SLRs from Galactic-scale star formation

Short-lived radioisotopes in meteorites from Galactic-scale correlated star formation

Yusuke Fujimoto, Mark R. Krumholz and Shogo Tachibana
Research School of Astronomy & Astrophysics, Australian National University, Canberra, Australian Capital Territory 2611, Australia
Department of Natural History Sciences, Hokkaido University, N10W8 Sapporo, Hokkaido 060-0810, Japan
Accepted XXX. Received YYY; in original form ZZZ

Meteoritic evidence shows that the Solar system at birth contained significant quantities of short-lived radioisotopes (SLRs) such as (with a half-life of 2.6 Myr) and (with a half-life of 0.7 Myr) produced in supernova explosions and in the Wolf-Rayet winds that precede them. Proposed explanations for the high SLR abundance include formation of the Sun in a supernova-triggered collapse or in a giant molecular cloud (GMC) that was massive enough to survive multiple supernovae (SNe) and confine their ejecta. However, the former scenario is possible only if the Sun is a rare outlier among massive stars, while the latter appears to be inconsistent with the observation that Al is distributed with a scale height significantly larger than GMCs. In this paper, we present a high-resolution chemo-hydrodynamical simulation of the entire Milky Way Galaxy, including stochastic star formation, H ii regions, SNe, and element injection, that allows us to measure for the distribution of and ratios over all stars in the Galaxy. We show that the Solar System’s abundance ratios are well within the normal range, but that SLRs originate neither from triggering nor from confinement in long-lived clouds as previously conjectured. Instead, we find that SLRs are abundant in newborn stars because star formation is correlated on galactic scales, so that ejecta preferentially enrich atomic gas that will subsequently be accreted onto existing GMCs or will form new ones. Thus new generations of stars preferentially form in patches of the Galaxy contaminated by previous generations of stellar winds and supernovae.

hydrodynamics – methods: numerical – Galaxy: disc – ISM: kinematics and dynamics – meteorites, meteors, meteoroids – gamma-rays: ISM
pubyear: 2018pagerange: Short-lived radioisotopes in meteorites from Galactic-scale correlated star formationA

1 Introduction

Short-lived radioisotopes (SLRs) – , , , , , , , , and – are radioactive elements with half-lives ranging from 0.1 Myr to more than 15 Myr that existed in the early Solar system (e.g., Adams 2010). They were incorporated into meteorites’ primitive components such as calcium-aluminum-rich inclusions (CAIs), which are the oldest solids in the Solar protoplanetary disc, or chondrules, which formed 1 Myr after CAI formation. The radioactive decay of these SLRs fundamentally shaped the thermal history and interior structure of planetesimals in the early Solar system, and thus is of central importance for core-accretion planet formation models. The SLRs, particularly , were the main heating sources for the earliest planetesimals and planetary embryos from which terrestrial planets formed (Grimm & McSween, 1993; Michel et al., 2015), and are responsible for the differentiation of the parent bodies of magmatic meteorites in the first few Myrs of the Solar system (Greenwood et al., 2005; Scherstén et al., 2006; Sahijpal et al., 2007). The SLRs are, moreover, potential high-precision and high-resolution chronometers for the formation events of our Solar system due to their short half-lives (Kita et al., 2005; Krot et al., 2008; Amelin et al., 2010; Bouvier & Wadhwa, 2010; Connelly et al., 2012).

Detailed analyses of meteorites show that the early Solar system contained significant quantities of SLRs. The presence of in the early Solar system was first identified in CAIs from the primitive meteorite Allende in 1976, defining a canonical initial ratio of (Lee et al., 1976, 1977; Jacobsen et al., 2008), far higher than the ratio of in the interstellar medium (ISM) as estimated from continuous galactic nucleosynthesis models (Meyer & Clayton, 2000) and -ray observations measuring the in-situ decay of (Diehl et al., 2006).

Compared to , the initial ratio of is still somewhat uncertain; analyses of bulk samples of different meteorite types produced a low initial ratio of (Tang & Dauphas, 2012, 2015), while other studies of chondrules using in situ measurements found higher initial ratio of than the ISM ratio (e.g., Mishra & Goswami 2014). Telus et al. (2016) found that the bulk sample estimates were skewed toward low initial ratios because of fluid transport of Fe and Ni during aqueous alteration on the parent body and/or during terrestrial weathering, and Telus et al. (2018) have found the initial ratios of as high as , although the initial value is still a matter of debate. If estimates in the middle or high end of the plausible range prove to be correct, they would imply a ratio well above the interstellar average as well.

It has been long debated how the early Solar System came to have SLR abundances well above the ISM average. The isotopes and , on which we focus in this paper, are of particular interest because they are synthesised only in the late stages of massive stellar evolution, followed by injection into the ISM by stellar winds and supernovae (SNe) (Huss et al., 2009). Other SLRs (e.g., , and ) can be produced in situ by irradiation of the protoplanetary disc by the young Sun (Heymann & Dziczkaniec, 1976; Shu et al., 1996; Lee et al., 1998; Shu et al., 2001; Gounelle et al., 2006).111Small amounts of can also be produced by this mechanism, but much too little to explain the observed ratio (Duprat & Tatischeff, 2007). Explaining the origin site of the and , and how they travelled from this site to the primitive Solar System before decaying, is an outstanding problem.

One possible origin site is asymptotic giant branch (AGB) stars (Wasserburg et al., 1994; Busso et al., 1999; Wasserburg et al., 2006). However, because AGB stars only provide SLRs at the end of their lives, and because their main-sequence lifetimes are long ( Gyr), the probability of a chance encounter between an AGB star and a star-forming region is very low (Kastner & Myers, 1994). For these reasons, the supernovae and stellar winds of massive stars, which yield SLRs much more quickly after star formation, are thought to be the most likely origin of and . Proposed mechanisms by which massive stars could enrich the infant Solar System fall into three broad scenarios: (1) supernova triggered collapse of pre-solar dense cloud core, (2) direct pollution of an already-formed proto-solar disc by supernova ejecta and (3) sequential star formation events in a molecular cloud.

The first scenario, supernova triggered collapse of pre-solar dense cloud core, was proposed by Cameron & Truran (1977) just after the first discovery of in Allende CAIs by Lee et al. (1976). In this scenario, a nearby Type II supernova injects SLRs and triggers the collapse of the early Solar nebula. Many authors have simulated this scenario (Boss, 1995; Foster & Boss, 1996; Boss et al., 2010; Gritschneder et al., 2012; Li et al., 2014; Boss & Keiser, 2014; Boss, 2017) and shown that it is in principle possible. A single supernova shock that encounters an isolated marginally stable prestellar core can compress it and trigger gravitational collapse while at the same time generating Rayleigh-Taylor instabilities at the surface that mix SLRs into the collapsing gas. However, these simulations have also demonstrated that this scenario requires severe fine-tuning. If the shock is too fast then it shreds and disperses the core rather than triggering collapse, and if it is too slow then mixing of SLRs does not occur fast enough to enrich the gas before collapse. Only a very narrow range of shock speeds are consistent with what we observe in the Solar System, and even then the SLR injection efficiency is low (Gritschneder et al., 2012; Boss & Keiser, 2014; Boss, 2017). A possible solution to overcome the mixing barrier problem is the injection of SLRs via dust grains. However, only grains with radii larger than 30 , which is much larger than the typical sizes of supernova grains (< 1 ), can penetrate the shock front and inject SLRs into the core (Boss & Keiser, 2010). Furthermore, analysis of Al and Fe dust grains in supernova ejecta constrains their sizes to be less than 0.01 (Bocchio et al., 2016).

The second scenario is a direct pollution: the Solar system’s SLRs were injected directly into an already-formed protoplanetary disc by supernova ejecta within the same star-forming region (Chevalier, 2000; Hester et al., 2004). Hydrodynamical simulations of a protoplanetary disc have shown that the edge-on disc can survive the impact of a supernova blast wave, but that in this scenario only a tiny fraction of the supernova ejecta that strike the disc are captured and thus available to explain the SLRs we observe (Ouellette et al., 2007; Close & Pittard, 2017). Ouellette et al. (2007) suggests that dust grains might be a more efficient mechanism for injecting SLRs into the disc, and simulations by Ouellette et al. (2010) show that about 70 per cent of material in grains larger than 0.4 can be captured by a protoplanetary disc. However, extreme fine-tuning is still required to make this scenario work quantitatively. One can explain the observed SLR abundances only if SN ejecta are clumpy, the Solar nebula was struck by a clump that was unusually rich in and , and the bulk of these elements had condensed into large dust grains before reaching the Solar System. The probability that all these conditions are met is very low, . Moreover, the required dust size of 0.4 is still a factor of 40 larger than the value of 0.01 obtained by detailed study of dust grain properties by Bocchio et al. (2016).

The third scenario is sequential star formation events and self-enrichment in a giant molecular cloud (GMC) (Gounelle et al., 2009; Gaidos et al., 2009; Gounelle & Meynet, 2012; Young, 2014, 2016). Gounelle & Meynet (2012) proposed a detailed picture of this scenario; in a first star formation event, supernovae from massive stars inject to the GMC, and the shock waves trigger a second star formation event. This second star formation event also contains massive stars, and the stellar winds inject and collect ISM gas to build a dense shell surrounding an H ii region. In the already enriched dense shell, a third star formation event occurs where the Solar system forms. Vasileiadis et al. (2013) and Kuffmeier et al. (2016) have modelled the evolution of a GMC by hydrodynamical simulations and shown that SN ejecta trapped within a GMC can enrich the GMC gas to abundance ratios of and , comparable to or higher than any meteoritic estimates. However, this scenario requires that the bulk of the SLRs that are produced be captured within their parent GMCs. This is enforced by fiat in the simulations (by the use of periodic boundary conditions), but it is far from clear if this requirement can be met in reality. In the simulations the required enrichment levels are not reached for Myr, but observed young star clusters are always cleared of gas by ages of Myr (e.g., Hollyhead et al., 2015). Moreover, the observed distribution of has a scale height significantly larger than that of GMCs, which would seem hard to reconcile with the idea that most remains confined to the GMC where it was produced (Bouchet et al., 2015).

The literature contains a number of other proposals (e.g., Tatischeff et al., 2010; Goodson et al., 2016), but what they have in common with the three primary scenarios outlined above is that they require an unusual and improbable conjunction of circumstances (e.g., a randomly-passing WR star, SN-produced grains much larger than observations suggest) that would render the Solar System an unusual outlier in its abundances, or that they are not consistent with the observed distribution of in the Galaxy.

Here we present an alternative scenario, motivated by two observations. First, is observed to extend to a significant height above and below the Galactic disc, suggesting that regions contaminated by SLRs much be at least kpc-scale (Bouchet et al., 2015). Second, there is no a priori reason why one should expect star formation to produce a SLR distribution with the same mean as the ISM as a whole, because star formation does not sample from the ISM at random. Instead, star formation and SLR production are both highly correlated in space and time (e.g., Gouliermis et al., 2010; Gouliermis et al., 2015, 2017; Grasha et al., 2017a, b); the properties of GMCs are also correlated on Galactic scales (e.g., Fujimoto et al., 2014, 2016; Colombo et al., 2014). That both SLRs and star formation are correlated on kpc scales suggests that it is at these scales that we should search for a solution to the origin of SLRs in the early Solar System.

In this paper, we will study the galactic-scale distributions of and produced in stellar winds and supernovae, and propose a new contamination scenario: contamination due to Galactic-scale correlated star formation. In section 2, we present our numerical model of a Milky-Way like galaxy, along with our treatments of star formation and stellar feedback. In section 3, we describe global evolution of the galactic disc and the abundance ratios of the stars that form in it. In section 4 we discuss the implications of our results, and based on them we propose a new scenario for SLR deposition. We summarise our findings in section 5.

2 Methods

We study the abundances of and in newly-formed stars by performing a high-resolution chemo-hydrodynamical simulation of the interstellar medium (ISM) of a Milky-Way like galaxy. The simulation includes hydrodynamics, self-gravity, a fixed logarithmic potential to represent the gravity of old stars and dark matter, radiative cooling, photoelectric heating, and stellar feedback in the form of photoionisation and supernovae. In the simulation, when self-gravity causes the gas to collapse past our ability to resolve, we insert “star particles" that represent stochastically-generated stellar populations drawn star-by-star from the IMF. Each massive star in these populations evolves individually until it produces a a mass-dependent yield of and at the end of its life. We subsequently track the transport and decay of these isotopes, and their incorporation into new stars. Further details on our numerical method are given in the following subsections.

We carry out all analysis and post-processing of the simulation outputs, and produce all simulations visualisations, using the yt222 software package (Turk et al., 2011).

2.1 Chemo-hydrodynamical simulation

Our simulations follow the evolution of a Milky-Way type galaxy using the adaptive mesh refinement code enzo (Bryan et al., 2014). We use a piecewise parabolic mesh hydrodynamics solver to follow the motion of the gas. Since the circular velocity of the galaxy necessitates strongly supersonic flows in the galactic disc, we make use of the dual energy formalism implemented in the enzo code, in order to avoid spurious temperature fluctuations due to floating point round-off error when the kinetic energy is much larger than the internal energy. We treat isotopes as passive scalars that are transported with the gas, and that decay with half-lives of 2.62 Myr for and 0.72 Myr for (Rugel et al., 2009; Norris et al., 1983).

The gas cools radiatively to 10 K using a one-dimensional cooling curve created from the cloudy package’s cooling table for metals and enzo’s non-equilibrium cooling rates for atomic species of hydrogen and helium (Abel et al., 1997; Ferland et al., 1998). This is implemented as tabulated cooling rates as a function of density and temperature (Jin et al., 2017). In addition to radiative cooling, the gas can also be heated via diffuse photoelectric heating in which electrons are ejected from dust grains via FUV photons. This is implemented as a constant heating rate of per hydrogen atom uniformly throughout the simulation box. This rate is chosen to match the expected heating rate assuming a UV background consistent with the Solar neighbourhood value (Draine, 2011). Self-gravity of the gas is also implemented.

2.2 Galaxy model

The galaxy is modelled in a three-dimensional simulation box of with isolated gravitational boundary conditions and periodic fluid boundaries. The root grid is with an additional 7 levels of refinement, producing a minimum cell size of 7.8125 pc. We refine a cell if the Jeans length, , drops below 8 cell widths, comfortably satisfying the Truelove et al. (1998) criterion. In addition, to ensure that we resolve stellar feedback, we require that any computational zone containing a star particle be refined to the maximum level. To keep the Jeans length resolved after collapse has reached the maximum refinement level, we employ a pressure floor such that the Jeans length is resolved by at least 4 cells on the maximum refinement level. In addition to the static root grid, we impose 5 additional levels of statically refined regions enclosing the whole galactic disc of 14 kpc radius and 2 kpc height. This guarantees that the circular motion of the gas in the galactic disc is well resolved, with a maximum cell size of 31.25 pc.

We use initial conditions identical to those of Tasker & Tan (2009). These are tuned to the Milky Way in its present state, but the Galaxy’s bulk properties were not substantially different when Solar system formed 4.567 Gyr ago (). The simulated galaxy is set up as an isolated disc of gas orbiting in a static background potential which represents both dark matter and a stellar disc component. The form of the background potential is


where is the constant circular velocity at large radii, here set equal to 200 , and are the radial and vertical coordinates, the core radius is , and the axial ratio of the potential is . This corresponding circular velocity is


The initial gas density distribution is


where is the epicyclic frequency, is the sound speed, here set equal to , is the one-dimensional velocity dispersion of the gas motions in the plane of the disc after the subtraction of the circular velocity, is the Toomre stability parameter, and is the vertical scale height, which is assumed to vary with galactocentric radius following the observed radially-dependent H i scale height for the Milky Way. Our disc is initialized with .

The initial disc profile is divided radially into three parts. In our main region, between radii of , is set so that . The other regions of the galaxy, from 0 to 2 kpc and from 13 to 14 kpc, are initialised with . Beyond 14 kpc, the disc is surrounded by a static, very low density medium. We set the initial abundances of and to , though this choice has no practical effect since the initial abundances decay rapidly. In total, the initial gas mass is , and the initial and mass are set to .

2.3 Star formation

We use a star formation algorithm based on Goldbaum et al. (2015). When the gas density exceeds a threshold density on the maximum refinement level, a star particle forms in a grid cell with the star formation rate density


where the star formation efficiency is as determined from observations (e.g., Krumholz & Tan, 2007; Krumholz et al., 2012; Heyer et al., 2016; Vutisalchavakul et al., 2016; Leroy et al., 2017), is the gas density of the cell, and is the local dynamical time. The star formation threshold density is chosen such that the Jeans length for gas on the maximum refinement level remains resolved by at least 4 cells. This threshold density depends on the maximum resolution: 12 for 31 pc, 25.4 for 15 pc and 57.5 for 8 pc.

To avoid creating an extremely large number of star particles whose mass is insufficient to have a well sampled stellar population, we impose a minimum star particle mass, , and form star particles stochastically rather than spawn particles in every cell at each timestep. In this scheme, a cell forms a star particle of mass with probability


where is the cell width, and is the simulation timestep. In practice, all star particles in our simulation are created via this stochastic method with masses equal to . Star particles are allowed to form in the main region of the disc between kpc.

2.4 Stellar feedback

Here we describe a subgrid model for star formation feedback that includes the effects of ionising radiation from young stars, the momentum and energy released by individual SN explosions, and isotope injections from stellar winds and SNe.

All star particles form with a uniform initial mass of 300 . Within each of these particles we expect there to be a few stars massive enough to produce SN explosions. We model this using the slug stellar population synthesis code (da Silva et al., 2012; Krumholz et al., 2015). This stellar population synthesis method is used dynamically in our simulation; each star particle spawns an individual slug simulation that stochastically draws individual stars from the initial mass function, tracks their mass- and age-dependent ionising luminosities, determines when individual stars explode as SNe, and calculates the resulting injection of and . In the slug calculations we use a Chabrier initial mass function (Chabrier, 2005) with slug’s Poisson sampling option, Padova stellar evolution tracks with Solar metallicity (Girardi et al., 2000), starburst99 stellar atmospheres (Leitherer et al., 1999), and Solar metallicity yields from Sukhbold et al. (2016).

We include stellar feedback from photoionisation and SNe, following Goldbaum et al. (2016). For the former, we use the total ionising luminosity from each star particle calculated by slug to estimate the Strömgren volume , and compare with the cell volume, . Here cm s is the case B recombination rate coefficient, is the number density, and and g are the mean particle mass and the mass of an H nucleus, respectively. If , the cell is heated to K. If , the cell is heated to a temperature of K, and then we calculate the luminosity that escapes the cell. We distribute this luminosity evenly over the neighbouring 26 cells, and repeat the procedure.

For SN feedback, we identify particles that will produce SNe in any given time step. For each SN that occurs, we add a total momentum of , directed radially outward in the 26 neighbouring cells. This momentum budget is consistent with the expected deposition from single supernovae (Gentry et al., 2017). The total net increase in kinetic energy in the cells surrounding the SN host cell are then deducted from the available budget of erg and the balance of the energy is then deposited in the SN host cell as thermal energy. In the higher resolution phases of the simulation ( 15 pc, 8 pc), we increase the momentum budget to in order to maintain approximately the same total star formation rate; given that the actual momentum budget is uncertain by a factor of due to the effects of clustering (Gentry et al., 2017), this value is still well within the physically plausible range.

We include isotope injection from stellar winds and SNe, which is calculated from the mass-dependent yield tables of Sukhbold et al. (2016). The chemical yields are deposited to the host cell. As discussed in Sukhbold et al. (2016), their nucleosynthesis model overpredicts333Sukhbold et al. (2016) compared their ejected mass ratio of (= 0.9) with the observed steady-state mass ratio of 0.34 (Wang et al., 2007), and stated that their yield should be corrected by a factor of three. However, a steady-state mass ratio should be used, not the ejected mass ratio, to compare with the observed mass ratio. The steady-state mass ratio can be obtained by multiplying the ratio of half-lives, as . This steady-state mass is ten times larger than the observed steady-state mass ratio. That is why we modify their tables by reducing the yield by a factor fo five and doubling the yield. the to compared to that determined from -ray line observations (Wang et al., 2007). To ensure that our ratio is consistent with observations, we modify their tables slightly by reducing the yield by a factor fo five and doubling the yield. This brings our Galaxy-averaged ratios of , , and into good agreement with observations.

3 Simulation Results

3.1 Evolution of the Disc

Figure 1: The time evolution of SFR and isotope mass. The black solid line shows the total SFR in the galactic disc. The blue dotted and red dashed lines show the total mass of and respectively. The sharp features at 600 and 660 Myr are transients caused when we increase the resolution.
Figure 2: The morphology of the galactic disc. Panels show the gas (left), (middle) and (right) surface densities of the face-on disc at 750 Myr. Each image is 28 kpc across. The galactic disc rotates anticlockwise. The two circles indicate Galactocentric radii of 7.5 kpc and 8.5 kpc, roughly bounding the Solar annulus.
Figure 3: Same as Figure 2, but zoomed in on a spot near the Solar Circle. Panels show the gas (top-left), star formation rate (top-right), (bottom-left) and (bottom-right) surface densities at 750 Myr. The two arcs show Galactocentric radii of 7.5 and 8.5 kpc, bounding the Solar annulus.

To determine the equilibrium distributions of isotopes in newly-formed stars, we use a relaxation strategy to allow the simulated galaxy to settle into statistical equilibrium at high resolution. We first run the simulation at a resolution of 31 pc for 600 Myr, corresponding to two rotation periods at 10 kpc from the galactic centre. This time is sufficient to allow the disc to settle into statistical steady state, as we illustrate in Figure 1, which shows the time evolution of the total star formation rate (SFR) and total and masses within the Galaxy. We then increase the resolution from 31 pc to 15 pc and allow the disc to settle back to steady state at the new resolution, which takes until 660 Myr. At that point we increase the resolution again, to 8 pc. These refinement steps are visible in Figure 1 as sudden dips in the SFR, which occur because it takes some time after we increase the resolution for gas to collapse past the new, higher star formation threshold, followed by sudden bursts as a large mass of gas simultaneously reaches the threshold. However, feedback then pushes the system back into equilibrium. In the equilibrium state the SFR is yr, consistent with the observed Milky Way star formation rate (Chomiuk & Povich, 2011), and the total SLR masses are 0.7 for and 2.1 for , respectively, consistent with masses determined from -ray observations (Diehl, 2017; Wang et al., 2007).

Figure 2 shows the global distributions of gas and isotopes in the galactic disc at 750 Myr, when the maximum resolution is 8 pc and the galactic disc is in a quasi-equilibrium state. Figure 3 shows the same data, zoomed in on a kpc-region centred on the Solar Circle. The Figures show that the disc is fully fragmented, and has produced GMCs and star-forming regions. The distributions of and are strongly-correlated with the star-forming regions, which correspond to the highest-density regions (reddish colours) visible in the gas plot. This is as expected, since these isotopes are produced by massive stars, which, due to their short lives, do not have time to wander far from their birth sites.

However, there are important morphological differences between the distributions of , , and star formation. The distribution is the most extended, with the typical region of enrichment exceeding 1 kpc in size, compared to pc or less for the density peaks that represent star-forming regions. The distribution is intermediate, with enriched regions typically hundreds of pc in scale. The larger extent of compared to is due to its larger lifetime (2.62 Myr versus 0.72 Myr for Al) and its origin solely in fast-moving SN ejecta (as opposed to pre-SN winds, which contribute significantly to Al).

3.2 Abundance ratios in newborn stars

To investigate abundance ratios of isotopes in newborn stars, whenever a star particle forms in our simulations, we record the abundances of and in the gas from which it forms, since these should be inherited by the resulting stars. We do not add any additional decay, because our stochastic star formation prescription does not immediately convert gas to stars as soon as it crosses the density threshold, and instead accounts for the finite delay between gravitational instability and final collapse. Figure 4 shows the probability distribution functions (PDFs) for the abundance ratios and ; we derive the masses of the stable isotopes and from the observed abundances of those species in the Sun (Asplund et al., 2009), and we measure the PDFs for star particles that form between 740 and 750 Myr in the simulation, at galactocentric radii from kpc (i.e., within kpc of the Solar Circle). However, the results do not strongly vary with galactocentric radius, as shown in Figure 5. We also show that the PDFs are converged with respect to spatial resolution at their high-abundance ends (though not on their low-abundance tails) in Appendix A.

Figure 4: The abundance ratios of short-lived isotopes in newly-formed stars. The central panel shows the joint PDF of and from our simulations, with colours showing probability density and black points showing individual stars in sparse regions. The top and right panels show the PDFs of and individually, with simulations shown in blue. All simulation data are for stars formed from Myr, at Galactocentric radii from 7.5 - 8.5 kpc. Green bands show the uncertainty range of Solar System meteoritic abundances (Lee et al., 1976; Tang & Dauphas, 2015; Telus et al., 2017; Mishra & Goswami, 2014); for , due to the wide range of values reported in the literature, we also show three representative individual measurements as indicated in the legend.
Figure 5: Dependence of the and PDFs on Galactocentric radius. The histograms are each measured for stars formed within a 1 kpc-wide annulus centred at the Galactocentric radius indicated in the legend, at the final time in the simulation.

In Figure 4 we also show meteoritic estimates for these abundance ratios (Lee et al., 1976; Tang & Dauphas, 2015; Telus et al., 2017; Mishra & Goswami, 2014). The PDF of peaks near , but is orders of magnitude wide, placing all the meteoritic estimates well within the ranges covered by the simulated PDF. The abundance distribution is similarly broad, but the measured meteoritic value sits very close to its peak, as . Clearly, the abundance ratios measured in meteorites are fairly typical of what one would expect for stars born near the Solar Circle, and thus the Sun is not atypical.

4 Discussion

Our simulations suggest a mechanism by which the SLRs came to be in the primitive Solar System that is quite different than proposed in earlier work based on smaller-scale simulations or analytic models. We call this new contamination scenario “inheritance from Galactic-scale correlated star formation". Our scenario differs substantially from the triggered collapse or direct injection scenarios in that both of these require unusual circumstances – the core that forms the Sun is either at just the right distance from a supernova to be triggered into collapse but well-mixed, or the protoplanetary disc was hit by supernova ejecta and managed to capture them without being destroyed. In either case stars with SLR abundances like those of the Solar System should be rare outliers, while we find that the Sun’s abundances are typical.

Figure 6: Distributions of gas, star formation, and SLRs in Galactic coordinates, as viewed from the position of the Sun (i.e., a point 8 kpc from the Galactic centre). Panels show the gas, star formation rate, and distributions (from top to bottom) in Galactic coordinates. Note that, although the absolute scales on the colour bars in each panel differ, all panels use the same dynamic range, and thus the distributions are directly comparable. The scalloping pattern that is visible at high latitudes and toward the outer galaxy is an artefact due to aliasing between the Cartesian grid and the angular coordinates in regions where the resolution is low.

However, the scenario illustrated in our simulations is also very different from the GMC confinement hypothesis. To see why, one need only examine Figure 3. Observed GMCs, and those in our simulations, are at most pc in size, whereas in Figure 3 we clearly see that regions of and contamination are an order of magnitude larger. This difference between our simulations and the GMC confinement hypothesis is also visible in the distribution of on the sky as seen from Earth. Figure 6 shows all-sky maps of the gas, star formation rate, , and as viewed from a point 8 kpc from the Galactic Centre (i.e., at the location of the Sun). If SLRs are confined by GMCs, then -rays from Al decay should have an angular thickness on the sky comparable to that of star-forming regions. Figure 6 clearly shows that this is not the case in our simulations: and extend to , while star forming regions are confined to . The difference in scale heights we find is consistent with observations. The Galactic CO survey of Dame et al. (2001) finds that most emission is confined to Galactic latitudes , while the -ray emission maps of (Plüschke et al., 2001; Bouchet et al., 2015) show a thick disc with . Our simulation successfully reproduces the observed difference in and CO angular distribution.

Figure 7: Mass distributions with respect to gas temperature versus density. Left is the gas, middle is and right is at 750 Myr.

We can make this discussion more quantitative by examining the distribution of and with respect to gas density and temperature, as illustrated in Figure 7. We find that only 30% of the and 56% of the by mass are found in GMCs (defined as gas with a density above 100 H cm), compared to a total GMC mass fraction of 16%; thus is overabundant in GMCs compared to the bulk of the ISM by less than a factor of 2, and by less than a factor of 3.5. These modest enhancements are inconsistent with the hypothesis that SLRs abundances are high in the Solar System because SLRs are trapped within long-lived GMCs.

Our simulations instead suggest that SLR abundances in newborn stars are large because star formation is highly-correlated in time and space (Gouliermis et al., 2010; Gouliermis et al., 2015, 2017; Grasha et al., 2017a, b). SN ejecta are not confined to individual molecular clouds, and instead deposit radioactive isotopes in the atomic gas over kpc from their parent molecular clouds. However, because star formation is correlated, and because molecular clouds are not closed boxes, and instead they continually accrete the atomic gas during their star forming lives (Fukui & Kawamura, 2010; Goldbaum et al., 2011; Zamora-Avilés et al., 2012), the pre-enriched atomic gas within kpc of a molecular cloud stands a far higher chance of being incorporated into a molecular cloud and thence into stars within a few Myr than does a random portion of the ISM at similar density and temperature. Conversely, the atomic gas in a galaxy that will be incorporated into a star a few Myr in the future does not represent an unbiased sampling of all the atomic gas in the galaxy. Instead, it is preferentially that atomic gas that is close to sites of current star formation, and thus is far more likely than average to have been contaminated with SLRs. It is the galactic scale correlation of star formation that is the key physical mechanism that produces high SLR abundances in the primitive Solar System and other young stars.

5 Conclusions

Short-lived radioisotopes (SLRs) such as and are radioactive elements with half-lives less than 15 Myr that studies of meteorites have shown to be present at the time when the most primitive Solar System bodies condensed. The most likely origin site for the and in meteorites is nucleosynthesis in massive stars, but the exact delivery mechanism by which these elements entered the Solar System’s protoplanetary disc are still debated.

To address this question, we have performed the first chemo-hydrodynamical simulation of the entire Milky Way Galaxy, including stochastic star formation and stellar feedback in the form of H ii regions, supernovae, and element injection. Our simulations have enough resolution to capture individual supernovae, so that we can properly measure the full range of variation in SLR abundances that results from the stochastic nature of element production and transport. From our simulations we measure the expected distribution of and ratios for all stars in the Galaxy. We find that the Solar abundance ratios inferred from meteorites are well within the normal range for Milky Way stars; contrary to some models for the origins of SLRs, the Sun’s SLR abundances are not atypical.

Our results lead us to propose a new enrichment scenario: SLR enrichment via Galactic-scale correlated star formation. We find that GMCs are at most 100 pc in size and their star forming regions are much smaller, while regions of and contamination due to supernovae are an order of magnitude larger. The extremely broad distribution of produced in our simulations is consistent with the observed distribution on the sky, which shows an angular scale height that is close to twice that of the molecular gas and star formation in the Milky Way. The SLRs are not confined to the molecular clouds in which they are born. However, SLRs are nonetheless abundant in newborn stars because star formation is correlated on galactic scales. Thus, although SLRs are not confined, they are in effect pre-enriching a halo of the atomic gas around existing GMCs that is very likely to be subsequently accreted or to form another GMC, so that new generations of stars preferentially form in patches of the Galaxy contaminated by previous generations of stellar winds and supernovae.

In future work, we will extend our simulations to include other SLRs such as and , which also have been claimed to place severe constraints on the birth environment of the Solar system (Huss et al., 2009).


Simulations were carried out on the Cray XC30 at the Center for Computational Astrophysics (CfCA) of the National Astronomical Observatory of Japan and the National Computational Infrastructure (NCI), which is supported by the Australian Government. Y.F. and M.R.K. acknowledge support from the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (project DP160100695). Computations described in this work were performed using the publicly available enzo code (Bryan et al. 2014;, which is the product of a collaborative effort of many independent scientists from numerous institutions around the world. Their commitment to open science has helped make this work possible. We acknowledge extensive use of the yt package (Turk et al. 2011; in analysing these results and the authors would like to thank the yt development team for their generous help.


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Appendix A Resolution study

To determine whether our stellar abundance distributions are converged, we compare the distributions we measure for stars formed at Myr of evolution, when our resolution is 8 pc at the galaxy has reached steady state, to those formed at Myr (steady state at 31 pc resolution) and Myr (steady state at 15 pc resolution). We show the results in Figure 8. We find that, although the peaks of the PDFs move to higher values with higher resolution, the high end tails converge to for , and for . Thus we are well-converged on the upper half of the abundance distribution. Moreover, given the broad range of uncertainties in the meteoritic abundance, the shifts we do see with resolution do not change the qualitative conclusion that Sun’s SLR abundances are within the normal range expected for Milky Way stars.

Figure 8: Resolution study for SLR abundance PDFs in newly-formed stars. The top panel is , and bottom is for . The black line shows the distribution of abundances at 31 pc resolution run ( Myr), the blue line is 15 pc resolution () Myr, and red line is at 8 pc resolution ( Myr).
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