Solar metallicity AGBs

Studying the evolution of AGB stars in the Gaia epoch

Abstract

We present asymptotic giant branch (AGB) models of solar metallicity, to allow the interpretation of observations of Galactic AGB stars, whose distances should be soon available after the first release of the Gaia catalogue. We find an abrupt change in the AGB physical and chemical properties, occurring at the threshold mass to ignite hot bottom burning,i.e. . Stars with mass below reach the C-star stage and eject into the interstellar medium gas enriched in carbon , nitrogen and . The higher mass counterparts evolve at large luminosities, between and . The mass expelled from the massive AGB stars shows the imprinting of proton-capture nucleosynthesis, with considerable production of nitrogen and sodium and destruction of and . The comparison with the most recent results from other research groups are discussed, to evaluate the robustness of the present findings. Finally, we compare the models with recent observations of galactic AGB stars, outlining the possibility offered by Gaia to shed new light on the evolution properties of this class of objects.

keywords:
Stars: abundances – Stars: AGB and post-AGB – Stars: carbon – Stars: distances
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1 Introduction

Stars of mass in the range , after the consumption of helium in the core, evolve through the asymptotic giant branch phase: above a degenerate core, composed of carbon and oxygen (or of oxygen and neon, in the stars of highest mass), a burning zone and a region with CNO nuclear activity provide alternatively the energy required to support the star (Becker & Iben, 1980; Iben, 1982; Iben & Renzini, 1983; Lattanzio, 1986). Because helium burning is activated in condition of thermal instability (Schwarzschild & Harm, 1965, 1967), CNO cycling is for most of the time the only active nuclear channel, whereas ignition of helium occurs periodically, during rapid events, known as thermal pulses (TP).

Though the duration of the AGB phase is extremely short when compared to the evolutionary time of the star, it proves of paramount importance for the feedback of these stars on the host environment. This is because it is during the AGB evolution that intermediate mass stars lose their external mantle, thus contributing to the gas pollution of the interstellar medium. In addition, these stars have been recognised as important manufacturers of dust, owing to the thermodynamic conditions of their winds, which are a favourable environment to the condensation of gas molecules into solid particles (Gail & Sedlmayr, 1999).
For the above reasons, AGB stars are believed to play a crucial role in several astrophysical contexts.
On a pure stellar evolution side, they are an ideal laboratory to test stellar evolution theories, because of the complexity of their internal structure. In the context of the Galaxy evolution, the importance of AGB stars for the determination of the chemical trends traced by stars in different parts of the Milky Way has been recognised in several studies (Romano et al., 2010; Kobayashi et al., 2011). Still in the Milky Way environment, massive AGB stars have been proposed as the main actors in the formation of multiple populations in Globular Clusters (Ventura et al., 2001). Moving out to the Galaxy, it is generally believed that AGB stars give an important contribution to the dust present at high redshift (Valiante et al., 2009, 2011); furthermore, these stars play a crucial role in the formation and evolution of galaxies (Santini et al. 2014).
It is for these reasons that the research on AGB stars has attracted the interests of the astrophysical community in the last decades.
The description of these stars is extremely difficult, owing to the very short time steps (of the order of one day) required to describe the TP phases, which leads to very long computation times. Furthermore, the evolutionary properties of these stars are determined by the delicate interface between the degenerate core and the tenuous, expanded envelope, thus rendering the results obtained extremely sensitive to convection modelling (Herwig, 2005; Karakas & Lattanzio, 2014).
There are two mechanisms potentially able to alter the surface chemical composition, namely hot bottom-burning (hereinafter HBB) and third dregde-up (TDU). The efficiency of the two mechanisms potentially able to alter the surface chemical composition, namely hot bottom burning (hereinafter HBB) and third dregde-up (TDU) depends critically on the method used to determine the temperature gradients in regions unstable to convective motions (Ventura & D’Antona, 2005a) and on the details of the treatment of the convective borders, for what concerns the base of the convective envelope and the boundaries of the shell that forms in conjunction with each TP, the so called ”pulse driven convective shell”. The description of mass loss also plays an important role in the determination of the evolutionary time scales (Ventura & D’Antona, 2005b; Doherty et al., 2014).
Given the poor knowledge of some of the macro-physics input necessary to build the evolutionary sequences, primarily convection and mass loss, the comparison with the observations is at the moment the only way to improve the robustness of the results obtained.
On this side, the Magellanic Clouds have been so far used much more extensively than the Milky Way (Groenewegen & de Jong, 1993; Marigo et al., 1999; Karakas et al., 2002; Izzard et al., 2004; Marigo & Girardi, 2007; Stancliffe et al., 2005), given the unknown distances of Galactic sources, which render difficult any interpretation of the observations. Very recent works outlines the possibility of calibrating AGB models based on the observations of the AGB population in dwarf galaxies in the Local Group (Rosenfield et al., 2014, 2016). The attempts of interpreting the observations of metal poor environments, typical of the Magellanic Clouds and of the galaxies in the Local Group, has so far pushed our attention towards sub-solar AGB models, published in previous works of our group (Ventura & D’Antona, 2008, 2009, 2011; Ventura et al., 2013). The main drivers of these researches were the understanding of the presence of multiple populations in globular clusters and the comparison of our predictions with the evolved stellar population of the Magellanic Clouds (Dell’Agli et al., 2015a, b; Ventura et al., 2015, 2016) and metal poor dwarf galaxies of Local Group (Dell’Agli et al., 2016). The advent of the ESA-Gaia mission will open new frontiers in the study of stars of any class, and in particular for the evolved stellar population of the Milky Way. Launched on December 2013, Gaia will allow constructing a catalogue of around more than 1 billion astronomical objects (mostly stars) brighter than 20 G mag (where G is the Gaia whitelight passband, Jordi et al. 2010), which encompasses of the Galactic stellar population. During the five year mission life time each object will be observed 70 times on average, for a total of photometric measurements in G band, the exact number of observations depending on the magnitude and position of the object (ecliptic coordinates) and on the stellar density in the object field. Gaia will perform as global astrometry for all the observed objects, thus allowing the determination of the distance of several AGB stars with unprecedented accuracy, refining the parallaxes determination of all the stars in the Hipparcos catalogue and dramatically increasing the number of accurately known parallaxes. The first release of the Gaia catalogue is foreseen by the end of summer 2016, and it will contain positions and G-magnitudes for all single objects with good astrometric behaviour. In order to benefit from the possibilities offered by the upcoming Gaia data, we calculated new AGB models with solar metallicity, completing our library, so far limited to sub-solar chemical composition models. The main goal of the present work is to explore the possibilities, offered by the comparisons with observations, to further constrain some of the still poorly known phenomena affecting this class of objects. This task is essential to be able to assess the role played by AGB stars in the various contexts discussed earlier in the section.
To this aim, after the presentation of the main physical and chemical properties of the solar chemistry AGB models, we will compare our theoretical results with a) the models available in the literature, to determine their degree of uncertainty and their robustness and b) recent observations of galactic AGB. In some cases we will also discuss how Gaia will help discriminating among various possibilities still open at present.

The paper is structured as follows: the description of the input used to build the evolutionary sequences is given in section 2; in section 3 we present an overall review of the evolution through the AGB ADD phase; the contamination of the interstellar medium determined by the gas ejected from these stars is discussed in section 4; section 5 presents a detailed comparison with two among the most largely used sets of models available in the literature; in section 6 we test our models against the chemical composition of samples of Galactic AGB stars; the conclusions are given in section 7.

2 Physical and chemical input

The evolutionary sequences used in this work were calculated with the ATON code; the details of the numerical and physical characteristics of the code are thoroughly documented in Ventura et al. (1998), while the most recent updates are presented in Ventura & D’Antona (2009). The interested reader is addressed to those papers for the details of the input adopted to build the evolutionary sequences. Here we provide the ingredients most relevant for the present analysis:

  • Chemical composition. The models presented here are representative of the solar chemical composition. The metallicity is , with initial helium . The distribution of the different chemical elements in the initial mixture is taken from Grevesse & Sauval (1998).

  • Mass range. The initial mass values are between and . We did not consider initial masses below , as their surface chemical composition is contaminated only by the first dredge-up, with scarce modification from TDU and no effects from HBB; the chemistry of the model reflect a modest contribution from TDU and never reaches the carbon star stage. On the other hand stars with initial mass above undergo core collapse, thus skipping the AGB phase.

  • Convection. In regions unstable to convective motions, the temperature gradient is determined via the full spectrum of turbulence (FST) model (Canuto & Mazzitelli, 1991). In convective zones where nuclear reactions are active we couple mixing of chemicals and nuclear burning in a diffusive-like scheme (Cloutmann & Eoll, 1976). The overshoot from the convective borders (fixed by the Schwarzschild criterion) is described by an exponential decay of convective velocities; the extent of the overshoot region is determined by the e-folding distance of such a decay, which in pressure scale height () units, is given by . During the core hydrogen-burning phase of stars of mass , we assume an extra-mixing from the external border of the convective core, with ; this is based on the constraint on core-overshoot necessary to reproduce the observed width of the main sequences of open clusters, given in Ventura et al. (1998). The same overshoot is applied during the core helium burning phases of the stars of any mass.

    During the AGB phase, we allow extra mixing from the internal border of the envelope and from the boundaries of the pulse driven convective shell; we use , in agreement with the calibration based on the observed luminosity function of carbon stars in the LMC, given by Ventura et al. (2014a).

  • Mass loss. The mass loss rate for oxygen-rich models is determined via the Blöcker (1995) treatment; the parameter entering the Blöcker (1995)’s recipe was set to , following Ventura et al. (2000). Once the stars reach the C-star stage, we use the description of mass loss from the Berlin group (Wachter et al., 2002, 2008).

  • Opacities. Radiative opacities are calculated according to the OPAL release, in the version documented by Iglesias & Rogers (1996). The molecular opacities in the low-temperature regime ( K) are calculated by means of the AESOPUS tool (Marigo & Aringer, 2009). The opacities are constructed to follow the changes of the envelop chemical composition, in particular carbon, nitrogen, and oxygen individual abundances.

1.25 0 0.28 0.51 0.59
1.5 4 0.32 0.51 0.61
1.75 4 0.39 0.51 0.615
2.0 4 0.46 0.49 0.62
2.25 5 0.48 0.49 0.63
2.5 10 0.62 0.49 0.65
3.0 15 0.81 0.56 0.67
3.5 0 0.58 0.66 0.78
4.0 0 0.32 0.79 0.86
4.5 0 0.27 0.83 0.89
5.0 0 0.23 0.86 0.91
5.5 0 0.21 0.89 0.94
6.0 0 0.18 0.93 0.97
6.5 0 0.13 0.99 1.02
7.0 0 0 1.04 1.08
7.5 0 0 1.14 1.16
8.0 0 0 1.21 1.25

Percentage of the duration of the C-rich phase; the maximum efficiency of TDU, defined as the ratio between the mass mixed in the surface convection region and the mass processed by CNO burning during the interpulse phase

Table 1: AGB evolution properties of solar metallicity models

3 The evolution through the AGB phase

Figure 1: Solar metallicity AGB model properties for various initial masses (full squares) are presented here. The individual panels show the maximum luminosity reached (top, left), the highest temperature experienced at the base of the external mantle (top, right), the duration of the TP-AGB phase (bottom, right) and the core masses at the beginning and at the end of the AGB evolution (bottom, left). The models at and metallicities are indicated, respectively, with blue full circles and red diamonds. For comparison, we also show the results from Cristallo et al. (2009, 2015) (triangles), Karakas & Lugaro (2016) (crosses) and Doherty et al. (2014) (open circles).

The evolution of stars of low- and intermediate mass through the AGB phase is mainly driven by the mass of the degenerate core, which determines the brightness of the star, the time required to lose the external mantle and the relative importance of the two mechanisms potentially able to alter the surface chemical composition, namely HBB and TDU. Exhaustive reviews, with detailed explanations of the most important properties of stars evolving through the asymptotic giant branch and the uncertainties related to their description, were published by Herwig (2005) and Karakas & Lattanzio (2014).

A summary of the main physical properties of the models presented here is reported in Table 1 and in Fig. 1, showing the duration of the AGB phase, the maximum luminosity experienced (), the core mass at the beginning and at the end of the AGB phase and the largest temperature reached at the base of the convective envelope (). In the same figure we also show the results of lower metallicity models (Ventura et al., 2013, 2014a, 2014b), and solar metallicity models calculated by other research groups (Karakas & Lugaro, 2016; Doherty et al., 2014; Cristallo et al., 2015).

All the physical quantities show clear trend with the initial mass (); an upturn in the core mass vs. relationship is found around , at the transition between lower mass stars, undergoing the helium flash, and more massive objects, experiencing core helium burning ignition in conditions of thermal stability.
Both vs and vs trend outlines an abrupt transition occurring for masses slightly above , consequently to the ignition of HBB. As thoroughly documented in the literature (Ventura & D’Antona, 2005a), the occurrence of HBB has a significant impact on the AGB evolution. Stars undergoing HBB evolve to brighter luminosities (Blöcker & Schöenberner, 1991) and experience a fast loss of their external mantle; on the chemical side, the surface composition reflects the outcome of the nucleosynthesis experienced at the bottom of the surface convective region. Based on these reasons, in the following we discuss separately the main properties of the stars experiencing HBB and the objects of mass below .

3.1 Massive AGB stars

Stars with initial mass experience HBB at the base of the convective envelope3. Within this mass interval we separate stars (which develop a carbon-oxygen core) and objects, which (after the carbon ignition in a partially degenerate off-center zone) develop an oxygen-neon core (Garcia-Berro et al., 1994, 1997; Siess, 2006, 2007, 2009, 2010).

Figure 2: The AGB evolution of the maximum surface luminosity reached by stars of different mass, experiencing HBB. On the abscissa we report the mass of the star (decreasing during the evolution). The various tracks correspond to model of initial mass (red), (blue), (magenta), (black), (orange), (green).

On general grounds, the maximum luminosity reached by stars undergoing HBB evolves to brighter and brighter luminosities during the initial AGB phases, as a consequence of the increase in the core mass; in more advanced phases the overall luminosity declines, owing to the gradual loss of the external mantle, which provokes a general cooling of the whole external zones, that reduces the efficiency of the CNO activity. This behaviour can be seen in Fig. 2, showing the AGB evolution of the surface luminosity of models of different initial mass; we used the (current) mass of the star as abscissa, to allow the simultaneous plot of all the models. As clear from Fig. 2 (see also top, left panel of Fig. 1) the highest luminosity experienced is extremely sensitive to , ranging from for the model, to for .
The luminosity dependency on initial mass is determined by the larger core masses of larger initial mass models, as shown in the left bottom panel of Fig. 1. Core masses range from () to (). Higher initial mass models experience a faster loss of the external envelop and thus a shorter AGB phase, because larger luminosities imply larger mass loss rates. While the AGB phase of a star lasts yr, in the case of the star it is limited to yr (see right, bottom panel of Fig. 1).4

The core mass also affects the temperature at the base of the convective envelope, which, as shown in the right,top panel of Fig. 1, increases linearly with mass, ranging from MK () to MK (). Models of higher mass are therefore expected to experience a stronger HBB, with a more advanced nucleosynthesis at the base of the convective envelope.

Fig. 1 allows to appreciate the effects of metallicity: lower metallicity models reach higher temperatures at the base of the envelope, thus they experience stronger HBB conditions, and their external regions are exposed to a more advanced nucleosynthesis.

The surface chemical composition of massive AGB stars is mainly determined by HBB, with a modest contribution from TDU. The effects of the latter mechanism are more evident towards the latest evolutionary phases, when HBB is turned off by the gradual consumption of the external envelope. In stars of mass around , with an initial mass just above the threshold necessary to activate HBB, the evolution of the surface chemistry is given by the balance of the two mechanisms.

Figure 3: The variation of the surface abundance of (left panel), (middle), (right) during the same AGB models shown in Fig. 2.

CNO cycling

Fig. 3 shows the variation with time of the CNO elements surface mass fraction in stars experiencing HBB. The surface carbon diminishes by during the first dredge-up episode and is further destroyed during the AGB phase, since the early TPs. Independently of the initial mass, an equilibrium is reached, where the surface carbon is smaller than the initial value and the ratio is ; as clearly shown in the figure, most of the mass ejected by these stars has this chemical composition. In the final AGB phases, when HBB is no longer active, some carbon is transported to the surface by TDU; this is particularly evident in the tracks corresponding to and models. The star follows a different behaviour, with the AGB evolution divided into three phases: a) the initial phase, when the surface carbon increases owing to the effects of TDU; b) an intermediate phase, when HBB destroys the carbon previously accumulated; c) the final TPs, when HBB is turned off and the surface carbon increases again.

M He
1.25 1.55(-2) 1.15(-4) 3.91(-5) 4.37(-4) -1.91(-8) 3.70(-5) 2.29(-6) -1.15(-6) 2.85(-5) 3.59(-7) 0 0 0 0
1.5 2.06(-2) 1.77(-3) 4.81(-5) 8.22(-4) -3.25(-8) 1.47(-4) 2.59(-6) -2.82(-6) 1.50(-4) 2.21(-6) -1.46(-7) 2.08(-6) 1.90(-6) 4.86(-8)
1.75 2.75(-2) 3.26(-3) 5.93(-5) 1.28(-3) -4.61(-8) 2.55(-4) 1.24(-5) -4.69(-6) 2.76(-4) 4.07(-6) -3.66(-7) 4.66(-6) 3.98(-6) 1.44(-7)
2.0 2.00(-2) 4.13(-3) 7.30(-5) 2.02(-3) -5.56(-8) 3.57(-4) 2.31(-5 -6.53(-7) 3.53(-4) 4.94(-6) -4.89(-7) 6.15(-6) 5.18(-6) 2.23(-7)
2.25 4.41(-2) 8.23(-3) 8.65(-5) 2.64(-3) -6.31(-8) -9.87(-5) 3.50(-5) -8.19(-6) 7.07(-4) 1.08(-5) -1.54(-6) 1.88(-5) 1.37(-5) 1.16(-6)
2.5 6.56(-2) 1.09(-2) 8.91(-5) 2.49(-3) -6.67(-8) -1.26(-4) 2.66(-5) -8.36(-6) 9.11(-4) 1.45(-5) -1.68(-6) 2.18(-5) 1.63(-5) 1.21(-6)
3.0 7.87(-2) 1.38(-2) 1.27(-4) 4.54(-3) -8.56(-8) -3.94(-4) 2.92(-5) -1.25(-5) 1.28(-3) 2.18(-5) -7.27(-6) 7.71(-5) 4.42(-5) 1.09(-5)
3.5 8.09(-2) -1.16(-3) 1.15(-3) 1.11(-2) -2.14(-7) -1.55(-3) 2.40(-5) -3.77(-5) 4.00(-4) 9.00(-5) -1.41(-5) 6.29(-5) 3.88(-5) 3.79(-5)
4.0 9.04(-2) -7.80(-3) 1.25(-4) 1.67(-2) -2.88(-7) -3.93(-3) 3.88(-5) -5.32(-5) -2.73(-4) 4.48(-4) -1.91(-5) 4.36(-5) 1.96(-5) 3.83(-5)
4.5 1.72(-1) -1.01(-2) 7.60(-5) 1.99(-2) -3.36(-7) -6.82(-3) 4.91(-5) -6.25(-5) -3.70(-4) 4.74(-4) -5.39(-5) 4.20(-5) 1.58(-5) 2.78(-5)
5.0 2.59(-1) -1.18(-2) 6.82(-5) 2.30(-2) -4.01(-7) -9.15(-3) 6.07(-5) -7.13(-5) -4.51(-4) 5.13(-4) -1.14(-4) 8.48(-5) 2.91(-5) 1.27(-5)
5.5 3.48(-1) -1.31(-2) 8.75(-5) 2.61(-2) -4.40(-7) -1.10(-2) 7.25(-5) -7.98(-5) -5.03(-4) 5.49(-4) -2.00(-4) 1.63(-4) 3.97(-5) 1.49(-5)
6.0 4.33(-1) -1.42(-2) 8.71(-5) 2.83(-2) -4.81(-7) -1.22(-2) 8.92(-5) -8.80(-5) -5.50(-4) 5.80(-4) -3.05(-4) 2.72(-4) 4.95(-5) 1.88(-5)
6.5 5.17(-1) -1.60(-2) 8.65(-5) 3.07(-2) -5.62(-7) -1.35(-2) 1.09(-4) -9.62(-5) -6.11(-4) 6.11(-4) -4.66(-4) 3.96(-4) 5.62(-5) 1.07(-5)
7.0 5.67(-1) -1.71(-2) 1.24(-4) 3.27(-2) -6.54(-7) -1.45(-2) 1.33(-4) -1.04(-4) -6.48(-4) 6.24(-4) -7.76(-4) 7.11(-4) 3.99(-5) 4.98(-5)
7.5 6.02(-1) -1.79(-2) 2.13(-4) 3.41(-2) -8.02(-7) -1.49(-2) 1.82(-4) -1.11(-4) -6.63(-4) 6.42(-4) -9.12(-4) 9.22(-4) 4.03(-5) 5.12(-5)
8.0 6.34(-1) -1.89(-2) 2.66(-4) 3.52(-2) -9.17(-7) -1.52(-2) 2.06(-4) -1.17(-4) -6.88(-4) 6.60(-4) -1.15(-3) 1.13(-3) 4.10(-5) 5.59(-5)
Table 2: Chemical yields of solar metallicity models

The destruction of the surface carbon is related to the relatively low temperatures required to activate carbon burning at the base of the envelope of AGB stars, namely MK; as shown in Fig. 1, these ’s are reached by all models experiencing HBB during the initial AGB phase. The only exception is the model, where the temperature necessary to start proton capture nucleosynthesis by nuclei is reached in more advanced AGB phases, after some TDU episodes occurred (see left panel of Fig. 3).

The activation of the CNO nucleosynthesis leads to the synthesis of nitrogen, which is increased (see middle panel of Fig. 3) almost by an order of magnitude at the surface of the stars. It is worth noticing that most of this nitrogen has a secondary origin in the present models, as N is essentially produced by the carbon originally present in the star.

The evolution of surface oxygen abundance is more complicated, as the activation of the whole CNO cycle (with the oxygen destruction) requires temperatures significantly higher than those necessary for the carbon burning ignition, namely MK. This makes oxygen depletion extremely sensitive to mass and chemical composition, as these are the two most relevant quantities in the determination of the temperature at which HBB occurs. Ventura et al. (2013) showed that massive AGBs at metallicity produce ejecta with an oxygen content a factor 10 smaller compared to the gas from which the stars formed. On the contrary, higher metallicity AGBs () were shown to undergo a less advanced nucleosynthesis and to eject gas with an oxygen content on average smaller than the initial value.
As discussed earlier in this section (see also top right panel of Fig. 1), solar metallicity models have a less efficient HBB compared to lower metallicity models. Therefore, the surface oxygen survives more easily in the solar metallicity models. As shown in Fig. 3, the lowest oxygen abundances ( below the initial values), are present in the most massive models evolution, in the final AGB phases. For the surface oxygen decreases during the second dredge-up event and is produced during the following AGB phase, owing to the effects of TDU.
Considering oxygen isotopes, the HBB nucleosynthesis is accompanied by a considerable destruction of the surface , which is rapidly consumed starting with the early TPs, when it reaches an equilibrium abundance of . The destruction of occurs at the same temperatures required for carbon burning ignition. On the contrary, is produced as soon as burning begins, the overall production factor ranging from 5 to 10, depending on the initial mass of the star. The variation of the ratio of the models discussed here is shown in the right panel of Fig.11.

Sodium production

The Ne-Na nucleosynthesis is activated at the same temperatures at which oxygen burning occurs. The evolution of surface sodium abundance during the AGB phase is complicated (Mowlavi, 1999) and depends on the balance between the production channel (i.e. the proton capture process by nuclei) and the destruction reactions ( and reactions, with the latter providing the dominant contribution). The production mechanisms prevail at temperatures lower than 90MK, whereas the destruction reactions, whose cross sections have a steeper dependance on temperature, become dominant for T90 MK. At the beginning of the AGB phase sodium is thus produced via burning, whereas it is destroyed in more advanced phases, when the destruction processes predominate (Ventura & D’Antona, 2006, 2008).

The variation of the sodium surface abundance during the AGB phase for the solar metallicity models is shown in Fig. 4. The dependency on initial mass offers an interesting example of how the temperature at the base of the convective zone is crucial to determine the nucleosynthesis in these stars. The dependency on shown in the top right panel of Fig. 1, explains the results of Fig. 4. In stars with , sodium is produced in the initial AGB phases and partly destroyed later on, when exceeds 90 MK and HBB reaches the strongest efficiency. In stars with sodium is produced during the whole AGB phase, with no destruction, because the temperature at the base of the external mantle is lower than 90 MK (see top, right panel of Fig. 1 and Table 1). For stars with initial mass just above the threshold to activate HBB (here represented by the star), only a small production of sodium occurs, because the temperature is not high enough to allow an efficient burning.

In summary, unlike the stars of lower metallicity (Ventura & D’Antona, 2011), here the destruction processes never really predominate, because of the lower temperatures reached at the bottom of the convective envelope. This results into a significant increase in the surface sodium, with final abundances 4-5 times larger than the initial values. The highest sodium production is reached in the model, because the destruction reactions are never activated during the entire AGB life.

Mg-Al nucleosynthesis

The magnesium-aluminum nucleosynthesis is activated at HBB temperatures close to 100MK: the proton capture by nuclei starts a series of reaction, whose outcome is the increase in the surface content of the two heavier isotopes of magnesium and the aluminum synthesis (Arnould et al., 1999; Siess & Arnould, 2008). Ventura et al. (2013) describes the extreme sensitivity of the Mg-Al nucleosynthesis efficiency to metallicity. As consequence of the different HBB strength at different chemical composition, in low metallicity stars a significant production of aluminum occurs, whereas in objects with higher metallicities magnesium burning is less efficient, with a more limited aluminum synthesis.

In the present solar metallicity models the activation the Mg-Al nucleosynthesis is limited to stars with . The largest depletion ( dex) is found in the largest initial mass models; in all cases no significant aluminum synthesis occurs.

Figure 4: The variation of the surface sodium mass fraction (in units) of AGB models experiencing HBB. The colour coding is the same as in Fig. 2.
Figure 5: Surface lithium abundance evolution for the same models shown in Fig. 2; the same colour coding is adopted. The quantity on the ordinate is . In the left panel we show the surface lithium as a function of the initial mass, whereas on the right we use the AGB time as abscissa. The horizontal line at indicates the limit above which the stars are considered lithium-rich.

Lithium

Lithium is synthetised during the AGB phase via the Cameron-Fowler mechanism, which is started by the activation of capture reactions by nuclei at the base of the surface convective zone (Cameron & Fowler, 1971). Sackmann & Boothroyd (1992) showed that the use of a self-consistent coupling between nuclear burning at the base of the envelope and mixing of chemicals in the same region, leads to production of great quantities of lithium in the surface layers of AGB stars, provided that a minimum temperature of MK is reached at the base of the external mantle. As shown in Fig. 1 and reported in Table 1, this property is shared by all the models presented here, with initial mass , do reach the required temperature.

Fig. 5 shows the variation of the surface lithium in our simulated stars during the AGB evolution: the results are shown as a function of the current mass of the stars and of the time counted from the beginning of the AGB phase.

Lithium is produced since the early TP-AGB phases, as soon as HBB is activated. The only exception to this behaviour is the model, in which lithium production occurs in more advanced AGB phases, after the star has experienced a C-star phase. In agreement with the general understanding of the lithium production in these objects, the surface lithium reaches a maximum abundance, after which it decreases below any detectability threshold. This apparently anomalous behaviour (the temperature at the base of the envelope keeps increasing until after the surface lithium is consumed, which would further favour the rate at which the Cameron-Fowler mechanism works) is due to the exhaustion of the surface which is at the base of the nuclear chain leading to lithium production.

AGB stars of solar chemical composition are expected to have a longer lithium-rich phase compared to metal poor AGBs because the smaller temperatures at the base of the envelope (see top, right panel of Fig. 1) delay the surface exhaustion.

As shown in the right panel of Fig. 5, the lithium-rich phase lasts for about half of the AGB evolution of these stars. The gas yields are therefore expected to show some lithium enrichment.

Stars with initial mass higher than are expected to be lithium-rich for the whole AGB phase because their large mass loss rates make the time scale for envelop consumption comparable to the destruction time scale. This result must be taken with some caution though, as it is strongly sensitive to the mass loss mechanism description.

Figure 6: The main physical and chemical properties of low-mass () AGB stars are shown as a function of decreasing initial mass. Individual panels show the behaviour of luminosity (top, left), effective temperature (top, right), mass loss rate (bottom, left) and C/O ratio (bottom, right). The tracks in the panels refer to models of initial mass (dotted, short-dashed, orange), (short-dashed, magenta), (dotted, long-dashed, blue), (dotted, green), (solid, red), (long-dashed, black),

3.2 Low mass AGB stars

The stars with initial mass below do not experience any HBB, thus their chemical composition is entirely determined by the repeated TDU events that follow each TP. This is going to affect not only their variation of the surface chemistry, but also their physics.

The main quantities related to the evolution of low initial mass AGB stars are shown in Fig. 6, where we report the variation of the luminosity, effective temperature, mass loss rate and the surface C/O ratio during the AGB phase.

The C/O ratio evolution shows that after each TP some carbon is dredged-up to the surface increasing the C/O ratio. Only stars with initial mass greater than reach the C-star stage; lower mass stars, while experiencing some carbon enrichment, lose the external mantle before C/O exceeds unity.

Reaching the C-star stage has important effects on the evolution of these objects. As shown in Fig. 6, the external regions of the star undergo a considerable expansion after the C/O ratio grows above unity: the effective temperature drops initially to K and decreases further below K while the surface carbon abundance increases. This behaviour is a consequence of the formation of CN molecules in C-rich regions, that favours a considerable increase in the opacity and in the mass loss rates. This effect was predicted in a seminal paper by Marigo (2002) and confirmed in more recent, detailed explorations by Ventura & Marigo (2009, 2010).

Figure 7: The variation of the surface ratio (left panel) and of the luminosity (right) for models with mass during the AGB phase. The two quantities are shown as a function of the surface C/O ratio. The same color coding of Fig. 6 was adopted. Crosses and crossed squares refer to C15 models with initial mass and , respectively.

As shown in the left bottom panel of Fig. 6, when stars become carbon rich, their mass loss rates increase up to /yr in the very final phases. The increase in the mass loss rate is due to two different effects: a) the expanded envelope becomes less and less gravitationally bound, thus overcoming the gravitational pull is easier and b) the lower effective temperatures favour the formation of large quantities of carbon dust in the wind, which in turn increases the effects of the radiation pressure on the dust particles in the circumstellar envelope.

Given the above, it is clear why the evolutionary time scales become significantly shorter when stars become C-rich: the envelope is lost rapidly, only a few (if any) additional TDU events can occur to further increase the surface carbon abundance.

The models with mass close to the threshold required to activate HBB, namely , undergo a higher number of TDU events before their mantle is lost. Consequently, they are the stars with the largest relative duration of the C-star phase () and with the highest final C/O ratio (, see Table 1).

Figure 8: The production factor (see text for definition) of the CNO isotopes in solar metallicity models. In the left panel we show the most abundant species, namely (black points), (blue diamonds) and (red squares). The right panel refers to (black points), (red squares), (blue diamonds) and (magenta pentagons).

Fig. 7 shows the surface ratio and the luminosity of the models becoming carbon stars during the AGB evolution, as the surface C/O, shown on the abscissa, increases. These results show that carbon stars are expected to evolve at luminosities . Furthermore, the surface ratio is expected to be above 50.
From the above arguments we understand that the evolution of the C-rich AGB stars is mainly driven by the surface C/O ratio, the latter quantity affecting directly the rate at which mass loss occurs, thus the time scale of this phase.
This is a welcome result for what concerns the robustness of the present findings. The increase in the C/O ratio depends on the treatment of convective borders during each TP, particularly of the assumed extra-mixing from the base of the envelope and the boundaries of the pulse driven convective shell; however, although a deeper overshoot would favour larger carbon abundances, this would be counterbalanced by the increase in the rate of mass loss, which would lead to an earlier consumption of the stellar mantle, thus reducing the number of additional TDU events.
On the statistical side, it is much more likely to detect a star when it is oxygen-rich than during the C-star phase. On the other hand, as will be discussed in next section, the latter is much more relevant for the gas and dust pollution determined by these objects, because, as shown in the bottom right panel of Fig. 6, it is during this phase that most of the mass loss occurs.

4 Gas pollution

The pollution from AGB stars is determined by the relative importance of HBB and TDU in modifying the surface chemical composition.

When HBB prevails, N-rich and C-poor yields are expected independently from the HBB strength. However at high temperatures ( MK), when the full CNO cycle and the Ne-Na and Mg-Al chains can occur, a modification of the mass fraction of elements heavier than oxygen is also expected. On the other hand, when TDU prevails C-rich yields are expected with minor contribution from O and N. Table 2 shows the net yields of the various chemical species. The production factor of the CNO elements, defined as the ratio between the average mass fraction of a given element in the ejecta and its initial quantity, are shown in Fig. 8. The left panels refers to , and , whereas on the right we show the less abundant isotopes.
In the low-mass regime () we find production of and . The production factor of both elements increases with the initial mass, up to a maximum of for . For what concerns carbon, as discussed in section 3.2, the reason is that higher mass models are exposed to more TDU events and experience a larger enrichment of carbon in the external regions (see bottom, right panel of Fig. 6). The null production of carbon found in the model stems from the balance between the first dredge-up, after which the surface carbon diminishes, and the following TDU’s, which increase in the external regions. The first dredge-up is also responsible for the production of and in low-mass AGB stars (see right panel of Fig. 8): in the first case the production factor is , fairly independent of , whereas for the latter isotope it reaches in the model. and are practically untouched in these stars.

In the high-mass domain the effects of HBB take over, changing the above picture substantially. Concerning the elements involved in CNO cycling, the results shown in Fig.8 can be understood based on the discussion in section 3.1.1. is found to be 10 times smaller in the ejecta, compared to the initial chemical composition. is also affected by HBB, with a maximum depletion of . The CNO nucleosynthesis has the effect of synthesising , which results to be increased by a factor . The activation of the HBB nucleosynthesis has also the effects of producing and via proton capture by and nuclei. Note that the significant production of (up to a factor in the most massive models) is not in contrast with the soft depletion of , given the disparity between the initial abundances of the two elements, which renders a small percentage destruction of sufficient to produce . is severely depleted in the ejecta of these stars, being 2-3 orders of magnitude smaller than the initial quantity

Turning to Ne-Na elements, the corresponding production factors are shown in the left panel of Fig. 9. We find that increases in low-mass stars (), as a consequence of TDU, which brings to the surface matter enriched in ; similarly to carbon, the production factor of is correlated to , ranging from for to for . Conversely, sodium is only scarcely touched, in this mass interval.

Like in the case of the CNO elements, the transition to the high-mass domain marks an abrupt change in the surface abundances of the Ne-Na elements, in conjunction with the shift from TDU- to HBB-dominated chemistry. In agreement with the discussion in section 3.1.2, we find for that the ejecta of exhibit depletion factors ranging from 3 to 10. Note that the trend of with mass is not monotonic, the most -poor ejecta being produced by models, despite the stronger HBB experienced by their higher mass counterparts. This is motivated by the very large mass loss rates suffered by stars, which render the loss of the envelope fast enough to compete with destruction.

The reduction of the surface favours the production of sodium, which is increased by a factor in the gas expelled from these stars. The most abundant isotope of neon, namely , is found to remain practically unchanged in all cases.

Finally, we examine the Mg-Al elements, shown in the right panel of Fig. 9. In the low-mass domain the surface mass fraction of these elements are only modestly changed, thus the corresponding production factor are close to unity. In models of higher mass proton-capture nucleosynthesis occurs, but for the solar metallicity the HBB temperatures are not sufficiently large to allow significant depletion of , which is the starting reaction of the whole cycle: as shown in the right panel of Fig. 9, the in the ejecta is barely depleted by more than , even in the models of highest mass. This partial nucleosynthesis is however sufficient to produce , which is found to be increased by a factor in the most massive models.

5 The robustness of the present generation of AGB models

The results from AGB evolution modelling are sensitive to the treatment of some physical mechanisms still poorly known from first principles, primarily convection and mass loss. Additional uncertainties come from the nuclear reactions cross-sections, though this is going to affect only the details of the chemical composition of the ejecta, because the nuclear rates of the reactions giving the most relevant contribution to the overall energy release are fairly well known (Herwig, 2005; Karakas & Lattanzio, 2014).

A reliable indicator of the predictive power of the present findings can be obtained by comparing with solar metallicity, AGB models found in the literature. On this purpose, in Fig. 1, reporting the main physical properties of the models presented here, we also show the results from Cristallo et al. (2015), Karakas & Lugaro (2016), Doherty et al. (2014). In the following, we will refer to the four sets of models, respectively, as ATON, C15, K16 and D14.

In the low-mass regime, the main difference between ATON and C15 and K16 results is that the ATON core masses at the beginning of the AGB phase are slightly smaller, thus the ATON models evolve at lower luminosities and the AGB phase is longer. The largest difference is found for the model, which in the ATON case experiences a maximum luminosity dex smaller than C15, and the AGB evolution is two times longer (4Myr vs. 2Myr). K16 models exhibit an intermediate behaviour in this range of mass.

Figure 9: The production factor of the elements involved in the Ne-Na and Mg-Al nucleosynthesis for the models presented here. Left: , and are indicated, respectively, with blue pentagons, red points and black squares; the sodium production factor by K16 (crosses), c15 (triangles) and D14 (circles) are also indicated. Right: the production factor of (black points), (red squares), (blue pentagons) and (magenta diamonds); the results for by D14 are indicated with open circles.

The most relevant differences are found in the high-mass domain, where HBB effects take over. In the comparison among the highest temperatures reached at the base of the convective envelope, ATON models in the range attain values of the order of MK, whereas in the C15 case we find . The K16 models exhibit temperatures closer to, though smaller than ATON, covering the range in the same interval of mass. Such a dramatic difference has an immediate effect on the luminosity, which for the ATON models, in the same range of mass, is , whereas in the C15 and K16 cases it is, respectively, and . Because the core masses at the beginning of the AGB phase are very similar in the three cases (see Fig.1), the differences outlined above must originate from the different description of the convective instability, particularly for what concerns the efficiency of convection in the innermost regions of the envelope. The ATON models are based on the FST treatment (Canuto & Mazzitelli, 1991), whereas the C15 and K16 computations used the mixing length theory (MLT) recipe. These results confirm the abalysis by Ventura & D’Antona (2005a), who discussed the outstanding impact of convection modelling on the efficiency of HBB experienced by AGB stars.

In the analysis of the behaviour of the core masses, we note that the ATON models present the greatest variation () during the whole AGB phase, compared to C15 and K16, for which we have : this is due to the deeper penetration of the convective envelope in the phases following each TP in the C15 and K16 cases, which slows the growth of the core during the AGB evolution.

We now focus on the evolution properties of those stars that develop a core made up of oxygen and neon, i.e. those of initial mass above . In this case we compare the ATON models with D14 and with the model by K165. The same initial mass does not correspond to the same core mass during the early AGB phases, because in the ATON case a larger extra-mixing from the border of the convective core during the H-burning phase was adopted, which results into a higher core mass at the beginning of the AGB phase. Taking into account this difference, we note that the values of the temperature at the base of the envelope and of the luminosity are similar in the ATON, D14 and K16 cases, whereas the D14 and K16 AGB evolutionary times are longer than ATON. The results from this comparison finds an explanation in the different modalities with which convection and mass loss are described. ATON models are based on a more efficient description of convection (FST, against the MLT treatment used by D14 and K16), which favours larger luminosities and HBB strength; however, ATON models also suffer a very strong mass loss, which provokes a fast loss of the external mantle, accompanied by a general cooling of the whole external regions, which acts against the achievement of very large HBB temperatures. The longer duration of the AGB phase found in the D14 and K16 models is due to the smaller mass loss rate adopted compared to ATON. The interested reader may find in D14 an exhaustive discussion of the impact of the mass loss description on the duration of the TP phase of super-AGB stars.

Figure 10: The production factor of , and of the models presented here (shown as black, full points), compared with results from Cristallo et al. (2015) (blue triangles), Karakas & Lugaro (2016) (red crosses) and Doherty et al. (2014) (magenta circles).

The differences discussed above have important effects on the yields expected from these stars, which show some differences among the results published by the different research groups.

In Fig. 10 we compare the production factors of the most abundant isotopes involved in CNO nucleosynthesis.

In the low-mass domain we find that the results concerning carbon are very similar. In all cases we find a positive trend of the carbon in the ejecta with the stellar mass, as higher mass stars experience more TDU events. ATON, C15 and K16 results are also similar on quantitative grounds, the largest enhancement being , reached by models.

The N-production factor of ATON, C15 and K16 are also similar: increases increase with the stellar mass, up to for the models.

In the same range of mass a few differences are found for what regards oxygen. In the ATON and K16 cases some oxygen enrichment occurs, whereas no production is found in C15 models.

For what concerns stars of mass above , the predictions are considerably different. In the ATON case carbon in the ejecta is severely reduced, almost by a factor 10. In the C15 and K16 models this reduction is much smaller, at most by a factor 4 in the , K16 model. The results from D14 also predict reduction factors not higher than 2.

Concerning nitrogen, in the mass range the ATON models produce more nitrogen, owing to the effects of HBB, not found in the C15 and K16 models of the same mass. In the ATON case, for massive stars, great amount of nitrogen are produced, with production factors in the range 6-8. This behaviour is shared by the D14 models. Conversely, the N-production factor is significantly smaller in the C15 case, where the production factor never exceeds . The largest production of nitrogen is found in the models by Karakas & Lugaro (2016): this is due to the combined effects of TDU, which increases the surface carbon, and HBB, which converts the dredge-up carbon into nitrogen.

In the large mass domain is only modestly reduced in C15 models, whereas in the ATON case the depletion factor in models is . The comparison between the ATON and K16 models is more tricky: for the ATON models predict more oxygen-poor ejecta, whereas in the range of mass the oxygen depletion is slightly higher in the K16 case. In the D14 models some oxygen depletion is found, though limited to .

Turning to sodium, in the large mass domain the results are significantly different, as can be seen in the left panel of Fig. 9: in the ATON case a great production of sodium is expected, the average Na in the ejecta being increased, with respect to the original chemistry, by a factor ranging from 3 to 5. In the K16 and D14 models the production factor is below 2, whereas in the C15 case it is slightly smaller.

In the range of masses experiencing HBB the extent of the Mg-Al nucleosynthesis is also model-dependent, as shown in the right panel of Fig. 9. The ATON models achieve some processing of , which is depleted by at most in the most massive case. This is in fair agreement with the results from D14, whereas in the C15 and K16 models processing of magnesium is negligible.

The differences in the expected chemical enrichment of the interstellar medium can be understood on the basis of the physical input used by the various research groups to calculate the evolutionary sequences. Convection is by far the biggest villain here, determining most of the differences found.

In the low-mass domain, the slight increase in the content found in the ATON and K16 models is due to the adoption of some overshoot from the base of the pulse driven convective shell, which further enhances the strength of the pulse and, more important, makes the internal regions of the convective envelope to be mixed with more internal zones touched by helium burning, with a higher oxygen content. In the same range of mass we find that the largest production factor of is similar in the ATON, C15 and K16 cases, indicating that those models experience TDU events of similar depth.

For masses above , the main reason for the differences among the various models is the strength of HBB and the description of mass loss. The large HBB temperatures are the main actors in the considerable depletion of carbon and production of nitrogen in the ATON models. The K16 models of mass above and the D14 models produce ejecta with nitrogen enhancement similar to ATON (see middle panel of Fig. 10), despite the carbon depletion is more reduced (left panel of the same figure). This is motivated by some TDU events active in the latter models, that transport to the external regions some carbon produced in the helium-burning shell, which is later converted into nitrogen: in summary, while the nitrogen produced in the ATON models is entirely of secondary origin, part of the nitrogen synthesised in the K16 and D14 cases has also a primary component. The best indicator of the efficiency of HBB is the behaviour of oxygen, which is depleted in the ejecta of the ATON and in some K16 models, whereas it is only scarcely touched in the C15 and D14 cases (see right panel of Fig. 10). Understanding the differences among the ATON and K16 results is not straightforward though. For the ATON models predict more oxygen-poor ejecta, because the K16 models are cooler at the base of the envelope (see top, right panel of Fig. 1), thus the latter is exposed to a less advanced nucleosynthesis. In the range of mass the oxygen depletion is slightly higher in the K16 case, compared to ATON, despite the latter models evolve at larger ’s. The reason for this apparently anomalous behaviour is once more in the large mass loss rates experienced by the ATON models, which makes the envelope to be lost before a great depletion of the surface oxygen may have occurred.

The efficiency of HBB is also the main factor determining the extent of the Ne-Na and Mg-Al nucleosynthesis experienced. The great enhancement of sodium found in the ejecta of ATON models is originated by the large HBB temperatures reached; conversely, in the other cases the temperatures required to activate the Ne-Na nucleosynthesis are barely reached, which determined a much smaller production of sodium (see left panel of Fig. 9).

6 Interpretation of observed Galactic AGB stars

The discussion of the previous sections outlines how far we are from a full understanding of the main evolutionary properties of AGB stars. The significant differences found between the present models and those by K16, C15 and D14 stress the importance of comparing the expectations from the models with the observations. As a first step towards this direction, we compare the most recent estimates of the CNO elemental and isotopic abundances in Galactic (solar metallicity) AGB stars with the ATON models presented here.

6.1 Extreme O-rich, AGB stars observed by Herschel

Justtanont et al. (2013) published Herschel Space Observatory (Herschel hereafter) observations of five visually obscured OH/IR stars6, using CO as a tracer of the thermodynamical structure of the circumstellar envelope. The combination with ground data allowed the determination of the dynamical and dust properties of the wind, and the derivation of the oxygen and carbon isotopic ratios.
To allow a clearer interpretation of the chemical composition of the stars in this sample we show in Fig. 11 the evolution of the surface (left panel) and of (right)the same models shown in Figg. 1 and 3. In all cases we see a significant reduction of the surface as soon as HBB begins, owing to the destruction of and the synthesis of ; eventually, the equilibrium value, , is reached. The activation of HBB also determines the destruction of the surface and the synthesis of : the surface is dramatically reduced compared to the initial value, . In the models of initial mass the surface raises again in the final evolutionary phases, after HBB was switched off: under the effects of a few late TDU events, carbon ratios are expected.

Figure 11: The evolution of the surface (left panel) and ratios, in the same models shown in Fig. 2. The same colour coding is adopted.

The surface chemistry of OH 127.8+0.0 and OH 30.1-0.7 shows the clear imprinting of HBB, with and below the detectability threshold. As shown in Fig. 11, this is a common feature of all the models experiencing HBB. The ignition of burning (with consequent synthesis of ) and the depletion of are active since the early AGB phases; as shown in Fig. 1, these temperatures at the base of the convective envelope are reached in all the models experiencing HBB. The surface chemistry observed in OH 127.8+0.0 and OH 30.1-0.7 is a common feature of all the models of initial mass , thus not allowing us discriminating among the possible progenitors. The upper limits for the (0.1) given by Justtanont et al. (2013) also support our interpretation of these stars being massive HBB stars. Our interpretation agrees with the Justtanont et al. (2013) conclusion of these stars being HBB AGB stars; the difference in the progenitor mass range (Justtanont et al. 2013 assume masses above ) is just because the minimum mass to activate HBB is model dependent; e.g., it is in the ATON models, while it is in the D14-like models used by Justtanont et al. (2013). We note, however, that these stars might be in a very advanced evolutionary stage, thus implying that their current mass could in principle be significantly smaller (down to ) than the initial mass.
Based on ISO spectra and IRAS photometry, the SED of these two stars shows up the silicate absorption feature at m, in agreement with the hypothesis that they are undergoing HBB: indeed Dell’Agli et al. (2014) showed that large dust formation occurs in stars during the HBB phase. The results by Dell’Agli et al. (2014) were based on models with sub-solar chemical composition; while the dust production by the present models will be addressed in a forthcoming paper, we may anticipate that the conclusions by Dell’Agli et al. (2014) can be safely extended to the present case, because the larger availability of silicon in the surface regions will further increase dust production in solar metallicity stars. We conclude that OH 127.8+0.0 and OH 30.1-0.7 are evolving through the AGB phases during which HBB is strongest, when dust production is large and the stars lose mass at high rates.
A significant support towards the identification of the precursors of OH 127.8+0.0 and OH 30.1-0.7 could be obtained by the knowledge of their distance, which would allow the determination of their luminosity. This is because, while undistinguishable on the basis of the surface isotopic ratios of carbon and oxygen, the stars of the various mass evolve at different luminosities during the AGB phase. This is clearly shown in Fig. 2, where the range of the luminosities of the various tracks is seen to vary substantially with the initial mass of the star: a luminosity would point in favour of the progeny of star, whereas a higher mass progenitor, , would require much higher luminosities, of the order of . It goes without saying that we mentioned only the two extreme cases, neglecting a number of intermediate situations.

The surface chemical composition of AFGL 5379 and OH26.5+0.6 indicates depletion of , as confirmed by the non detection of the line in the spectra. Unlike the two previous stars, the isotopic carbon ratio, , is significantly higher than the equilibrium value.
A possible interpretation of these data is that AFGL 5379 and OH26.5+0.6 descend from progenitors and are in the phases following the ignition of HBB, when carbon burning started, but there was no time to reach the equilibrium value. In this case we expect that the current mass of the stars are close to the initial mass and that the stars are actually lithium-rich7. We believe this possibility unlikely, for the following reasons: a) at the ignition of HBB these stars would evolve at effective temperatures K, significantly higher than the temperatures deduced by Justtanont et al. (2013), which are slightly above 2000 K; b) during the same phase, we find that these stars have radii of the order of , smaller than found by Justtanont et al. (2013); c) the mass loss rates in the initial HBB phases are at most a few , whereas AFGL 5379 and OH26.5+0.6 are currently loosing mass with rates much higher than .
Our favourite interpretation is that AFGL 5379 and OH26.5+0.6 are the progeny of stars, and are currently evolving during the final AGB phases. The observed is larger than the equilibrium value, because HBB is switched off when the mass of the envelope drops below and a few TDU events are sufficient to increase the surface , thus lifting the ratio (see left panel of Fig.11). The effective temperatures during the late AGB phases are K, in better agreement with those indicated by the authors, i.e. K. An additional point in favour of this hypothesis is that the radius of the star is expected to be , very close to the values proposed by Justtanont et al. (2013). A last argument supporting this conclusion is that the SED of these stars show up a deep silicate feature, suggesting the presence of significant quantities of dust, as expected based on the cool temperatures of the models, favouring dust formation. Interestingly, if this hypothesis proves correct, it is possible to constrain the current mass and the luminosity of AFGL 5379 and OH26.5+0.6: in the final AGB phases of stars the mass is reduced to and the luminosity is .

This could be confirmed by an accurate determination of the distances which is not yet available, at the moment, for this type of stars.

Among the stars observed by Justtanont et al. (2013) WXPsc is the least obscured and is still visible in the optical. The carbon ratio for this star is ; this is not highly significant, as it ranges from the values typical of CNO equilibria to those of incomplete CN burning. The information on the ratio is hard to interpret: Justtanont et al. (2012) give , at odds with the results derived by Justtannont et al. (2015) in a larger sample of extreme OH/IR stars, where they found upper limit for the oxygen isotope ratio of the order of 0.1. An additional information on this star is that the optical spectrum displays a strong Rb line at 7800A (Garcia-Hernandez 2016, private communication), which suggests that it has already experienced some TPs and TDU episodes, and it is Rb-rich. Confirmation of the given by Justtanont et al. (2012) would rule out any contamination from HBB; in this case the most likely possibility is that WXPsc descends from a progenitor of mass just above the threshold required to activate HBB () and has already experienced some TDU events, whereas HBB has not yet started.

This interpretation has some problems though, mainly related to the degree of obscuration of the star (, according to Ramstedt & Oloffsson, 2013), as witnessed by the silicate feature, which is about to be converted into absorption, owing to the increasing thickness of the circumstellar shell: this evidence would rather indicate that WXPsc is evolving through the final AGB phases and is surrounded by great quantities of silicate dust. If this understanding is correct, the surface chemistry of the star should display evidences of HBB, which seems in contrast with the large given by Justtanont et al. (2012). On the other hand, Justtannont et al. (2013) mentioned that there were problems with the observations and analysis of WX PsC, related to possible assymetries of the circumstellar shell, which may alter their result. In conclusion, any definite interpretation of the evolutionary history of this star will be possible only when a more robust determination of the oxygen isotopic ratio will be available.

6.2 Lithium abundances in O-rich AGB stars

García-Hernández et al. (2007) presented results from high-resolution spectroscopy of a large sample of O-rich AGB stars, for which the lithium and zirconium abundances were measured. The latter element increases under the effects of TDU, thus its content can be used as a reliable indicator of the efficiency of TDU in the stars observed.

Among the sources observed by García-Hernández et al. (2007), 25 show evidence of lithium, with , whereas in 32 of them the lithium line was not detected, thus indicating that . The distribution of the periods observed is d for lithium-rich objects, whereas the AGB stars with no lithium have periods below 500 d, with the single exception of IRAS 18050-2213, which has a period of 732 d.

The lithium-rich stars in the García-Hernández et al. (2007) sample are interpreted as the progeny of stars, currently evolving through the lithium-rich phase, when the Cameron-Fowler mechanism is active. Based on the discussion in section 3.1.4, we know that this phase extends for about half of the AGB evolution of stars of solar metallicity. While on general grounds we cannot identify the mass of the progenitors, statistical arguments suggest that most of the lithium-rich stars descend from stars. As shown in the right panel of Fig. 5, the duration of the lithium-rich phase is longer the lower is the mass of the progenitors: it is yr for , yr for and yr for . Given these time scales and the functional form of any realistic mass function, we deduce that the stars observed likely descend from progenitors of mass below , and have current masses between and

The distribution of the periods of the stars in the sample by García-Hernández et al. (2007) further supports this interpretation. The stars with no lithium are either stars of mass below , which do not experience any HBB, or more massive objects in the initial AGB phases, before the Cameron-Fowler mechanism is activated: during these early TP-AGB phases the stars are more compact and less luminous, thus their periods are shorter. This is fully consistent with one of the main results of the Garcia-Hernandez et al. (2007) analysis, i.e. lithium-rich stars have larger periods than their lithium-rich counterparts. The lack of any strong s-process enrichment in the lithium-rich stars observed by García-Hernández et al. (2007), as deduced by the absence of significant zirconium enrichment, further supports our models. Indeed this is in agreement with our results, that TDU is scarcely efficient in solar metallicity, massive AGB stars (see the values of reported in Table 1).

A final comment concerns the luminosities of lithium-rich stars. Because the ignition of the Cameron-Fowler mechanism requires a minimum temperature at the bottom of the envelope MK, this reflects into a minimum luminosity , i.e. ; this stems from the tight relationship between and . We note that, although Galactic massive HBB-AGB stars may display strongly variable luminosities and their distances are unknown (García-Hernández et al., 2007), similar truly massive HBB-AGB stars in the Magellanic Clouds consistently display extremely high luminosities of (García-Hernández et al., 2009).

6.3 C isotopes in different types of AGB stars from radio transitions

The group of Galactic AGB stars by Ramstedt & Olofsson (2014) are the most complete sample presented so far, with ratios available for stars in different phases of the AGB evolution. This sample includes both carbon stars and oxygen-rich objects. The results are based on radiative transfer modelling of the observed and radio transitions; the solution of the energy balance equation allowed the determination of the circumstellar , the rate of mass loss and the expansion velocity. These information can be used to constrain the evolutionary models.

Before entering the discussion, we believe important to stress at this point that the observational data in the optical/near-IR are more representative of the photosphere, while the radio data, such as those presented in this section, trace the chemistry of the circumstellar envelope. This is confirmed by recent results, showing that in some cases both values do not agree (e.g., Vlemmings et al. 2013). Furthermore, the interpretation of the radio data is subject to several assumptions and modelling. Typically, it is assumed that the radio transitions are optically thin and the flux ratio is equivalent to the ratio, which is not always the case; in case that the radio transitions are optically thick, the real ratio is generally underestimated.

We will discuss the stars in the sample separately, according to their being M- or C-star. We do enter into the discussion of the possible origin of J stars, i.e. the carbon-rich objects in the sample with unusually low (below 15) ratios: these sources, as discussed in section 6.2.3, likely belong to binary systems, thus they cannot be understood on the basis of the single star models used here.

O-rich M-type AGB stars

The carbon ratio of these objects () exhibits the signature of HBB, tracing the equilibria of proton capture nucleosynthesis. As shown in Fig. 11 (see left panel), this is a common behaviour of all the models of initial mass above discussed here.

The possibility that these objects descend from stars with mass just above the threshold required to activated HBB, i.e. , is unlikely, because these stars reach the surface corresponding to the equilibrium of proton capture nucleosynthesis only in the final TPs, thus for a limited fraction of the AGB life (see the track corresponding to the case in the left panel of Fig. 11).

We believe more probable that IRC+10529 and IRC+50137 descend from stars and are currently evolving through the AGB phases following the ignition of HBB. This hypothesis is supported by the optical depth given by the authors, , indicating a large degree of obscuration, thus the presence of great amounts of silicate dust in the wind. The mass loss rates indicated by Ramstedt & Olofsson (2014) (in the range ) rule out very massive progenitors, which shifts our attention towards objects. This conclusion is further supported by statistical arguments, based on the duration of the AGB phase of stars of different mass, reported in Table 1 and in the bottom, right panel of Fig. 1.
If this interpretation proves correct, the luminosity expected is , significantly higher than those adopted by the authors (, see Table 3).

R Leo exhibits a surface , similar to IRC+10529 and IRC+50137, indicating that the surface material was exposed to CN cycling. Unlike IRC+10529 and IRC+50137, the star is not heavily obscured () and the given mass loss rate () is a factor of smaller.
The possibility that R Leo is currently experiencing HBB is not supported by the latter two evidencies, unless it is currently evolving through a phase when mass loss and dust production are temporarily interrupted. If this is the case, the luminosity should be not below , almost a factor 10 higher than the value indicated by Ramstedt & Olofsson (2014).
An alternative possibility is that this star descends from a progenitor and is currently evolving through the initial AGB phases, before becoming a carbon star. Cool bottom burning during RGB ascending might account for the reduction of : this process, proposed by Boothroyd & Sachmann (1999), is originated by deep circulation mixing below the base of the convective envelope, and has the effects of mixing material enriched in and depleted in to the surface. A problem with this interpretation is that the observed is smaller than the lowest predictions from cool bottom burning modelling, i.e. .

GX Mon, IK Tau, IRC-30398, IRC+10365 share several properties in common with IRC+10529 and IRC+50137: the measured shows up the effects of HBB and the optical depths, in the range , trace the presence of significant quantities of silicate dust in the circumstellar envelope. We discuss these 4 stars separately, because the carbon ratios given by the authors, , are higher than expected on the basis of a pure CNO equilibria, although the errors associated to individual abundances are compatible with a pure HBB chemistry. In the latter case the interpretation of these sources would be similar to what was proposed earlier in this section for IRC+10529 and IRC+50137.
Alternatively, the large degrees of obscuration and carbon isotopic ratios are obtained in the final AGB phases of stars (see the track in the left panel of Fig. 11): the interpretation of these stars would be similar to the scenario proposed for AFGL 5379 and OH26.5+0.6, in section 6.1. The effective temperatures of the stars in the late AGB phases, K, are only slightly in excess of the temperatures indicated by Ramstedt & Olofsson (2014).
According to this scenario, the stars in this group should have present masses of the order of . The expected luminosity is , a factor of 2 higher than proposed by Ramstedt & Olofsson (2014).

CIT4, IRC+60169 and IRC+70666 have ratios in the range . They exhibit a significant degree of obscuration, with , revealing the presence of silicate dust in the wind. While the large ’s indicate the effects of TDU, the presence of significant quantities of dust in the circumstellar envelope suggests advanced AGB stages of stars with progenitors of mass above : indeed lower mass stars reach the C-star stage, and little dust formation occurs in the early AGB phases, when the star is still oxygen-rich.
The carbon ratios and the mass loss rates proposed by Ramstedt & Olofsson (2014) are reproduced by models with initial mass , just above the threshold to activate HBB; as shown in Fig. 11 (see left panel), these stars first experience a series of TDU events, favouring the increase in the surface , then produce via HBB. If this understanding is correct, the stars should have a current mass of and a luminosity .
Alternatively, the degree of obscuration and the rate of mass loss proposed are reproduced by models of initial mass , in the final evolutionary phases: similarly to the stars discussed in the previous point, the large might be the effect of late TDU episodes, occurring when HBB is turned off. If this interpretation is correct, we may fix the current mass and luminosity of these stars, that are, respectively, and .
In both cases the luminosities expected are significantly in excess of the suggestion by the authors, that give for IRC+60169 and IRC+70666.

SW Vir and RX Boo have , which is compatible with the chemistry of any star at the beginning of the AGB phase, when the chemical composition was modified solely by the first and, possibly, the second dredge-up episodes.
Based on the luminosities given by the authors, , we conclude that SW Vir and RX Boo descend from objects and are currently at the beginning of the AGB evolution, before reaching the C-star stage. This interpretation is also in agreement with the very small optical depths given by Ramstedt & Olofsson (2014), .
However, the same isotopic ratios and small degree of obscuration are also reproduced by higher mass models in the early AGB phases, before the ignition of HBB. In this case the luminosities would be , larger than the values given by Ramstedt & Olofsson (2014).

Concerning W Hya, R Dor, RT Vir, R Cas, the material in the surface regions of these stars were exposed to partial CN cycling, as confirmed by the observed isotopic carbon ratios, . The luminosities given by the authorsfor these stars are in the range If these luminosities will be confirmed by precise distance measurements (see next section) the possibility that the observed ’s are determined by HBB would be ruled out beacuse significantly smaller than those reached by the stars experiencing HBB. A valid alternative is that the stars in this group descend from low-mass progenitors: the main arguments supporting this conclusion are: a) all the stars of mass in the range evolve at luminosities similar to those observed, in the AGB phases previous to the increase in the surface via TDU (the latter mechanism would increase the , far above the observed values); b) the degree of obscuration and the mass loss rate indicated by Ramstedt & Olofsson (2014) are very small, which is typical of the AGB evolution of low-mass stars, before the C-rich phase is reached.
On the theoretical side, we expect that the surface of these objects is modified by the first dredge-up, after which according to standard modelling of mixing we have ; this is a factor higher than observed. A solution for this discrepancy could be that the stars in this group experienced cool bottom processing during the RGB ascending (Boothroyd & Sachmann, 1999).

C-rich N-type AGB stars

LP And, V Cyg, CW Leo, RW LMi, V384 Per, UU Aur have a surface C/O above unity, the signature of repeated TDU events. The mass loss rate is correlated to the surface , which spans the range ; this is what we expect from the AGB evolution of low-mass stars, as discussed in section 3.2. These 6 objects are therefore experiencing advanced evolutionary phases of the AGB life, after becoming carbon stars.

The observed ’s are attained by all the star with initial mass in the range , although the luminosities and the mass loss rates given by Ramstedt & Olofsson (2014) suggest progenitors. The optical depths given by the authors are in the range , which indicates the presence of significant quantities of carbon dust in the wind; this is expected on the basis of AGB+dust modelling of stars evolving through the C-star phase (Dell’Agli et al., 2014).

The interpretation of UU Aur and V Cyg poses some problems. UU Aur has the largest in the overall sample, namely . Such large carbon abundances are reached by all the low-mass stars models considered here. The luminosity of this object is an issue though: while according to our modelling the C-star stage is not reached as far as the luminosity is below , Ramstedt & Olofsson (2014) indicate .

The luminosity of V Cyg given by Ramstedt & Olofsson (2014), , is also not reproduced by our models. If confirmed, the low luminosities of these two objects would be a strong indication that TDU is more efficient in the AGB stars of solar metallicity, compared to the predictions given here.

S-type AGB stars

The sample by Ramstedt & Olofsson (2014) includes 17 S-type stars, with a surface C/O around unity. The interpretation of these objects is not straightforward, because the and the luminosities given in the above paper are not consistent with our predictions. Concerning the chemical composition, Fig. 2 in Ramstedt & Olofsson (2014) shows that the average of this group of stars is slightly above 20, whereas according to our models carbon stars should have . This is shown in Fig. 7 (right panel); note that the same chemistry is also expected on the basis of C15 models, which adds more robustness to this general conclusion. This systematic difference can be explained only by invoking some ad hoc mechanism, such as cool bottom burning, acting to increase the in the envelope of low-mass stars before they become enriched in ; we believed this possibility unlikely though, because all the S-stars in the Ramstedt & Olofsson (2014) sample present such a low , thus indicating that this mechanism should be active in all low-mass stars. Alternatively, the circumstellar is not a reliable tracer of the surface cratio, at least for S-type stars. The interpretation of the results by Ramstedt & Olofsson (2014) is further complicated by the differences among the luminosities expected based on our models and those given by the authors. As discussed in section 3.2, and shown in Fig. 7, carbon stars of solar chemistry are expected to evolve at luminosities . This is at odds with the luminosities adopted by Ramstedt & Olofsson (2014) (see their Table 1), which are in the range . Note that use of C15 models (shown in the same figure) would hardly improve this mismatch, as in that case luminosities not below are expected.

6.4 Distance estimates within Gaia mission

This detailed analysis shows that reliable measurements of the distance of Galactic AGB, especially of those with recent estimates of CNO elemental and isotopic abundances, is urgently needed. The knowledge of the distance will allow a robust determination of the luminosity, which, as discussed in the previous sections, is crucial to the characterization of the observed stars in term of mass and evolution.
In Table 3 we summarized the characteristics of the Ramstedt & Olofssson (2014) sample discussed in details in subsection 6.3. The authors report the predicted absolute luminosity, however only in a few cases (starred with an asterisk in the table) the luminosities were estimated from accurate Hipparcos parallax measurements or by VLBI maser spot astrometry. In all other cases, the luminosity was either derived from Groenewegen & Whitelock (1996) period-luminosity relation (Mira variables) or assumed to be equal to 4000L (semi-regular, irregular variables, variables of unknown type or period). The uncertainty in the observed luminosity estimates makes the comparison between observed and predicted luminosities inconclusive.
As mentioned in the introduction, this problem will be addressed when Gaia astrometry for these stars will be available 8. The accuracy of Gaia parallaxes depends in a complicated way on several factors: number of observations, environment (i.e. stellar density), brightness, colour and so on. The number of end-of-mission observations based on Gaia scanning law9 are reported in the last column of Table 3. A good fraction of the Ramstedt & Olofssson (2014) sample stars will probably be observed enough times to reach the nominal astrometric error for bright stars of their spectral type (=10 as). However, given that most of the stars in our sample are Mira or semi-regular variables, it is not possible at present to evaluate the actual parallax accuracy for them. If accurate parallaxes will be available, then it will be possible to derive accurate luminosities, to discriminate among different model scenarios and to assign an evolutionary mass in several cases.

Name S-type L/L N
IRC+10529 M 7 10600 57
IRC+50137 M 6 9900 46
R Leo* M 6 2500 30
GX Mon M 11 8200 21
IK Tau M 10 7700 48
IRC-30398 M 13 8900 21
IRC+10365 M 13 7700 39
CIT4 M 29 4000 57
IRC+60169 M 29 4000 82
IRC+70066 M 66 4000 76
SW Vir* M 18 4000 45
RX Boo* M 17 4000 47
W Hya* M 10 6000 24
R Dor* M 10 4000 36
RT Vir* M 9 4500 39
R Cas* M 19 4000 82
LP And C 56 9600 68
V Cyg C 38 6000 47
CW Leo C 71 9800 27
RW Lmi C 45 10000 52
V384 Per C 43 8300 43
UU Aur C 100 4000 22
Table 3: Sample sources discussed in detail in subsection 6.3 with their spectral type (S-type), the derived (assumed to be equal to the measured ) and computed absolute magnitude given by Ramstedt & Olofsson (2014). In the last column are shown the predicted number of end-of-mission Gaia observations. Stars with parallax measurements by Hipparcos or by more precise estimates as VLBI maser spot astrometry are labelled with an asterisk.

7 Conclusions

We present solar metallicity models of the AGB phase of stars with mass in the range . This investigation integrates previous explorations by our group, focused on sub-solar chemistries.

The main physical and chemical properties of AGB stars are extremely sensitive to the stellar mass. A threshold mass separates two distinct behaviours.

The chemical composition of stars of mass is altered by the TDU mechanism, which favours a gradual increase in the surface carbon content. We find that the stars with mass in the range become carbon stars during the AGB phase. Once the C-star stage is reached, the consumption of the envelope is accelerated by the expansion of the external regions and by the effects of radiation pressure acting on the carbonaceous dust particles in the circumstellar envelope. This effects prevent further significant enrichment in the surface carbon, keeping the C/O ratio below . The gas ejected by these stars is enriched in carbon and nitrogen by a factor compared to the material from which the stars formed. The luminosities of carbon stars fall in the range .

Stars of mass experience HBB at the bottom of the convective envelope. The strength of the HBB increases with the mass of the star. The pollution from these stars reflects the equilibrium abundances of the HBB nucleosynthesis experienced. On general grounds, we expect carbon-poor and nitrogen-rich ejecta, owing to CN cycling. In stars of mass above the HBB temperatures are sufficiently large to activate the full CNO and the Ne-Na nucleosynthesis: the gas expelled by these stars is enriched in sodium, whereas the oxygen content is smaller than it was when the star formed. These stars are expected to evolve as lithium-rich sources for a significant fraction of the AGB phase.

The comparison with results in the literature outlines some similarities but also significant differences, particularly for what regards the strength of the HBB experienced, thus the luminosities at which these stars evolve and the kind of pollution expected. The carbon, nitrogen and sodium content of stars of mass above are extremely different from the results from other research teams, stressing the importance of confirmation from the observations.

We compare the models presented here with the CNO elemental and isotopic abundances in different types of Galactic AGB stars as estimated from observational data at very different wavelengths (from the optical to the radio domain);this part of the research has the double scope of adding more robustness to the present results and to characterise to stars observed, in terms of mass and age of the progenitors. The comparison with the observations is hampered by the unknown distances of the sources discussed.

Acknowledgments

MDC acknowledges the contribution of the FP7 SPACE project ASTRODEEP (Ref.No:312725), supported by the European Commission. 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. FD acknowledges support from the Observatory of Rome.

Footnotes

  1. pagerange: Studying the evolution of AGB stars in the Gaia epochLABEL:lastpage
  2. pubyear: 2012
  3. This mass range depends on metallicity, i.e. lower-Z stars achieve HBB conditions more easily . The lower mass limit to experience HBB decreases to for metallicities below .
  4. A word of caution is needed here: the short duration of the AGB phase of massive AGBs, particularly of the stars whose initial mass is close to the threshold limit to undergo core collapse, is partly due to the steep dependence on luminosity of the mass loss rate used here (Blöcker, 1995) ; the interested reader can find in Doherty et al. (2014) an exhaustive discussion on this subject.
  5. The ATON and K16 models of, respectively, and , produce indeed an hybrid O-Ne core: they undergo an off-centre ignition of carbon, but the temperatures are not sufficient for the convective flame that develops to reach the centre of the star.
  6. These stars are obscured in the optical range (e.g. Garcia-Hernandez et al. 2007) and they are expected to be the more massive AGB stars, experiencing extreme mass-loss rates.
  7. This information is however of little help because, as we noted above, these sources are completely obscured in the optical (García-Hernández et al., 2007), leaving no chances of any reliable lithium measurement.
  8. Seven stars of the Ramstedt & Olofssson (2014) sample will probably already be included in Gaia’s first data release, foreseen by the end of summer 2016, which will include parallaxes for the large majority of the Hipparcos and Tycho-2 stars.
  9. Computed with the Observation Forecast Tool available at

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