On the nature of the most obscured C-rich AGB stars in the Magellanic Clouds
The stars in the Magellanic Clouds with the largest degree of obscuration are used to probe the highly uncertain physics of stars in the asymptotic giant branch (AGB) phase of evolution. Carbon stars in particular, provide key information on the amount of third dredge-up (TDU) and mass loss. We use two independent stellar evolution codes to test how a different treatment of the physics affects the evolution on the AGB. The output from the two codes are used to determine the rates of dust formation in the circumstellar envelope, where the method used to determine the dust is the same for each case. The stars with the largest degree of obscuration in the LMC and SMC are identified as the progeny of objects of initial mass and , respectively. This difference in mass is motivated by the difference in the star formation histories of the two galaxies, and offers a simple explanation of the redder infrared colours of C-stars in the LMC compared to their counterparts in the SMC. The comparison with the Spitzer colours of C-rich AGB stars in the SMC shows that a minimum surface carbon mass fraction must have been reached by stars of initial mass around . Our results confirm the necessity of adopting low-temperature opacities in stellar evolutionary models of AGB stars. These opacities allow the stars to obtain mass-loss rates high enough () to produce the amount of dust needed to reproduce the Spitzer colours.
keywords:Stars: abundances – Stars: AGB and post-AGB, galaxies: Magellanic Clouds
The recent years have witnessed a growing interest in the evolution of stars of low and intermediate mass (), which evolve through the asymptotic giant branch (AGB) after the end of core helium burning. While this evolutionary phase only accounts for a very small percentage of the overall lifetime, it is extremely important because it is during the AGB when the richest nucleosynthesis occurs as well as the most intense mass loss. This means that AGB stars are able to enrich their environment with gas chemically altered by internal nuclear processes and with the dust formed in their wind.
The unsolved problems of galaxy formation and chemical evolution at all redshifts requires a full understanding of the topic of stellar evolution and nucleosynthesis of AGB stars. Particular areas where AGB stars have proven useful include inferring the masses of galaxies at high redshifts, owing to their large infrared luminosities (Maraston et al. 2006); chemical evolution of galaxies (Romano et al. 2010), owing to the ability of AGB stars to enrich their environment with stellar winds; because of the efficiency of the dust formation process in their winds, AGB stars play a crucial role in the formation and evolution of galaxies (Santini et al. 2014); recent studies suggested a relevant contribution from AGB stars to the dust content of high-redshift quasars (Valiante et al. 2011), contrary to earlier investigations, which stressed the dominant role of supernovae (SNe) (Todini & Ferrara, 2001; Nozawa et al., 2003; Maiolino et al., 2004); finally, AGB stars are one of the favoured polluters for providing the gas required to form second generation stars in globular clusters (Ventura et al., 2001).
While theoretical models of AGB stars have seen significant progress over the last few years (e.g., Karakas & Lattanzio 2014), the results are still not completely reliable. This is primarily because we still do not understand how mass loss or convection work in stars. The problem with convection manifests itself in two important ways in AGB stars. The first is through the efficiency of third dredge-up (TDU), which is the inward penetration of the convective envelope following each thermal pulse. The efficiency or depth of TDU depends on how convective borders are treated numerically (e.g., Frost & Lattanzio, 1996). The second is through temperature gradients in convective regions, which cannot be calculated from first principles (Ventura & D’Antona 2005). Therefore comparing theoretical AGB models with observations is crucial in order to substantially improve the predictive power of the stellar evolution models.
The Magellanic Clouds (MCs) are an ideal environment to test theoretical predictions, because they are relatively close (51 kpc and 61 kpc respectively, for the LMC and SMC, Cioni et al. 2000; Keller & Wood 2006) and the low reddening ( mag and 0.04 mag, respectively, for the LMC and SMC, Westerlund 1997). Furthermore, the study of the MCs provides a wider range of possibilities in comparison with the Milky Way, because the interstellar medium of our Galaxy is highly obscuring and the distances of the stars are unknown. Also, the MCs probe a lower metallicity than the disc of our Galaxy.
Various dedicated surveys have been devoted to observe the AGB population of the MCs: the Magellanic Clouds Photometric Survey (MCPS, Zaritsky et al., 2004), the Two Micron All Sky Survey (2MASS, Skrutskie et al., 2006), the Deep Near Infrared Survey of the Southern Sky (DENIS, Epchtein et al., 1994), the Surveying the Agents of a Galaxy’s Evolution Surveys with the Spitzer telescope for the LMC (SAGE–LMC, Meixner et al., 2006) and the SMC (SAGE–SMC, Gordon et al., 2011), and HERschel Inventory of The Agents of Galaxy Evolution (HERITAGE, Meixner et al., 2010, 2013).
These surveys have produced a wealth of data on AGB stars, which can be used to compare to the results of theoretical calculations. To reproduce the observed infrared (IR) colours, which are sensitive to the amount of dust formed in the circumstellar envelope, some research groups couple the description of the internal star with the dust formation process in the wind. This approach was first set up by the Heidelberg team (Ferrarotti & Gail, 2001, 2002, 2006) and later used by other independent investigators (Ventura et al., 2012a, b; Di Criscienzo et al., 2013; Ventura et al., 2014a; Nanni et al., 2013a, b, 2014).
Against this background, we have started a research project aimed at constraining the uncertain physics of AGB evolution, by focusing our attention on the most obscured AGB stars in the MCs.
This study follows Marigo et al. (2008), who built theoretical isochrones which included the AGB phase and extended the isochrones to the IR bands. Here we take a step forward by relaxing some of the assumptions made by Marigo et al. (2008). These include determining the expansion velocity of the wind and the final dust to gas ratio, and we model the AGB phase by the full integration of the stellar structure equations, rather than using a synthetic approach. We base our analysis on AGB models calculated from two independent stellar evolution codes which made a significant contribution to the literature of AGB stars over the past couple of decades: MONASH (Frost & Lattanzio, 1996) and ATON (Ventura et al., 1998). The two codes have been developed and updated independently and include numerous differences between each other in the numerical structure and in the physical ingredients used. This procedure provides us with a much more complete and critical analysis because: a) it adds robustness to common findings; b) the discrepancy between results provide an estimate of the uncertainty associated with that result; and c) the comparison with the observations may allow us to select the most appropriate description of a given phenomenon (e.g., the treatment of convective borders).
In the first paper of this series (Ventura et al., 2015a) we focused on oxygen-rich stars in the LMC with the brightest IR emission, interpreted as the progeny of stars experiencing hot bottom burning (HBB).
In this paper we turn to the carbon star population in the MCs. The goal of the present investigation is to use the sample of numerous C-rich AGB stars to reconstruct the various stages of their evolutionary history. In particular, we are interested in studying the amount of carbon accumulated in the external mantle and the rate at which their envelope has been gradually lost by stellar winds.
We will preferentially concentrate on the C-stars with the largest degree of obscuration, for which the mass and chemical composition of the progenitors can be established; this makes the comparison with the models easier and more reliable.
The paper is organised as follows. Section 2 presents an overview of the observations of the AGB population of the MCs, with a summary of the interpretative analysis proposed so far. The physical ingredients used to calculate the evolutionary sequences presented here and the method followed to describe the dust formation process and to produce synthetic spectra are given in Section 3. Section 4 presents the results concerning the main evolution and dust properties of the stars currently evolving through the C-rich AGB phase in the MCs. The comparison between the AGB stars with the largest degree of obscuration and the results from theoretical models is given in Section 5, while Section 6 discusses our interpretation in terms of other observational parameters as well as future observations to test it. Conclusions are presented in Section 7.
2 AGB stars in the Magellanic Clouds
The results from the surveys MCPS, 2MASS and DENIS have been used to derive information on the internal structure and on the efficiency of the mechanisms that are altering the surface chemical composition of AGB stars.
Studies focused on the interpretation of the luminosity function of carbon stars in the LMC and SMC have provided important information on the efficiency of TDU and the core mass at which TDU begins (Groenewegen & de Jong, 1993; Marigo et al., 1999; Karakas et al., 2002; Izzard et al., 2004; Marigo & Girardi, 2007; Stancliffe et al., 2005).
The mid-IR Spitzer data, combined with near-IR 2MASS photometry, have been extensively used to derive the main properties of the stars observed, specifically the luminosity, the rate of mass loss, and the dust injection rate (Groenewegen et al., 2007; Riebel et al., 2010, 2012; Srinivasan et al., 2009, 2011; Boyer et al., 2011, 2012). Various methods have been proposed to classify the observed stars and separate carbon stars from their oxygen-rich counterparts (Cioni et al., 2000a, b, 2006). The stars with the highest degree of obscuration have been traditionally referred to as ”extreme” (Blum et al., 2006), owing to their extremely red IR colours and the uncertain surface chemical composition.
In a series of papers (Dell’Agli et al., 2014, 2015a, 2015b) we tackled the problem of interpreting the IR observations of the MCs AGB star population by confronting the observational evidence with results of full AGB evolutionary models. The models also account for dust formation in the circumstellar envelope. The latter ingredient is mandatory because radiation from the central object is reprocessed to longer, infrared wavelengths by dust.
Based on the results by Dell’Agli et al. (2015a), Ventura et al. (2015a) performed an extensive exploration of the various input used to build AGB evolutionary sequences of oxygen-rich intermediate-mass stars in the LMC. The study, which used results from different evolutionary codes, found that the expected position in the various IR colour–colour planes occupied by oxygen-rich AGB stars during the phase with the strongest obscuration is practically independent of the details of AGB modelling.
In this paper we turn our attention to the C-star population in the LMC and SMC. Dell’Agli et al. (2014) characterised the AGB stars populating the diagonal band in the CCD of the two galaxies, extending to (LMC, Srinivasan et al., 2011) and (SMC, Boyer et al., 2011), as carbon stars (see also Dell’Agli et al., 2015a, b). The scenario proposed by Dell’Agli et al. (2014) is that the observed bands represent obscuration sequences: the stars move across the diagonal band as they become more enriched in carbon, owing to the effects of TDU. The subsequent investigations by Dell’Agli et al. (2015a, b) followed a population synthesis approach, which allowed us to determine the expected distribution of stars in the colour–colour and colour–magnitude planes obtained with the Spitzer bands. These studies are based on the star formation history of the MCs by Harris & Zaritsky (2004, 2009) and on the evolutionary times of stars of various mass and metallicity, reported in Table 1 in Dell’Agli et al. (2015a).
One general result is that the regions of the observational planes where highly-obscured carbon stars are found are not well populated. This is because the evolutionary time scales get shorter as the star becomes enriched in carbon, owing to the considerable increase in the rate of mass loss. This has important consequences on the (current) mass distribution of the carbon stars observed. All the stars with initial mass in the range evolve as carbon stars from a given stage of the evolution until the removal of the envelope, where the final stellar mass is . On the other hand, for the reasons given above, the very final evolutionary phases have a very short duration. The combination of these two factors makes the mass distribution of the LMC to peak around , in nice agreement with the analysis based on pulsation periods by Boyer et al. (2015).
Dell’Agli et al. (2015a) found that in the LMC the C-rich AGB stars with the reddest infrared colours formed during the Myr long epoch of high star formation, which occurred Myr ago, when most of the stars formed from gas with metallicity . An age of Myr corresponds to stars with initial masses .
By applying to the SMC the same population synthesis analysis, Dell’Agli et al. (2015b) found that the stars exhibiting the largest obscuration descend from stars, formed Gyr ago, when the dominant metallicity of the interstellar medium was . Contrary to the LMC, only a negligible fraction of stars descending from objects are expected to evolve nowadays through the very final AGB phases of highest obscuration, because the SFR of the SMC exhibits a much narrower peak than the LMC at Myr ago.
We will focus on these masses and metallicities in the following sections.
3 Numerical and physical inputs
3.1 Stellar evolution models
This work is based on evolutionary sequences calculated with the ATON code (Ventura et al., 1998) and with the Monash version of the Mount Stromlo Stellar Structure Program (MONASH, Frost & Lattanzio, 1996). Exhaustive discussions on the numerical and physical input adopted are found in the papers by Ventura et al. (2013) and Karakas (2010), which also provide a detailed description of the chemical and physical properties of the AGB evolution of these stars.
The main differences between the two sets of models are the treatment of convection, the description of mass loss, and the calculation of molecular opacities in the low-temperature region of the envelope:
In the ATON code the convective instability is described by means of the Full Spectrum of Turbulence model developed by Canuto & Mazzitelli (1991), whereas in the MONASH case the traditional mixing length theory is used.
The ATON sequences are calculated by coupling nuclear burning and mixing of chemicals in a diffusive-like scheme. Overshoot of convective eddies into radiatively stable regions is described by means of an exponential decay of velocities from the convective/radiative interface, fixed by the Schwarzschild criterion. The e-folding distance is assumed to be (where is the pressure scale height calculated at the formal boundary of convection), in agreement with the calibration based on the observed luminosity function of carbon stars in the LMC, given by Ventura et al. (2014a). The MONASH models of Karakas (2010) assume instantaneous mixing and no overshoot beyond the formal Schwarzschild boundary is applied. However, the MONASH models implement an algorithm to search for a neutrally stable point (e.g. Lattanzio, 1986), which has been shown to increase the amount of TDU relative to models without (Frost & Lattanzio, 1996). Note that in low-mass AGB models the amount of TDU found by this algorithm is still less than required to match the C/O transition luminosity of MC AGB stars and some formal overshoot had to be applied (Kamath et al., 2012).
In the ATON sequences, molecular opacities in the low-temperature regime (below K) are calculated by means of the AESOPUS tool (Marigo & Aringer, 2009). The opacities are suitably constructed to follow the changes in the chemical composition of the envelope, particularly of the individual abundances of carbon, nitrogen, and oxygen. The MONASH models from Karakas (2010) include an approximate treatment for the molecular opacities (in particular CN, CO, HO and TiO) using the formulations from Bessell et al. (1989) with the corrections by Chiosi et al. (1993). These fits do include some compositional dependence, but do not account for large variations in the CNO species.
3.2 Dust formation in the winds of AGB stars
The growth of dust particles in the circumstellar envelope is described following the pioneering explorations by the Heidelberg group (Gail & Sedlmayr, 1985, 1999; Ferrarotti & Gail, 2001, 2002, 2006; Zhukovska et al., 2008). The wind is assumed to expand isotropically from the surface of the star; the velocity is held constant until gas molecules enter the region where condensation into dust particles is favoured. As far as a minimum amount of dust is formed, the results are independent of the adopted initial velocity.
The model is based on the equation of momentum conservation and on a differential relation for the radial variation of the optical depth:
accounts for the effects of radiation pressure on dust grains, while is the extinction coefficient.
The description of the wind is completed by the equation giving the radial variation of temperature and by the mass continuity relation:
Here we focus on carbon-rich environments, where the surface carbon abundance exceeds oxygen. In this case the two main dust species formed are solid carbon (C) and silicon carbide (SiC). The condensation reactions by which the two species form are, respectively, and (see, e.g. Ferrarotti & Gail, 2006). The condensation temperatures are 1100 K (C) and 1400 K (SiC). The growth rate of dust grains ( and ) is proportional to the least abundant among the species involved in the condensation reactions, namely and silicon. Considering the high stability of CO and SiS molecules, we have
In the above equations () indicates the fraction of carbon (silicon) molecules condensed into dust particles.
SiC is the most stable species and forms at higher temperatures, thus closer to the surface of the star. Equation 6 indicates an upper limit to the growth of SiC particles, reached when the fraction of silicon molecules condensing into SiC approaches . Because neither silicon nor sulphur undergo significant variations along the life of stars of intermediate mass, this quantity remains constant during the AGB phase.
While the formation of SiC grains is important for the IR properties of the SED of AGB stars, it does not influence the dynamical status of the wind. This is because SiC particles are extremely transparent to electromagnetic radiation and thus do not contribute to the acceleration of the wind via radiation pressure.
Solid carbon is less stable than SiC, therefore the zone where the formation of carbon grains occurs is more external than the region where SiC particles begin to form. Because the surface carbon abundance is generally much higher than that of silicon, contrary to SiC, no saturation in the carbon dust formation process occurs. The only exception is at the very beginning of the C-rich phase, when the carbon excess with respect to oxygen is very small, which prevents the formation of significant quantities of carbon dust (see equation 5).
However, because of the very large values attained by the extinction coefficient of solid carbon grains, the growth of these particles is commonly halted by the considerable expansion of the wind, which determines a fast drop in the gas density, according to equation 4.
We may safely assume in this case (e.g., equation 5) that the key quantity is the density of molecules111This is consistent with mid-IR spectroscopic observations of Galactic and MCs AGB stars, which show that CH is very abundant in their circumstellar envelopes (e.g., van Loon et al. 1999; Yang et al. 2004; Lagadec et al. 2007; van Loon et al. 2008).. The density of in turn depends on the surface carbon mass fraction and on the density of the wind in the region where condensation occurs, i.e., the zone where the temperature is K; we refer to the density of this region as .
Because the typical distance from the surface at which solid carbon forms is , we may safely expand equation 3 assuming that , to obtain
The first term on the right hand side of equation 8 is dominant. Therefore, the number of molecules available to form solid carbon is determined by the carbon mass fraction, X(C) and the ratio.
We may therefore conclude that the winds of carbon stars have the following stratification:
SiC forms in an internal zone, at a temperature of K. In most cases the growth of SiC particles is halted by saturation, which occurrs when the fraction of gaseous silicon condensing into dust approaches (see discussion in the previous section). The wind is modestly accelerated by formation of SiC, because this species is highly transparent to radiation.
Solid carbon particles form in more external regions, where the temperature is K. In this case the wind is greatly accelerated owing to the high values of the extinction coefficient of carbon dust. The factors mostly relevant to formation of solid carbon are the ratio and the surface carbon mass fraction.
3.3 Synthetic spectra
To determine the magnitudes in the Spitzer bands used in the present analysis we follow the same approach used in Ventura et al. (2015a) and discussed in detail in Dell’Agli et al. (2015a). Based on the values of mass, luminosity, effective temperature, mass-loss rate and surface chemical composition calculated from the MONASH and ATON codes, we apply the model of dust formation described in Section 3.2 to determine the size of the dust grains formed and the optical depth (here we use the value at m, ).
These ingredients are used by the code DUSTY (Nenkova et al., 1999) to calculate the synthetic spectra of each selected point along the evolutionary sequence. The magnitudes in the various bands are obtained by convolution with the appropriate transmission curves. DUSTY needs as input parameters the effective temperature of the star, the radial profile of the density of the gas and the dust composition of the wind, in terms of the percentage of the various species present and of the size of the dust particles formed. All these quantities are known based on the results of stellar evolution and of the description of the wind.
4 Carbon stars in the Magellanic Clouds: evolution and dust properties
We focus now on the stars that account for most of the C-star population in the LMC and SMC. For the LMC we consider models of initial mass and metallicity . To compare models with the same core mass, while in the ATON case we show models of initial mass and , in the MONASH case we present the and models; this is due to a slight difference in the mass vs core mass relationships found with the two codes in the range of masses close to the limit to experience the helium flash. For the SMC we analyse the evolution of stars of metallicity .
4.1 Physical properties of carbon stars
The evolution of these models is shown in Fig. 1, where we plot the luminosity, effective temperature, mass-loss rate and surface carbon abundance as a function of time from the beginning of the thermally-pulsing AGB phase.
The top, left panel of Fig. 1 shows that the ATON and MONASH models evolve at similar luminosities, an indication that the core masses are similar. Note that in this case we do not expect any effect of convection modelling on the behaviour of luminosity, because stars in this range of mass do not experience HBB. This is at odds with the analysis by Ventura et al. (2015a), where the ATON and MONASH models of stars were shown to evolve at different luminosities. The only meaningful difference difference is the duration of the whole AGB phase, which is systematically longer in the MONASH models; we will come back to this point shortly. The duration of the AGB phase is not monotonic with mass: the model evolves for a longer time compared to their and counterparts. This is because the relationship between the core mass at the beginning of the AGB phase and the initial mass of the stars has a minimum at , which makes the growth of the luminosity of the model in the initial AGB phases slower than in the other cases.
In the phases before the C-star phase is reached, the effective temperatures of models of the same mass are similar in the MONASH and ATON cases (see top, right panel of Fig. 1). After the C/O ratio exceeds unity, the effects of the different low-temperature opacities takes over: the ATON models, owing to the expansion of the external regions triggered by the increase in the opacity, evolve to lower temperatures, down to K, whereas in the MONASH models we find K. This effect is extensively discussed in Ventura & Marigo (2009, 2010).
The difference in the surface temperature has a direct effect on the rate of mass loss. As shown in the bottom, left panel of Fig. 1, exceeds /yr in the ATON models of , whereas in the MONASH case it is times smaller; in the model of metallicity the difference is smaller (/yr and /yr in the MONASH and ATON models, respectively). This is not only due to the more expanded, hence less gravitationally bound, configurations of lower ’s models; a further reason for the higher ’s of the ATON models is the use of the formulation by Wachter et al. (2002, 2008), which favours large rates of mass loss in carbon rich, low stars. The rate of mass loss in the ATON models is generally larger than in the MONASH cases also during the early AGB phases. This is due to the differences between the Blöcker (1995) and Vassiliadis & Wood (1993) formulae for M stars. This is not a major problem here because little mass is lost during the oxygen-rich phase of these stars and, as will be shown in the following, the amount of dust formed during these evolutionary phases is negligible in comparison to the late evolutionary phases, when the stars are carbon-rich.
4.2 The change in the surface chemistry
Concerning the surface chemistry, we show in the bottom, right panel of Fig. 1 the variation of the carbon abundance in the same models shown in the other panels. The most relevant difference between the results found with the two evolution codes is found in the case, for which the MONASH and ATON models reach final carbon mass fractions of and , respectively. This situation is reversed in lower mass models; indeed in the ATON case the final surface carbon is , a factor of 2 higher than MONASH. This is because the MONASH models do not show very efficient dredge-up at the minimum mass for C-star production, a problem that has been discussed extensively in Kamath et al. (2012) and Karakas et al. (2010b). The 1.5 model only dredges up of material from the He-intershell, with a minimum core mass for TDU of 0.6. Kamath et al. (2012) found that the minimum mass for TDU in LMC AGB stars should be lower, at 0.58, indicating that convective overshoot should probably be applied (see also, e.g., Marigo et al., 1999). To reach surface carbon mass fractions an extra-mixing zone extending over two pressure scale heights below the base of the convective envelope needs to be applied. This is entirely consistent with the analysis by Kamath et al. (2012), who invoked an overshoot of similar extension to match the observations of AGB stars in MCs clusters.
These dissimilarities between the results obtained with the two evolution codes are not surprising, given the considerable sensitivity of the carbon enrichment of the surface layers to the details of the treatment of convective borders, as thoroughly documented in the literature (Karakas & Lattanzio, 2014).
4.3 Dust formation in the circumstellar envelope
The changes in the spectral energy distribution of AGB stars are correlated with evolution properties. This reflects the variation of the main physical parameters (e.g., mass loss) and of the quantity of dust in the circumstellar envelope.
Fig. 2 shows the evolution of the size of the dust grains formed (left panel) and the optical depth at wavelength m, , for the same models shown in Fig. 1. For clarity, we only show the dimension of the dust particles formed in greater quantities, which provide the dominant contribution to the acceleration of the wind, i.e., olivine (oxygen-rich phases) and solid carbon (C-stars). is plotted on a logarithmic scale, which allows us to discuss the early AGB phase, which is otherwise undetectable on a linear scale plot. On the abscissa we show the surface mass fraction of carbon, which increases during the AGB phase.
The following results are in common between the MONASH and ATON models:
(i) little dust formation occurs until the C/O ratio is close to unity. As shown in Fig. 2, the olivine grains barely exceed a nanometer size and the optical depth is very small. The SED of the star is unaffected by dust during these phases. This holds independently of mass and metallicity.
(ii) The quantity of carbon dust formed increases during the subsequent C-star evolution, as confirmed by the rise of the grain size and , shown in Fig. 2. This can be understood based on the discussion in Section 3.2, because both factors affecting formation of carbonaceous dust, namely the surface carbon abundance and the ratio, increase after becoming C-rich (see Fig. 1).
(iii) The amount of dust formed in the winds of the star is significantly smaller than in their counterparts of higher mass. This is because the models, particularly during the final AGB phases, attain a higher surface carbon abundance, which in turn leads to lower effective temperatures and higher rates of mass loss; this can be clearly seen in Fig. 1.
4.4 Thermodynamic and chemical structure of the wind
To understand how the conditions in the wind evolve, we show in Fig. 3 the stratification of the circumstellar envelope in three distinct stages of the carbon star phase of the , (top panel) and the , ATON models. The plots illustrate conditions at the beginning of the AGB phase, the very end of the AGB evolution and an intermediate phase. In the same figure we also show the MONASH models of mass and during the final AGB phases. The panels of the figure show the radial distribution of the grains size of SiC and solid carbon, the velocity of the wind, and , the quantity entering equations 2 and 3.
Formation of SiC occurs in an internal zone, stellar radii away from the surface, where the temperature is K. Because SiC is highly transparent to stellar radiation, the velocity of the wind stays constant in the region of SiC formation. At the very beginning of the carbon star phase SiC is produced in modest quantities, with grains of a few nanometers in size. In more advanced phases saturation condition occurs, the dimension of SiC grains grow to m and m in the and cases, respectively. This is because silicon in the envelope is either locked into SiS molecules or condensed into SiC particles. The difference in the SiC grain size is due to the dependence of the surface silicon abundance on initial metallicity.
Formation of carbon grains occurs stellar radii away from the surface, where the temperature is K. Carbon is produced in greater quantities compared to SiC, owing to the higher availability of carbon molecules in comparison to silicon. The formation of carbon dust is accompanied by the acceleration of the wind. The location of the carbon condensation zone is gradually shifted outwards during the AGB evolution; this is because the slope of the T(r) relation is smaller for lower effective temperatures and the higher also result in pushing out the region where K (see equation 3). The typical size of the carbon grains formed, , is of the order of m and increases during the AGB evolution. In the final evolutionary phases of the model we find m, whereas we get a maximum dimension m in the case.
In the comparison between the SiC and solid carbon dust formed, we note that the amount of SiC, after saturation conditions occur, stays constant during the AGB evolution. On the other hand larger and larger quantities of solid carbon grains are formed as the star accumulates carbon in the surface regions. Therefore, we expect that the SiC/C ratio decreases during the AGB evolution (see Fig. 4 and section 6).
The velocity reached by the wind also increases during the evolution of these stars, spanning the range km/s.
4.5 An overview of MONASH and ATON results
The comparison between the MONASH and ATON results allows us to study the main factors affecting carbonaceous dust formation in AGB stars.
The evolution of the infrared properties of these stars is strongly related to the amount of dust formed. As discussed in section 3.2, formation of solid carbon is determined by the surface carbon abundance and the ratio. The former is relevant at the beginning of the C-star phase, as confirmed by the steep slope of the vs X(C) and vs X(C) relations shown in Fig. 2. This is because the growth rate of carbon dust is proportional to the density of molecules, which in turn, is given by the carbon excess with respect to oxygen (see equation 5). For small carbon abundances even a small change of X(C) favours a high percentage increase in , which results in a significant rise in the growth rate of carbon grains. After the surface carbon exceeds the relative weight of this factor diminishes, because any additional change will result in a smaller percentage increase in the number density of particles; the ratio plays a dominant role here.
Fig 2 shows that at the end of the AGB evolution higher values of are reached in the ATON models. For we find in the MONASH model, whereas we obtain in the ATON case. In this case the star reaches relatively small carbon abundances, . Following the above discussion, we know that this is the domain most affected by the carbon content. The ATON model produces more dust than MONASH (see left panel of Fig. 2), owing to the higher availability of carbon in the surface regions, as shown in the bottom–right panel of Fig. 1. The infrared emission is consequently more intense in the ATON case.
Turning to models of higher mass and metallicity, we find that the MONASH model evolves to , while the ATON model reaches at the end of the AGB phase. Stars of this mass undergo more TDU events, thus becoming more C-rich during the AGB evolution. The rate of mass loss plays a dominant role here in affecting dust formation. This is confirmed by the comparison between the MONASH model of with the ATON, case: despite the former experiences a larger carbon enrichment (see Fig. 1), the latter reaches higher optical depths in the final phases, owing to the higher rate of mass loss experienced.
5 Spitzer colours of carbon stars in the MCs
As discussed in the previous sections, the evolution of AGB stars with progenitors of mass below is driven by the progressive enrichment of carbon in the surface regions. The SED of these stars gradually shifts to the IR, with the peak of the emission moving to longer wavelengths. This is illustrated in Fig. 4, where we show the SED of the , (left panel) and , models, in four evolutionary phases from the beginning of the AGB evolution, with practically no dust effects, to the very final phases. At the end of the AGB phase the SED of the model peaks at longer wavelengths compared to the case, for the reasons given in Section 4.3.
Fig. 5 shows AGB stars in the SMC (left panel) and LMC (right) on the colour–colour () plane. The regions delimited by the dashed lines are the C-star locii, according to Dell’Agli et al. (2015a, b). As discussed in section 2, most of the obscured C-stars in the LMC descend from progenitors, whereas in the SMC the objects with the reddest IR colours are the progeny of stars. Therefore the SEDs, corresponding to the end of the AGB phase (dashed lines), shown in Fig. 4, provide an indication of the typical colours of the most obscured AGB stars in the two galaxies. The synthetic SEDs confirm that the most obscured LMC AGB stars reach redder colours than their SMC counterparts. This explains why the C-star locus in the LMC is more extended towards the red (up to ) than in the SMC ()
This explanation is in constrast to the interpretation by van Loon et al. (2008), who invoked a metallicity dependence on dust formation to explain the stronger dust emission shown by carbon stars in the LMC compared to the SMC. Note that the present working hypothesis is focused on stars with the reddest colours, thus it is not in contrast with the assumption that C-star formation is easier in the SMC becaue of the lower average metallicity (Sloan et al., 2008).
The overall population of C-stars in the MCs is composed of a range of masses and chemistries (Dell’Agli et al., 2015a, b), which in the general case prevents us from identifying the progenitors of the individual sources observed. To overcome this difficulty we focus on the AGB stars populating the terminal side of the obscuration sequences of C-stars. As discussed in section 2, each star becoming C rich spends only a very small percentage of the AGB in the last evolutionary phase with the highest degree of obscuration. Therefore only stars of masses and metallicities given above can be observed in such advanced evolutionary phases.
Fig. 5 shows the evolutionary tracks corresponding to the same MONASH and ATON models shown in Fig. 2. All the evolutionary sequences reproduce the diagonal band where C-stars evolve. The only discrepancy between models and the observations concerns the C-stars populating the bluest region of the CCD, centred at . This group of stars present no signature of dust, consequently the synthetic spectrum is entirely determined by the GRAMS SED used to model the atmosphere of the central star. The reason for the difference is the absorption feature due to CO and C molecules, which is not included in the GRAMS models. This is however not an issue for the present analysis, because this feature vanishes when dust is present in the circumstellar envelope (Boyer et al., 2011).
The fact that both MONASH and ATON sequences trace the observations further reinforces the main conclusions by Dell’Agli et al. (2015a, b): the diagonal bands in the CCD of the LMC and SMC are obscuration sequences. The stars with the reddest colours correspond to those more enriched in carbon, with a larger amount of carbonaceous dust in the circumstellar envelope.
Fig. 5 shows that the ATON models nicely reproduce the observations, the evolutionary tracks reaching the terminal points of the observed sequences, both in the SMC and LMC cases. The MONASH models reproduce most of the AGB stars along the obscuration sequences, yet they do not extend to the reddest IR colours observed. This can be explained on the basis of the discussion in the previous section and of the results shown in Fig. 2 and 3. For the SMC, the reason for the higher degree of obscuration reached by the ATON sequences is mainly related to the higher quantity of carbon accumulated in stars during the AGB. For the LMC case, the main reason for the discrepancy among MONASH and ATON models is the difference in the description of the low-temperature molecular opacities in C-rich environments and in the mass-loss modelling (see section 3). These in turn affect the IR properties of the reddest AGB stars in the LMC, which reflects the mass-loss rate experienced in the final AGB phases, which, in turn is related to the effective temperature.
These arguments lead us to conclude that reproducing the IR colours of the most obscured AGB stars in the SMC requires models of stars of initial mass to achieve a surface carbon abundance . In order to reproduce the IR colours of the LMC AGB stars, we conclude that the main physical ingredient is the low-temperature opacities used in the calculations. The use of low-temperature opacities that follow the chemical composition of the envelope is especially important for stars with masses , which in the last phases reach surface carbon abundances . Furthermore, the description of mass loss in C-rich environments, where significant amounts of dust form, must be based on hydrodynamical wind models including dust formation in radiative transfer equations.
We stress that the results obtained by MONASH and ATON codes are fairly similar for most of the AGB phase, for the masses and metallicities investigated here. Significant differences are found only during the two last interpulse phases. For this reason, the change in the physical ingredients discussed are crucial for a correct determination of the dust properties of these stars and, more generally, for the interpretation of IR properties of more complex stellar populations, where a significant population of C-stars is expected. On the other hand, we expect little effects for the other results not directly related to dust, primarily the stellar yields, which reflect the whole AGB phase.
6 What do we learn from obscured carbon stars in the MCs?
The models presented here nicely reproduce the mid–infrared colours for the SMC and LMC. According to our schematization AGB stars become more and more obscured as the carbon in the envelope increases. If this is correct, the LMC proves the ideal environment to host C-stars with an extremely intense infrared emission. This is because the SFH of the LMC peaks at Myr (Harris & Zaritsky, 2009), the formation epoch of stars which are those reaching the largest abundances of carbon in the final evolutionary phases (see Fig. 1). If this understanding is confirmed, we reach the general conclusion that the degree of obscuration of the reddest stars in the LMC is the highest among C-rich AGB stars; for stars exhibiting a higher degree of obscuration, an AGB origin can be disregarded.
Table 1 reports the main properties of the individual stars which according to our interpretation populate the reddest portion of the C-star sequence in the CCD of the MCs. Observational confirmation of these quantities (in particular of the predicted radial stratification of the SiC and carbon grains) would be ideal to assess the robustness of our modelling and interpretation. Unfortunately this is challenging with present astronomical instrumentation.
Concerning the synthetic SEDs of the stars examined here, we note that the dashed track in the right panel of Fig. 4 is extremely similar to the SED of the extreme carbon star shown in the top-left panel of Figure 7 by Riebel et al. (2012), which is taken as a representative member of the group of most obscured C-stars in the LMC. Interestingly, in SMC C-rich AGB stars the CH and SiC features are observed to be stronger and weaker, respectively, than in the LMC stars (e.g., Lagadec et al. 2007; Zijlstra et al. 2006, van Loon et al. 2006, 2008). Indeed, our synthetic SEDs, which show an intermediate stage after becoming C-rich (red-dotted lines in Fig. 4), reproduce well this observation. The 3.1 m CH HCN absorption feature is stronger in a SMC AGB star than in the LMC case, while the opposite is seen for the 11.5 m SiC feature. This is in agreement with our framework because the production of SiC (see discussion in section 3.2) scales with the amount of silicon available at the surface, which in turn, is proportional to the metallicity of the stars. Therefore production of SiC is favoured in the LMC, because the metallicity of the C-stars in this galaxy, particularly those forming the largest quantities of dust, is generally larger than their counterparts in the SMC. On the other hand carbon dust production is approximately independent of metallicity, because the carbon accumulated to the surface of these stars is of primary origin.
As for the global properties of these objects, Riebel et al. (2012) find that the luminosities of the most obscured C-stars in the LMC are within the range , which nicely overlaps with the range of luminosities for the LMC reported in Table 1.
Concerning the mass loss rates, Riebel et al. (2012) find that the C-stars in the LMC with the highest degree of obscuration inject into the interstellar medium carbonaceous dust with a rate of yr. This is translated into an overall mass-loss rate of yr222To find the mass-loss rate from the dust rate we adopted a gas/dust ratio . This is indeed what we find based on our models, with a carbon mass fraction slightly above and a percentage of gaseous carbon condensed into dust of .. This quantity is significantly smaller than the result reported in Table 1, which is in much better agreement with the results published by Gullieuszik et al. (2012); van Loon (2006); Groenewegen et al. (2007).
On the chemical side, we have seen that the conclusions we may draw for the SMC and LMC are different. In the former case, we showed that within the context of our description of the AGB and dust systems the colours of the C-stars exhibiting the highest degree of obscuration are reproduced only if the amount of carbon accumulated at the surface exceeds of the total mass. This C abundance this corresponds to a C/O ratio above 3. The IR colours of the most obscured LMC C-stars are however less sensitive to the surface carbon abundance than their SMC counterparts. The uncertainties affecting the degree of carbon enrichment are still significant, which is confirmed by the differences between the MONASH (surface carbon mass fraction slightly below 0.02, C/O10) and ATON (X(C)0.01, C/O3) models.
The most obscured C-stars in the MCs are very faint in the optical domain but much brighter in the near-IR. Thus the best observational way to test the different nature (i.e., progenitor masses) of the obscured C-stars in the SMC and LMC would be to obtain follow-up high-resolution (20,000) near-IR (JHK bands) spectroscopy of these stars. This can be done with actual instrumentation (e.g., CRIRES at ESO/VLT). From such spectra one could get the CNO elemental abundances, which are expected to be different in both types of stars (see e.g., Ventura et al. 2015b).
On the other hand, an analysis of the chemical composition of PNe in the MCs would provide important complementary information on the chemical enrichment of C-stars in these galaxies. This is because only small surface abundance changes are expected from the final AGB phase to the PN stage. For example, Ventura et al. (2015b) showed that the most C-enriched PNe in the LMC display carbon abundances below X(C)0.01, in agreement with the and ATON models and with the MONASH model (see the bottom-right panel in Fig. 1). The extension of this type of analysis to a much wider sample of PNe in the LMC (and also to the SMC PNe) will help us to understand whether this upper limit in the carbon abundance is real, or due to the limited sample of PNe examined.
We use Spitzer IR data of C-stars in the Magellanic Clouds to improve our understanding of the evolution of AGB stars with masses below , which become carbon stars through repeated TDU events. We focus on the objects with the highest degree of obscuration, because it is easier to characterise their progenitors in terms of their initial masses and metallicities. This is due to differences in the SFH between the SMC and the LMC, allowing us to investigate stars of different mass. The analysis of the SMC permits to study the evolutionary properties of AGB stars of mass , whereas we use the LMC to investigate higher mass stars, with .
The LMC sequence of C-stars extends to redder IR colours () compared to the SMC (). According to our interpretation, this is because of the higher quantity of carbonaceous dust forming in the circumstellar envelope of stars, in comparison with their lower mass () counterparts evolving in the SMC.
The comparison between models and observations suggests the following: a) in AGB stars TDU must be efficient enough to produce a surface carbon abundance above before the end of the AGB phase; b) to correctly model the late AGB phases of stars of mass it is mandatory to include the carbon enrichment in the calculation of the low-temperature molecular opacities (Marigo, 2002; Ventura & Marigo, 2009, 2010; Kamath et al., 2012). In addition, the description of mass loss must rely on hydrodynamical simulations, which take into account dust formation. These physical ingredients are crucial in order to reproduce the extremely red colours of the C-stars in the LMC with the largest degree of obscuration. Based on our modelling, these stars evolve at effective temperatures close to K and loose their external mantle with a rate slightly above yr.
If our understanding is correct, we expect that the most obscured stars in the SMC are surrounded by a more internal region with SiC dust grains m sized, and a more external zone, stellar radii from the surface of the star, where SiC grains and m sized, solid carbon particles are present. In the counterparts in the LMC, the higher metallicity favours a larger growth of SiC grains, which reach dimensions of the order of m. Solid carbon grains on the other hand can grow to m, because these stars are more enriched in gaseous carbon than their counterparts of smaller mass.
High-resolution near-IR spectroscopy of the most obscured C-stars in the SMC and LMC as well as the analysis of a wider MC PNe sample will allow us to test the conclusions reached here; i.e., the most obscured C-rich AGB stars in the LMC are the descendants of stars with higher initial masses than their SMC counterparts.
The authors are indebted to the referee, J. Th. van Loon, for the careful reading of the manuscript and for the several comments, that help improving significantly the quality of this work. P.V. was supported by PRIN MIUR 2011 ”The Chemical and Dynamical Evolution of the Milky Way and Local Group Galaxies” (PI: F. Matteucci), prot. 2010LY5N2T. A.I.K. was supported through an Australian Research Council Future Fellowship (FT110100475). DAGH was funded by the Ramón y Cajal fellowship number RYC201314182 and he acknowledges support provided by the Spanish Ministry of Economy and Competitiveness (MINECO) under grant AYA201458082-P. F.D. and M.D.C. acknowledge support from the Observatory of Rome.
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