Abstract
Dust-obscured star formation has dominated the cosmic history of star formation, since \(z \simeq 4\). However, the recent finding of significant amount of dust in galaxies out to \(z \simeq 8\) has opened the new frontier of investigating the origin of dust also in the earliest phases of galaxy formation, within the first 1.5 billion years from the Big Bang. This is a key and rapid transition phase for the evolution of dust, as galaxy evolutionary timescales become comparable with the formation timescales of dust. It is also an area of research that is experiencing an impressive growth, especially thanks to the recent results from cutting edge observing facilities, ground-based, and in space. Our aim is to provide an overview of the several findings on dust formation and evolution at \(z > 4\), and of the theoretical efforts to explain the observational results. We have organized the review in two parts. In the first part, presented here, we focus on dust sources, primarily supernovae and asymptotic giant branch stars, and the subsequent reprocessing of dust in the interstellar medium, through grain destruction and growth. We also discuss other dust production mechanisms, such as Red Super Giants, Wolf–Rayet stars, Classical Novae, Type Ia Supernovae, and dust formation in quasar winds. The focus of this first part is on theoretical models of dust production sources, although we also discuss the comparison with observations in the nearby Universe, which are key to put constraints on individual sources and processes. While the description has a general applicability at any redshift, we emphasize the relative role of different sources in the dust build-up in the early Universe. In the second part, which will be published later on, we will focus on the recent observational results at \(z > 4\), discussing the theoretical models that have been proposed to interpret those results, as well as the profound implications for galaxy formation.
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1 Introduction
Dust is a fundamental component of the interstellar medium. Dust extinction and reddening at optical and UV wavelengths, as well as its thermal emission at infrared and sub-millimeter wavelengths, have important implications on the observational properties and detectability of galaxies, especially at high redshift. Dust has a fundamental role in the cooling of the interestellar medium and, therefore, facilitating the gravitational collapse, hence the formation of stars across a broad range of masses.
Dusty galaxies have been extensively studied in the local Universe and across the cosmic epochs. Obscured systems are found to dominate the cosmic star formation budget out to \(z \simeq 4\) (Zavala et al. 2017). This is an interesting timescale from a theoretical perspective; indeed, it is comparable with the timescales of some of the most prominent star formation processes, hence opening different scenarios on the relative contribution of various dust formation channels at such early epochs. Therefore, the first 1.5 Gyr after Big Bang represent a key and rapid transition phase in the production and processing of dust grains.
This area of research has recently experienced an impressive growth, especially thanks to the several recent observational results from the Atacama Large Millimeter/submilli-meter Array (ALMA) and from the James Webb Space Telescope (JWST), which have triggered the development of several models to explain the content and properties of dust in the early Universe, as well as their implications for galaxy formation and observability.
Although this field is evolving very rapidly, we believe that it is now a proper time to provide an overview of the several findings on early dust formation and evolution, and of the theoretical efforts to explain the observational results. As this is a massive area of research, we have organized the review in two parts.
The first part is presented here and aims at reviewing the landscape of the theoretical models of the possible sources of dust in the early Universe. This is meant to provide the essential backbone required for understanding the observations at high redshift, as well as the key ingredient for the models specifically aimed at interpreting in detail the high-redshift observations. In this part, we focus on the theoretical scenarios describing nucleation and growth of dust grains in different sources of dust, primarily various models for dust formation in atmospheres of Asymptotic Giant Branch (AGB) and Supernova (SN) ejecta. However, we will also discuss models of additional sources of dust that might be relevant in the early phases of galaxy formation, such as Red Super Giants, Wolf–Rayet stars, and also dust formed in the quasar-driven winds, and we will also discuss the dust reprocessing in the interstellar medium. Our presentation can be useful to describe dust formation and evolution at any redshift. However, we will emphasize their specific role in the context of the timescales available in the early Universe. Figure 1 gives a quick glimpse of the timescales involved in the dust formation associated with some of these sources (see Sect. 5 for more details); while the figure is highly incomplete, it serves to illustrate the timescales at play and why these sources of dust are relevant in different stages of galaxy formation in the early Universe, hence the motivation for this part of the review.
In this part of the review, we do not cover in detail the observational aspects associated with the sources of dust, through the extensive observational studies of dust formation and destruction in various classes, which would require a separate review, and out of the scope of our primary goals of providing the information for the early Universe. However, we do briefly compare the expectations of different theoretical models with observations, which are mostly confined in the nearby Universe, for each category of dust sources.
In the second part of the review, which will be published later on, we will focus on the recent observational results investigating the dust content and properties in different classes of galaxies at \(z > 4\), out to the earliest epochs for which such constraints have been obtained. We will also discuss the theoretical models and cosmological simulations that have been proposed to interpret those results, as well as the profound implications for galaxy formation.
We clarify that this is not, by any means, the first review on the dust sources and dust reprocessing. Many other extensive reviews have been presented in the past, starting from Draine (2003), which discussed the observed properties of interstellar dust grains (wavelength-dependent extinction, scattering, emission, and polarization), and their implications for dust models (Draine 2009); dust production by supernovae (Gall et al. 2011; Sarangi et al. 2018), and its subsequent processing and survival in supernova remnants (Micelotta et al. 2018); dust formation and mass loss of stars on the asymptotic giant branch (Höfner and Olofsson 2018); and the properties of dust in the interstellar medium of nearby galaxies (Galliano et al. 2018), which provide an invaluable laboratory to explore fundamental dust processes across a diversity of environmental conditions (metallicity, star formation activity, etc.), hence constituting a necessary intermediate step toward understanding distant galaxies.
Here, we leverage on those reviews, by expanding and updating them in some areas, with the specific focus of exploring the nature and origin of dust in the early Universe.
2 Supernovae
2.1 Models of dust formation in supernova ejecta
Since the explosion of SN1987A, direct observations of dust formation in core-collapse SNe have motivated theoretical investigations of dust condensation in SNe. Three main approaches have been followed, with increasing degree of complexity.
2.1.1 Classical nucleation theory
The simplest approach adopts the so-called classical nucleation theory (CNT), which was first applied by Kozasa et al. (1989, 1991) to model dust formation in SN 1987A. In CNT, when a gas becomes supersaturated, particles (monomers) aggregate in a seed cluster that subsequently grow by accretion of other monomers.
For grain materials whose molecules are not present in the gas phase, the rates of nucleation and grain growth are controlled by one chemical species, which is referred to as the key species. This is the species of the reactants that has the least collisional frequency onto a target nuclei (Kozasa and Hasegawa 1987). Under these conditions, the steady-state nucleation rate (that is the number of critical clusters formed per unit volume and unit time) is given by
and the grain growth rate is
In these expressions, \(\alpha\) is the sticking coefficient (the probability that when a collision occurs, the collider sticks to the target), \(\varOmega = 4/3 \pi a_0^3\) is the volume of the monomer of the key species in the condensed phase, \(\sigma\) is the surface tension of the condensed material, \(m_{{\rm k}}, c_{{\rm k}},\) and \(v_{{\rm k}}\) are the mass, concentration, and velocity of the key species monomers, \(\upmu = 4 \pi a_0^2 \sigma /(k_B T)\) is a parameter, T is the ejecta temperature, and S is the super-saturation ratio, expressed as
where \(\varDelta G_{{\rm r}}\) is the Gibbs free energy for the condensation reaction \(\varSigma _i \nu _i \, A_i =\) solid (\(A_i\) are the chemical species of the reactants and products in the gas phase and \(\nu _i\) are the stoichiometric coefficients, which are positive for the reactants and negative for the products), and \(P_i\) are the partial pressures of the ith species.
The grain properties that are generally included in SN dust formation models are reported in Fig. 2.
The presence of CO and SiO molecules in SN ejecta is very important for dust formation, because carbon atoms bound in CO molecules are not available to form Amorphous Carbon (AC) grains and SiO molecules take part in the reactions that lead to the formation of oxide grains, such as MgSiO\(_3\), Mg\(_2\)SiO\(_4\), and SiO\(_2\). In some of the models, the CO and SiO abundance is computed under the assumption of chemical equilibrium, balancing radiative association rates with destruction rates through collisions with energetic electrons and, for SiO, charge transfer with positive Ne ions (Todini and Ferrara 2001; Schneider et al. 2004). Other models have computed the CO and SiO abundance under non-steady-state conditions (Bianchi and Schneider 2007), including in the reaction network additional species, such as C\(_2\) and O\(_2\), and bimolecular neutral–neutral reactions (Marassi et al. 2014, 2015, 2019). When applied to the same SN progenitor, the CO abundance predicted by this upgraded molecular network at the onset of dust nucleation is in good agreement with the result of chemical kinetic model (Sarangi and Cherchneff 2013; see Sect. 2.1.3). Finally, some of the models perform dust formation calculations assuming that the formation of CO and SiO molecules is complete, so that no carbon-bearing grains condense if C/O \(< 1\), and no Si-bearing grains—except for oxide grains—condense if Si/O \(< 1\) (Nozawa et al. 2003, 2010).
In general, at the beginning of the nucleation process, the gas is moderately supersaturated, the nucleation rate is small, and large seed clusters, made of N monomers, tend to form. Due to the expansion, the volume of the ejecta increases, and the super-saturation rate grows and smaller clusters form with a larger formation rate. This occurs until the gas becomes sufficiently rarefied (because of expansion and/or exhaustion of monomers in the gas phase), and the formation rate drops. This sequence of events, together with accretion, results in a typical log-normal-like grain size distribution (Bianchi and Schneider 2007).
Thanks to its relative simplicity, CNT has been applied to perform systematic explorations of dust condensation in 1D spherically symmetric SN explosion models with varying progenitor mass, metallicity, rotation rate, explosion energy, and supernova type. Todini and Ferrara (2001) used it to model dust formation in core-collapse supernovae starting from the grid of explosion models by Woosley and Weaver (1995), hence assuming progenitors masses in the range \([12 - 40] \, M_\odot\), and initial metallicities \(Z = 0, 10^{-4} Z_\odot , 10^{-2} Z_\odot , 1 Z_\odot\). Using the same grid of SN explosion models, Bianchi and Schneider (2007) explored the additional effect of the partial destruction by the SN reverse shock (see Sect. 2.3 for more details). CNT has been also applied to explore dust formation in pair-instability (Schneider et al. 2004) and faint SN explosions (Marassi et al. 2014) with massive metal-free (Population III) stellar progenitors, to provide a formation pathway of iron-poor stars in the Galactic halo (see, e.g., de Bennassuti et al. 2017), and to explain their observed surface elemental abundances. Finally, Marassi et al. (2019) has applied CNT on a new extensive grid of core-collapse SN models (Limongi and Chieffi 2018)Footnote 1 to investigate how metallicity, rotation, and fallback impact the nucleosynthetic output of the explosion, and the total mass, size, and composition of dust formed in the ejecta.
The applicability of CNT in astrophysical environments has been questioned due to the lack of chemical equilibrium resulting from the low number density (and collision rate) of monomers (Donn and Nuth 1985). However, recent calculations show that even when the number of critical clusters was artificially depressed far below than the value predicted by CNT, the resulting grain size distribution and mass are little affected, with changes in the mean grain radius smaller than 15% (Paquette et al. 2011). In addition, Nozawa and Kozasa (2013) have demonstrated that a steady-state nucleation rate is a good approximation in SN ejecta, at least until the collisional timescales of the key species \(\tau _{{\rm coll}}\) are much smaller than the timescale with which the super-saturation ratio increases, \(\tau _{{\rm sat}}\); otherwise, the effects of non-steady state lead to lower condensation efficiencies and larger average radii of newly formed grains. Since the dust destruction efficiency by the SN reverse shock heavily depends on the grain size distribution (see Sect. 2.3), the knowledge of the size distribution of newly formed dust is critical to predict the mass and sizes of grains that survive and enrich the interstellar medium (ISM). The analysis performed by Nozawa and Kozasa (2013) shows that the steady-state nucleation rate is applicable only if \(\varLambda (t_{{\rm on}}) \equiv \tau _{{\rm sat}}(t_{{\rm on}})/\tau _{{\rm coll}}(t_{{\rm on}}) \gtrsim 30\), and \(\varLambda (t_{{\rm on}})\) can be expressed as a function of the gas density and temperature at the time \(t_{{\rm on}}\) when dust formation startsFootnote 2. When applied to the physical conditions predicted by Type-IIp or Type-IIb SN models, \(\varLambda (t_{{\rm on}})\) is generally found to be \(\gtrsim 100\), and the steady-state approximation is found to be appropriate.
2.1.2 Kinetic nucleation theory
A second method to model dust formation in SN ejecta is the so-called kinetic nucleation theory (KNT). Compared to CNT, KNT is more realistic as it does not assume a steady state between condensation and evaporation: the condensation rate of clusters of \(N \ge 2\) atoms is computed from kinetic theory and the evaporation rate by applying the principle of detailed balance. The method is fully described in Nozawa et al. (2003) where it has been applied to model dust formation in Population III core-collapse SN explosions with progenitor masses \([13 - 20] \, M_\odot\) and in pair instability SN explosions with progenitor masses of 170 and \(200 \, M_\odot\).
Dust formation is expected to depend on the type of core-collapse SN explosion, and in particular on the mass of the outer H-rich envelope (Kozasa et al. 2009). A less massive outer envelope leads to larger expansion velocities of the He-core, causing a rapid decrease in the temperature and density of the expanding ejecta. Investigation of dust formation applying KNT to a SN-Ib explosion model similar to the observed SN 2006jc (Nozawa et al. 2008), and to a SN-IIb explosion model similar to Cas A (Nozawa et al. 2010), show that dust formation can occur earlier than in Type-IIp SN explosions, the total dust mass formed is comparable, but the grain sizes are strongly reduced, with important implications for their destruction by the reverse shock (see Sect. 2.3). An exploration of the dependence of dust formation on the properties of the SN explosions (progenitor mass, explosion energy) has been recently carried out by Brooker et al. (2022), who applied KNT to a large database of SN explosion models based on the work by Fryer et al. (2018), with 15, 20, and 25 \(M_\odot\) progenitor masses and covering a wide range of explosion energies. They generally find that the bulk of dust production, irrespective of individual grain species, occurs earlier for more energetic explosions, as these explosions evolve more rapidly owing to higher initial kinetic velocity. As a result, for a given progenitor mass, there is also a clear dependence of grain size of individual species on the explosion energy, where less energetic models ultimately produce larger dust grains, as their ejecta experience the physical conditions amenable to dust production over a longer period of time. Because the energy of the SN explosion sensitively impacts the resulting nucleosynthesis, both the dust composition and dust mass are found to depend on the explosion energy, consistent with the previous findings (Marassi et al. 2019).
Despite the encouraging results discussed above, CNT and KNT do not consider the actual chemical pathway that leads to the formation of the molecular precursors and seed nuclei. To overcome this limitation, Lazzati and Heger (2016) developed a formalism that is able to join the chemical phase with the grain growth phase using KNT. As a proof of concept, they applied this hybrid approach to the formation of carbonaceous grains in the ejecta of a 15 \(M_\odot\) SN explosion with initial solar metallicity. Compared to CNT, they find a more gradual dust formation, extending from a few months up to a few years after the explosion, in closer agreement with observations of local SN remnants (see Sect. 2.4).
2.1.3 Molecular nucleation theory
The third method to compute dust formation is the chemical kinetics model or molecular nucleation theory (MNT), where the chemical pathway proceeds through simultaneous phases of nucleation and condensation. The nucleation phase, which leads to the formation of molecular and cluster precursors, is described by an extended non-equilibrium chemical network. In the condensation phase, the small clusters formed in the gas phase condense through coagulation and coalescence to form large grains, provided that suitable conditions are met. The method was introduced by Cherchneff and Lilly (2008), which applied it to investigate the nucleation phase in the ejecta of a Population III pair-instability supernova explosion with progenitor mass of 170 \(M_\odot\). Cherchneff and Dwek (2009) and Cherchneff and Dwek (2010) applied the same approach to investigate the formation of molecules and early dust precursors in the ejecta of Population III supernova explosions with progenitor masses of 20 and 170 \(M_\odot\), studying the effect of different levels of heavy element mixing in the ejecta. The model was then applied to the stratified ejecta of Type-IIp SN explosions with progenitor masses of 12, 15, 19, and 25 \(M_\odot\) and initial solar metallicity (Sarangi and Cherchneff 2013), and then extended from the nucleation phase to the condensation phase by Sarangi and Cherchneff (2015). In this approach, the condensation phase occurs through coagulation between small clusters rather than grow through adsorption of gas monomers or molecules, as in CNT, KNT, and in the hybrid model by Lazzati and Heger (2016). In the latter model, it is found that monomers are more abundant than clusters, and, being lighter, have a larger thermal velocity that makes collisions more frequent. The formation of large grains likely requires coagulation and growth to be taken into account simultaneously in the condensation phase (see Sluder et al. 2018 and the discussion below).
In all the models described above, the physical properties of the expanding SN ejecta were based on fully mixed one-zone models or on 1D spherically symmetric models where the elemental abundances are distributed in concentric shells, with different degrees of mixing and a uniform or clumpy gas distribution. Attempt to incorporate dust formation into more sophisticated description of the ejecta has been made by Sluder et al. (2018), who developed a model to account for anisotropic \(^{56}\)Ni dredge-up, the so-called “nickel bubbles”, that arise as a consequence of the strongly a-spherical explosion geometry (see Sluder et al. 2018 and references therein). Using MNT in a framework where the nucleation phase is joined to the condensation phase through both coagulation and grain growth, they modeled dust formation in SN1987A adopting a \(25 M_\odot\) core-collapse SN model with LMC initial metallicity (\(Z = 0.007\)).
2.1.4 Models’ comparison
A comparison between the predictions of all these theoretical models is shown in Fig. 3. For each model, we report the total mass of dust predicted in core-collapse SN explosions with different initial progenitor masses (hereafter we refer to \(m_{{\rm star}}\) as the zero-age main sequence stellar mass) and assuming that stars have initially a solar metallicity (except for the model by Sluder et al. 2018). When reporting the results of each study, we attempted to select the SN models with explosion energies as close as possible to \(10^{51}\) erg. The predicted dust masses are scattered between \(\sim 0.03 \, M_\odot\) and \(\sim 1 - 2 \, M_\odot\), with no clear coherent trend. In general, at least for the few stellar progenitors where the comparison is possible, models based on CNT (Bianchi and Schneider 2007; Marassi et al. 2019) (represented with the blue color palette) tend to predict larger dust masses compared to models based on MNT (Sarangi and Cherchneff 2015, red color palette) or on KNT (Lazzati and Heger 2016; Brooker et al. 2022, pink and violet). Note, however, that the results of Brooker et al. (2022) and Sluder et al. (2018) for the \(25 \, M_\odot\) progenitor are very close to what expected on the basis on CNT by Bianchi and Schneider (2007). At the same time, the comparison between the results of Bianchi and Schneider (2007) and Marassi et al. (2019) shows that—even assuming a very similar approach to follow dust formation—the resulting dust masses are sensitive to the adopted SN explosion models and to the assumed rotation rate of the progenitor star, at least for stars with initial masses \(\le 25 \, M_\odot\). Similarly, assuming a clumpy rather than a homogeneous ejecta can increase the dust mass by almost 0.5 dex for the same progenitor mass (see the difference between the dark and light red points, corresponding to the clumpy and homogeneous ejecta model for a \(19 \, M_\odot\) progenitor predicted by Sarangi and Cherchneff 2015). The figure also shows that the most efficient dust factories are SN explosions from low-mass rotating stellar progenitors (\(13-15 \, M_\odot\)), as a consequence of rotational mixing, which leads to more metal-enriched ejecta. This also causes stronger mass loss by stellar winds in the pre-SN evolution of more massive progenitors (\(\gtrsim 20 \, M_\odot\)), reducing the mass of the ejecta and of the newly synthesized dust compared to non-rotating models. Finally, above \(\sim 30 \, M_\odot\), the strong fallback experienced during the SN explosion is the main limiting factor to dust production, at least in models based on CNT.
In Fig. 4, we show a comparison of the grain composition predicted by different theoretical models when applied to SN explosions with three initial progenitor masses, \(15 \, M_\odot\) (top row), \(19-22 \, M_\odot\) (middle row), and \(25 \, M_\odot\) (bottom row). The symbols and color-coding of theoretical models are the same as the one adopted in Fig. 3. Here, we have broadly classified the grain species into carbon grains, silicates (which comprise enstatite, MgSiO\(_3\), forsterite, Mg\(_2\)SiO\(_4\), silicon dioxide SiO\(_2\), pure silicon, Si, and silicon carbide, SiC), and other grain types, which comprise alumina (Al\(_2\)O\(_3\)), pure iron (Fe), iron sulfide (FeS), iron oxide (FeO), magnetite (Fe\(_3\)O\(_4\)), pure magnesium (Mg), and magnesia (MgO). The figure shows that a large variety of grain species are predicted to form. For the SN model with \(15 M_\odot\) progenitor, all the non-rotating models predict the formation of more carbon grains than silicates, although the mass of carbon dust depends on the dust formation scheme adopted, being larger for models based on CNT (Bianchi and Schneider 2007; Marassi et al. 2019), and becoming progressively smaller for models based on KNT (Lazzati and Heger 2016; Brooker et al. 2022) and MNT (Sarangi and Cherchneff 2015). For rotating models, instead, the abundance of heavier and more internal elements is very sensitive to rotational mixing, and the dominant grain species in the \(15 M_\odot\) model are predicted to be magnetite and forsterite. Even for non-rotating models, silicate formation by the \(15 \, M_\odot\) progenitor depends on the adopted SN explosion model, being negligible for Bianchi and Schneider (2007) and Brooker et al. (2022), and small but not negligible for Sarangi and Cherchneff (2015) and Marassi et al. (2019), despite the different microphysical approach to dust nucleation adopted in the latter models. Similar considerations apply for the 20 and \(25 M_\odot\) progenitorsFootnote 3. All the models predict the formation of carbon, silicates, and other grains, with masses that are larger when CNT is adopted.
2.2 The case of SN 1987A
When comparing the predictions of different SN dust models, it is important to consider the grain size distributions expected for different grain species. In fact, depending on the properties of the ejecta and on the timing of dust nucleation, the condensation phase via coagulation and/or accretion may lead to very different predictions regarding the characteristic grain sizes. This aspect is important when comparing with observational indications of the time evolution of dust formation in young SN remnants, and to estimate the fraction of newly formed dust that will be able to survive the passage of the reverse shock, with larger grains generally being more resistant to destruction (see Fig. 20 in Kirchschlager et al. 2023 for a discussion on the impact of gas density and magnetic field on the survival fraction of grains as a function of their sizes).
To this aim, we selected a few studies where the supernova model (progenitor mass, metallicity, and explosion energy) has been chosen to provide a fair counterpart to SN 1987A (Sarangi and Cherchneff 2015; Bocchio et al. 2016; Sluder et al. 2018; Brooker et al. 2022). Depending on the model, both the time evolution of dust formation and the final dust mass, composition and sizes, can vary significantly. Bocchio et al. (2016) select a \(20 \, M_\odot\) progenitor exploding with an energy of \(10^{51}\) erg, and releasing a \(^{56}\)Ni mass of \(0.075 \, M_\odot\). Using CNT, they find that \(0.84 \, M_\odot\) of dust forms in the ejecta (see their Table 2), mostly composed by Mg\(_2\)SiO\(_4\) (\(0.43 \, M_\odot\)), SiO\(_2\) (\(0.19 \, M_\odot\)), Fe\(_3\)O\(_4\) (\(0.11 \, M_\odot\)), and carbon grains (\(0.07 \, M_\odot\)). The grain species follow a log-normal-like size distribution function, with central (peak) grain size which depends on the grain species, and which is larger for carbon grains (90.4 nm), Mg\(_2\)SiO\(_4\) (68.9 nm) and SiO\(_2\) (55.5 nm), and smaller for Fe\(_3\)O\(_4\) (9.3 nm), reflecting the ejecta initial composition, and the timing of dust nucleation.
A similar SN model was considered by Brooker et al. (2022) (see their M20cE1.00 model). Using KNT, they find that \(0.0378 \, M_\odot\) forms, mostly in the form of carbon (\(0.0237 \, M_\odot\)), forsterite (\(4.44 \times 10^{-3}\, M_\odot\)) and alumina grains (\(9.61 \times 10^{-3} \, M_\odot\)). They do not show the time evolution of the dust mass and the final grain size distribution for this specific model, but based on the results of other \(20 \, M_\odot\) SN models with the closest explosion energies, they predict silicate (carbon) grains to form \(\sim 400\) (\(\sim 900\)) days after the explosion, and average grain sizes which range from \(\sim 2 - 7 \upmu\)m (\(\sim 0.8 - 3 \upmu\)m) for forsterite (alumina) grains, to \(\sim 8 - 10 \upmu\)m for carbon grains. Hence, not only the total dust mass and composition is different, but also the average grain sizes are considerably larger compared to Bocchio et al. (2016).
The results of SN 1987A models based on MNT have been discussed by Sluder et al. (2018) (see their Sects. 7.1 and 7.2), who compare their 20 \(M_\odot\) SN model with the 19 \(M_\odot\) clumpy SN model considered by Sarangi and Cherchneff (2015). In Figs. 5 and 6, we show the mass evolution as a function of the post-explosion time for different grain species as predicted by Sarangi and Cherchneff (2015) and Sluder et al. (2018), respectively. In the same figures, we also show the dust mass per logarithm of the radius (\(dM/d{\rm ln}\,a\)) for different species at the end of the simulations. This corresponds, respectively, to \(t = 2000\) days and \(t = 10^4\) days after the explosion.
At 2000 days after the explosion, the total dust mass predicted by Sluder et al. (2018) is 0.44 \(M_\odot\), while it is 0.14 \(M_\odot\) in the model by Sarangi and Cherchneff (2015). This difference is attributed to the effect of grain growth by accretion, which is not considered by Sarangi and Cherchneff (2015). The final dust composition predicted by Sarangi and Cherchneff (2015) is dominated by forsterite (\(5.3 \times 10^{-2} M_\odot\)), pure magnesium (\(2.6 \times 10^{-2} M_\odot\)), alumina (\(1.8 \times 10^{-2} M_\odot\)), pure silicon (\(1.2 \times 10^{-2} M_\odot\)), and iron (\(1.2 \times 10^{-2} M_\odot\)). Carbon grains represent only \(\sim 5.3 \%\) of the total dust mass (\(7.3 \times 10^{-3} M_\odot\)).
In the model by Sluder et al. (2018), the dust mass at the end of the simulation (\(10^4\) days) is 0.51 \(M_\odot\), mostly composed by magnesia (0.16 \(M_\odot\)), pure silicon (\(0.15 \, M_\odot\)), forsterite (\(9 \times 10^{-2} \, M_\odot\)), iron sulfide (\(3.8 \times 10^{-2} \, M_\odot\)), carbon (\(3 \times 10^{-2} \, M_\odot\)), and silicon dioxide (\(2.2 \times 10^{-2} \, M_\odot\)).
In both models, dust formation starts at 100–200 days after the explosion, but for most species appears to be more gradual in Sluder et al. (2018), as a consequence of the lower densities in the ejecta compared to Sarangi and Cherchneff (2015). The overall evolution of forsterite, alumina, iron sulfide, pure iron, and silicon grains appears similar, despite the resulting masses are different. A striking difference is that C and SiC grains start to form at \(\sim 300\) days in Sluder et al. (2018) and only at \(\sim 900\) days in Sarangi and Cherchneff (2015), and that magnesium grains do not form in Sluder et al. (2018) due to the rapid formation of magnesia grains. These differences may be due to the different SN model considered, as well as to the inclusion of additional physical processes in Sluder et al. (2018), such as accretion of the grains, grain sublimation, and grain charge (which may affect the coagulation rate, see Sluder et al. 2018 for more details).
If we compare the final dust mass distribution as a function of the grains radii, we find that the peak radii agree to within a factor of a few for some grain species (forsterite, carbon, alumina, iron, and iron sulfide), while they differ significantly for others (silicon). In general, the bulks of the grains are found to have radii ranging between \(\sim 10^2\) to \(\sim 5 \times 10^4\) Å in Sluder et al. (2018), and between \(\sim 10^2\) to \(\sim 5 \times 10^3\) Å in Sarangi and Cherchneff (2015). These figures extend to significantly larger radii compared to the predictions of Bocchio et al. (2016), but are at the lower end of the range of grain sizes obtained by Brooker et al. (2022). It is hard to discriminate to what extent these differences can be attributed to the different microphysical processes implemented in the various models, and to what extent these depend on the adopted physical properties of the expanding SN ejecta. Whatever the cause, these differences have important consequences for grain survival and ejection in the ISM.
It is important to comment on the comparison between model predictions and observations of dust formation in SN 1987A. This can be done by looking at the left panel of Fig. 6, where observationally estimated dust masses are reported by the colored data points, as explained in the legend. These values have been obtained by fitting the observed spectral energy distribution (SED) at different epochs, as derived from observations made by the Kuiper Airborne Observatory (KAO) at \(t = 60\), 250, 415, 615, and 775 days after the explosion (Wooden et al. 1993), and at later time by Spitzer (\(t \gtrsim 5800\) days, Dwek et al. 2010), Herschel (\(t \gtrsim 8000\) days, Matsuura et al. 2011, 2015), and ALMA (\(t \gtrsim 9000\) days, Indebetouw et al. 2014; Cigan et al. 2019).
The analyses have been made under different assumptions and using different methodologies. Wesson et al. (2015) use a 3D radiative transfer model to fit the SED, finding a gradual increase in the dust mass, from \(0.001\,M_\odot\) at 615 days, \(0.02\,M_\odot\) at 1300 days, \(0.6\,M_\odot\) at 8515 days, to \(0.8\,M_\odot\) at 9200 days (see the red crosses in the left panel of Fig. 6 indicated by W15 in the legend). This gradual increase has been confirmed by Bevan and Barlow (2016) (green open squares, B16), who used a 3D Monte Carlo model to estimate the dust mass from the observed blueshifting of the emission lines.
None of the models that we have discussed above predict a sufficiently slow gradual increase of the dust mass to be in agreement with these findings. However, the above interpretation has been questioned by Dwek (2016); Dwek et al. (2019), who argued that dust grains could have formed promptly, but could be hidden in optically thick clumps. Using a simple analytic approach to estimate the probability that a photon can escape a dusty sphere, they estimated that at 615 days, the ejecta already contain \(0.4 M_\odot\) of enstatite and \(0.047 M_\odot\) of carbon dust, but the clumps are optically thick, and remain so until—at 8815 days—they become optically thin and enstatite and carbon grains have coagulated to form composite grains with masses \(0.42 M_\odot\) at 8815 days and \(0.45 M_\odot\) at 9090 days. Yet, studies based on radiative transfer modeling find it hard to hide early dust formation in clumps while at the same time reproducing the observed spectral energy distribution (SED) and emission line profiles of SN 1987A (Ercolano et al. 2007; Wesson et al. 2015; Bevan and Barlow 2016). After a large parameter exploration of dust models with pure composition and a variety of spatial configurations, Wesson and Bevan (2021) show that at an epoch of \(\sim 800\) days, a carbon dust mass of \(\sim 2 \times 10^{-3} M_\odot\), a clump volume filling factor of \(f = 0.05\), and grain radius \(a = 0.4 \upmu\)m is the only parameter set accounting for both the observed constraints on the SED and emission line profiles. Even if assuming carbon–silicate mixture would be consistent with a slightly higher dust mass, these constraints are still a factor of 50–100 below the masses estimated using the most recent observations of SN 1987A with Herschel (Matsuura et al. 2011, 2015) and ALMA (Indebetouw et al. 2014). Hence, these studies support a scenario in which dust formation in SN 1987A continues for many years after the supernova explosion and it is largely dominated by carbon grainsFootnote 4, at odds with most (if not all) the theoretical models. Note, however, that these results assume spherically symmetric ejecta, while the 3D distribution of H, He, O, Mg, Si, Ca, and Fe has been found by Larsson et al. (2016) to be sufficiently anisotropic at \(10^4\) yrs after the explosion to explain on its own the spectral line asymmetries that are generally attributed to dust (Bevan and Barlow 2016; Wesson and Bevan 2021).
A more general discussion on observations of SN remnants is presented in Sect. 2.4.
2.3 Dust processing and survival in supernova remnants
It has been known since many years that not all the dust newly formed in SN ejecta will be able to enrich the ISM. On longer timescales, compared to the ones discussed above, the ejecta where dust resides is crossed by the reverse shock generated by the interaction between the expanding SN blast wave and the ISM. Depending on the grain properties (compositions and sizes) and on its spatial distribution, the processing by the reverse shock can lead to significant dust destruction. The effective SN dust yield (the dust mass that survives the passage of the reverse shock) is expected to have a different total mass, composition, and grain size distribution compared to the newly formed grains that we have discussed above.
The processing and survival of dust formation in SN remnants have been recently reviewed by Micelotta et al. (2018), where an extensive description of the observational evidences and theoretical models can be found. Here, we provide a critical discussion of the main findings with the aim of providing a synthetic picture of our current understanding of the effective SN yield.
2.3.1 Physical processes at work
When dust grains are invested by the reverse shock, their interaction with gas particles and with other grains is mediated by different physical processes, such as: sputtering (grain collision with high-velocity atoms and ions which leads to the erosion of the grains via ejection of atoms from its surface), sublimation due to collisional heating to high temperatures, shattering (grain–grain collisions that lead to fragmentation in smaller grains), and vaporization (due to the intense heating generated during grain–grain collisions, that leads to partial or complete return of grain constituents to the gas phase). Sputtering is defined as kinetic when the collision velocities are determined by the relative motion between the grains and the gas (when the grain-gas relative velocity is much larger than the gas thermal speed, generally in cold/warm gas phase, with \(T \lesssim 10^4\) K), and as thermal when the collision velocities arise from the thermal motion of the gas (when the gas thermal speed is much larger than the grain-gas relative velocity, generally in the hot gas phase, with \(T \gtrsim 10^6\) K). Dust grains in the ionized shocked gas are heated mainly by collisions with electrons. If the grains are small, heating is stochastic and an equilibrium temperature does not exist. Instead, a broad temperature distribution establishes, but only a negligible fraction of the grains is found to exceed the sublimation temperatures (Bianchi and Schneider 2007).
The relative importance of these physical processes in SN remnants depends on the assumed initial dust spatial distribution: assuming a smooth, uniform distribution within the ejecta, Bocchio et al. (
Notes
The grid of SN models comprises progenitor masses in the range [13 - 120] \(M_\odot\) with initial equatorial rotational velocities of \(v = 0\) and \(v = 300\) km/s, and four different initial progenitor metallicities, \(Z = 10^{-3} Z_\odot , 10^{-2} Z_\odot , 10^{-1} Z_\odot , 1 Z_\odot\) (see Marassi et al. 2019 for more details).
Nozawa and Kozasa (2013) also provide fitting formulae to their non-steady-state models, that express the final average grain size and condensation efficiency as a function of \(\varLambda (t_{{\rm on}})\) and that can be used to estimate the typical size and mass of newly formed grains formed in different astrophysical environments.
Note that, according to Dwek et al. (2019), if most of the dust forms within 2 years after the explosion, and the IR emission from the dust is initially self absorbed, the lack of the 9.7 and 18 \(\upmu\)m silicate emission features in the spectra of SN 1987A is not evidence for the absence of silicate dust, but due to the large optical depth of the ejecta (Dwek and Arendt 2015).
The dust masses are \(\propto a^3\), so even a relatively small variation in the adopted grain sizes can lead to a significant variation in the inferred dust mass.
A star is classified as a C-star when carbon is more abundant than oxygen in its atmosphere. M-stars are oxygen-rich and S-stars are an intermediate class, when C/O \(\sim 1\).
Here, we have assumed a solar metallicity of \(Z_\odot\)=0.0142 (Asplund et al. 2009).
The total dust yields of TP-AGB stellar evolution models as a function of the stellar mass and metallicity are available online at https://ambrananni085.wixsite.com/ambrananni/online-data-1.
In Ferrarotti and Gail (2006), dust species that can react with hydrogen molecules can be chemi-sputtered and this process inhibits dust condensation unless \(T_{{\rm dust}} < 1000\)K.
All the ATON models are based on the full spectrum of turbulence and evolve at larger luminosities, on more expanded configurations, in comparison with their counterparts calculated with the traditional mixing length theory. This partially limits the efficiency of TDU for masses close to the limit for HBB (Ventura et al. 2014).
The adopted BH evolutionary tracks are meant to be indicative of possible evolutionary scenarios which lead to the formation of super-massive black holes powering the observed Active Galactic Nuclei (AGNs) and quasars at \(z \simeq 6\). See Inayoshi et al. (2020) and Volonteri et al. (2021) for recent reviews on early BH formation and growth.
A derivation of this expression can be found in McKee (1989) and in Slavin et al. (2015). It is based on the idea that the warm gas is confined into clouds (with filling factor \(f_{{\rm cloud}} = f_{{\rm w}}\)) embedded in the hot intercloud medium (with filling factor \(f_{{\rm h}}\)), and that the shocked cloud is at the same pressure of the shocked hot gas, so that \(\rho _{{\rm cloud}} v_{{\rm s,cloud}}^2 \simeq \rho _{{\rm h}} v_{{\rm s,h}}^2\), where \(\rho _{{\rm cloud}}\) (\(\rho _{{\rm h}}\)) and \(v_{{\rm s,cloud}}\) (\(v_{{\rm s,h}}\)) are the mass density and shock velocity in the cloud (hot gas). The cloud shocks can be radiative, but the blast wave in the hot gas is not. Hence, Eq. (15) in the hot phase can be written as: \(M_{{\rm s, h}} = f_{{\rm h}} \, \rho _{{\rm h}} \, V_{{\rm s}} = E_{{\rm SN}}/(\sigma v_{{\rm s, h}}^2)\), and the shocked cloud mass can be written as: \(M_{{\rm s, cloud}} = f_{{\rm cloud}} \, \rho _{{\rm cloud}} \, V_{{\rm s}} = (f_{{\rm cloud}}/f_{{\rm h}}) \, (\rho _{{\rm cloud}}/\rho _{{\rm h}}) \, M_{{\rm s, h}} = (f_{{\rm cloud}}/f_{{\rm h}}) \, E_{{\rm SN}}/(\sigma v_{{\rm s, c}}^2)\), which then leads to Eq. 16, with \(f_{{\rm eff}} = f_{{\rm cloud}}/f_{{\rm h}} = f_{{\rm w}}/f_{{\rm h}}\).
We do not show the results by Martínez-González et al. (2019) here, as they predict grain destruction timescales that are longer than the age of the Universe, when applied to Milky Way conditions.
Following De Vis et al. (2017), AGBs are assumed to condense 15% of their heavy elements into dust.
There is another set of model parameters that are fitted to each individual galaxy, and that control its particular star formation history (see Table 6 in Galliano et al. 2021).
Following Galliano et al. (2021), we adopt here a solar metallicity value of 12 + log(O/H) = \(8.69 \pm 0.05\), so that \(Z/Z_\odot = 2.04\times 10^{-9} \times 10^{(12+ \text {logO}/\text {H})}\).
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Acknowledgements
The authors dedicate this review to the memory of Stefania Marassi, a brilliant and enthusiastic scientist, who has given important contributions to the understanding of dust formation and survival in supernovae. She will be greatly missed. The authors are grateful to the referees for their careful reading and useful suggestions. The authors warmly thank Simone Bianchi, Ilse De Looze, Florian Kirchschlager, Fred Galliano, Mikako Matsuura, Hiroyuki Hirashita, Arka Sarangi, Isabelle Cherchneff, and John Slavin for their constructive and insightful comments, and for allowing us to reproduce some of their figures. RS thanks the Kavli Institute for Cosmology in Cambridge for their support and kind hospitality. RM acknowledges support by the Science and Technology Facilities Council (STFC), by the ERC through Advanced Grant 695671 “QUENCH”, and by the UKRI Frontier Research grant RISEandFALL. RM also acknowledges funding from a research professorship from the Royal Society.
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Schneider, R., Maiolino, R. The formation and cosmic evolution of dust in the early Universe: I. Dust sources. Astron Astrophys Rev 32, 2 (2024). https://doi.org/10.1007/s00159-024-00151-2
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DOI: https://doi.org/10.1007/s00159-024-00151-2