The origin of dust in galaxies revisited: the mechanism determining dust content
© 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. 2011
Received: 8 November 2010
Accepted: 25 February 2011
Published: 2 February 2012
The origin of cosmic dust is a fundamental issue in planetary science. This paper revisits the origin of dust in galaxies, in particular, in the Milky Way, by using a chemical evolution model of a galaxy composed of stars, interstellar medium, metals (elements heavier than helium), and dust. We start from a review of time-evolutionary equations of the four components, and then, we present simple recipes for the stellar remnant mass and yields of metal and dust based on models of stellar nucleosynthesis and dust formation. After calibrating some model parameters with the data from the solar neighborhood, we have confirmed a shortage of the stellar-dust-production rate relative to the dust-destruction rate by supernovae if the destruction efficiency suggested by theoretical works is correct. If the dust-mass growth by material accretion in molecular clouds is active, the observed dust amount in the solar neighborhood is reproduced. We present a clear analytic explanation of the mechanism for determining dust content in galaxies after the activation of accretion growth: a balance between accretion growth and supernova destruction. Thus, the dust content is independent of the uncertainty of the stellar dust yield after the growth activation. The timing of the activation is determined by a critical metal mass fraction which depends on the growth and destruction efficiencies. The solar system formation seems to have occurred well after the activation and plenty of dust would have existed in the proto-solar nebula.
Cosmic dust grains are negligible in mass in the Universe. Nevertheless, they play a significant role in many astronomical, astrophysical, and astrochemical aspects: extinction (absorption and scattering) matter of radiation, an emission source in infrared wavelengths, a coolant and a heat source in the interstellar medium (ISM) and intergalactic medium (IGM), and a site for the formation of molecules. Therefore, dust is one of the most important constituents of the Universe. Dust is also important for planetary science because grains are material for planets.
Dust grains are formed in rapidly-cooling gas of stellar outflows (Draine and Salpeter, 1977; Yamamoto and Hasegawa, 1977). We call such grains ‘stardust’. Sources of the stardust are asymptotic giant branch (AGB) stars, su-pernovae (SNe), red supergiants, novae, Wolf-Rayet stars, and so on (e.g., Gehrz, 1989). The main source of the star-dust in the present Milky Way and the Magellanic Clouds is thought to be AGB stars (Gehrz, 1989; Draine, 2009; Matsuura et al., 2009).
SNe may also produce a significant amount of stardust (Kozasa and Hasegawa, 1987; Todini and Ferrara, 2001; Nozawa et al., 2003, 2007; Schneider et al., 2004; see also Kozasa et al., 2009). Stardust from SNe was particularly important in the early Universe because the time for stars to evolve to the AGB phase is typically about 1 Gyr, but the cosmic time in the early Universe is less than this (Morgan and Edmunds, 2003; Maiolino et al., 2004; Dwek et al., 2007; but see also Valiante et al., 2009). The ‘first’ star-dust may have also played an important role in changing the mode of star formation from massive-star dominated to present-day Sun-like-star dominated (Schneider et al., 2003, 2006).
However, dust formation by SNe remains observation-ally controversial. The first detections of a few M⊙ dust freshly formed, which is much larger than expected, in Cassiopeia A (Cas A) and Kepler SN remnants (SNRs) by submillimeter observations with SCUBA (Dunne et al, 2003; Morgan et al., 2003) were almost contaminated by foreground dust in the ISM on the sight-lines (Krause et al, 2004; Gomez et al, 2009). Recent infrared observations with the Spiter Space Telescope and AKARI and sub-millimeter observations with Herschel and BLAST of Cas A and other SNRs are in agreement with theoretical expectations of 0.01–0.1 M⊙ per one SN (Rho et al, 2008; Sakon et al., 2009; Nozawa et al, 2010; Barlow et al, 2010; Sibthorpe et al, 2010).
Once stardust grains are injected into the ISM, they are processed there. The grains in hot gas are bombarded by thermally-moving protons and sputtered (Onaka and Kamijo, 1978; Draine and Salpeter, 1979). SN shockwaves probably destroy dust grains by grain-grain collisional shattering as well as sputtering (e.g., Dwek and Arendt, 1992; Jones et al, 1994, 1996; Nozawa et al, 2006; Silvia et al, 2010). This destruction process is widely accepted and observational evidence of the destruction has been found in several SNRs, especially with the Spitzer Space Telescope (Arendt et al, 1991,2010; Borkowski et al, 2006; Williams et al., 2006; Dwek et al, 2008; Sankrit et al., 2010; but see Mouri and Taniguchi, 2000).
Assuming the destruction efficiency predicted theoretically, the life-time of dust grains is found to be of the order of 100 Myr (McKee, 1989; Draine, 1990; Jones et al., 1994, 1996). On the other hand, the injection time of stardust is of the order of 1 Gyr (e.g., Gehrz, 1989). Thus, another efficient channel of dust formation is required to maintain dust content in galaxies. The most plausible mechanism is accretion growth in the ISM (Draine, 1990, 2009); in dense molecular clouds, atoms and molecules of some refractory elements and compounds accrete onto pre-existing grains and may change from the gas phase to the solid phase. Note that, unlike the sticking growth of grains well studied in protoplanetary disks, this accretion growth causes an increase in dust mass. This type of growth is favored to explain the observed depletions of some elements in the gas phase of the ISM relative to solar abundance. The correlation between the degree of depletion and the density in the ISM particularly suggests this process (e.g., Savage and Sembach, 1996; Jenkins, 2009). It is also suggested that an efficient growth is required to explain the massive dust mass observed in the early Universe (Michalowski et al., 2010).
Since the pioneering work by Dwek and Scalo (1980), much theoretical work on dust-content evolution in galaxies has been carried out (Dwek, 1998; Edmunds and Eales, 1998; Lisenfeld and Ferrara, 1998; Hirashita, 1999a, b, c; Hirashita et al., 2002; Edmunds, 2003; Inoue, 2003; Morgan and Edmunds, 2003; Dwek et al., 2007; Calura et al., 2008; Zhukovska et al, 2008; Valiante et al., 2009; Asano et al., 2011; Dwek and Cherchneff, 2011; Gall et al, 2011a, b; Mattsson, 2011; Pipino et al, 2011). These works are based on the evolutionary model of elemental abundance in galaxies called the chemical evolution model (Tinsley, 1980 for a review) and incorporate some (or all) of the three processes of formation, destruction, and growth of dust. One of the main results from recent works is the importance of accretion growth.
This paper presents a new interpretation of the mechanism for determining dust content in galaxies. Previous works imply that the mechanism is a balance between dust destruction by SNe and accretion growth in the ISM. However, to date, this point has not been discussed clearly. This paper analytically justifies this implication. For this aim, a simple one-zone model is sufficient. In addition, we present new simple recipes describing stellar remnant mass and yields of elements and dust from state-of-the-art models of stellar nucleosynthesis and the formation of stardust.
Section 2 presents a review of the basic equations. In Section 3, we present new simple recipes of stellar remnant mass and yields. In Section 4, we calibrate some model parameters to reproduce the observed properties of the solar neighborhood. Section 5 presents our analytical interpretation of the mechanism for determining dust content in galaxies, and further discussions are presented in Section 6. Experts in this field may go straight to Section 5 which is the new result of this paper.
Throughout this paper, we call elements heavier than helium ‘metal’ according to the custom of astronomy. We adopt the metal mass fraction (so-called metallicity) in the Sun of Z⊙ = 0.02 (Anders and Grevesse, 1989) conventionally, although recent measurements suggest a smaller value of 0.0134 (Asplund et al., 2009).
2. Chemical and Dust Evolution Model of Galaxies
2.1 Equations of chemical and dust amount evolution
I, I Z , and Id are the ISM, metal, and dust infall rates from the IGM, respectively. O, O Z , and Od are the ISM, metal, and dust outflow rates to the IGM, respectively. In this paper, we do not consider any outflows (O = O Z = Od = 0), but consider only an ISM infall I (no metal and dust in the infalling gas: I Z = Id = 0), which is required to reproduce the metallicity distribution of stars nearby the Sun. 1 1 The reason why we omit any outflows is that we do not know the transport mechanism of metal and dust from galaxies to the IGM (e.g., Bianchi and Ferrara, 2005). However, this omission may be inconsistent with detections of metal and dust in the IGM (e.g., Songaila and Cowie, 1996; Menard et al., 2010). 2 2
In the dust mass equation (Eq. (4)), there are two additional terms; Dsn is the dust-destruction rate by SNe and Gac is the dust-growth rate in the ISM by metal accretion. These two terms are discussed in Section 2.5 and Section 2.6 in detail.
2.2 Star formation and infall rates
Parameters and values for the solar neighborhood.
(1, 50), (2, 20), (3, 15), and (5, 10)
(1.5, 1), (1.5, 2), (3, 0.5), (3, 1), (3, 2), (6, 0.5), and (6, 1)
0.01, 0.02, and 0.04
0.01, 0.1, and 1
2.3 Stellar mass spectrum and returned mass rate
The stellar life-time τ1f(m) is calculated by the formula of Raiteri et al. (1996) which is a fitting function of Padova stellar evolutionary tracks (Bertelli et al., 1994). This formula is a function of stellar mass m and metallicity Z. However, the Z-dependence is weak. Thus, we neglect it (we always set Z = Z⊙ in the formula).
2.4 Stellar yields of ‘metal‘ and dust
2.5 Dust destruction by supernova blast waves
The effective mass swept by a dust-destructive shock wave, ϵmsn is the important parameter. It is estimated to be ~ 1000 M⊙, namely ϵ ~ 0.1 and msn ~ 104M2299; (McKee, 1989; Nozawa et al., 2006). Recent models for starburst galaxies in the early Universe often assume an effective mass of ϵmsn ~ 100 M⊙ which is a factor of 10 smaller than our fiducial value (Dwek et al, 2007; Pipino et al, 2011; Gall et al, 2011a). Their argument is that starburst activity produces multiple SNe which make the ISM highly inhomogeneous and the dust-destruction efficiency decreases in such a medium. However, the solar neighborhood is not the case, and, thus, we keep ϵmsn ~ 1000 M⊙.
2.6 Dust growth by ‘metal’ accretion in the ISM
This time-scale is very uncertain, but we will obtain τac,0 = 3 × 106 yr as the fiducial value in Section 4.2 in order to reproduce the dust-to-metal ratio in the solar neighborhood with an SN destruction efficiency of ϵmsn = 1000 M⊙. This value can be obtained with a set of parameters of a = 0.1 μm (typical size in the ISM of the Milky Way), σ = 3 g cm−3 (compact silicates), sZ = 1, vZ = 0.2 km s−1 (56 Fe as an accreting metal atom and thermal temperature of 100 K), , and Xcold = 0.2. This data set is just an example, but ensures that the time-scale is not outrageous.
There is a discussion that the lifetime of dense clouds (or the recycling time-scale of dense gas) should be longer than the accretion growth time-scale for an efficient dust growth (Zhukovska et al., 2008; Dwek and Cherchneff, 2011). According to these authors, the lifetime is long enough to realize an efficient dust growth in the Milky Way and even in starburst in the early Universe. Another issue is the effect of grain-size distribution which is discussed in Hirashita (2011).
3. Stellar Remnant and ‘Metal’ and Dust Yields
In this section, we present new simple formulas to describe the stellar remnant mass and yields of metal and dust which are useful to input into the chemical evolution codes. We represent all elements heavier than helium as just a ‘metal’ in the formulas for simplicity, while yields of various elements are presented in the literature. We consider three types of stellar death: white dwarfs through the AGB phase, core-collapse Type II SNe, and a direct collapse leading to a black-hole called a ‘collapser’ (Heger et al., 2003). In this paper, we assume the mass range for the SNe to be 8–40 M⊙ (Heger et al., 2003). The stars with a mass below or above this mass range become AGB stars, or ‘collapsers’, respectively.
We neglect Type Ia SNe for simplicity. This population of SNe is the major source of the element iron (Iwamoto et al, 1999) and may be the source of iron dust (Calura et al., 2008). However, in respect of the total stardust mass budget, the contribution of SNe Ia relative to SNe II is always less than 1–10% (Zhukovska et al., 2008; Pipino et al., 2011). Since we are dealing with metal and dust each as a single component, we can safely neglect the contribution of SNe Ia.
4. Milky Way Analog
Let us calibrate the parameters in the chemical and dust evolution model of galaxies so as to reproduce the properties of the solar neighborhood in the Milky Way. There are two parameters in the chemical evolution part: the time-scales of star formation, τsf, and infall, τin. There are two additional parameters in the dust-content evolution: the time-scale of the ISM accretion growth, τac,0, and the efficiency of the dust destruction, ϵmsn. In addition, there are two parameters reflecting the uncertainties of the metal and dust yields, f Z and ξ. Table 1 is a summary of these parameters and values.
Note that we do not apply any statistical method to justify the goodness of the reproduction of the observational constraints throughout this paper because our aim is not to find the best fit solution for the constraints but to demonstrate the dust-content evolution in galaxies qualitatively. This is partly due to the weakness of the observational constraints and due to the large uncertainties of dust physics itself.
4.1 Chemical evolution at the solar neighborhood
From these three comparisons, we finally adopt the case of (τSF/Gyr, τin/Gyr) = (3, 15) as the fiducial set for the Milky Way (or more precisely, for the solar neighborhood) in this paper.
4.2 Dust content evolution at the solar neighborhood
If there is neither destruction nor accretion growth of dust, the dust-to-gas ratio evolution is just the metallicity evolution multiplied by the condensation efficiency of star-dust, ξ, as shown by the dotted line. We have assumed ξ = 0.1 for this line. Once the SN destruction of dust is turned on with a standard efficiency as ϵmsn = 1 × 103M⊙ (McKee, 1989; Nozawa et al., 2006), the dust amount is reduced by a factor of ten as shown by the dot-dashed line. This confirms that the dust destruction is very efficient and the stardust injection is too small to compensate for the destruction (e.g., Draine, 1990; Tielens, 1998). Then we need the accretion growth in the ISM to reproduce the dust-togas ratio, ~10−2, in the present Milky Way. If we assume a time-scale of τac,0 = 3 × 106 yr, the dust-to-gas-ratio evolution becomes the solid line and reaches ≃ 10−2 which, after several Gyr, is almost two orders of magnitude larger than the case without growth.
5. Determining Dust-to-Metal Ratio
Equation (30) shows that the final value of δ is determined by the equilibrium between the SN destruction and the accretion growth in the ISM. The time-scale to reach equilibrium is 1/(b – a). This is relatively short in the fiducial case. For example, it is 0.3 Gyr when Z = 0.02. This means that the δ evolution proceeds with keeping the equilibrium between SN destruction and the accretion growth, or equivalently, δ = δ∞ after Z exceeds Zc. This behavior is also found by comparing the two time-scales, τsn and τac in Fig. 8; once τac becomes shorter than τsn at about 4 Gyr at which Z exceeds Zc, τac turns around and approaches τsn again. This is realized by the reduction of the term (1 − δ) in τac (see Eq. (17)) when δ increases from ~0 to δ∞. Such a kind of self-regulation process determines the dust-to-metal ratio δ.
6.1 Effect of uncertainties of yields
6.2 What kind of dust is formed by the ISM growth?
We have shown that the main production channel of dust is the accretion growth in the ISM of the present-day Milky Way. This conclusion has also been reported in the literature. For example, Zhukovska et al. (2008) argued that the mass fraction of stardusts in the total dust is only 0.1–1% based on a more sophisticated chemical evolution model than in this paper (see their figure 15); more than 99% of dust is originated from accretion growth in the ISM. It is also well known that some interplanetary dust particles show a highly-enhanced abundance of deuterium and 15N relative to the solar composition, which is a signature of a molecular cloud origin because such isotopic fractiona-tions are expected in a low temperature environment (e.g., Messenger, 2000). Therefore, dust produced by the ISM accretion exists. Then, we have a very important question; what kinds of dust species are formed by the accretion growth in the ISM?
In molecular clouds, many kinds of ices such as H2O, CO, CO2, CH3OH have been detected (e.g., Gibb et al., 2000). These ices are condensed onto pre-existent grains. In these ices, some chemical reactions and ultraviolet photolysis (and cosmic rays) process the material and may make it refractory. As a result, so-called ‘core-mantle grains’ coated by refractory organics would be formed (e.g., Li and Greenberg, 1997). Indeed, such a grain has been found in cometary dust: olivine particles produced by a Type II SN coated by organic matter which seems to be formed in a cold molecular cloud (Messenger et al., 2005). Therefore, the ISM dust probably has core-mantle or layered structures. Moreover, the composition can be heterogeneous: for example, graphite coated by silicate, silicate coated by graphite, silicate coated by iron, etc. The formation of such grains does not seem to be studied well. Much more experimental and theoretical work is highly encouraged.
If we can find signatures of the dust accretion growth in the ISM of galaxies by astronomical observations (i.e. very distant remote-sensing), it proves the growth to be ubiquitous. Possible evidence already obtained is a huge mass of dust in galaxies which requires accretion growth as discussed in this paper. It is worth studying how to distinguish stardust grains (or grain cores) and ISM dust (or mantle) by observations, e.g., spectropolarimetry, in the future.
6.3 Dust amount in the proto-solar nebula
We have shown that the dust amount is very small before ISM growth becomes active. For example, the dust-to-gas mass ratio is of the order of 10−4 during the first few Gyr following the formation of the Milky Way (or the onset of the major star formation in the solar neighborhood). If the dust-to-gas ratio in the proto-solar nebula was 10−4, planet formation might have been difficult. Fortunately, the activation of ISM growth is considered to have been about 8 Gyr ago in the solar neighborhood. Thus well before the solar-system formation. Indeed, we expect a dust-to-gas ratio of several times 10−3 at 4–5 Gyr ago (see Fig. 7). Moreover, the dust-to-gas ratio may be much enhanced in the proto-solar nebula relative to the average ISM. This is because the accretion growth is more efficient at a higher density and the density in the proto-solar nebula is several orders of magnitude higher than that in molecular clouds. Therefore, even if the solar-system formation occurred before the activation of ISM growth globally, dust growth might have been active locally in the proto-solar nebula. In this case, the planet formation is always possible if there is enough metal to accrete onto the pre-existent seed grains, even before global growth activation. This is an interesting issue to relate to the Galactic Habitable Zone where complex life can be formed (Lineweaver et al., 2004). We will investigate this more in the future.
1 Without gas infall from intergalactic space, we would expect a much larger number of low-metallicity stars in the solar neighborhood than is observed. This is called the ‘G-dwarf problem’ (e.g., Pagel, 1989).
2 The origin of intergalactic metals and dust is galactic outflows and the amount ejected from galaxies is the same order of that remained in galaxies (e.g., Ménard et al., 2010 for dust; see also Inoue and Kamaya, 2003, 2004, 2010). Dust grains may be ejected from galaxies more efficiently than metals because the grains receive momentum through radiation pressure (Bianchi and Ferrara, 2005). Even in this case, our discussion about the dust-to-metal ratio in Section 5 would not be affected essentially by the omission of this selective removal of dust, although the set of model parameters which can reproduce the observations would change. In any case, this point would be interesting for future work.
3 The micro-process of the destruction considered in Nozawa et al. (2007) is sputtering by hot gas.
4 The terms ‘mixed’ and ‘unmixed’ refer to the elemental mixing in the SN ejecta (Nozawa et al., 2003). In the ‘mixed’ case, there is no layer where C is more abundant than O, so only silicate, troilite, and corundum grains can be formed. On the other hand, the ‘unmixed’ case has a C-rich layer and Fe layer and can form carbon and iron grains as well as silicate.
The author thanks anonymous referees for their many suggestions which were useful to improve the presentation and the quality of this paper. The author is grateful to T Kozasa and A. Habe for interesting discussions and for their hospitality during my stay in Hokkaido University, Sapporo, where this work was initiated, to R. Asano, H. Hirashita, and T T Takeuchi for many discussions, to T Nozawa for providing his dust yields in SNe, and to H. Kimura, the chair of the convener of the ‘Cosmic Dust’ session in the AOGS 2010 meeting, for inviting me to the interesting meeting in Hyderabad, India. This work is supported by KAKENHI (the Grant-in-Aid for Young Scientists B: 19740108) by The Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.
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