The metal and dust yields of the first massive stars

The metal and dust yields of the first massive stars

Stefania Marassi, Raffaella Schneider, Marco Limongi, Alessandro Chieffi, Marco Bocchio, Simone Bianchi
INAF/Osservatorio Astronomico di Roma, Via di Frascati 33, 00040 Monteporzio, Italy
INAF/IASF, Via Fosso del Cavaliere 100, 00133 Roma, Italy
Kavli Institute for the Physics and Mathematics of the Universe, Todai Institutes for Advanced Study,
The University of Tokyo, Kashiwa 277-8583, Japan
INAF/Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy

We quantify the role of Population (Pop) III core-collapse supernovae (SNe) as the first cosmic dust polluters. Starting from a homogeneous set of stellar progenitors with masses in the range , we find that the mass and composition of newly formed dust depend on the mixing efficiency of the ejecta and the degree of fallback experienced during the explosion.

For standard Pop III SNe, whose explosions are calibrated to reproduce the average elemental abundances of Galactic halo stars with , between 0.18 and 3.1  () of dust can form in uniformly mixed (unmixed) ejecta, and the dominant grain species are silicates. We also investigate dust formation in the ejecta of faint Pop III SN, where the ejecta experience a strong fallback. By examining a set of models, tailored to minimize the scatter with the abundances of carbon-enhanced Galactic halo stars with , we find that amorphous carbon is the only grain species that forms, with masses in the range () for uniformly mixed (unmixed) ejecta models.

Finally, for all the models we estimate the amount and composition of dust that survives the passage of the reverse shock, and find that, depending on circumstellar medium densities, between 3 and 50% (10 - 80%) of dust produced by standard (faint) Pop III SNe can contribute to early dust enrichment.

stars:low-mass, supernovae: general, ISM: cloud, dust, Galaxy: halo, galaxies:evolution
pagerange: The metal and dust yields of the first massive starsAppendix: Final dust grids and tablespubyear: 2015

1 Introduction

Dust grains play a fundamental role in the evolution of stellar populations at high redshift. Population III stars (hereafter Pop III), so far undetected, are responsible of the first chemical enrichment of the high-redshift interstellar medium (ISM). Given the current theoretical limits on the mass of the first stars (Hosokawa et al. 2011; Hosokawa et al. 2012), early metal enrichment is likely to be mostly driven by the first core-collapse supernovae (SNe), with a possible contribution from more massive pair-instability supernovae (although this may strongly depend on the poorly constrained tail of the stellar initial mass function, Hirano et al. 2014, 2015; Susa et al. 2014).

Yet, the amount and properties of grains that can be injected in the high-redshift ISM and contribute to the enrichment depend on the dust condensation efficiencies in SN ejecta and on the destruction suffered by thermal and non-thermal sputtering during the passage of the reverse shock of the SN, on timescales of (Bianchi & Schneider 2007; Nozawa et al. 2007). Depending on the density of the circumstellar medium where the explosion takes place, the mass fraction of newly formed dust that is able to survive ranges between and for circumstellar medium densities in the range , which corresponds to number densities in the range (Bianchi & Schneider 2007; Nozawa et al. 2007; Silvia et al. 2010; Silvia et al. 2012; Marassi et al. 2014). In addition, the passage of the reverse shock significantly alters the grain size distribution and modifies the grain cross section, changing the dust cooling efficiency (Schneider & Omukai 2010).

Dust formation in SN ejecta has been investigated following two different methods: classical nucleation theory (CNT) and a chemical kinetic approach (Cherchneff & Dwek 2009; Cherchneff & Dwek 2010; Sarangi & Cherchneff 2013). Theoretical models, developed in the framework of CNT, have shown that dust formation can take place in SN ejecta a few hundred days after the explosions and provide predictions on the mass, composition and size distribution of the newly formed grains (Kozasa et al. 1989, 1991; Todini & Ferrara 2001; Nozawa et al. 2003,  2008, 2010, 2011; Schneider et al. 2004; Bianchi & Schneider 2007). These models predict dust masses M for SN progenitors with masses and metallicities (Schneider et al. 2014), in agreement with the dust mass inferred from recent Herschel and ALMA observations of SN 1987A (Matsuura et al. 2011; Indebetouw et al. 2014) and Cas A (Barlow et al. 2010). Although in the past the applicability of CNT in astrophysical context has been questioned (Donn & Nuth 1985; Cherchneff & Dwek 2009), mainly due to the assumption of chemical equilibrium at nucleation, recently Paquette & Nuth (2011) showed that this assumption has a lower impact on the grain mass and size distribution than previously thought. Similarly, Nozawa & Kozasa (2013) demonstrated that CNT is a good approximation in SN ejecta, at least until the collisional timescales of the key molecule is much smaller than the timescale with which the supersaturation ratio increases.

The goal of the present study is to investigate the role of Pop III core-collapse SN as dust polluters, adopting a homogeneous set of metal-free progenitors with masses in the range . Under the assumption that the observed metal poor stars likely formed from gas clouds enriched by Pop III SNe, we use properly calibrated SN explosion models (Chieffi & Limongi 2002) to calculate the formation of dust in the ejecta, applying CNT and accounting for the process of grain growth. We quantify the impact of ejecta mixing on the final dust masses and grain size distributions, analyzing both uniformly mixed models within the helium core and unmixed/stratified cases. To obtain a more realistic estimate of the dust mass that is able to enrich the ISM, we also consider the effects of the reverse shock (Bianchi & Schneider 2007).

Motivated by the observed surface elemental abundances of Carbon Enhanced Metal Poor (CEMP) stars, i.e. stars with an observed overabundance of light elements compared to Fe and - in particular - with [C/Fe] (Beers & Christlieb 2005), we also investigate dust formation in the ejecta of faint Pop III SN, where the ejecta experience mixing and fallback (Umeda & Nomoto 2002; Umeda & Nomoto 2003). Recently, Marassi et al. (2014) showed that dust can be produced in faint Pop III SN ejecta (see Kochanek 2014 for dust formation in solar metallicity faint SNe.)

Here, we extend this previous analysis and we simulate a large set of faint Pop III SN models, searching for a combination of mixing and fallback that provides the best-fit to the observed abundance pattern of all currently known C-enhanced hyper-iron-poor stars (Beers & Christlieb 2005; Yong et al. 2013; Keller et al. 2014; Ishigaki et al. 2014). For these faint SN models we also explore the impact, on the final dust masses, of ejecta mixing and reverse shock.

The plan of the paper is as follows. In Section 2 we briefly summarize the Bianchi & Schneider (2007) dust nucleation model and we describe the upgrated molecular network. In Section 3 we illustrate the main features of Pop III SN progenitors that are modeled using FRANEC stellar evolutionary code (Limongi & Chieffi 2006; Limongi & Chieffi 2012) and their calibration. In Section 4 we present the resulting dust yields for Pop III core-collapse SNe. In Section 5 we describe how we construct, using the mixing and fallback procedure (Umeda & Nomoto 2002), faint Pop III ejecta calibrated with the same procedure described in Marassi et al. (2014). In Section 6 we show the results on dust yields obtained in Pop III faint SN ejecta. In Section 7 we discuss all the results and their dependence on the fallback, ejecta mixing, and reverse shock and we draw our conclusions. In the Appendix we present our final dust data grids that will be available to the community.111The resulting dust and metal yields will be available in electronic format for interested researchers upon request.

2 Dust formation model

To model dust formation in SN ejecta we follow the Bianchi & Schneider (2007) model, where classical nucleation theory in steady state conditions was applied (see Nozawa et al. 2003; Bianchi & Schneider 2007 and references therein). For our calculation, we use a previously developed code that has been applied to core-collapse (Todini & Ferrara 2001; Bianchi & Schneider 2007) and pair-instability SNe (Schneider et al. 2004). This theoretical model has allowed to successfully reproduce the dust masses observed in SNe and young SN remnants (Schneider et al. 2014; Valiante & Schneider 2014). In Bianchi & Schneider (2007) the chemistry of molecular formation is implemented following Todini & Ferrara (2001), but relaxing the assumption of steady state. In the gas-phase, the formation of carbon oxide (CO) and silicon oxide (SiO) was assumed to be driven by radiative association reactions and destroyed by Compton electrons coming from radioactive decay of Co. Seven different grain species are formed in SN ejecta: amorphous carbon (AC), iron, corundum (AlO), magnetite (FeO), enstatite (MgSiO), forsterite (MgSiO) and quarz (SiO). In this work, we follow the formation of the above grain species assuming that seed clusters are formed by a minimum of two monomers, which subsequently grow by accretion of other monomers. The accretion process is regulated by the collisional rate of the key species and depends on the sticking coefficient (defined as the probability that an atom colliding with a grain will stick to it) which we have assumed equal to 1 for all grain species. A discussion of the dependence of the dust yields on these two parameters can be found in Bianchi & Schneider (2007), where is also possible to find a description of the adopted properties of SN dust species to which we refer for more details.

RA1 k Dalgarno et al. (1990)
RA3 k Andreazza & Sigh (1987)
RA4 see text Babb & Dalgarno (1994)
NN4 see text -
Table 1: Molecular processes considered in this work: the rate coefficients are taken from the UMIST database for astrochemistry 2012; where the origin of the reaction rates is different the corresponding reference is indicated.
D1 W=125
D2 W=110
D3 W=125
D4 W=125
Table 2: Compton Electron destruction reactions and the corresponding mean energy per ion pair .

2.1 Upgrated Molecular Network

It is well known that CO and SiO molecules play a fundamental role in the dust formation process: CO formation subtracts C-atoms and limits the formation of AC grains. SiO is required to form silicates, such as MgSiO and MgSiO. Due to the important role of molecules in the dust formation pathway, we have enlarged our molecular network taking into account other formation/destruction processes involving CO/SiO molecules and their interactions with O and C. These molecular processes are crucial in subtracting gas-phase elements from the ejecta (in particular oxygen and carbon, which are very abundant, see left panel of Fig. 2), that otherwise are free to form dust. We follow the evolution of CO, SiO, O and C which form through different channels (reaction rates), respectively: (i) radiative association reactions where the formation of molecules takes place through the emission of a photon which carries off the excess energy released during the formation process; (ii) bimolecular, neutral-neutral reactions that involve molecules and atoms. For these two-body reactions, the formation rates of molecules k(T) are given by the usual Arrhenius-type expression,


where T is the temperature of the ejecta gas in K and the activation energy in K. In Table 1 we report the rates expressed in the Arrhenius form according to the UMIST database for astrochemistry 2012222 This database is a compilation of molecular rates that have different origin, some are theoretically calculated, others are directly measured in the laboratory. Clearly, there is a degree of uncertainty related to the rate calculations: in some cases we decided to refer to other rate estimates present in the literature that are more robust. This is the case for the radiative association rate coefficient of O (RA4), for which we have chosen to fit the expression of the rate coefficient, as a function of temperature, obtained from theoretical calculations in Babb & Dalgarno (1994). In addition, we found that the neutral backward reaction NN4 is negligible (K. Omukai, private communication).

In standard nucleation theory, dust condensation is described in terms of a nucleation current that depends on the abundance of the key species. Hence, contrary to other studies which adopt a chemical kinetic approach (Cherchneff & Dwek 2009, 2010; Sarangi & Cherchneff 2015), we do not follow the formation of carbon chains as a pathway to solid carbon clusters. Thermal fragmentation of the chains through collisions with gas particles, in addition to oxydation reactions similar to NN2, may limit the formation of carbon chains. However, if all C were to contribute to carbon dust formation, the estimated carbon dust mass would need to be corrected upward by .

We take into account the destruction due to Compton electrons coming from the Ni decay in the ejecta. As observed in SN 1987A, destruction by Compton electrons has a deep impact on the ejecta chemistry. As shown by Woosley et al. (1989), the explosion of SN 1987A has produced Ni which decays in days into Co; the subsequent decay of Co into Fe deposits energy as rays in the SN ejecta, powering the observed light curve. In SN 1987A, the emitted light curve is very well reproduced if mass of Co was ejected during the SN explosion.

Here we assume molecules to be destroyed by the impact with energetic electrons produced by the radioactive decay of Co, with a rate coefficient k that depends also on the mean energy per ion pair W. According to Woosley et al. (1989), this rate coefficient can be estimated as follows: the thermalized -ray energy input rate for a given Co mass is given by,


where was the adopted mass of Co produced in the original Woosley et al. (1989) model, days is the e-folding time of Co decay, and the function is the deposition function and it is given by one minus the fraction of energy that escapes in photons in the X-ray and -ray bands,


where represents the column depth of the SN at some fiducial time (for s gr/cm) and cm gr is an average opacity to rays from Co decay. The above quoted values of and have been derived by Woosley et al. (1989) for SN 1987A and we will assume these to hold for all the explored SN progenitors. In particular, we assume that once a -ray Compton scatters with electrons, it is completely absorbed. Thus, the can be considered as the electron energy input and the energy transferred to a single gas particle per unit time can be computed as,


where is the number of gas particles in the ejecta. To compute the destruction rate, , it is necessary to divide by the mean energy per dissociation, . For example, to compute the destruction rate of neutral CO we divide L by the mean energy per dissociation W, obtaining


Finally, we assume that all the radioactive energy is deposited uniformly in the ejecta. As it will be clear in what follows, the efficiency of molecule formation/destruction processes depends on the chemical composition and on the thermodynamics of the ejecta. In Section 4, we give a detailed description of the relevant processes for some selected SN models.

Figure 1: Pre-supernova chemical structure for three selected models: (left panel), (central panel), (right panel). The shaded region extends up to the mass coordinate of the He core. Different shaded regions indicate the layers that we will consider in the unmixed SN models (layers A, B, and C from left to right). Colour versions of the figures are available online.

3 PopIII SN progenitors models

Figure 2: Left panel: initial metal abundances in the ejecta of the adopted SN models as a function of the progenitor stellar mass (the abundance of Al has been multiplied by ). Right panel: mass of dust grains, before the passage of the reverse shock, as a function of the progenitor mass. is the total mass in silicates, including MgSiO, MgSiO and SiO.
Figure 3: Temperature (left panel) and number density (right panel) evolution for (solid), (dotted), (dashed) ejecta models.

The presupernova models adopted in this paper are the ones presented and discussed in details in Limongi & Chieffi (2012). These models span a range of mass between 13 and 80   M and have a pristine Big Bang initial composition. The evolution of these models has been followed from the pre-main sequence up to the onset of the iron core collapse by means of the FRANEC stellar evolutionary code (Limongi & Chieffi 2006). The explosion of the mantle and the consequent explosive nucleosynthesis have been computed in the framework of the ”artificially induced explosion”. Then, for each model, the mass cut (), i.e. the mass coordinate which separates the final remnant from the ejected portion of the mantle, has been fixed by requiring a best fit to the element abundance pattern of the Cayrel average star, as extensively described in Limongi & Chieffi (2012). In Table 3 we summarize the main properties of the SN explosion models.

We construct the Pop III ejecta models, requiring that the thermal, dynamical and chemical evolution of the ejecta evolve consistently with the explosive nucleosynthesis simulation (see next section for details). We have performed dust formation calculations assuming uniform mixing of the elemental abundances in the He core. However, due to the uncertainties related to the efficiency of mixing in metal-free SNe (Joggerst et al. 2009, Heger & Woosley 2010), for some models we also present the results obtained assuming unmixed ejecta. In Fig. 1 we show the chemical structure (elemental mass fraction) as a function of the mass coordinate for three selected pre-supernova models, (for a detailed description of the differences emerging in the convective zones we refer the reader to Limongi & Chieffi 2012). The shaded region extends up to the mass-coordinate of the He core, different colours indicate the layers that we will consider in the unmixed SN models, in Section 4. The left boundary of the innermost shaded region corresponds to the adopted mass-cut coordinate. In the left panel of Fig. 2 we show, for each SN model, the initial abundance of metal species which participate to molecules and dust formation; for all the SN models, the ejecta are very rich in carbon and oxygen and the total mass of metals is an increasing function of the progenitor mass. The ejecta mass , as expected, is an increasing function of the progenitor mass and explosion energy (see Table 3).

4 Results: PopIII SN dust yields

Figure 4: Time evolution of molecular (dashed lines) and dust masses (solid lines) for three metal-free SN progenitors: 15  M (left panel), 30  M (middle panel), 50   M (right panel).

This section presents the calculated dust yields that we obtain for Pop III core-collapse SN models. As stated in the previous section, we construct the ejecta models using as initial conditions the thermo-dynamical properties obtained by the SN explosion simulation outputs (Limongi & Chieffi 2012). The ejecta follow an adiabatic expansion and the temperature evolution is given by,


is the ejecta expansion velocity, is the adiabatic index, and and are the temperature and radius of the He core at the initial time . This initial time is fixed by requiring that the gas temperature at the radius of the He core, reaches a temperature of  K. For all uniformly mixed SN ejecta models (labelled with the progenitor mass) Table 3 reports the thermodynamical properties, the metal yields of the key elements in the nucleation process, the total amount of dust, the mass of molecules and the mass of dust in each grain species. In what follows, we discuss these results in details.

Dust formation in uniformly mixed ejecta

Figure 5: Time evolution of molecular (dashed lines) and dust (solid lines) masses for the unmixed model: layer A (left panel), layer B (middle panel), layer C (right panel). Colour versions of the figures are available online.

In the right panel of Fig. 2 we plot the mass of dust for different grain species as a function of the progenitor mass. We find that: (i) the total dust mass produced increases with the progenitor mass, ranging between  M, and it is dominated by silicates; (ii) the second most abundant dust species is magnetite, due to the initially high iron abundance present in the ejecta (see left panel of Fig. 2) plus the iron produced by decay; (iii) amorphous carbon forms only in less massive models, with progenitor masses . This is due to the larger mean ejecta density of more massive progenitors, which increases the rates of the major processes leading to the formation of CO molecules, locking carbon atoms and preventing the formation of AC grains (we will return to this point later); (iv) alumina is the less abundant dust species, reflecting the lower abundance of Al in the ejecta.

Using three representative SN progenitors with masses and , Fig. 3 shows the evolution of the ejecta temperature and number density: when the He core of the three SN progenitors reaches K, we fixed the initial time , which varies between (1.78 - 3.96)s (see Table 3). At these initial times, the three ejecta models have radii of (15 M), (30 M), and (50 M) cm, and start the adiabatic expansion with velocities in the range (2960-3086)km s (see eq. 6), and the temperature decreases. As shown in the right panel of Fig. 3, the initial number densities, 7.18(15 M), (30 M), (50 M) cm, also decreases, showing a step-decrease corresponding to the condensation of the gas-phase elements.

In standard nucleation theory, dust grains condense when the gas becomes supersaturated. For each grain species, this depends on the temperature, density and abundances of the corresponding key element in the ejecta. Fig. 4 shows that grains form between 45 and 120 days after the explosions. Although these timescales are smaller than the values found by Nozawa et al. (2003) for core-collapse Pop III SN with a 25 progenitor, due to the different thermal evolution of the ejecta, the resulting dust masses and grain size distribution are consistent because grain condensation occurs in similar physical conditions.

Molecules form according to the formation/destruction rates described in Section 2.1 and are also partially destroyed by the interaction with Compton electrons produced by destruction reactions rates (see Table 2), up to the point where the temperature reaches the condensation window and dust grains start to form. The ejecta density is a strong function of the initial progenitor mass: when the ejecta temperature enters the condensation regime, at around T  K, the corresponding density can vary by one order of magnitude, although the dependence on the progenitor mass is not monotonic. Clearly, the chemical evolution of the ejecta depends on the temperature and density at each given time: in Fig. 4 we show, for the same set of SN models, the time dependence of the mass of CO, SiO and of the newly formed dust species.

We start analizing the model plotted in the left panel of Fig. 4: CO and SiO start forming at around 27 days after the explosion, when . At this time, the CO formation rate is dominated by the neutral process NN2 that rapidly depletes all the available . SiO molecules form through the neutral channel NN5 and radiative association process RA2. At around 44 days, when , the impact with Compton electrons () dominates over the other rates and partially destroys CO molecules. The free carbon atoms form AC, which is the first dust species to form, due to its higher condensation temperature. When the temperature decreases to , alumina grains form, which rapidly deplete aluminum from the ejecta. When T drops to  K, MgSiO starts forming - at the same time of MgSiO- but MgSiOreaches supersaturation first (because it has the largest nucleation current), rapidly consuming Mg and SiO and inhibiting the growth of MgSiO. Finally, when  K, FeO  and SiO  forms, depleting completely the remaining SiO and iron from the ejecta.

The central panel of Fig. 4 shows the evolution of molecules and dust grains for the model: at days, when , the dominant process is radiative association of which - due to the large oxygen abundance - is then rapidly depleted in CO through the reaction . When T decreases, at around 66 days, the dominant CO formation process becomes radiative association RA1. Around 93 days, the temperature reaches , nucleation starts, D1 efficiently destroys the CO molecule, leaving C atoms free to form AC and - as in the model - the CO formation processes are not equally efficient in re-forming the molecule. As a result, AC grains form.

For the more massive model the evolution changes, as shown in the right panel of Fig. 4. The interplay between the larger ejecta density and the richer oxygen content (the mass of oxygen is of the mass of the ejecta) leads to the efficient formation of molecules through radiative association RA4 and also activates efficiently the bimolecular process NN1, which exceeds the destruction rate D1, and becomes the leading process in CO formation. This depletes all the C atoms, inhibiting AC grains condensation. As for the two previous models, at the main CO formation channel is . When T decreases, it becomes and it remains so for the subsequent evolution. At 64 days, the nucleation process starts, the grain condensation proceeeds as described for the two previous models, because the condensation sequence of the grain species reflects the corresponding condensation temperatures (Todini & Ferrara 2001; Schneider et al. 2004).

We summarize our results on mixed ejecta models in Table 3. In general, the total mass of CO molecules ranges between , increasing with the mass of the ejecta due to the initial abundances of oxygen and carbon. SiO molecules form efficiently through NN5 (at early times) and through RA2, but it is completely depleted in silicates at the end of the nucleation process. molecules are consumed at very early time in the formation process of CO, through the channel NN2. For models less massive than , is under-produced (and consumed rapidly in CO formation process), with respect to more massive models. When the higher mean ejecta density and oxygen abundance cause radiative association rate RA4 to become the dominant process. This enables a very efficient reaction rate which overcomes the destruction rate , locking all carbon atoms in CO molecules.

Dust formation in umixed ejecta

The mixing efficiency in SN events is still debated, due to complexity of physical processes associated to core-collapse, such as asphericity and growth of Rayleigh-Taylor instabilities which accompany shock propagation. Besides, these effects are multi-dimensional and this adds an extra source of uncertainty related to emerging differences in 1D-3D numerical simulations (see Joggerst et al. 2009, Heger & Woosley 2010 and references therein). In particular, the occurence and the growth of Rayleigh-Taylor instabilities depends on stellar mass and metallicity. It has been shown that the more compact is the star, the more rapid is the reverse shock propagation, giving less time to these hydrodynamical instabilities to grow (Joggerst et al. 2009). For this reason, we have decided to investigate the impact of ejecta mixing on dust formation and we have considered stratified models, as the limiting cases when Rayleigh-Taylor instabilities do not grow. The unmixed case is based on the hypothesis that, due to inefficient mixing, the elemental abundances reflects the pre-supernova stratified composition: this means that more internal elements, such as magnesium and silicon are not present or present in very little amount in the more external layers of the star, reducing the probability to form silicates.

Figure 6: Mass of dust grains, before the passage of the reverse shock, as a function of the progenitor mass for the three selected unmixed models. is the total mass in silicates, including MgSiO, MgSiO and SiO.

In Fig. 1, for each progenitor model, the shaded regions represent the layers that we consider in the stratified models, which extend from the mass cut coordinate to the outer radius of the He core (). The number and extent of the layers have been selected based on the criterium of constant abudances of the relevant elemental species within each layer. Hence, the outer radius of layer A corresponds to the mass coordinate where the Si abudance rapidly drops, and the outer radius of layer B is where the abundance of C (Ne) rapidly increases (decreases).

For the and models, we report in Tables 45 and  6 the thermodynamical properties, the initial elemental composition, the masses of molecules and dust for all the layers. The time evolution of the molecular and dust masses for each of the three layers of the progenitor is shown in Fig. 5. In the stratified ejecta, due to the different temperature evolution of the layers, CO starts to form earlier in the evolution with respect to the corresponding mixed case, and the same is true for SiO, where present. It is worth to note that, compared to the mixed case where is completely depleted in CO, in layers A and B the molecule forms, while AC forms only in layer C. Silicates and alumina form in the two internal layers A and B where Al, Si and Mg are present. Magnetite forms only in layer A where iron is present. The total mass of dust for the progenitor is , about of the mass formed in the mixed case.

Fig. 6 summarizes the results obtained for unmixed ejecta models. The mass of dust for different grain species is shown as a function of the progenitor mass. We find that the total dust mass ranges between  M, and it is dominated by silicates. Contrary to the fully mixed cases, for the and SN progenitor models, solid iron is able to form due to the initially high iron abundance present in the most internal layer of the ejecta plus the iron produced by decay. As a result, in these models the total dust mass formed is larger than in the mixed case. The CO mass, differently from the mixed case, is not increasing with the progenitor mass, but varies depending on rate formation efficiency which is a function of temperature, mean density and composition of each layer.

Dust destruction by the reverse shock

Figure 7: Left panel: the mass of dust at the end of nucleation, and after the passage of a reverse shock of increasing intensity for all the mixed SN models considered in the present study. From top to bottom: no reverse shock models (no-rev), models with a circumstellar medium density of (rev1), ,(rev2), and (rev3). Right panel: size distribution function of the grains for a progenitor model before (no-rev, left) and after the passage of the reverse shock (rev1, right).

To describe the impact of the reverse shock on the dust grains formed inside the expanding ejecta and to estimate the surviving dust mass, we follow the approach described in Bianchi & Schneider (2007) for which we summarize the key points: (i) the dynamics of the reverse shock is treated using Truelove & McKee analytic approximations (Truelove & Mckee 1999) which follows the forward and reverse shock evolution as a function of the main ejecta parameters, such as kinetic energy, , ejecta mass, , and density of the ISM, ; (ii) the distribution of dust grains in the ejecta is uniform and the size distribution is the same everywhere; (iii) to quantify the role of we analize three different cases with . As previously shown in Todini & Ferrara (2001) and Nozawa & Kozasa (2003), the nucleation and accretion processes lead to a typical lognormal grain size distribution: in the right panel of Fig. 7 we show the grain size distribution of the SN model with mixed ejecta, before and after the passage of the reverse shock. The grain sizes range between , depending on the grain species and on the SN ejecta models. Since AC is the first grain species to condense, it has sizes larger than the other grains because grain accretion is more efficient at larger densities. For the same reason, alumina grains have the smallest sizes due to the low initial abundance of Al in the ejecta. As a result, the latter grain species is almost completely destroyed by the reverse shock, while the other grain species suffer a partial destruction, with the grain size distribution flattening towards smaller grain sizes.

The dust mass which survives the impact of the reverse shock is reported for all mixed SN models in Table 7, where we have also specified the dust mass of each grain species. In the left panel of Fig. 7 we show, for all Pop III mixed SN models, from top to bottom, the total mass of dust at the end of nucleation and after the impact of the reverse shock for the three increasing values of . In the worst scenario, when the SNe explode in the densest ISM, the reverse shock travels faster and encounters a higher density gas inside the ejecta, increasing the sputtering and causing that only of the newly formed dust mass survives. Clearly, the percentage of surviving dust depends on the ejecta model and ranges from to . In Fig. 9 the same histograms are reproduced for and mixed models, showing the impact of the reverse shock on the different grain species. We can see that alumina grains are completely destroyed. Depending on , after the passage of the reverse shock, we see that: (i) in the model the dominant species becomes AC, differently from the no-rev case, where AC and silicates have comparable masses; (ii) in the model silicates always dominate the mass of dust; however, the smaller destruction suffered by AC grains, compared to other grain species, alters the original dust composition and after the passage of the reverse shock the mass of AC and silicates are comparable and AC grains are more abundant than grains; (iii) in the model, silicates dominate all the grain species, as in the no-rev case.

Fig. 8 illustrates the dust mass which survives to the impact of the reverse shock for the three selected unmixed models (see also Table 8 for the amount of grains of different species in the three layers). After the passage of the reverse shock, depending on the density of the ISM and on the progenitor mass, the percentage of surviving dust ranges from to . Also, compared to the fully mixed models, we note that in each case dust is destroyed to a minor degree. In fact, in all the three unmixed models, most of the dust mass is produced in the innermost layer (layer A). At the time the reverse shock reaches this region of the ejecta, density is low and the effect of the reverse shock is less destructive. In Table 8 we note that, while layer B and C are highly affected by the passage of the reverse shock, dust in layer A survives in large quantities and represents almost the totality of the survived dust mass. These calculations have been performed with an updated version of the code by Bianchi & Schneider (2007) which considers also stratified ejecta, taking into account the gas (density, temperature, elemental abundances) and dust (composition, size distribution) properties in each shell depending on the position within the ejecta.

These results suggest that the effect of the reverse shock must be taken into account in order to have a reliable estimate of the final dust mass and composition.

Figure 8: Mass of dust grains, after the passage of the reverse shock, as a function of the progenitor mass for the three selected unmixed models. From top to bottom: no reverse shock models (no-rev), models with a circumstellar medium density of (rev3).

5 PopIII faint SN progenitors

We know from observations that a fraction of of iron-poor stars observed in the Galactic Halo with are carbon-rich (Yong et al. 2013; Placco et al. 2014 and references therein). Most notably, the observed frequency of CEMP stars that do not show overabundances of neutron-capture elements, the so-called CEMP-no stars, increases to at , with interesting implications for chemical evolution models and the formation pathway of these hyper-iron poor stars (de Bennassuti et al. 2014).

Different scenarios have been proposed to explain the observed elemental abundances of CEMP-no stars (see Norris et al. 2013 and references therein). Among these, stellar winds of fast-rotating massive stars (Maeder, Meynet & Chiappini 2015), a single Pop III supernova, experiencing mixing and fallback after the explosion (Umeda & Nomoto 2002; Iwamoto et al. 2005; Tominaga et al. 2007; Tominaga 2009; Heger & Woosley 2010; Tominaga et al. 2014; Yong et al. 2013; Ishigaki et al. 2014; Marassi et al. 2014), or in terms of an almost failed Pop III SN (with a large fallback) exploding in an environment pre-enriched by one or more normal Pop III supernovae (Limongi et al. 2003).

In Marassi et al. (2014) we intepreted the surface element abundances of SMSS J031300, the recently discovered CEMP-no stars with [Fe/H] (Keller et al. 2014), in the framework of the mixing-fallback scenario. In particular, in that paper dust formation in the ejecta of Pop III faint SNe was investigated for the first time, showing that - depending on the extent of mixing experienced by the ejecta and on the partial destruction by the SN reverse shock - between and of carbon dust forms. These dust masses are large enough to activate dust-driven fragmentation (Schneider et al. 2012) in the parent star-forming cloud of SMSS J031300, even accounting for the dilution and mixing of the SN ejecta with the surrounding pristine gas (Marassi et al. 2014).

In this section, we use the same procedure applied in Marassi et al. (2014) to estimate the mass and composition of dust that forms in the ejecta of faint Pop III SNe. The SN models have been selected by comparing the predicted elemental yields with the observed surface elemental abundances of the four C-enhanced, hyper iron-poor stars currently known, namely: HE1327-2326 (Frebel et al. 2005), HE0107-5240 (Christlieb et al. 2002), HE0557-4840 (Norris et al. 2007) and SMSS J031300 (Keller et al. 2014). For each of these, we vary the mixing and fallback efficiencies so as to minimize the scatter between the observed abundance pattern and the elemental yields predicted by Pop III SN models (Limongi & Chieffi 2012)333In Marassi et al. (2014) we estimate that in less than 1 Myr the ejecta material can be well mixed and diluted with pristine gas, enriching the gas cloud out of which second generation C-enhanced stars form with a [Fe/H] consistent with the observed values.

The surface chemical abundances of HE1327-2326, HE0107-5240, and HE0557-4840 have been taken from the recent compilation by Norris et al. (2013) (see their Table 4; here we normalize to the solar abundances of Asplund et al. 2009), which are based on high-resolution data, but are determined using 1D, LTE model-atmosphere analysis. The upper limit on silicon for HE1327-2326, HE0107-5240 and HE0557-4840 is taken from Yong et al. (2013). For consistency, we consider the observed elemental abundances of SMSS J031300 as derived from 1D model atmosphere (Marassi et al. 2014). In Fig. 10 we show the comparison between the observed elemental abundances and the best fit models for each of the four stars. We find that the data are reproduced by Pop III SNe with progenitor masses in the range that experience strong fallback. For all the models we have identified the mass-coordinates that defines the extent of mixing and fallback that better reproduce the observed abundaces, with particular attention on [C/Ca], [Mg/Ca] and [O/Ca] - that are extremely important for dust formation - without exceeding the upper limits on [Fe/Ca]. In the following, we discuss the properties of the faint Pop III SN progenitors inferred from the observed abundances of each star, which we also report in Table 9.

Figure 9: Histograms showing the mass of dust in the different compounds at the end of nucleation, and after the passage of a reverse shock of increasing intensity for three mixed SN models of 15M, 30M and 50M. From top to bottom: no reverse shock models (no-rev), models with a circumstellar medium density of (rev3).
Figure 10: Comparison between the observed elemental abundance ratios of the CEMP-no stars and the chemical yields of Pop III faint SN with progenitor masses of . Mixing and fallback are chosen so as to minimize the scatter with the observations (black points). Dots with arrows show upper limits and filled points with errorbars indicate the detections.

For HE1327-2326, nitrogen has been detected and the observed abundance shows comparable value of [N/Ca] and [C/Ca]. Since a substantial amount of N is produced only by Pop III SN models with progenitor masses in the range (see Limongi & Chieffi 2012 for more details), we have limited the exploration of the mixing and fallback procedure to this mass range. The best agreement for HE1327-2326 is provided by the progenitor model with a mass-cut of and an ejected mass of of . Note that a [Si/Ca] ratio close to the observed upper limit implies a substantial under-production of [(Na,Mg,Al)/Ca] ratios. Since the amount of Si in the ejecta plays a crucial role in the dust formation process, we chose to fit the [Si/Ca] ratio, even if the abundances of Na, Mg and Al are underproduced.

The same procedure has been applied to HE0107-5240 finding the best agreement for a SN progenitor model with a mass-cut of and a mass of , which reproduces the observed [C/Ca] and [O/Ca] and predicts a [Na/Ca] ratio close to the observed one.

For HE0557-4840 we have searched for progenitors which favors low [N/Ca] due to the low upper-limit inferred from observations. We select a progenitor with and , that reproduces also the observed [C/Ca] and [Mg/Ca] abundances. We note that none of the models is able to reproduce, at the same time, the observed [O/Ca] and [Mg/Ca] abundances (see also Limongi & Chieffi 2012 and Ishigaki et al. 2014), particularly the low-mass progenitors, which have lower value of [Mg/O] in the ejecta.

Figure 11: Left panel: the mass of dust at the end of nucleation for mixed and unmixed ejecta for the four faint SN progenitors. Central panel: the mass of dust at the end of nucleation and after the passage of a reverse shock of increasing intensity for the four faint SN progenitors with mixed ejecta considered in this study. Right panel: the same as in the central panel but for faint SN models with stratified ejecta. From top to bottom: no reverse shock models (norev), models with (rev3)


Finally, for SMSS J031300 we have reported only the best-fit obtained for the model ( and ) selected by Marassi et al. (2014), to which we refer the reader for a detailed discussion.

6 Dust yields from faint Pop III SN

This section presents the results of the dust formation calculation for Pop III faint SN progenitors. To enable a comparison with the results by Marassi et al. (2014), we first discuss the results for uniformly mixed ejecta, which are presented in Table 9 in the Appendix, where we give - for each of the four selected faint SN progenitors - the explosion parameters, the thermodynamical properties, the metal yields of the key elements in the nucleation process, the total amount of dust and the masses of molecules. Similarly to Marassi et al. (2014) we find that for all the progenitor models investigated, the only grain species that is able to condense and grow is amorphous carbon. This is a consequence of the extensive fallback, which determine an ejecta composition dominated by carbon atoms, with an amount of Mg, Si and Al which is too low to enable the condensation of other grain species (Marassi et al. 2014). We find that the molecular reactions involving SiO are negligible. The mass of AC is in the range , depending on the initial carbon abundance and on the mean ejecta density and temperature evolution. Due to the interplay of these quantities it is not possible to establish a direct correspondence between progenitor mass, ejected mass and the dust mass produced. As shown in Marassi et al. (2014), AC grains do not forms if the formation channels of carbon monoxide are efficient in subtracting carbon atoms from the ejecta, and this efficiency is greater when the mean ejecta density is larger. As a consequence, we note that HE0557-4840 have the greater condensation efficiency but the smaller AC mass produced. Equally important is the temperature evolution which, in the case of HE0107-5240, enables the formation of , subtracting C atoms from the ejecta.

In faint SNe, mixing occurs due to Rayleigh-Taylor instabilities up to a mass-coordinate that is very close to the mass-cut (Umeda & Nomoto 2002); as a consequence, the material beyond the mass-cut is likely to be stratified, and dust nucleation in unmixed ejecta gives a more reliable estimates of the total mass of dust produced. Table 10 shows the results for the unmixed ejecta model. For three of the four progenitor models, the stratified ejecta is composed of two layers A and B that have different average temperature, density and chemical composition. In particular, in all three unmixed models analyzed, the internal layers A have mean ejecta density larger compared to the external layers B, enabling a very efficient formation of CO which inihibits the formation of AC.

The consequence of stratification is a reduction of the total mass of dust produced, that ranges between . In the left panel of Fig. 11, we plot the total mass of dust before the passage of the reverse shock for mixed and unmixed models. Similarly to what done in Section 4, we have studied the impact of the reverse-shock on the above dust masses. The grain sizes originally follow a log-normal distribution in the range . As expected, after the passage of the shock the distribution flattens and shifts to lower grain sizes, due to the erosion of the larger grains caused by sputtering. In the central and right panels of Fig. 11, we show the mass of dust that survives in uniformly mixed and stratified ejecta models, respectively. We find that, depending on the progenitor model, dust can be totally destroyed (as in the case of ) or that between 10 to 80 of the original mass can survive. The passage of reverse shock in the unmixed case is less destructive than in the case of the fully mixed model. As discussed in Section 4, dust in external layers is highly affected by the reverse shock. On the contrary dust produced in internal layers, as in the case of , is able to survive in large quantities, finding itself in milder conditions compared to the external layers.

Figure 12: Mass of the SN progenitor, of the remnant, of metals and dust mass as a function of the progenitor mass for standard (left panel) and faint (right panel) Pop III SNe. Note that the mass of metals and dust have been multiplied by (see text).

7 Conclusions

In this study we have estimated the dust mass produced in the early Universe by Pop III standard and faint core-collapse SNe. For standard core-collapse events, which do not experience a strong fallback, the metal-free progenitors are calibrated to reproduce the average elemental abundances of Galactic halo stars with . We have enlarged our study to include Pop III faint SNe, which are fine-tuned to reproduce the abundance patterns observed on the surface of the sub-sample of carbon-enhanced hyper iron poor stars.

To estimate the dust mass produced that survives the subsequent impact of the reverse shock, we have updated the previously developed code of Bianchi & Schneider (2007) to include formation/destruction processes of CO, SiO, and molecules that are crucial in subtracting gas-phase elements from the ejecta. We have investigated how our poor knowledge of mixing can affect the resulting dust yields by analyzing both uniformly mixed and stratified ejecta. Finally, to have a more realistic estimate of the dust mass that will be injected into the ISM, we have analized the effect of the passage of the reverse-shock. Our main results are that:

  • Standard core-collapse Pop III SNe are efficient dust producers when the ejecta are uniformly mixed; the newly formed dust mass ranges between [0.18 - 3]  M and is dominated by silicates. Depending on the density of the interstellar medium, the impact of the reverse shock on the newly formed dust is to reduce the original dust mass by a factor which ranges between to , changing the relative abundance of different dust species. The mass of dust produced depends on the degree of mixing experienced by the ejecta. In general, silicates, magnetities and alumina grains are formed in the internal layers, while amorphous carbon forms only in the external layers that are carbon and oxygen dominated. In stratified ejecta dust does not form at the same time in each layer, with silicates forming in the inner layers before AC in the external ones. For the same SN progenitor model, the mass of dust formed in unmixed ejecta can be smaller or higher than in the corresponding mixed case, with variations which amount to .

  • We confirm the results found by Marassi et al. (2014) that dust can form in the ejecta of faint Pop III SNe. As a consequence of the larger fallback experienced with respect to standard core-collapse Pop III SNe, the ejecta is lacking in silicate, magnesium and alumina and the only dust grain that forms is amorphous carbon. The total amount of carbon dust produced in the uniformly mixed case varies between []M, and in the stratified case between []M depending on the model. After the passage of the reverse shock, the dust that survives ranges between to .

    The mass and composition of dust formed in the ejecta of Pop III SNe depends on the degree of fallback. In standard Pop III SNe, the mass-cut corresponds to a mass coordinate in the range . As a result, almost all the mantle is ejected with a greater amount of internal elements, such as silicon and magnesium, favoring the condensation of silicates. The observed elemental abundances of CEMP stars with require Pop III SN progenitors with masses in the range which experience a strong fallback, with mass-cut which correspond to mass coordinates in the range . These faint SNe leave a much larger remnant behind and eject a smaller amount of metals, with mantles dominated by light elements. These properties of the SNe largely affect the mass and composition of dust which condense in the ejecta, as shown by Fig. 12, where we summarize our results showing the mass of metals and of the dominant grain species produced by standard (left panel) and faint (right panel) Pop III SNe. Note that for each SN model, we have rescaled the mass of metals and dust as and , to clearly display these physical quantities.

    Finally we have constructed, starting from our set of metal-free progenitors, a dust data grid for Pop III SNe which provides the initial conditions required to simulate the properties of the first metal-enriched star forming regions at high-redshift. In addition, we plan to extend this analysis to higher metallicity to incorporate these new mass- and metallicity-dependent yields in chemical evolution models with dust.


We thank the anonymous Referee for her/his careful reading of the manuscript and useful comments. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 306476. We aknowledge financial support from PRIN MIUR 2010-2011, project “The Chemical and dynamical Evolution of the Milky Way and Local Group Galaxies”, prot. 2010LY5N2T


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Appendix: Final dust grids and tables

In this appendix we report all the useful tables: for all progenitors we report chemical composition (yields), mass of molecules, mass of dust etc.

Pop III SN - Fully Mixed Ejecta Models
0.65 0.896 1.25 1.45 3.36 5.66
- - - - - - - -
- - - - -
- - - - - - - -
- - -
- -
Table 3: Properties of the Pop III SNe, including the explosion energy [ erg], the ejecta velocity [], the mass of the ejecta, the mass cut and the mass of the helium core [], the gas number density [] and the radius of He core, [cm] at [sec] when adiabatic expansion starts (see text); the initial masses of C, O, Mg, Si, Al, Fe, and Ni which decays in Co fueling -luminosity (see eq. 2), the mass of molecules, CO, SiO, , and the grains formed in the expanding ejecta []. Each model name identifies the progenitor mass.
Unmixed Ejecta Model
=0.7 = 3.40 = 2960 = 13.38
zone A zone B zone C
- -
- -
- - -
- -
- -
- - -
- -
- -
- -
Table 4: Properties of the 15 Pop III SN unmixed ejecta model. In unmixed models and are the mean radius and density of the layers.
Unmixed Ejecta Model
=1.6 = 7.22 = 3086 = 28.14
zone A zone B zone C
- -
0.22 - -
- - -
- - -
- -
- - -
- -
- -
- - -
Table 5: Properties of the 30 Pop III SN unmixed ejecta model.
Unmixed Ejecta Model
=2.6 = 18.11 = 3017 = 47.84
zone A zone B zone C
- -
- -
- -
- - -
0.46 3.46
- - -
- - 0.12
- -
0.26 -
0.20 - -
0.82 - -
- -
0.31 - -
1.61 0.12
Table 6: Properties of the 50 Pop III SN unmixed ejecta model.
Pop III SN - Reverse Shock - Fully Mixed Ejecta Models
0.10 - - -
- -
0.17 0.39 0.24 0.27
0.15 0.37 0.47
- - -
- -
0.16 0.17