Astron. Astrophys. 362, 921-936 (2000)

4. Comparison to observations

In this section we compare our results to the observed abundance profiles of various elements across the galactic disk. Tracers of abundance profiles include emission-line objects (HII regions and planetary nebulae), as well as stars and stellar associations (B-stars and open clusters, respectively). In most cases, those tracers are relatively young objects (HII regions, B-stars and planetary nebulae of type I), younger than 1 Gyr; they provide then information about the current abundance profile of the Milky Way disk. In other cases (planetary nebulae of type II or III, open clusters), the objects involved are several Gyr old and provide information about the past status of the disk (albeit with much larger uncertainties than in the former case).

In Sect. 4.1 we present briefly the available observational data from various sources. In Sect. 4.2 we compare the data for young objects to our results at T = 13.5 Gyr; we show, in particular, how the results for C (and to a much lesser extent, N and O) may be affected by the M92 metallicity-dependent yields of massive, mass losing stars. In Sect. 4.3 we discuss the profiles of the corresponding abundance ratios of elements to Oxygen. In Sect. 4.4 we discuss the history of the abundance profiles, comparing our results to observations of old objects (of rather uncertain ages).

4.1. Observational data

One of the first comprehensive optical surveys of HII region abundances was performed by Shaver et al. (1983). They have found strong abundance gradients for N/H, O/H and Ar/H in the range of galactocentric distances R_G = 5 - 12 kpc. Those results were later confirmed by the surveys of Fich & Silkey (1991) and Vílchez & Esteban (1996), extending the data up to distances of R_G 17 kpc. Those authors suggested that the N/H and O/H gradients show a tendency for flattening between 11 and 18 kpc. Taking advantage of the small extinction in the infrared, Simpson et al. (1995) and Afflerbach et al. (1997) studied objects towards the center of the Galaxy. Simpson et al. (1995) observed 12 HII regions in R_G = 0 - 10 kpc and found a somewhat better fit with a step function than with a smoothly decreasing one. On the contrary, after adding five outer Galaxy HII regions (R_G = 13 - 17 kpc), Rudolph et al. (1997) concluded that the single slope profiles for N/H and S/H are more likely than step functions. The existence of a gradient in the oxygen abundance profile obtained from HII regions is not in doubt at present, but its magnitude has been recently challenged by the work of Deharveng et al. (2000), who report a value about half as large as previous measurements.

Observations of B-type stars in young clusters and associations in the late 90ies confirmed the existence of an abundance gradient. Smartt & Rolleston (1997) found an oxygen abundance gradient similar to the one obtained in HII regions (except for the work of Deharveng et al. 2000), in the galactocentric distance range R_G = 6 - 18 kpc. This was confirmed by Gummersbach et al. (1998) who detected significant abundance gradients for C, O, Mg, Al and Si in galactocentric distances R_G = 5 - 14 kpc.

Several works have been devoted to the study of the abundance patterns of planetary nebulae (PN, see e.g. Maciel & Quiroza 1999 and references therein). According to a classification scheme originally suggested in Peimbert (1978) and revised in Pasquali & Perinotto (1993), planetary nebulae are subdivided into types I, II and III. PNI have He/H 0.125 and log(N/O) -0.3, are located in the galactic thin disk and their progenitors are probably associated with stars in the mass range 2.5 - 8 . PNII belong also to the thin disk, are not particularly enriched in nitrogen or He and are thought to evolve from stars in the 1.2 - 2.5 range. Finally, PNIII are associated with the galactic thick disk and thought to originate from low mass progenitors, in the 1 - 1.2 range. The estimated progenitor masses imply ages of 1 Gyr for PNI, 1 - 8 Gyr for PNII and 8 Gyr for PNIII, respectively. These differences should allow, in principle, to use PN as tracers of the chemical evolution of the galactic disk. However, the mass and age differences between the various PN types are not quite well defined, as we shall see in Sect. 4.3. Moreover, all PN are expected to be auto-enriched in products of the CN cycle (i.e. N-rich and C-poor), while PNI (especially those originating from relatively massive progenitors, in the 5 - 8 range) are probably auto-enriched in products of the NO cycle (N-rich and O-poor). For those reasons, we shall not consider at all in the following the abundances of C and N from PN of all types and the abundances of O from PNI. For the purpose of this work, we shall use PNI (along with HII regions and B-stars) as tracers of the young disk in Sects. 4.2 and 4.3. PNII and PNIII will be discussed in Sect. 4.4.

Table 1 summarizes the currently available observational data on the abundance profiles across the Milky Way disk. Two points should be noticed:

Table 1. Observed and calculated abundance gradients in the Galactic disk (dlog(X/H)/dR, in dex/kpc).
References:
(1) Shaver et al. 1983; (2) Simpson et al. 1995; (3) Rudolph et al. 1996; (4) Afflerbach et al. 1997; (5) Deharveng et al. 2000; (6) Esteban et al. 1999; (7) Smartt & Rolleston 1997; (8) Gummersbach et al. 1998; (9) Hibbins et al. 1998; (10) Smartt et al. 2000; (11) Maciel & Koppen 1994; (12) Maciel & Quireza 1999; (13) Smarrt (2000). Ref. 9 and 10 give only the abundance of individual objects (shown by "x") and the derived gradients come from the combinations with the data of Rolleston et al. (2000).
Results :
a) Woosley & Weaver (1995) yields; b) Maeder (1992) yields for He, C, N, O

1) Contrary to other authors, we did not consider data on Fe from open clusters, since the situation is rather uncertain at present: for instance, in the solar neighborhood, open cluster data show no evolution of the Fe abundance with age (e.g. Friel 1999), contrary to the familiar age-metallicity relation suggested by data for F-stars (Edvardsson et al. 1993). In view of that dicrepancy, we chose not to consider Fe in this work (although we do calculate its abundance profile, as shown in Fig. 4).

2) Data in Table 1 are adopted directly from the references listed and no attempt has been made to homogenize them by recalculating the abundances in a consistent way. In general, differences in techniques and atomic data employed produce an abundance scatter which is smaller than observational uncertainties in the line strengths. Therefore, we believe that direct comparison between our models and those inhomogeneous data can still provide statistically meaningful results.

4.2. Current disk abundance profiles

The observational data of Table 1 concerning "young" objects (HII regions, B-stars, PNI) are plotted in Fig. 6, along with our model results, obtained with the WW95 yields, at T = 13.5 Gyr. In Fig. 7 we also plot the same data for He, C, N and O and we show the corresponding results obtained with both WW95 and M92 yields; as discussed in Sect. 2.2, the metallicity dependenence of massive star winds has an effect on the yields of those elements.

Fig. 6. Present day abundance profiles in the Milky Way disk (obtained in the framework of the model presented in Sect. 2 and with the WW95 metallicity dependent yields) and comparison with observations. Data sources are given in Table 1. The HII region data of Deharveng et al. (2000) suggest an oxygen abundance gradient by 40% less steep than the commonly accepted one of dlog(O/H)/dR -0.065 dex/kpc. The typical observational uncertainties for different elements and data sets are shown with error bars in the bottom left corner of each panel.

Fig. 7. Abundance profiles of He, C, N and O, at T = 9 Gyr (dashed curves ) and T = 13.5 Gyr (solid curves ), obtained with the WW95 yields (thin curves , same as e.g. in Fig. 3), and the M92 yields (thick curves ), in the framework of the model presented in Sect. 2. It can be seen that, compared to the WW95 yields, the M92 yields lead to considerably different results for C, to slightly different results for N, and to quasi-identical results for He and O. In particular, the M92 yields may explain completely the carbon abundance profile, with no need for any contribution from intermediate mass stars; on the contrary, nitrogen observations suggest that another source is mandatory.

Since the prescriptions for the radial dependence for infall and SFR of the BP99 model adopted here were such as to reproduce the observed oxygen abundance profile, we start the description of our results with this element.

Oxygen: As can be seen from Table 1, data from both HII regions and B-stars suggest an abundance gradient dlog(O/H)/dR -0.07 dex kpc^-1 (see the recent review by Smarrt 2000 on B-stars). Maciel & Quiroza (1999) include PNII (despite the fact that these objects are, in principle, older than 1 Gyr) and find an average gradient of dlog(O/H)/dR -0.065 dex kpc^-1 for all tracers of the "young" population. However, Deharveng et al. (2000), after a consistent analysis of their own data on HII regions, as well as of those of previous works, conclude that the gradient should be 40% smaller than generally thought, i.e. -0.04 dex kpc^-1. The data of Deharveng et al. (2000) concern the galactocentric distance R_G = 5 - 15 kpc, i.e. the same as the one of the work of Shaver et al. (1983) on HII regions or studies on B-stars; the difference in the resulting abundance gradient cannot then be attributed in the studied galactocentric distance range. As stressed by Deharveng et al. (2000), their derived O/H abundances depend strongly on their two-temperature HII region model (one temperature for the high excitation O zone and another temperature for the low excitation O⁺ zone); an alternative HII region model (with temperature fluctuations) would lead to larger O/H abundances. We also notice that in their recent work covering B-star in the inner Galaxy, Smartt et al. (2000) find oxygen abundances compatible to those of B stars in the solar neighborhood, that is no gradient for the inner disk.

As explained in Sect. 2, our model is based on the radial variation of the SFR (Eq. 3) and infall rate (Eq. 1). A different prescription would lead to different results for the abundance gradients (as in e.g. Prantzos & Aubert 1995, who used a radially independent infall time-scale and found a smaller gradient of dlog(O/H)/dR -0.03 dex kpc^-1). Also, by adopting the same prescriptions, but assuming radial inflows, one would obtain smaller values for the abundance gradient (e.g. Tsujimoto et al. 1995, Portinari & Chiosi 2000). Obviously, the magnitude of the abundance gradient is crucial in fixing the parameters entering the current phenomenological chemical evolution models. In particular, a strong gradient does not support the idea of important radial inflows induced by a galactic bar (such as those found e.g. in the calculations of Friedli & Benz 1995); the Milky Way bar must then have formed relatively recently and/or played a negligible role in driving gaseous flows in the disk.

The only published successful chemodynamical model for the Milky Way (Samland et al. 1997) predicts an oxygen abundance gradient that flattens considerably in the outer disk. Despite some claims for such a flattening (Vilchez & Esteban 1996), no convincing observational evidence exists up to now (see the discussion in Deharveng et al. 2000). Our model predicts no flattening of the gradient in the outer disk. It does predict a small flattening in the inner disk. As explained in Prantzos & Aubert (1995), this is due to the fact that all metal abundances are diluted in the inner disk by the late ejection of metal-free material by the numerous low-mass, long-lived stars of the first stellar generations; the ejection rate of that material at late times is larger than the metal production rate, since most of the gas in the inner disk has been consumed at that time. This is not the case in the outer disk, which is formed late.

As can be seen in Fig. 7, the M92 yields lead to results for oxygen that are almost indistinguishable from those of WW95. Only in the inner (more metal-rich) zones a slight difference is obtained in the oxygen abundance profile. As already discussed in Prantzos et al. (1994) the metallicity dependent stellar winds have a negligible impact on the oxygen yields.

Finally, another aspect of the observed oxygen abundances (Fig. 6) has been discussed in several places: all "young" objects in the local disk have lower oxygen abundances (in the range O/H 3.2-5 10^-4) than the Sun ( = 10^-4, Grevesse & Sauval 1998). For instance, Gies & Lambert (1992) derive an oxygen abundance O/H 4.8 10^-4 for local B stars, while Esteban et al. (1998) give O/H = 10^-4 for Orion nebula. This is difficult to understand in the framework of conventional models of chemical evolution, where metallicity increases monotonically with time. The idea that the Sun was born in the metal-rich inner disk and subsequently migrated outwards (Wielen et al. 1996), has been recently rejected by Binney & Sellwood (2000), on the grounds of dynamical arguments but their work seriously underestimated the ability of spiral arms to shift the radii of stars that corrotate with them. At present, there is no satisfactory explanation for the "super-metallicity" of the Sun relative to young objects in the solar neighborhood.

Carbon: There are very few studies of carbon abundances, either in HII regions or B-stars. Based on only two nearby HII regions (Orion and M17), Peimbert et al. (1992) first derived an abundance gradient of dlog(C/H)/dR -0.080.02 dex kpc^-1 in the solar vicinity. Adding another HII region (M8) to that sample, Esteban et al. (1999) obtain -0.1330.022 dex kpc^-1. However, both those studies concern a very limited range of galactocentric distances (6 - 9 kpc), and the derived abundance gradients cannot be considered as representative of the disk as a whole. On the other hand, the study of Gummersbach et al. (1998) suggests a rather small C gradient for B-stars in the range R_G = 6 - 12 kpc: dlog(C/H)/dR -0.045 dex kpc^-1; this is half as steep as the oxygen abundance gradient derived for those same B-stars in that study. If the Gummersbach et al. (1998) value is correct, it should then be difficult to understand the corresponding disk profile of the C/O ratio, which should decrease in the inner disk. Indeed, observations of low mass stars in the solar neighborhood show that C/O increases with metallicity (e.g. Gustafsson et al. 1999 and references therein), and we would expect to see the same effect in the inner, metal-rich disk. Hibbins et al. (1998) performed a differential analysis of C and N abundances of B-stars in the outer disk (10 - 17 kpc). They found that C correlates with N, but not with O. However, their absolute values of C/H for nearby stars are systematically lower by a factor 2 3 than those of other studies; they suggest then that their data (and data coming from different samples, in general) should be used with caution in studies of galactic chemical evolution.

In summary, the carbon abundance profile in the Milky Way disk is poorly determined. The few available data sets cover limited galactocentric distance ranges and are not derived in a consistent way. If all the data are plotted, as in Fig. 6 and Fig. 7, a carbon abundance gradient larger than the one of oxygen appears; but this may well be an artifact. We note that in his recent review, Smartt (2000) suggests a gradient of dlog(C/H)/dR -0.07 dex kpc^-1, based on the recent work of Rolleston et al. (2000) on B-stars (see also Smartt et al. 2000).

Our model results (Fig. 6) show a carbon abundance gradient of dlog(C/H)/dR -0.06 dex kpc^-1, i.e. comparable to the one of oxygen, when the WW95 yields are used. However, the absolute value of the local carbon abundance at the Sun's birth is underproduced in that case (by a factor of 2); another C source is then required. Intermediate mass stars (IMS) are well known net producers of carbon, but in recent years, several works (Prantzos et al. 1994, Carigi 1994, Gustaffson et al. 1999, Henry et al. 2000a) suggested that the M92 metallicity dependent yields of massive stars fit better the observed C/O abundance patterns in extragalactic HII regions and low-mass stars in the solar neighborhood. This is confirmed in Fig. 7, where it can be seen that the use of the M92 yields allows indeed to reproduce the absolute abundance of carbon in the solar neighborhood, with no need for a contribution by IMS. In that case, the resulting C abundance gradient is much steeper: -0.086 dex kpc^-1. Clearly, the abundance profiles of carbon vs. oxygen in the Milky Way disk are crucial in any attempt to evaluate the role of massive star winds in the production of carbon.

Nitrogen: There is a large number of works concerning N abundances in HII regions; the N abundance profile seems to be steeper, in general, than the corresponding O profile (see Table 1). Observations of B-stars (Gummersbach et al. 1998) support this conclusion, but the error bars are much larger in that case. Smarrt (2000) suggests a gradient of dlog(N/H)/dR -0.080.002 dex kpc^-1, i.e. compatible with the one of oxygen. Our models also produce a steeper gradient of N (with respect to that of O), with the yields of both WW95 (Fig. 6) and M92 (Fig. 7). As can be seen in Fig. 7, the differences resulting from the use of those two sets of yields are rather small (slightly larger than in the case of oxygen, but considerably smaller than in the case of carbon). Two important points should be noticed:

i) The absolute value of the N abundance obtained with both sets of yields is too low compared with observations in the solar neighborhood and in the disk. Contrary to the case of carbon, the M92 yields are not sufficient to account for the current abundance of N in the Milky Way. Unless the N yields are seriously underestimated in both WW95 and M92 (which is improbable, since they consist of the sum of the initial C+N+O), another N source is required. Intermediate mass stars are the obvious candidate, but their yields are notoriously difficult to estimate (in view of the many uncertainties concerning mass loss rates, "hot-bottom burning", etc.). Our calculations clearly show what is the magnitude of the expected contribution of IMS, in order to complement the (presumably better understood) yields of massive stars: on average, IMS have to produce 3-4 times more N than massive stars.

ii) We stress again (see also Sect. 3) that the flattening of the N abundance profile obtained in our calculations for the inner disk is due to the fact that, since yields of WW95 and M92 are available only up to Z = , for higher metallicities we use the yields at Z = ; thus, in our models N is produced in the inner disk (where high metallicities are developed) with the same yield always, i.e. as a primary element and its abundance follows the one of oxygen. Clearly, this is an artifact of the calculation, due to the lack of appropriate input data; if N were treated correctly, as a secondary, its abundance profile would not flatten in the inner disk [Notice : we could simply scale the N yields of WW95 with metallicity, but it would be more difficult to do the same thing with the M92 yields, since the effect of the stellar wind on the yield is not simply proportional to metallicity].

Magnesium, Aluminium, Silicon: The abundance profiles of those elements have been studied by Gummersbach et al. (1998), who observed B-stars in galactocentric distances 5 - 14 kpc. In view of the large uncertainties (see Table 1), all those gradients can be considered as compatible with the oxygen gradient of -0.07 dex kpc^-1, at the 1 level; this is particularly true for Mg. On the other hand, taken at face value, the Al profile seems to be considerably flatter than the one of Si (-0.045 dex kpc^-1 vs. -0.107 dex kpc^-1, respectively). This is rather surprising, taking into account that Al is an odd-Z element and its yield depends slightly on metallicity (the "odd-even" effect, see Fig. 1). Because of this effect, our models produce a steeper gradient for Al than for Si. The latter is comparable to the one of oxygen, as expected.

We note that in his recent review Smarrt (2000) suggests gradients of similar magnitude for Al and Si (-0.050.02 dex kpc^-1 and -0.060.01 dex kpc^-1, respectively), based on B-star data. In that case the problem is alleviated, although not completely solved. We also note that low-mass stars in the solar neighborhood do not exhibit the theoretically expected behaviour of the Al/O abundance pattern (e.g. Goswami & Prantzos 2000 and references therein). It may well be then that the odd-even effect has been overestimated in the WW95 yields of Al.

In summary, the observed abundance profiles of Al and Si run opposite to theoretical expectations, but in view of their large uncertainties, it is difficult to draw firm conclusions on stellar nucleosynthesis.

Neon, Sulphur, Argon: These elements have been observed through their emission lines in both HII regions and PN of all types. In general, HII region abundances suggest a radial profile similar to the one of oxygen for all three elements, i.e. a gradient of -0.07 dex kpc^-1 (the flat S profile of Shaver et al. 1983 is an exception to this general agreement). Data from PNI and PNII support gradients of this magnitude also for S and Ar, but suggest a smaller gradient for Ne (-0.036 dex kpc^-1, according to Maciel & Quiroza 1999).

Our model leads to S and Ar abundance gradients similar to the one of O (0.05 dex kpc^-1 in both cases). In the case of Ne, the (unexpected) small metallicity dependence of the WW95 yields (Fig. 1) leads to a steeper profile: dlog(Ne/H)/dR -0.08 dex kpc^-1, exactly as in the case of Mg.

In summary, the observed S and Ar abundance profiles are in agreement with theoretical expectations, while Ne remains problematic, both theoretically and observationally.

Helium: For the sake of completeness, we present here the He profiles of our models. As can be seen in Fig. 7, there is no difference between the profiles obtained with the WW95 and M92 yields. In both cases a flat He/H profile is obtained. However, the lack of IMS yields in our model does not allow us to draw conclusions about He.

The observational situation concerning the He abundance profile is not clear. The flat profile of the He⁺/H⁺ ratio found by Shaver et al. (1983) was confirmed by the recent work of Deharveng et al. (2000). However, the true He/H gradient depends also on the unknown amount of the corresponding neutral species. The data on Fig. 6 and Fig. 7 are from the work of Gummersbach et al. (1998) on B-stars. The error bars are quite large (0.3 dex for log(He/H)) and do not allow us to draw any conclusion on the existence of an abundance gradient for He.

Fig. 8 summarizes the discussion of this section, concerning observed and calculated abundance profiles in the Milky Way disk. If the values of Smartt (2000) are adopted for the C and Si gradients from B-stars, then there is satisfactory agreement between the model and observations for all elements but Al (taking into account error bars); He and N require another source to account for their absolute abundances, even if the gradient has the correct value. But the main "message" of Fig. 8 is that homogeneous data sets are required for a meaningful comparison between theory and observations.

Fig. 8. Present day abundance gradients in the Milky Way disk: summary of models vs. observations. Model results are shown by open symbols (asterisks , for the WW95 yields, connected by a solid curve , and pentagons for the M92 yields, only for C, N and O). Observations (Table 1 for references) are shown by filled symbols . Notice the large discrepancy between the carbon gradients observed in B-stars and HII regions, respectively. An average gradient of -0.070.02 dex kpc-1 is compatible with most of the data and the model results. Most of the observed abundance gradients are rather well reproduced by the model, but the case of Al is problematic (see text).

4.3. Abundance ratios along the Galactic disk

Abundance ratios between metals are, in principle, more reliable tracers of the chemical evolution than absolute abundances, since they do not depend on the star formation efficiency and they allow to identify if e.g. an element has a secondary origin, whether it is produced in long-lived sources (low-mass stars or SNIa) or whether it is affected by the "odd-even" effect, etc. These properties have been widely used as diagnostic tools of the history of the halo + solar neighborhood system (se e.g. Pagel 1997). In practice, the situation is complicated due to various theoretical and observational uncertainties (e.g. Goswami & Prantzos 2000 and references therein), except for a few trivial cases.

This is also the case for the Milky Way disk, as can be seen in Fig. 9: of the nine element abundance ratios to oxygen displayed in the figure, not a single one shows any clear trend with galactocentric distance. Although in most cases this is expected on theoretical grounds (e.g. for Ne, Mg, Si, S, Ar, which are primary elements), for others (N and, to a smaller extent, He and Al) this is rather surprising. Even worse is the large scatter obtained for all elements and at all galactocentric distances. There is a striking difference with F stars in the solar neighborhood, which display very small dispersion in their abundance ratios (Edvardsson et al. 1993). The inhomogeneity of the data sets displayed in Fig. 9 contributes certainly to that scatter. However, even in cases where only one tracer is involved (B-stars for Mg, Al and Si), the dispersion is rather large: it is about twice as large as the typical uncertainty of individual abundance ratios, estimated here to be 0.2 dex (see also Henry & Worthey 1999).

Fig. 9. Profiles of abundance ratios versus oxygen (normalised to the corresponding solar ratio: in the Milky Way disk. Observations are shown and compared to model results of this work. In all panels, the thin curves indicate results obtained with the WW95 yields, while the thick curves on the left side panels indicate results obtained with the M92 yields (leading to larger He/O, C/O and N/O abundance ratios). [Note: The flattening of theoretical profiles of abundance ratios in the inner disk is due to our use of yields for Z= even at metallicities larger than solar, because yields for such metallicities are not available in WW95 and M92]. Data (from references given in Table 1) concern HII regions (triangles ), PNI (crosses ) and B-stars (pentagons ). The typical observational uncertainties for different element ratios are shown with error bars in the upper left corner of each panel. Notice that for Ne/O, the best values from type I PNs are given by the lower envelope of the data (see discussion in Sect. 4.3).

A meaningful comparison between theory and observations is difficult in such conditions. However, Fig. 9 allows us to draw some conclusions:

i) The theoretical abundance ratios of Si/O, S/O and Ar/O are constant across the disk, as expected for primaries; their absolute value is always solar and compatible with available observations. The WW95 yields reproduce well the current average abundance ratios of those elements.

ii) The theoretically expected "odd-even" effect for Al/O is not manifested in the available observational data, i.e. no trend of Al/O with galactocentric distance (or metallicity) is observed. The WW95 yields reproduce correctly the current local Al/O ratio ( solar), and lead to a small dependence on metallicity (or radius), because of the "odd-even" effect.

iii) The WW95 yields underproduce the observed Ne/O and Mg/O ratios (as anticipated from Fig. 1); this is also the case for the solar neighborhood, as discussed in Goswami & Prantzos (2000). The discrepancy is not large, taken into account the various uncertainties of stellar nucleosynthesis calculations (see Prantzos 2000 for a review) as well as in observational data. Our Ne/O data come mainly from PN I, where this ratio is usually determined under the assumption that Ne/O = Ne/O. The Ne/O values probably are upper limits to the Ne/O value for central stars hotter than 50,000 degrees, due to the presence of charge exchange reaction O + H⁰ O⁺ + H⁺ that allows some O⁺ to coexist with Ne; this is particularly the case for PNs of type I with low density (Peimbert et al. 1995). Therefore the best values from type I PNs are given by the lower envelope of the data presented in Fig. 9 (M. Peimbert, private communication). On the other hand, the WW95 yields of Ne and Mg manifest an unexplained dependence on metallicity. Put together, these discrepancies point to some problems in the WW95 yields of Mg and Al. One possibility is that the extent of the C-shell (where both elements are mainly synthesized) is underestimated by the Ledoux criterion for convection employed in the WW95 calculations.

iv) The WW95 yields underproduce the local C/O ratio, while the M92 yields of massive stars reproduce it fairly well (with no need for a C contribution by IMS). However, if WR stars are the main producers of C, one expects this ratio to decrease with galactocentric distance (as indicated by the thick curve for C/O in Fig. 9), and this trend is not seen in currently available data. On the other hand, if IMS produce the bulk of C as primary, no variation of the C/O ratio with galactocentric distance is expected. It should be noted that gradients of C/O (in fact, variations of C/O with O/H) have been observed in extragalactic HII regions (e.g. Garnett et al. 1999) and are also expected in the case of the Milky Way disk. Thus, accurate determination of the C/O ratio across the Milky Way disk is crucial in determining the roles of IMS and Wolf-Rayet stars in carbon production. [Note: the flattening of the theoretical C/O profile in the inner disk is due to our use of M92 yields for Z = even when the metallicity is larger than solar; in principle, the C/O ratio should continue increasing in the inner disk. C and O yields for metallicities higher than solar are required for a proper calculation].

v) Both WW95 and M92 yields underproduce the N/O ratio in the disk and lead to a N/O profile declining with radius. IMS are expected to be the main N producers in the disk. The dispersion of presently available data on N/O in the disk does not allow to conclude whether they produce N as primary (i.e. through hot-bottom burning), or as a secondary. As with the case of C, observations of N/O in extragalactic HII regions show that N behaves as secondary at high metallicities (Henry et al. 2000a). This does not seem to be the case in the inner regions of the Milky Way disk, at least with currently available data.

vi) The observed He/O ratio in B-stars is higher than the corresponding solar value at all galactocentric distances. This is obviously related to the fact that the O abundances of those young objects are (somewhat surprisingly) systematically lower than solar. Since no satisfactory explanation for that exists up to now (at least in the framework of conventional chemical evolution models), we do not expect our results to match the average observed value of He/O. On the other hand, the B-star data show a flat He/O profile (as a result of the similar He/H and O/H gradients shown on Fig. 6 and Fig. 7). In our calculations, the amount of He produced by massive stars alone (either with the WW95 or the M92 yields) is negligible relative to the primordial one of the infalling gas. Thus, the final He/H profile is flat (Fig. 6 and Fig. 7) and the final He/O profile (Fig. 9) is decreasing in the inner disk; obviously, the contribution of intermediate mass stars is mandatory to account for He observations.

4.4. Evolution of abundance gradients

As already mentioned in Sect. 4.1, abundances in planetary nebulae of various types (I, II and III) allow, in principle, to follow the history of the abundance profile of the Milky Way disk. However, the progenitor masses and lifetimes of PNs are not well known. For instance, Allen et al. (1998) assume that both PNII and PNIII have progenitors of similar mass range (M2 ) and classify them in terms of their kinematical properties: PNII have peculiar velocities 60 km/s and PNIII have 60 km s^-1. To account for these properties as well as for the relative frequency of the various PN types, Allen et al. (1998) propose a "dynamical" model for the Milky Way disk, simulating orbital diffusion. They find good agreement with observed gradients of PN (classified according to that scheme), provided that not all IMS go through the PN stage. In that same paper, they also explore the "conventional" scheme, classifying PN in terms of progenitor mass: 1.3M/8.4 and 3 Gyr for PNI, 0.9M/1.3 and 3 9 Gyr for PNII and 0.8M/0.9 and 9 Gyr for PNIII. They find that their model fails to reproduce observations of the various PN types in that case.

In our model we have no information on the kinematical properties of the gas or the stars. We adopt then the classification scheme of Pasquali & Perinoto (1993) for PN, already presented in Sect. 4.1. We are aware that this scheme is not necessarily the most appropriate one (uncertainties in ages may be larger than stated and kinematics may play a non negligible role), but we adopt it for the sake of comparison to our model results. This comparison is presented in Fig. 10. It can be seen that:

Fig. 10. Abundance profiles in the Milky Way disk at various epochs according to our model and comparison to objects of (hopefully) corresponding ages. From left to right, profiles are shown for young (Column A), intermediate (Column B) and old age (Column C) objects. In Case A belong B-stars, HII regions and planetary nebulae of type I; in Case B belong planetary nebulae of type II; and in Case C belong planetary nebulae of type III (see Sect. 4.4 for a discussion on ages). The corresponding model results are shown at time T = 12.5-13.5 Gyr or age = 0-1 Gyr (shaded area in A), T = 5.5-12 Gyr or age = 1.5-8 Gyr (shaded area in B) and T = 0.5-5.5 Gyr or age = 8-13 Gyr (shaded area in C). References for data are given in Table 1.

i) The model describes relatively well the O, Ne, S and Ar abundance gradients of young objects (left hand panels, Column A), as already discussed in the previous sections. However, the observed scatter at all galactocentric distances is much larger than the range of values given by the model for the last 1 Gyr (the shaded region in Fig. 10). It should be noted that the observed scatter ( 0.6 dex) is larger than the corresponding one for young stars in the solar neighborhood (e.g. Garnett & Kobulnicky 2000). Probably, systematic effects and uncertainties in distance estimates contribute largely to the observed scatter of "young" tracers in Fig. 10.

ii) Model predictions are compatible with observations for O and Ar in PNII, as can be seen in the middle panels of Fig. 10 (Column B). In fact, there is very little difference between the data for PNII and those for PNI. Predictions for S are slightly above the data points, while predictions for Ne are clearly below the corresponding data. The reason for the latter discrepancy is obviously the unexplained underproduction of Ne in the low metallicity yields of WW95, already discussed in Sects. 2.2 and 4.3. In the other 3 cases (O, S and Ar) there is fairly good agreement between theory and observations concerning all properties of the observed abundance profiles (absolute values, gradient, scatter).

iii) Observations show that, on average, abundances in PNIII are lower and present a larger dispersion than in PNII. Both features are relatively well reproduced by our models, as can be seen on the right hand panels in Fig. 10 (Column C), with the exception of Ne (for the reasons already mentioned in the previous paragraph).

Our models, as some other models of this kind ( Mollá et al. 1997, Portinari & Chiosi 1999) suggest that abundance gradients are steeper for older objects. Other works (e.g. Chiappini et al. 2000) reach an opposite conclusion, although they are based on the same assumption, namely an "inside-out" formation of the disk; clearly, the adopted time-scales for star formation and infall play an important role in this discrepancy. Although our model results are compatible with available data on PN, the large scatter in those data does not allow to conclude on the temporal variation of the gradients (see Maciel & Quireza 1999). However, our model makes a new, and perhaps testable, prediction: if the observed abundance scatter at a given galactocentric distance is to be attributed, at least partially, to intrinsic age differences between the tracers (e.g. PN) then we expect that scatter to be smaller in the inner disk than in the outer one (as indicated by the extent of the shaded areas in Fig. 10).

© European Southern Observatory (ESO) 2000

Online publication: October 30, 2000
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