown in the middle left panel of Fig. 8, in the presence of neutrons the only stable isotope of I, I captures a neutron to produce I. This is unstable with a half-life of 25 minutes, too short to allow any further neutron captures, at least in -process conditions. Similarly to the case of Fe discussed above, the case of the I branching point is quite typical. Here, 1/s and mbarn. The branching factor reaches above 1%, 50%, and 90% only when is above , , and n/cm, respectively. In general, a branching factor also depends on the temperature since both and can have a temperature dependence, and also a density dependence for . In the case of I, both and have a small dependence on the temperature, with a variation of less than 60% for typical -process temperatures between 100 and 300 MK [takahashi87]111111It should be noted that there is a third path of the branching point because I can also electron capture into Te. This channel however is roughly 20 times less likely than the , so we did not consider it in the calculation of the branching point. However small, the branching factor of I in -process conditions has been carefully investigated because it affects the accuracy of the -process contribution to Xe, in principle an isotope produced mostly by the -process, but with a potential 10% -process contribution [reifarth04]..

The neutron densities required to produce I are not achieved in the typical AGB stars that produce the bulk of the process in the Galaxy. Consequently, the bulk galactic production of I has been attributed to the process. Still, in other sites such as CCSNe, neutron “bursts” can occur with neutron densities up to the values that allow I production (Table 3). For accurate predictions in these cases, the contribution of higher energy levels in I to the total neutron-capture cross section should be considered [rauscher12], which may modify the measured cross sections in stellar plasma conditions. These sites do not produce the bulk of I in the Galaxy because there are not enough neutrons released to convert Fe into heavier elements, but only small numbers of neutrons are released iin total, which allow some capture by the initial inventory of I itself.

Also the reference isotope, I, is a major process product. Thus, in spite of the issues and problems currently related to the modelling of the process, both from the stellar site and the nuclear physics point of view, the I/I ratio produced by the process is well constrained. This is because it can be derived on the basis of the -process residuals method, whereby the -process component of the Solar System abundance distribution is obtained by subtracting from the total abundance of each isotope (derived from meteoritic analysis) the -process component, which is relatively well known, often controlled mostly by the neutron-capture cross section of the stable isotope (e.g., [arlandini99, bisterzo11]). In the case of the radioactive I, its -process abundance can be simply derived from the -process residual of Xe, since all of the -process abundance of Xe is first produced as I. Due to all these advantages, the I/I ratio represents a textbook case to be used for the derivation of cosmic timescales, as will be described in more detail in Sec. 4.2. Furthermore, any constraints from it can be cross checked with those from Pu and Cm, providing possibly three different independent evaluations of a given time interval.

3.7 The SLRs with an -process contribution: Pd, Hf, and Pb

The ESS abundance of Hf has been relatively well determined for some time, and the value we provide in Table 2 is in agreement within error bars with the value given by [burkhardt08]. For Pd there are still problems related to the determination of the age of the iron meteorite on which the Pd/Pd ratio has been determined with a precision of better than 3% [matthes18]. In Table 2 we have considered the higher value given by [matthes18] for the initial ratio, which is in agreement with the value of (5.9 2.2) based on the analysis of carbonaceous chondrites [schonbachler08]. The case of Pb is more problematic because both the elements involved in the analysis (Pb and Tl) are somewhat volatile and Pb in particular is prone to contamination so that a mixing line produced by contamination could be incorrectly interpreted as an isochrone. Furthermore, Tl has only two stable isotopes, which means that it is not possible to correct directly for possible artificial or natural mass fractionation effects, and it is more difficult also to recognise potential nucleosynthetic anomalies. To address this problem, for the mass spectrometric analysis, [andreasen12] added an element of similar mass (Pt) in order to infer the instrumental mass fractionation for Tl. These authors obtained a value for the Pb/Pb ratio in agreement with the previous value [baker10], but an order of magnitude higher than that given by the older analysis [nielsen06]. The value in Table 2 is that reported by [palk18] and obtained combining the results of [andreasen12] and [baker10].

From the point of view of stellar production, the galactic abundances of these three nuclei have significant contributions from the process. Specifically, Pd and Pb are produced directly by neutron-captures onto the stable Pd and Pb, respectively (top left and bottom right panels of Fig. 8). On the other hand, production of Hf requires the activation of a branching point at Hf (bottom left panel of Fig. 8). The half-life of this nucleus was believed to greatly decrease from roughly 42 days to 30 hours in stellar conditions due to the population of an excited state at 68 keV [takahashi87]. In this case the branching factor leading to the production of Hf reaches above 3% only for above n/cm and the bulk of the production of Hf needs to be attributed to the process. This was leading to a strong disagreement in the time intervals derived from I and Hf and to solve this problem different components for the -process were proposed [wasserburg96], as well as different local sources for Hf [meyer00] (see also [ott08]). However, according to more recent experimental data [bondarenko02] such a 68 keV state in Hf does not exist, thus the half-life of Hf should not vary greatly with the temperature. In this case, the branching factor is above 3% already for above n/cm and a significant production of Hf occurs in the AGB stars that produce the bulk of the process in the Galaxy, with Hf/Hf ratios around 0.15. This removes the issue of the time discordance with I [lugaro14].

Pd and Hf have significant contributions from both the and the process. As in the case of I, their -process production ratios relative to their reference stable isotope can be derived using the -residual method and considering the -process residuals of their daughter nuclei, Ag and W, respectively. Since the -process residual depends on the -process contribution to each specific isotope, the -process Hf/Hf ratio had to be readjusted after the discovery that Hf has a significant -process production, which in turn increases the -process contribution to W. On the other hand, Pb is effectively a nucleus produced only by the process, being shielded from -process production by Tl. However, this does not mean that its production can exclusively occur in AGB stars: small neutron bursts in CCSNe and WR stars can also produce this isotope, although these are minor production sites since there is no conversion of Fe nuclei into Pb. The main problem with the production of Pb is that its electron-capture half-life is predicted to vary by several orders of magnitudes in stellar conditions: from 17 Myr in terrestrial conditions down to roughly 15 years for temperatures above 50 MK, and also depending on the density, although this temperature and density dependence is uncertain by an order of magnitude [goriely99]. This makes it difficult to save Pb to be carried to the stellar surface, but production is still be expected [yokoi85]. Finally, we note that in both the cases of Hf and of Pb, population of higher energy levels can modify the total neutron-capture cross sections in stellar conditions [rauscher12], which needs to be considered as an additional model uncertainty.

3.8 The -process SLRs: Nb, Sm, and Tc

The ESS values of both Nb and Sm are well determined. In the case of Nb the value of Nb/Nb given in Table 2 is derived from rutiles and zircons with well known ages and is in agreement with the less precise value of [iizuka16] from angrites and eucrites. The Sm/Sm value, on the other hand, has been measured directly in a CAI (Fig. 2), removing previous issues related to the age adjustment. For Tc, only upper limits are available. The half-life of Sm is poorly determined. A recent experiment [kinoshita12] shortened the previous recommended value by approximately 50%, however there is better agreement with the suite of meteoritic data with different ages (from Pb-Pb dating) when the older half-life is employed [marks14]. The half-life of Nb appears to be well determined, being the weighted average of two experiments that produced similar results, in spite of different approaches.

The stellar production of all these isotopes is broadly ascribed to the process – although a minor production process for Tc is also neutron capture on the relatively abundant Ru, followed by the electron capture decay of Ru [arnould97]. Model predictions and the usage of these isotopes as cosmochronometers have been discussed in detail by [lugaro16]. In summary, Sm is most likely produced by the process, although the site is still debated between SNIa [travaglio14] and CCSNe, with SNIa being favoured [travaglio18]. The accuracy of the theoretical predictions is hampered for this isotope by the uncertain Gd(,)Sm reaction, which controls the (,n)/(,) branching at Gd. The current resulting uncertainty on the Sm/Sm production ratio from SNIa models is a factor of two [travaglio14], but owing to the lack of experimental data it could be even higher, up to one order of magnitude. These nuclear uncertainties, together with the half-life uncertainty, currently hamper the opportunity of using Sm, the longest lived of the SLRs considered here, as an accurate cosmochronometer.

When considering the lighter -process isotopes up to Ru, different flavours and sites of -process nucleosynthesis need to be considered [travaglio18], particularly to explain the relatively high Solar System abundance of the -process isotopes of Mo (at masses 92 and 94) and Ru (at masses 96 and 98). In particular, another source of Nb is required in the Galaxy because only considering the process in SNIa results in inconsistent timescales when the other SLR predominantly produced by SNIa, Mn, is also considered [lugaro16]. For example, low-mass CCSNe could be a significant cosmic source of Nb. In summary, also the opportunity to use Nb as an accurate cosmochronometer is hampered, in this case by the current large uncertainties related to the modelling of CCSNe. Finally, the upper limits available for the ESS abundance of Tc do not allow the use of these SLRs as meaningful chronometers [lugaro16].

3.9 Sn and Cs

Establishing and interpreting the ESS initial abundances of Sn and Cs is challenging for a number of reasons. Concerning Sn, measuring Te isotopic ratios precisely is especially difficult, and compounded by the fact that given the short half-life of Sn we may not expect a large excess signal. The most recent work [brennecka17b] reports an upper limit for the Sn/Sn ratio of 3. Even so, this value is significant when compared to the stellar production of Sn and may be used to rule out nearby stellar sources. So far, most authors have ascribed the production of Sn to the process in supernovae (see [fehr09] and references therein), since the branching isotope Sn has a half-life of 9.6 days, too short to allow for significant capture of neutrons in -process conditions (Fig. 8). However, a non-detection of Sn cannot be used to rule out a nearby CCSN source of SLRs because, as discussed above, the process is not believed to occur in standard CCSNe, but rather in NSMs or peculiar CCSNe. The branching point may still open during neutron burst conditions in CCSNe. In fact, considering the theoretically calculated of Sn of around 70 mbarn, and the strong temperature dependence of the half-life [takahashi87], which decreases to 2.5 hours at 200 MK, the probability of Sn to capture a neutron is above 10% for neutron densities above 10 n/cm, which are possible during a neutron burst. A detailed analysis of the production of Sn in CCSNe also considering the nuclear uncertainties is still missing and urgently needed to exploit the new experimental ESS upper limit.

The situation for Cs is similar and also open. The difficulty in measuring its initial ESS abundance is mostly related to the fact that Cs is a volatile element, which does not easily fully condense into solids. Recently a new approach to the problem was used by [brennecka17b], who inferred a new upper limit for the Cs/Cs ratio by analysing volatile-depleted material (rather than material in which the radionuclide should be enhanced, as is usually done), which should show a deficit in Ba with respect to the bulk of Solar System matter, in which Cs fully contributed to the abundance of Ba. The derived upper limit is much lower than that previously proposed based on direct measurements of Ba isotopes in CAIs (e.g., [bermingham14]). Similarly to the case of Sn, Cs is produced by a branching point located at an isotope, Cs, whose T presents a strong theoretically estimated temperature dependence. It decreases from 2 years at laboratory temperatures, down to 12 days at 200 MK, due to the population of levels at 60 and 177 keV in stellar condition. The uncertainty in the evaluation of the rate is of an order of magnitude [goriely99]. The of Cs is approximately 800 mbarn, as derived from statistical model calculations aided by the experimentally determined cross section of Cs [patronis04]. However, the population of higher energy levels can modify the total of Cs in stellar conditions by 50% [rauscher12]. Using such values, the branching factor for the production of Cs is above 10% already for -process neutron densities above N n/cm. In fact, the activation of the branching point at Cs is required to match the Ba/Ba isotopic ratio in the Solar System, where both Ba and Ba are isotopes that can be only be produced by the process [bisterzo15]. This branching point is also of interest for the interpretation of Ba isotopic anomalies measured in mainstream stardust silicon carbide grains (SiC) that originated from AGB stars and show the signature of the process [liu15, lugaro17]. Overall, while the largest contributor to the cosmic abundance of Cs is the -process, in relation to the ESS we need to consider also the minor potential production sites, both the -process and the neutron burst in CCSNe. A detailed analysis also of the related nuclear uncertainties and their impact is still missing and, again, urgently required to be able to properly interpret the meteoritic data.

4 The galactic chemical evolution of radioactive isotopes

4.1 General models and considerations

The simplest way to compute the evolution of the abundances of radioactive nuclei in the Galaxy is based on the concept of steady-state equilibrium, for which a simple derivation can be made as follows. The rate of change in time of the number of a given radioactive nucleus in the ISM is given by:

(7)

where the first (negative) term represents the decay, with the mean-life constant in time, and the second (positive) term represents the stellar production rate, as stars inject freshly produced radioactive nuclei into the ISM. This equation is a typical self-regulating equation because the larger the positive term, the larger the abundance, and the larger the negative term. This means that the abundance