ISM dust feedback from low to high mass stars

Astronomy & Astrophysics manuscript no. ms February 2, 2008

c ESO 2008

The role of stellar mass and mass functions on the ISM dust feedback
D. Falceta-Gon?alves c

arXiv:0710.5103v1 [astro-ph] 26 Oct 2007

N?cleo de Astrof? u ?sica Te?rica, CETEC - Universidade Cruzeiro do Sul, Rua Galv?o o a Bueno 868, CEP 01506-000 S?o Paulo - Brazil a received ; accepted ABSTRACT Context. The dust component of the interstellar medium (ISM) has been extensively studied in the past decades. Late-type stars have been assumed as the main source of dust to the ISM, but recent observations show that supernova remnants may play a role on the ISM dust feedback. Aims. In this work, we study the importance of low and high mass stars, as well as their evolutionary phase, on the ISM dust feedback process. We also determine the changes on the obtained results considering di?erent mass distribution functions and star formation history. Methods. We describe a semi-empirical calculation of the relative importance of each star at each evolutionary phase in the dust ejection to the ISM. We compare the obtained results for two stellar mass distribution functions, the classic Salpeter initial mass function and the present day mass function. We used the evolutionary track models for each stellar mass, and the empirical mass-loss rates and dust-to-gas ratio. Results. We show that the relative contribution of each stellar mass depends on the used distribution. Ejecta from massive stars represent the most important objects for the ISM dust replenishment using the Salpeter IMF. On the other hand, for the present day mass function low and intermediate mass stars are dominant. Conclusions. We con?rm that late-type giant and supergiant stars dominate the ISM dust feedback in our actual Galaxy, but this may not the case of galaxies experiencing high star formation rates, or at high redshifts. In those cases, SNe are dominant in the dust feedback process. Key words. ISM: evolution, dust; Stars: mass function, mass-loss, winds

1. Introduction
RGB and AGB stars are known as the major continuous dust producers in the Universe, but also SN remnants have shown fast grain growth and dusty shells of Md ? 10?2 ?101 M⊙ (Nozawa et al. 2003). From the classical nucleation theory, the timescale for grain growth in the ISM can be estimated by τg = 4sa(f ni mi vi )?1 , where a is the dust mean size, s is
Send o?print requests to: diego.goncalves@unicsul.br


D. Falceta-Gon?alves: ISM dust feedback from low to high mass stars c

the material density, f the sticking probability, ni the gas phase density, mi the atom mass and vi the velocity of the i-th atom to be added onto the grain surface. Considering typical ISM parameters, a ? 0.1 ? 1 ?m, s ? 2 g cm?3 , ni ? 1 cm?3 , T ? 10 K, and assuming an e?ciency f = 0.1 ? 1, we ?nd τg < 109 yr. Dust particles are likely to be destroyed by shock waves (Draine & Salpeter 1979; McKee 1989). Grain-grain or ion-grain collisions will lead to the shattering process, reducing or destroying dust particles. Jones et al. (1994, 1996) described the shattering process of ISM dust induced by SN blasts, obtaining destruction timescales of τd ? 4 ? 6 × 108 yr. Actually, as mentioned in these works, the accurate derivation of destruction timescales depends on the velocity of the shock waves, the frequency of SNe and the physical properties of the ISM, as density and temperature. Hence, the destruction timescales are shorter than the dust growth scale, the observed dust could not be explained by nucleation in loco, but had to be recently (< 109 yr) injected into the ISM (Tielens 1998). It is commonly suggested that the ISM dust should be mostly originated from evolved low and intermediate mass stars but recent observations showed the presence of large quantities of dust (Md = 108 M⊙ ) in the early Universe (z > 5) (Hughes et al. 1998; Archibald et al. 2001; Dunne et al. 2003; Bertoldi et al. 2003; Maiolino et al. 2004). At that age low and intermediate mass stars were not evolved yet and, therefore, SNe are recognized as responsible for such material ejections (Todini & Ferrara 2001; Morgan & Edmunds 2003; Sugerman et al. 2006; Dwek et al. 2007). In the post-shock phase of the SN remnant, the gas is generally cool and dense enough to allow dust formation and growth (Falceta-Gon?alves et al. 2003, 2005). Observationally, c it is con?rmed for SN1987A, which shows a 10?3 M⊙ dust shell with a dust to gas ratio for heavier elements ? 0.3. The same result was obtained for several other galactic and extragalactic SNe (Barlow et al. 2005; Gomez et al. 2007). Therefore, SNe seem to play an important part on the ISM dust replenishment process (Dwek 1998). However, if the short dust destruction timescale is taken into account, SNe could only be the main source of dust of the Galaxy if it presented a high star formation rates in its recent history. In this work we present a semi-empirical model, in which we study the role of di?erent stellar mass functions in the output of dust ejected to the ISM. The model is described in Sect. 2, in Sect. 3 we show the main results and present a brief discussion, followed by the conclusions.

2. The Model
To obtain the total amount of dust ejected by a certain star during all its evolution we have to integrate the dust mass loss rates of each evolutionary phase over the evolutionary time. The di?culties on performing such calculation lie on the determination of the dust mass loss rates at each evolutionary phase of the star, as well as its duration. To accomplish this we used the evolutionary tracks given by Schaller et al. (1992), which take into account the mass loss during the stellar evolution. These numerical calculations also provided the abundance of heavier elements on the stellar surface at each epoch of the stellar evolution.

D. Falceta-Gon?alves: ISM dust feedback from low to high mass stars c


Fig. 1. Evolutionary tracks for stars with masses ranging from 1 to 120 M⊙ for metallicity ˙ of 0.02. The box shows the values of log(M ). We used these numerical results to determine the amount of material able to be added into the dust grains that is being ejected from the stars. The total dust mass ejected by each star over its lifetime can be determined by integrating the mass loss rate at each stellar evolutionary phase, determined by:
M2 M1 t2 t1

˙ Φ(m)Md (m) dt dm,


˙ where Φ(m) is the stellar population mass distribution, Md (m) is dust mass loss rate of a given star of mass m at the time t, M1 and M2 are the limits of the mass range and t1 and t2 are the limits of the time interval. To compute the dust mass loss rates we used: ˙ ˙ Md (t, m) = M (t, m)fd (t, m)χ(t, m), (2)

˙ where M is the total mass loss rate, which is obtained empirically as described in the following subsection, fd is the dust-to-gas fraction of elements heavier than He and χ is the wind metallicity, of an star with mass m at an evolutionary time t. In Fig. 1 we illustrate the evolutionary track given by Schaller et al. (1992) for stars with masses ranging from 0.8 to 120 M⊙ used in this work, for an initial metallicity of 0.02, and the empirical stellar mass loss rates. Di?erent models of homogeneous and heterogeneous condensation theories have been proposed but the actual dust-to-gas fraction of stellar winds is still not completely understood. The gas acceleration is responsible for the gas rarefaction at the base of the stellar atmosphere and, depending on the model used, may result in very di?erent pressure and temperature pro?les, which are critical to the derivation of the condensation rates. As an


D. Falceta-Gon?alves: ISM dust feedback from low to high mass stars c

approximation, we introduce a single dust-to-gas fraction for each stellar mass, depending on the chemical composition. The yields for dust-to-metal fraction (fd ) for the massive stars were the same used by Dwek et al. (2007) (table 2), and for low and intermediate mass stars we used the data from Morgan & Edmunds (2003) (table 1). 2.1. The stellar mass-loss rates The mass loss rates, for each stellar mass at each evolutionary phase, were introduced empirically. For low and intermediate mass stars during the main sequence, giants and supergiants evolutionary phases, we used the data from de Jager et al. (1988). The wind velocities for giant and supergiant stars are, in general, v < 200 km s?1 and dust is not destroyed at heliopause. At the end of their lives, intermediate mass-stars present very high mass loss rates at the post-AGB’s phases (? 10?4 M⊙ yr?1 ) (Wachter et al. 2002), and are known as progenitors of the planetary nebulae. Massive stars are also know to present dust in their winds, mainly at the later stages of their evolution. WR and LBV stars present high mass loss rates in unstable and clumpy winds that favor dust nucleation and survival. For these objects we used the data given by Crowther (1997). Also, about 30% of these objects are in binary systems, and Marchenko et al. (2002) found that binary systems present high dust production rates due to the wind-wind shock, with 4 ? 6% of the wind mass condensed into grains at WR+OB systems. On the other limit, low mass protostars were also considered since their jets and disks are dust growth sites. Typically, these objects present a mass-loss rate of 10?8 M⊙ yr?1 during 106 ? 107 yr (Mundt et al. 1987). 2.2. The stellar mass distributions To compute the total contribution for the ejected material by all stars we may de?ne a mass distribution function. To simulate the distribution of a young stellar population we used the typical Salpeter single component IMF (Salpeter 1955): Ψ (log M ) = AM ?x for M? > 1M⊙ , where A = 4.43 × 10?2 and x = 1.3, and: Ψ (log M ) = B exp ? (log M ? log Mc ) /2σ 2



for M? < 1M⊙ , where B = 0.158, Mc = 0.079 and σ = 0.69. For the old populations, which exhibit a signi?cantly lower number of massive stars, we used the Present Day Mass Function (PDMF). For the PDMF Eqs. (3) and (4) are still valid but, A = 4.4 × 10?2 and x = 4.37 for 0 ≤ log M ≤ 0.54, A = 1.5 × 10?2 and x = 3.53 for 0.54 < log M ≤ 1.26 and A = 2.5 × 10?2 and x = 2.11 for log M > 1.26 (Chabrier 2003; Elmegreen 2004).

3. Results and Discussion
If one assumes that the dust is rapidly destroyed in the ISM (τd ? 108 yr), it is possible to naively separate in two the possible scenarios of the galactic history: i- old feedback process, which occurred in the presence of a large number of massive stars and, ii- recent feedback

D. Falceta-Gon?alves: ISM dust feedback from low to high mass stars c




Feedback (%)





1.E-03 0 20 40 60 80 100 120 140 M (solar)

Fig. 2. Dust mass, relative to total (in percent), ejected to the ISM by each stellar mass range during its complete evolution. The solid line represents the model using a typical Salpeter IMF, and the dotted line represents the model for the present day mass function (PDMF).

process, with a relatively larger number of low and intermediate mass stars. Therefore, we must study the dependence of di?erent stellar mass distributions on the dust feedback process. We performed the calculation of Eqs. (1) and (2) computing the ejected material during the evolution of all stars using the IMF and PDMF distributions. In Fig. 2, we show the relative amount of dust ejected by each stellar mass range to the ISM during all its evolution, for the IMF and the PDMF. It is noticeable that the high mass component is the major source of dust for the Salpeter IMF distribution. These stars evolves rapidly and eject large amounts of heavy atoms during the SN phase, and their remnants evolve to form shells of few solar masses of dust particles. On the other hand, the result is the opposite if use the present stellar distribution of the Galaxy. There are few high mass stars, and as a consequence SNe are not so frequent. Using the PDMF, the low and intermediate mass stars, as they leave the main sequence, are the main contributors of dust to the ISM. Intermediate mass stars at supergiant phase have been assumed to be the most important source of dust but, surprisingly, the results for the PDMF show that stars with M? < 3 M⊙ are dominant. It can be explained by the overabundance of low mass stars in this distribution. In the present stage of the Galaxy as the dust is destroyed, or severely changed, in short timescales (τd ? 108 yr ), the PDMF would give more accurate abundances of dust in the ISM. Since the dust generated from high mass stars in the past was recycled, and with the absence of these objects in the current population, we may conclude that low mass stars are the main source of the dust observed in the present stage of the Galaxy. In Table 1 we show the quantitative results of the calculations described above. For a typical IMF the high mass stars (M? > 8 M⊙ ) are responsible for 68% of the dust that


D. Falceta-Gon?alves: ISM dust feedback from low to high mass stars c

Table 1. Relative and absolute dust ISM feedback contribution for di?erent stellar component mass functions. Stellar mass range Md (M > 8 M⊙ ) Md (M < 8 M⊙ ) Md
a a total

IMF 68% 32% 7 × 10

PDMF 1% 99% 2 × 107

(M⊙ )

assuming a total stellar population of 1 × 1010 M⊙ .

returns to the ISM. On the other hand, considering a PDMF, this contribution falls to less than 1%. To determine the absolute feedback mass, we used a total stellar population of 1 × 1010 M⊙ , which gives a total dust mass Md ? 7 × 107 for the IMF distribution, and 2 × 107 for the PDMF. Interestingly, the results indicate that in recent starburst regions, one should expect a larger dust-to-gas ratio when compared to an evolved population. It could possibly be the reason for irregular and spiral galaxies, which present high star formation activity, have more dust than the evolved elliptical galaxies (Seaquist et al. 2004). However, since we have very di?erent scenarios here, with di?erent feedback and destruction timescales for each type of galaxy, this statement needs more detailed calculations to be tested. 3.1. Time evolution In the previous calculations, to obtain the total amount of dust ejected to the ISM we had to assume the mass function of the stellar population, which translates the evolutionary phase of the stellar component at the epoch we are studying as the dust is recycled in short timescales. However, in order to obtain the time evolution of the ISM dust component, we have to include in Eq. (1) the star formation rate function over history. We performed the evolutionary calculation assuming a constant star formation rate of 5 M⊙ yr?1 , as used by Morgan & Edmunds (2003). However, di?erently of that work we took into account the dust destruction and studied its role on the total dust ejected to the ISM. At each time step, we calculate the total ejection from each stellar mass range of the current population, add new stars using the Salpeter IMF, remove stars that have already evolved and, ?nally remove the destroyed dust from the total solid component. In the present calculations, in order to simulate the chemical enrichment of the stars, a metallicity of z = 0.01z⊙ was arbitrarily used for the initial population (t < 107 yr), and z = z⊙ for t > 106 yr. In Fig. 3 we show the results for the absolute dust mass ejected to the ISM. In both cases we can identify the dominance of massive stars on the total ejections at the earlier stages of the galaxy evolution. On both models, it is also noticeable the appearance of substantial dust amount from low and intermediate mass stars only after ? 108 yr. These objects become the major dust producers on the last 0.5 billion years on both models. The main di?erences appear on the later stages, where for considering dust destruction, massive stars would be responsible for 3 times less dust mass than obtained by previous

D. Falceta-Gon?alves: ISM dust feedback from low to high mass stars c


winds Sne total

winds Sne total



M (solar)


M (solar)







1.E+02 1.E+06





T (yr)

T (yr)

Fig. 3. Absolute dust mass ejected to the ISM. The modeled ejection by high mass stars (solid thin), low and intermediate mass stars (dashed) and total (solid thick), without dust destruction (left panel) and considering dust destruction (right panel).

calculations, while this proportion for low and intermediate mass stars is negligible. After 10 billion years of evolution, we obtained a current dust mass of ? 6 × 107 M⊙ without dust destruction, and ? 107 M⊙ taking into account the dust destruction.

4. Conclusions
It is still unclear what is the main source of the dust feedback in our Galaxy. The dust must be formed in stars and ejected to the ISM and some authors have argued favoring cool latetype stellar winds, which present high mass-loss rates and dust is proved to be formed in these sites by observations. On the other hand, other plausible sources are the SNe ejecta. During the ?nal evolutionary phases, high mass stars explode and supersonically eject a very rich gas to the ISM. Firstly, to determine the relative amount of dust ejected to the ISM for each stellar mass at each evolutionary phase we calculated the dust ejection during each evolutionary phase of the stars for di?erent stellar mass distributions. As main result we showed that SNe are the main source of ISM dust feedback if a classic Salpeter IMF distribution is assumed. On the other hand, if we use the present day mass function, we show that the main sources of dust to the present Galaxy are the low and intermediate mass stars, representing more than 90% of the total dust mass. Secondly, we studied the dust feedback process along the galactic time evolution, as done by Morgan & Edmunds (2003), but including the e?ects of dust destruction by SN blasts. For simplicity we used a constant destruction rate, consistent with the current galactic physical parameters. During previous ages the SNe ejecta are dominant, in agreement with previous works. We showed that, considering the dust destruction, low and intermediate


D. Falceta-Gon?alves: ISM dust feedback from low to high mass stars c

mass stars are dominant for a galactic age of t > 109 yr, in a much higher proportion. The total dust mass of ? 107 M⊙ is obtained for a star formation rate of 5 M⊙ yr?1 . The dust destruction timescale depends on the SNe frequency, as well as the ISM density and temperature. It is probable that the destruction rate was higher earlier during the galactic evolution. In this case, the presented conclusions will stand, and the role of low and intermediate mass stars in later stages will be even higher.
Acknowledgements. D.F.G thanks FAPESP (No. 06/57824-1) for ?nancial support, also A. Jones and the referee for the comments and suggestions.

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