Dust formation history of galaxies: A critical role of metallicity* for the dust mass growth by accreting materials in the interstellar medium
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2012
Received: 7 November 2011
Accepted: 27 April 2012
Published: 12 March 2013
This paper investigates the main driver of dust mass growth in the interstellar medium (ISM) by using a chemical evolution model of a galaxy with metals (elements heavier than helium) in the dust phase, in addition to the total amount of metals. We consider asymptotic giant branch (AGB) stars, type II supernovae (SNe II), and dust mass growth in the ISM, as the sources of dust, and SN shocks as the destruction mechanism of dust. Furthermore, to describe the dust evolution precisely, our model takes into account the age and metallicity (the ratio of metal mass to ISM mass) dependence of the sources of dust. We have particularly focused on the dust mass growth, and found that in the ISM this is regulated by the metallicity. To quantify this aspect, we introduce a “critical metallicity”, which is the metallicity at which the contribution of stars (AGB stars and SNe II) equals that of the dust mass growth in the ISM. If the star-formation timescale is shorter, the value of the critical metallicity is higher, but the galactic age at which the metallicity reaches the critical metallicity is shorter. From observations, it was expected that the dust mass growth was the dominant source of dust in the Milky Way and dusty QSOs at high redshifts. By introducing a critical metallicity, it is clearly shown that the dust mass growth is the main source of dust in such galaxies with various star-formation timescales and ages. The dust mass growth in the ISM is regulated by metallicity, and we emphasize that the critical metallicity serves as an indicator to judge whether the grain growth in the ISM is the dominant source of dust in a galaxy, especially because of the strong, and nonlinear, dependence on the metallicity.
Stellar light, in particular at shorter wavelengths, is absorbed by dust and re-emitted as a far-infrared thermal emission from the dust (e.g., Witt and Gordon, 2000, and references therein). Therefore, dust affects the spectral energy distributions of galaxies (e.g., Takagi et al., 1999; Granato et al., 2000; Noll et al., 2009; Popescu et al., 2011). The existence of dust in galaxies also affects the star-formation activity. Dust grains increase the molecular-formation rate by two orders of magnitude compared to the case without dust (e.g., Hollenbach and McKee, 1979), and the interstellar medium (ISM) is cooled efficiently by molecules and dust. Consequently, star formation is activated drastically by dust. Hence, dust is one of the most important factors for the evolution of galaxies (e.g., Hirashita and Ferrara, 2002; Yamasawa et al., 2011).
The amount of dust in galaxies is one of the crucial factors to interpret the observational information of galaxies, since dust exists ubiquitously and the radiation from stars is always affected by dust attenuation. However, in spite of its importance, the evolution of the amount of dust has not been completely established yet. There are some key factors involved in understanding the dust evolution of galaxies. One of these is the ratio of the metal (elements heavier than helium) mass to the ISM mass, which is referred to as the “metallicity”. Since dust grains consist of metals, it is natural to think that the evolution of dust is closely related to metallicity. In general, galaxies are believed to evolve from a state with a very low metallicity and a very small amount of dust to one with higher amounts of metal and dust. Hence, it is mandatory to model the formation and evolution of dust grains in galaxies along with the evolution of metallicity (e.g., Dwek and Scalo, 1980; Hirashita, 1999a, b; Inoue, 2003; Yamasawa et al., 2011).
Dust grains are formed by the condensation of metals. A significant part of the metals released by stellar mass loss during stellar evolution, or supernovae (SNe) at the end of the life of stars, condense into dust grains. Dust grains not only originate from stars, but are also destroyed by SNe blast waves (e.g., Jones et al., 1994, 1996; Nozawa et al., 2003; Zhukovska et al., 2008). In addition, we should consider the dust mass growth in the ISM by the accretion of atoms and molecules of refractory elements onto grains (e.g., Liffman and Clayton, 1989; Dwek, 1998; Draine, 2009; Jones and Nuth, 2011).
What kind of dust formation processes are dominant at each stage of galaxy evolution is a very important question for understanding the evolution history of the ISM and star formation in galaxies. However, since dust evolution depends strongly on the age and metallicity of a galaxy, it is not an easy question to answer. Up to now, dust evolution has been studied with various models. For example, in young galaxies, SNe have been considered as the source of dust because they are the final stage of massive stars whose lifetime is short, and asymptotic giant branch (AGB) stars have been neglected because of their longer lifetime. However, Valiante et al. (2009) showed that the AGB stars also contribute to the dust production in young galaxies, and cannot be neglected even on a short timescale of ~500 Myr. A more elaborate survey of the parameter space for the dust formation by SNe and AGB stars has been carried out by Gall et al. (2011a). They showed that the contribution of AGB stars exceeds that of SNe II, at several 100 Myr, if the ratio between the metal and dust mass produced by SNe II is less ~0.01 and mass-heavy IMF with a mass range 1-100 M⊙.
As for the dust mass growth, the ISM is considered to be the main source of dust in various galaxies. for example, the present dust amount observed in the Milky Way cannot be explained if the source of dust was only stars, suggesting that we must consider the dust mass growth in the ISM in evolved galaxies (e.g., Liffman and Clayton, 1989; Dwek, 1998; Draine, 2009; Jones and Nuth, 2011). Recently, dusty quasars (total dust mass > 108 M⊙) have been discovered at high redshifts (e.g., Beelen et al., 2006; Wang et al., 2008), and theoretical studies on dust sources at high red-shifts are currently carried out actively (e.g., Michalowski et al., 2010b; Gall et al., 2011a, b; Pipino et al., 2011; Valiante et al., 2011). These have shown that it is difficult to explain the total dust amount in these QSOs only with stellar contributions, and the importance of dust mass growth in the ISM has been discussed. The next question is what controls the point where the dust mass growth in the ISM dominates the total dust mass production in galaxies. Therefore, although each physical process has already been extensively discussed, there emerges the crucial question: what kind of dust production process is dominant at each stage of galaxy evolution? And, in particular, when does dust mass growth become dominant as a source of dust mass?
The central aim of this work is to address this question. In this paper, we investigate what is the main driver of dust mass growth in the ISM. Since all sources of dust production are tightly related to each other in dust evolution, it is crucial to treat these processes in a unified framework to understand the evolution of dust in galaxies. Here, we adopt a model based on a chemical evolution model in a same manner as Hirashita (1999b), Calura et al. (2008), and Inoue (2011). This is because their models consider the main dust production/destruction processes that affect the dust evolution of galaxies, which makes it easy to compare our results to previous ones. From this work, we find that the dust mass growth in the ISM is regulated by a critical metallicity, the details of which are described in Subsection 3.2. Although dust mass growth can occur at any time during the age of a galaxy, there is a moment at which the dust mass growth becomes greater than the contribution from other sources of dust.
This paper is organized as follows. In Section 2, we describe the model developed for this work. In Section 3, we describe, and discuss, the basic results obtained by our model. The main topic of this paper, critical metallicity, is introduced and extensively examined in Subsection 3.2. Section 4 is devoted to the conclusions. The solar metallicity is set to be Z⊙ = 0.02 (Anders and Grevesse, 1989) throughout this paper.
2. Dust Evolution Model of Galaxies
In this section, we describe a simple chemical evolution model with dust which examines what determines the point where the dust mass growth in the ISM becomes dominant. The dust evolution model is developed in the same manner as in Hirashita (1999b) and Inoue (2011).
2.1 Equations of galaxy evolution
In this section, we describe the equations of the mass evolution of stars and the ISM which contains metal and dust in galaxies. We use a simple one-zone model, because we are interested in the global properties of galaxies. Also, we assume a closed-box model. Thus, the total baryon mass Mtot (the sum of the stellar mass and the ISM mass) is a constant. However, since Mtot is just a scale factor in our model, this value does not affect the physical properties of galaxies nonlinearly.
In this work, we do not consider the effects of inflow and outflow. However, they may not influence the properties of dust and metal enrichment in galaxies for the following reasons: An inflow makes not only the metallicity, but also the dust-to-gas mass ratio, small, because usually an inflow is considered to be metal- and dust-poor. As for an outflow, it expels ISM components (gas, metal and dust) out of a galaxy. However, if all ISM components flow out together, the metallicity and the dust-to-gas mass ratio do not change.
In this work, we consider AGB stars and SNe II as stellar sources, but we neglect the SNe Ia for simplicity. Nozawa et al. (2011) recently proved that SNe Ia produce little dust. Furthermore, Calura et al. (2008) have shown that the dust destruction rate by SNe Ia is about 1/10 of that by SNe II. As for the metals ejected by SNe Ia, they play an important role in the chemical evolution of galaxies (e.g., Matteucci et al., 2009). However, since we do not discuss the abundance ratio of each metal but, rather, the total metallicity, we do not take into account the contribution of SNe Ia.
In this paper, we assume that the mass ranges of AGB stars and SNe II are 1–8 M⊙ and 8-40 M⊙, respectively. Also, we assume that all stars with initial masses m > 40 M⊙ evolve to black holes without SN explosions (Heger et al., 2003).
As for the remnant and metal masses, the data are taken from van den Hoek and Groenewegen (1997) for AGB stars with a mass range 1–7 M⊙ and metallicities Z = (5.0 × 10−2, 0.2, 0.4, 1.0) Z⊙, and from Woosley and Weaver (1995) for SNe II with a mass range 12–40 M⊙ and metallicities Z = (5.0 × 10−2,0.1, 1.0) Z⊙. As for the dust mass, the data is taken from Zhukovska et al. (2008) for AGB stars with a mass range 1–7 M⊙ and metallicities Z = (5.0 × 10−2, 0.1, 0.2, 0.4, 0.75, 1.0) Z⊙, and from Valiante et al. (2009) for SNe II with a mass range 12–40 M⊙ and metallicities Z = (5.0 × 10−2, 1.0) Z⊙, which are quoted from Bianchi and Schneider (2007).
Although stardust yields are not completely understood, theoretical predictions of SNe II recently show a good agreement with observations of nearby supernova remnants (SNRs) (e.g., Nozawa et al., 2010). We considered the current model based on these latest results. However, some problems still remain unsolved (e.g., nucleation efficiency). As for the dust yield of AGB stars, we take similar star-dust yields to those of (Valiante et al. 2009, 2011) and Gall et al. (2011a) whilst their yields may be uncertain. However, we note that after the dust mass growth in the ISM becomes dominant, the dust abundance is insensitive to star-dust yields (Inoue, 2011). Thus, although there exist slight uncertainties in dust yields, we can discuss the activation mechanism for dust mass growth in the ISM without ambiguity.
2.2 Dust destruction timescale
It is thought that SNe are the main source of dust destruction. This dust destruction process depends on various parameters (density and temperature of the ISM, the explosion energy of the SNe, etc.), and is very complex (e.g., Jones et al., 1994, 1996; Nozawa et al., 2006). In this work, we adopt the equations presented by Mckee (1989).
The range of the integration is the mass range where the SNe can occur (Heger et al., 2003). So, if t < τ40 M⊙, γSN(t ) = 0.0.
2.3 Metal accretion timescale
As mentioned above, we conservatively adopt ā = 0.1 μm as a fiducial value (e.g., Inoue, 2011). Small grains may be depleted by coagulation in molecular clouds (Hirashita and Yan, 2009), which strengthens the importance of large grains. The importance of large grains is further enhanced given that the grain size distribution tends to be biased towards a large (a ~ 0.1 μm) size by the destruction within SN remnants (Nozawa et al, 2007). Thus, we assume ā ~ 0.1 μm to estimate the dust mass growth timescale. Although we basically adopt ā = 0.1 μm, we also examine ā = 0.01 μm for a quick growth case, later. Indeed, the MRN grain size distribution (Mathis et al, 1977) has ā = 0.01 μm (Hirashita and Kuo, 2011). In reality, the grain size distribution in galaxies changes with time due to some processes (e.g., SN shocks, accretion, etc.). As for the contribution of the evolution of the grain size distribution, this is discussed in a paper in preparation (Asano et al, 2012).
In this paper, we consider only η = 0 (no accretion growth), or 1, in order to avoid any fine-tuning. In fact, the effect of a different choice of η can be offset by a different choice of nH and T. This allows us to merge the uncertainties of η, nH, and T into the value of τacc, 0. We set τacc, 0 = 4.0 x 105 yr as a fiducial value (e.g., Inoue, 2011). Other choices of τacc, 0 result in a different timing of the growth activation. This is explicitly expressed in Eq. (27) later.
3. What Drives Dust Mass Growth in the ISM?
In this section, we investigate what determines the point where the grain growth in the ISM dominates the total dust mass production in galaxies.
3.1 Contribution of each physical process to the total dust mass in galaxies
From these figures, we find that although the ejected-by-stars contribution is the biggest in the early stages, as time passes, the main contributor to the dust production becomes the dust mass growth in the ISM at a given point referred to as the “switching point”. For example, Liang and Li (2009) pointed out that dust produced by SNe II predominates the dust budget in galaxies in a high-z Universe (z > 5) using the extinction curves of GRB host galaxies at high redshifts. Their results are in good agreement with our work. Furthermore, the process of dust mass growth is expected to explain the dust amount in the Milky Way or dusty QSOs at high redshifts (e.g., Zhukovska et al., 2008; Draine, 2009; Michalowski et al., 2010a; Valiante et al., 2011). So, what determines the switching point? We will discuss this in the next section (this is the main topic in this paper).
After dust mass growth has taken place, the effect of dust destruction by SN shocks approaches that of dust mass growth. Thus, after dust mass growth becomes efficient, the dust amount in galaxies determines the balance between the effect of dust destruction and that of dust mass growth in the ISM (see also Inoue, 2011).
As shown in Fig. 2, the values of δ for all τSFs converge to ~ 1. In contrast, the value for the Milky Way is about 0.5. However, since it can be adjusted by adopting a different η, we do not try to fine-tune the convergence value of δ in this study. Inoue (2011) showed that the convergence value of δ is determined by the balance between the contribution of dust destruction by SN shocks and that of the dust mass growth (for details, the product of τacc, 0 and ϵmswept).
3.2 Critical metallicity for dust mass growth
In this section, we introduce the main topic of this paper, the critical metallicity. This is the metallicity at the switching point (see Subsection 3.1). In our model, the sources of dust are stars (AGB stars and SNe II) and the dust mass growth in the ISM.
This equation is exact if SFR is constant.
Thus, if the metallicity of a galaxy is larger than the above metallicity, we should consider the effect of dust mass growth in the galaxy. Here, we refer to the metallicity as the critical metallicityZcr, which is the metallicity at the switching point. To obtain the value of Zcr, hereafter, we adopt δ = 0.02 and D = 5 × 10−4. As for the value of δ, from Fig. 2, the value of δ is in the range of 0.01–0.04 at the switching point for each τSF. Furthermore, although δ is dependent on time, before the dust mass growth becomes effective to the total dust mass, δ is determined only by the contribution of stars (see Appendix A). This contribution is in the range 0.01–0.04 in our calculation (Fig. A.1 in Appendix A). Thus, we take δ = 0.02 as a representative value. Also, since we found from numerical calculation that the range of D is 10−4 to 10−3, we take D = 5 × 10−4 as a representative value.
For reasons of clarification, we compare our discussion with a similar work by Inoue (2011). Inoue (2011) defined a critical metallicity to compare the contribution of dust destruction by SN shocks with that of dust mass growth. Thus, the critical metallicity of Inoue (2011) is the metallicity at which the contribution of dust mass growth exceeds that of dust destruction. In contrast, our critical metallicity is the metallicity at which the dust mass growth becomes the main source of the increase of dust (the contribution of dust mass ejected by stars is the main source of dust at an early stage of galaxy evolution). Those interested in both works should bear this difference in mind.
In the above discussion, we have focused on the critical metallicity. One may, however, be interested in its relation to the time, tcr, which is the galactic age when the metallicity in a galaxy reaches the critical metallicity. Here, in order to understand, more clearly, the importance of the dust mass growth in various galaxies with various star-formation timescales, we demonstrate the relation between the critical metallicity Zcr and the time tcr. However, we stress that the metallicity is more fundamental because tcris determined by the critical metallicity.
From Fig. 7, we find that the evolutionary tracks with different ā show almost the same behavior if we introduce the critical metallicity for each value of ā. Thus, although Hirashita and Kuo (2011) showed that the critical metallicity is sensitive to the grain size distribution, the mechanism that the critical metallicity determines the point at which the dust mass growth becomes the dominant factor in the growth of the total dust mass in a galaxy does not change. As for the dust evolution considered the evolution of the grain size distribution (including the effects of stellar dust, SN destruction and accretion) in a galaxy, this issue will be extensively discussed in a work in preparation (Asano et al. 2012, in preparation).
In this work, we have constructed a galaxy evolution model taking into account the metallicity and age dependence on the various dust sources (AGB stars, SNe II and growth in the ISM) to investigate what is the main driver of the grain growth which is expected to be the dominant source of dust in various galaxies with various star-formation timescales.
We have found that the point at which the dust mass growth in the ISM becomes dominant is determined by the metallicity. If the metallicity in a galaxy exceeds a certain critical value, the critical metallicity, dust mass growth becomes active and the dust mass rapidly increases, until metals are depleted from the ISM. This critical metallicity is larger for a shorter star-formation timescale. Dust mass growth is thought to be the dominant source of dust in evolved galaxies, such as the Milky Way and young, but dusty and massive, QSOs at high redshifts. The importance of the dust mass growth in such a diversity of galaxies can be explained clearly in terms of the critical metallicity. The dust mass growth in the ISM is regulated by the metallicity, and we emphasize that the critical metallicity works as an indicator to judge whether the grain growth in the ISM is the dominant source of dust in a galaxy, especially because of a strong and nonlinear dependence on the metallicity.
1This temperature corresponds to ⟨v⟩ = 0.14 km s−1. We assume AmH⟨v⟩2 = kT and adopt A = 20 (AmH is the mean mass of the colliding atoms) (Spitzer, 1978).
3Indeed, their equations (4) and (5) have the metallicity dependence. However, their adopted timescales in table 1 seem to omit the dependence finally.
We thank the anonymous referees for their helpful comments which improved the presentation and content of this paper. We are grateful to Takashi Kozasa, Takaya Nozawa, Daisuke Yamasawa, Asao Habe, and Takako T. Ishii for fruitful discussions. RSA has been supported from the Grant-in-Aid for JSPS Research under Grant No. 23-5514. RSA and TTT have been also partially supported from the Grant-in-Aid for the Global COE Program “Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos” from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. TTT and AKI have been supported by Program for Improvement of Research Environment for Young Researchers from Special Coordination Funds for Promoting Science and Technology, and the Grant-in-Aid for the Scientific Research Fund (TTT: 20740105, 23340046, AKI: 19740108) commissioned by the MEXT. HH is supported by NSC grant 99-2112-M-001-006-MY3.
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