VARIABLE YIELDS AND THE PROBLEM OF NITROGEN PRODUCTION
C. F O R I E R I
International School for Advanced Studies, Trieste, Italia
(Received 6 February, 1985) Abstract. In this paper we study the effect of metal-dependent stellar models on chemical yields and in particular on the history of nitrogen and oxygen abundances. We find that N yield decreases with increasing metal content. This effect somewhat balances the growth of secondary enrichment in nitrogen and leads to a relation between oxygen and nitrogen in fair agreement with observational data for galactic H I! regions.
1. Introduction Nitrogen is one of the commonest elements in the Universe; its abundance has been determined for a large sample of galactic and extragalactic H II regions and planetary nebulae. While nitrogen is considered to be a secondary product of stellar nucleosynthesis, requiring oxygen and carbon seeds to be synthesized, it is difficult to account for the observational data in terms of current stellar models. Two different solutions have been suggested to explain the observed abundances: either that a large fraction of nitrogen is primary origin (being directly synthesized from hydrogen and helium initially present in the stars), or a large fraction of nitrogen comes from low-mass stars, of long lifetime; and its present abundance reflects the nitrogen production of metal-poor stars. In this paper, after a brief summary of the various explanations put forward by different authors, we suggest a new approach, which takes into account the different nitrogen production by stars of different metallicity and, therefore, allows for time variations of the nitrogen yield. Evolutionary models in the range of intermediate mass stars (IMS; Renzini and Voli, 1981) predict that the amount of both primary and secondary nitrogen depend on the initial chemical composition of the star. If we take this fact into account in chemical evolutionary models, the indication arises of a nitrogen production mimicking the primary origin of this element.
2. Simple Mathematical Formulation Before reviewing the current observational information on elemental abundances and on nitrogen in particular, we present here a simple mathematical formulation of chemical evolution, in order to facilitate the forthcoming discussion. The synthesis of heavy elements takes place in stellar interiors. If ejected, these new elements, mixed with interstellar gas, enrich subsequent generations of stars. Ejection generally occurs only at the final stages of a star life. In addition to the stellar contriAstrophysics and Space Science 114 (1985) 119-133. 0004-640X/85.15 9 1985 by D. Reidel Publishing Company
120
c. FORIER1
bution, exchanges of material between different regions within the same galaxy or with the external environments modifies the chemical abundances. Chemical elements can be divided into two classes: namely, the primary and secondary ones. The former are directly synthesizes from hydrogen and helium, as carbon, oxygen, and iron. The latter require the presence of some seeds to be synthesized. The most common among those secondary elements is nitrogen which, once CNO cycle has set to equilibrium, is more abundant then C and O in virtue of the low rate of the ~4N(p, 7 ) 1 5 0 reaction. To compute the time variation of an element i, one must know the fraction of gas Ei ejected in this form by each dying star. Following Tinsley's (1980) notation, E i can be written as mu
E; = t
[(m
- M r - mpzm)Z(t
-
zm) + mpzm]O(t
-
Zm)~O(m)din,
(1)
ml
where Pzm is the fraction of a star of mass m ejected as new-synthesized metals; Zm, the lifetime of a star of mass m; Mr, the mass of the remnant; ~, the star formation rate (SFR); and ~0, the initial mass function (IMF). In the usual instantaneous recycling approximation, simple mathematical relations are possible: assuming that the system is closed (no gas losses or infall) and initially formed by nonenriched gas, one obtains the so-called standard solution Z = y In G - 1
,
(2)
where G is the ratio of gas mass to total mass, and y is the yield of the heavy elements, defined as mu
ml
In this case Z may become much greater than y as the gas mass declines by star formation. A different analytical solution is found when star formation is exactly balanced by gas inflow - i.e., if the mass of gas keeps constant. In this case the solution is easily expressed in terms of the ratio between accreted and initial mass, M and M o, respectively -
i.e.,
v = (M - Mo)/M o .
(4)
Therefore, it follows that Z = y(1 - e-V).
(5)
In this case the metallicity tends to the yield as v grows by infall in the course of evolution. The above expressions hold good for primary elements. For secondary elements the
VARIABLE YIELDS AND THE PROBLEM OF NITROGEN PRODUCTION
121
ejection rate of newly-formed material is given by
E~ = f mps,,,[Z(t- Zm)/Zo]~r(t- z,,,)cp(m)dm.
(6)
In the case of the simple closed models, one gets
Xs = 89
2,
(7)
where Xs is the abundance of a given secondary element and y~ its yield. As suggested by Serrano and Peimbert (1983), in the case of nitrogen and oxygen, one can write Log(N/O) = a Log(O/H) + b,
(8)
with a = 1 for the standard model.
3. The Observational Information and N Problem
The best information on the abundance distribution across the galactic disk comes from H II regions. They are generally taken as indicators of the interstellar medium (ISM) composition. Good data are derived also from planetary nebulae (PN) and supernova remnants (SNR). However, those objects might be self-enriched: in particular PNs due to mixing during the phase of asymptotic giant branch (AGB). Although contrasting results have been presented over the past years, a negative gradient is always found for log(N/H) - 0.23 + 0.06
(Peimbert et al., 1978) ;
- 0.10 + 0.03
(Hawley, 1978) ;
- 0.08 _+ 0.02
(Talent and Dufour, 1979) ;
- 0.095 + 0.03
(Binette et aL, 1982) ;
- 0.09 + 0.015
(Shaver et al., 1982).
While in the past the gradient in nitrogen was thought to be steeper than the gradient in oxygen, recent observations seem to indicate about equal gradients in the two dements. In fact, Shaver et al. (1982) give for the gradient in oxygen the value of -0.07 + 0.015. This fact is quite surprising as according to the classical picture, nitrogen is expected to be a secondary product having 12C and 1 6 0 a s seeds. A different gradient in nitrogen is indicated by PNe abundances: namely, - 0.18 + 0.06 (Torres-Peimbert and Peimbert, 1977). However, self-enrichment caused by external mixing during late evolutionary phases of these stars, when H-burning in CNO cycle transforms carbon and oxygen into nitrogen, may alter nitrogen abundances. In such a case, PN nitrogen gradient is expected to be steeper because further contribution by carbon and oxygen transformations has to be added to the initial value.
122
c. FORIERI
z~ -~o
g
ao o
9
r
9 8
o:
-1.5
!
I
8.5
9,0
I 9.5
12+ log (O/H) Fig. 1. The N/O abundance ratio versus the total oxygen abundance for galactic H ]] regions from Shaver et al. (1982).
In Figure 1, data for galactic H II region s :are compared in the [ O/H ]-[ N/O ] diagram. They do not agree with the predictions from the standard model. In fact N/O appears to be almost constant across the galactic disk, as it is for primary dements, for which
(X, tX2) = (y, tY2),
(9)
if the yields are constant in time. However, the disagreement is not surprising owing to the crude assumptions in the standard model. Abundance determination in external spiral galaxies show similar behaviour, in the sense that they exhibit almost constant N/O ratios, the mean value of N/O, however, varying from galaxy to galaxy. The spread in the N/O ratio among regions with the same oxygen abundance is up to a factor of 4. On the contrary, all H II regions in irregular and blue compact galaxies are underabundant in nitrogen and populate an approximativdy triangular region of the [O/H]-[N/O] diagram, and no evident relation between nitrogen and oxygen content can be found. The whole set of data, when galactic and extragalactic regions are included, is shown in Figure 2. As pointed out by Serrano and Peimbert (1983), the data are confined between two 45 ~ lines, however, with very large dispersion. For objects with 12 + logO/H > 9. Ray 9 etal. (1982) suggest that the calibration procedure could underestimate the effective temperature of H II regions and thus overestimate the oxygen abundance. However, it is quite clear that it is difficult to extend this explanation to a whole set of the data. The indication emerges that, to explain the observational data, one must relax some of the approximations made in standard models. Several ways out are possible, as suggested by different authors. (i) The first explanation is that a part of nitrogen is of primary origin. In fact, primary
123
VARIABLE YIELDS AND THE PROBLEM OF NITROGEN PRODUCTION
I
I
!
I 0 Ao
9
-1.0
9
9
9
9
~
0
9
0
0
9
go 9
*
9 8
#ee ~
Z
-1.5
+~k
~,
§
4."1"
+
~,
§
+
+
+ +A
+
+A
++*
9
+ "F
13
I~A
13 ~
9
9 9
9 9 GALAXY 9
+ Irr- & Cofnl~lCt
~M3.3
+
OM83 ~"
AMI01
A NGC300 n NGC13~ r l NGC 7793
I
J
I
f
&O
8.5
9.0
9.5
12. ,og (o~)
Fig. 2. The N/O abundanceratio versus the total oxygenabundanceboth for galactic(Shaver et al., 1982) and extragalacticH I1 regions (Edmunds and Pagel, 1981; and referencegiven therein).
synthesis can take place in IMS during AGB phase (Iben and Renzini, 1983, 1984), although the efficiency of this process is not very well established. On the other hand, the situation is not clear from the observational point of view as well. In fact, while there are several highly reliable examples of primary production of nitrogen, in many others the evidence is weak. HD 192 163, the ionizing WN star of the PN NGC 6888, shows X, = 0.035 and XC = 0.001 (Willis and Wilson, 1978), that is a nitrogen abundance much greater than the solar global abundance of C, O, and N. In general, however, the PN compositions provide evidence for efficient nitrogen synthesis, but not for efficient primary production. In fact, N/O never exceeds Z in PN of type I (Peimbert and Serrano, 1979) and the evidence for a substantial primary production is very weak. PNe of types II and III, though showing C + N + O abundances higher than the solar values, have not undergone substantial production of nitrogen, although exception s (NGC 6803 with 12 + log(O/H) = 9.02 and 12 + log(N/H) = 8.76) are known to exist. On the other hand, classical novae generally show overabundance of nitrogen - a fact which requires primary production, as was suggested by William (1982). He found that novae seem to be mainly responsible for nitrogen abundance in M31 and in MCs, if we assume that the ejecta in external galaxies have the same composition as in the Galaxy. However, even for galactic novae, the composition of the ejecta is rather uncertain. There is a wide dispersion of data, even if CNO elements seem to be more abundant than the cosmic value. (ii) Edmunds and Pagel (1978, 1984) suggest that primary production may explain not only galactic data, but also those of NGC 300, M33, and M101, if the assumption
124
c. FORIERI
of intantaneous recycling approximation is relaxed. In fact, while oxygen is essentially formed by massive stars of very short lifetimes, nitrogen might be produced by long-lived stars. In such a case the nitrogen production should be expressed by a law different from Equation (8) - i.e., taking into account the time delay of nitrogen ejection X,/X o = (y,/yo)f(t) ;
(10)
where f ( t ) , initially equal to 0, tends to 1 with increasing age. Differences between galaxies could be explained in terms of different ages, that is the time elapsed since the main event of star formation. However, large differences among N/O ratios in different galaxies, and strong dependence of stellar ages on the mass, do not allow us to determine the mass range in which primary nitrogen is produced and, in turn, the epoch of the dominant star formation event. Unless the age of magellanic clouds (CMs) is lower than 1 Gyr, the effective mass ranges between 1 and 2 M e. This conclusion does not agree with current theory of stellar evolution. In particular, Renzini and Voli (1981) found a lower mass limit for envelope burning, under which primary nitrogen synthesis does not occur at all. This mass limit depends on initial chemical composition and on mixing-length parameter ~, being 4 M e for Z = 0.02 and 3.25 M e for Z = 0.004. (iii) A more complex model has been proposed by Alloin et al. (1979), assuming both primary and secondary N, an arbitrary SFR, a power law for the IMF and finally the closed model of galactic evolution, initially composed only by unenriched gas. The result is a curve less steep than the 45 ~ line in the N/O vs O/H diagram. A single relationship does not reproduce all the data; but allowing for suitable variations across the disk, one may obtain the observed feature - even it is not clear how IMF variations may yield a N/O ratio constant across the galaxy disk. However, it is worth mentioning that gradients in oxygen and nitrogen in other galaxies are also customarily explained in terms of a suitable choice for SFR and IMF. For instance for M33, which shows abundances lower than expected, Alloin et al. (1979) assume a large number of low mass stars in the IMF, even if the SFR history could play an important role in N production. On the contrary, for M101 they assumed a large fraction of massive stars to explain the low nitrogen content compared with oxygen abundance in the Galaxy. Alternatively, a primordially peaked SFR must be invoked. In those cases, in which observational evidence of substantial production of primary nitrogen is not very strong, the above assumptions can be easily avoided. In fact, Serrano and Peimbert (1983), using a secondary production of nitrogen (although a moderate contribution by primary N cannot be excluded) and a chemical model with infall and without instantaneous recycling approximations, suggest a different solution. They consider the possibility of a metal-dependent yield Yz and assume that Yz = Yo + a Z .
(11)
This variation is thought of to be given by a variable IMF. If nitrogen is produced by long-lived stars, and oxygen by massive stars, in Equation (8) b is a function of time, whose value is - ~ at the beginning, when only oxygen was produced, and constant
VARIABLE YIELDS AND THE PROBLEM OF NITROGEN PRODUCTION
125
afterwards. Considering models with constant ratio between the accretion rate and effective SFR (excluding low mass stars that are long-lived), Serrano and Peimbert (1983) found that the main contributors to nitrogen nucleosynthesis are stars with masses larger than 1.2-1.3 Mo and, therefore, with lifetimes shorter than about 3 Gyr. While, at low metallicities, models with constant or variable metallicity are equivalent, in metal-rich regions only models with variable yields seem to agree with the observational data, as the others lead to higher N/O ratios. The solar N/O ratio suggests an infall rate comparable with SFR, while the O/H gradient indicates that infall becomes relatively more important in external regions. Serrano and Peimbert (1983) conclude that, while O/H is essentially determined by gas fraction (unless the accretion rate is very high) N/O depends both on time and on the relative efficiency of accretion. On time because the delay effect decreases with increasing time, and on accretion as this controls the time necessary to reduce the gas fraction. The scatter among irregular galaxies can be interpreted in terms of age increasing from NGC 6822 to the LMC, and ofinflox efficiency increasing from NGC 4449 to the SMC. The comparison between theoretical models and observations for these galaxies is rather uncertain as SFR could be highly time dependent. (iv) A completely different approach has been undertaken by White and Audouze (1983). They included stochastic effects in chemical evolution of galaxies. They did not specify the type of chemical inhomogeneity but they used a simple model to describe the mixing process. Like in the model of Lynden-Bell (1975) and Larson (1972), here infall exactly balances the star formation and, therefore, the surface density of gas keeps constant. The instantaneous recycling approximation is relaxed, and gas can be slightly inhomogeneous due to inefficiency of the mixing process. The effect of such an inhomogeneity is to make constant the ratio of secondary to primary elements, as is perhaps indicated by the observational distribution of abundances in H II regions. A purely secondary nitrogen synthesis could explain the relation between N/O and O/H. White and Audouze (1983) consider their model only as a preliminary approach to the study of the effects of inhomogeneities. Concluding this section, we should like to comment briefly on a few additional points that are important in modeling the chemical history of the galaxies. The usual assumption made about infaUing gas is that this gas is of primordial composition. As a matter of fact, a gas with such a composition is not observed; while there is no evidence for a stellar population with primordial composition (Bond, 1981). This fact is generally explained by postulating an early enrichment caused by a population of massive or very massive stars - namely, a hypothetical Population III. The implications of primordial enrichment have been studied by several authors. It is worth recalling that an IMF enriched in massive stars would imply yields completely different from those of the present stellar population, in particular, massive and very massive stars are strong oxygen producers. In support to this, metal-poor stars are observed to be relatively more abundant in oxygen than in other primary elements.
126
c. FORIERI
What about nitrogen? In a sample of eight old Population II stars, Barbuy (1983) found that both oxygen and nitrogen are overabundant. This is true not only for giants, where the carbon deficiency can indicate the presence of self-enrichment in secondary nitrogen, but also for unevolved stars. A mechanism of primary nitrogen production is, therefore, involved, as indicated by the study of Bessel and Norris (1982). They found a value [N/Fe] = + 1.7- + 2.0 for two dwarfs having [Fe/H] = - 2.0, implying too a high initial value [O/Fe] > 0.7-1.0 in the case of secondary production. Sneeden (1974) came to the same conclusion, finding too large a difference in the ratio N/H between unenriched dwarfs and enriched subgiant. These latter data have, however, been questioned by Barbuy (1983). Moreover, if stars with [Fe/H] < - 2 . 0 are always overabundant in nitrogen, the situation is drastically different in the case of[Fe/H ] > - 2.0. There is a wide dispersion in the ratio N/Fe; nitrogen can be found even underabundant with respect to iron, for both subgiants (as in the case of v Ind; Harmen and Pagel, 1970) and subdwarfs (Clegg, 1977).
4. Variable Yields for Z-dependent Models In models of chemical evolution, the direct influence of the chemical composition on stellar evolution and consequent variation of the yields are, in general, neglected. This is due first to the practical difficulty of including variable yields in evolutionary computations; and, secondly, to the lack of sufficiently extensive grids of stellar models. Although metal-dependent yields have been already considered by Serrano and Peimbert (1983), this was thought of to be only the consequence of a variable IMF. A variation in the lower or upper limit of mass can modify the fraction of stars which are able to enrich the interstellar medium: increasing this fraction, one can increase the yield. By changing the slope of the IMF, a specific range of masses is favoured with respect to the others: in particular, a flatter IMF increases the number of massive stars as well as the oxygen yield. The effect of the star initial metallicity on the final nucleosynthetic enrichment has been customarily neglected. On the contrary, it might be worth of interest to evaluate its effect on models of chemical evolution of the Galaxy. As it will be shown in what follows, this may be crucial in the case of nitrogen. This suggestion arises from the analysis of the model computed by Renzini and Voli (1981), in which stellar models as well as the final enrichment of the interstellar medium have been considered for IMS with two different metal contents: Z = 0.02 and Z = 0.004. It would be important to test the influence of the star's initial chemical composition on galactic models not only restricted to IMS but also extended to all ranges of mass. 4.1. MASSIVE STARS From a theoretical point of view, the evolution of massive stars depends on the initial metal content. Due to the lower efficiency of H-burning in the CNO-cycle, metal-poor stars have smaller radii and higher central densities and temperatures to balance the
VARIABLE YIELDS AND THE PROBLEM OF NITROGEN PRODUCTION
127
reduction of produced energy. A small contraction, interesting the whole star, suffices to reach the equilibrium condition due to the strong dependence on temperature of the efficiency of CNO cycle. As a consequence, the model is hotter and a slightly more luminous. In addition to this, the extension of the convective core during the H-burning phase is greater than in metal-rich stars. If mass loss is included in the models, there can be a new dependence on Z of the evolution, as the mechanism of mass loss might be metal dependent. Theoretically, those mechanisms based on metal ions, like mass loss by radiation pressure on lines of Castor et al. (1975), predict a variation in the mass loss rate. A change in effective temperature and luminosity, implied by a different metal content, can also influence the mass loss rates. In a preliminary investigation, assuming Abbott's (1982) Z-dependent expression for the mass loss, we found (cf. Forieri, 1982) that the rates suites to star of solar composition cannot be extended to objects with Z = 0.001. In fact, there are both direct and indirect indications that mass-loss rates in supergiants of LMC are smaller than in their galactic counterparts. It is known from current evolutionary models (Arnett, 1978; Weaver etal., 1978; Weaver and Woosley, 1980; Woosley and Weaver, 1982) that the final nucleosynthetic enrichment by massive stars depends on (and can be parametrized by) the mass of the He core built in the course of early stages. Since this turns up to depend on mass loss (Chiosi, 1981) it follows that the stellar wind may significantly affect the enrichment process. The most important element synthesized by massive stars - that is, oxygen may be ejected in lower amounts by strong stellar wind. Moreover, massive stars could contribute to the chemical evolution of the Galaxy during the WC phase with the nuclear products of the 3e-reaction present in the stellar wind, especially 12C and 22Ne (Maeder, 1981). As WC's are customarily considered the descendants of massive stars through mass loss, metal-dependent winds should imply yields variable with stellar metallicity. In fact, the observations indicate a decreasing fraction of WC's relatively to O-type stars from the solar vicinity to SMC and LMC (Vanbeveren and Conti, 1980), that is for environment with decreasing Z. However, models of massive stars of different metal content and computed to the final evolutionary stages, are needed to quantitatively estimate the variation in the yields. 4.2. INTERMEDIATEMASS STARS Alcock and Paczynski (1978)first investigated the influence of metal content on stellar models in the mass range of 2 to 10 M o. As in massive stars, models with lower metaUicity are more compact; the increase in T is stronger than the increase in p, and the core of metal-poor models is less degenerate, with important consequences on the final evolution. More precisely, while a different chemical composition would imply only a small change in the yields from massive stars, for IMS the change may be more important owing to its effect on the mass range, within which explosive nucleosynthesis may take place. In fact, as shown by the case ofa 7 Mo, with Population I chemical composition,
128
c. FORIERI
carbon burning is explosive, while it ignites quietly in metal-poor stars (Alcock and Paczynski, 1978). Furthermore, Renzini and Voli (1981) computed the evolution beyond the exhaustion of the central helium, considering the thermal pulse and the third dredge-up phases, for various mixing length parameters in the outer convection and mass loss rates. They found that nitrogen production is strongly dependent on the metal content; in particular, the production of primary nitrogen during the process of envelope burning. The lower limit of mass for envelope burning becomes smaller with decreasing metallicity, while the mass range for primary nitrogen production gets larger. Furthermore, within a given mass, the production of primary nitrogen is larger as the metallicity decreases. Renzini (1984) suggests that even a lower rate of mass loss can increase the nitrogen yield in metal-poor models; but this is not yet supported by observations. The effect of metallicity on N production is not very important in the case of secondary nitrogen, since this latter is proportional to the initial metal content - even though a more efficient production is expected in metal-poor stars. The ratio between the mass of ejected nitrogen and initial metal abundance grows in models with Z -- 0.004. Furthermore, this trend is slightly larger in models with a higher mixinglength. Moreover, a more substantial mass loss could lower nitrogen nucleosynthesis in metal-rich stars even in the case of secondary nitrogen production. 5. Chemical Evolution of the Galaxy In order to investigate the importance of yields dependent on the stellar metal content, we study the dependence of nitrogen abundance on Z. First, we assume instantaneous recycling - in the sense that we compute the yield corresponding to the current metal content. This approximation is not particularly critical, because we considered 3.25 M o to be the lowest mass to have yield variation. This star has a lifetime of about 250 x 106 yr, which is short in comparison with the time-scale of chemical evolution. As only two grids of models with different Z are given in Renzini and Voli (1981), we assume the yield of N to linearly depend on Z. The new yields have been used in a model of galactic chemical evolution, based on the numerical procedure suggested by Talbot and Arnett (1971). For a complete description of the mathematical formulation, see also Chiosi and Matteucci (1982). The major characteristics of the model when applied to disk galaxies are summarized as follows. The galactic disk is assumed to be well-mixed by rotation; all quantities, such as chemical composition, gas content, total mass, are functions of the radial distances and not of angular coordinates. This is not rigorously true, but the time-scale of homogeneization by rotation is thought of to be shorter than that of chemical evolution. Additional assumption is that radial mixing cannot significantly alter the chemical abundances and, therefore, there is no exchange of matter between regions at different distances from the galactic centre, while flows of mass both from outside and to inside the system are allowed. In our model the disk is gradually built up by infall of gas of primordial chemical composition. Following dynamical models of disk galaxies by
VARIABLE YIELDS A N D THE PROBLEM O F NITROGEN P R O D U C T I O N
129
Larson (1976), we assume a long time-scale for this process, possibly longer in the outer parts of the disk than in the inner ones. Accordingly, we describe the disk with the superposition of many cylindrical shells, each of them considered as an isolated system with its independent evolution. Gradients of chemical abundance are given by the contribution of each ring. The model was preliminarily calibrated on observations available for the solar vicinity in order to fix the value of several parameters. Quantities which cannot be easily inferred from observations are the SFR, IMF, and infall laws. For the SFR we assume the dependence on gas and total density of Talbot and Arnett (1973), while we fix its adjustable parameters by comparing the rate with the observational determination for the solar vicinity. The choice of IMF can be critical in determining the relative abundance of elements. In our models we considered two classes of IMF: with variable and constant slope (Miller and Scalo, 1979; Salpeter, 1955). Another parameter is the fraction of stars with a mass smaller than M,., not contributing to nucleosynthesis. Here we assume 0.55 and 0.10, respectively, in order to reproduce the present O/H ratio in solar vicinity. However, as a variable slope (that is, a relatively smaller fraction of massive stars) produces too high N/O ratio, in the following only the case of the Salpeter IMF is considered. Finally, we must specify the infall time-scale. In order to obtain a reasonable agreement with the features observed in the solar vicinity, Chiosi (1977, 1980) found that it must range from 2 to 3 Gys. Sufficiently steep metallicity gradient requires a time-scale increasing outwards, as suggested by Larson's (1976) dynamical collapse model. The age of the Galaxy is assumed to be 12 Gys. For the total mass distribution we use the recent determination of Caldwell and Ostriker (1982). 6. Results Although our approach is very preliminary, still some interesting results relative to the nitrogen are possible. Although the main properties of this model resemble those of Chiosi and Matteucci (1982), there are several novel features that deserve some attention. In particular, the gradient in oxygen abundance (d logO/dr = - 0.07) is obtained only if the infall time-scale increases outward from the galactic centre by a factor of 4 within 6 kpc around the Sun. The present abundances of O and N are compared in Figure 3 which shows the O/H vs N/O diagram, applying both constant yields obtained from Z = 0.004 and Z --- 0.02 models of Renzini and Voli (1981) and variable yields. If we follow Renzini and Voli, nitrogen nucleosynthesis is partly secondary over the whole range of mass, and partly primary in the range 3.25-8 M o for Z --- 0.004 and 4-8 MQ for Z = 0.02. Two possibilities are examined for metal-rich stellar model, that is either with moderate mass loss (r/-- 0.333) or stronger stellar wind (r/= 0.667), corresponding to caseA and case B. Tables 3A and 3D or 3F and 3G in Renzini and Voli (1981), are used, respectively. Table I summarizes some present relevant quantifies of the computed models at
130
c. FORIERI I
I
9
.
9
9
-
9
I
9
--1~)
~,. .................,,-.~,
9
o let
s " ,,s
~1
-1.5
I 8.5
I 9.0 12 + I ~
I 9.5
(O/H)
Fig. 3. Theoretical relation between the N/O ratio and total oxygen abundance for models and observational data for H n regions between 6 and 12 kpc from the galactic centre. Solid (case D) and dotted (case E) lines denote models with variable yields. Case A: dottes dashed line. Case B: dashed line. Case C: dotted dashed line. Open circles denote $38 and $48.
different distances from the galactic centre. Mass density and infall time-scale is the same at a given radius for all the models. GAS is the fraction of mass in gas. [O/H] and [N/O] have the usual meaning of 12 + log(O/H) and log(N/O), respectively. Partial contribution of secondary and primary nitrogen is given too. In the case of constant yields, secondary nitrogen is dominant. This fact occurs for different metal contents, depending on the stellar models used in yield computations. As long as Z is low, the secondary N production is less important than the primary. The opposite occurs for greater values of Z. The most interesting result of the assumption of variable yield is its effect on nitrogen production. The choice of a linear dependence, leads to a N/O ratio almost constant even for high metal contents. There is a very moderate increase in log (N/O) between 6 and 12kpc, confirming the observational constraint of a mean gradient of - 0.02 + 0.01 in the same range. In case A, an almost constant ratio log(N/O) = - 1.0 is obtained under the assumption of Salpeter's mass-function with x = 1.3, which agrees only marginally with observations. In case B the constant ratio log (N/O) is slightly lower, that is - 1.1. This value is in better agreement with the observational data, although always higher than the mean observational value. One could think that a different IMF should provide a better fit between models and observations. However, in such a case, the frequency of massive stars relatively to IMS should be increased as the former are the only producers of oxygen and the latter are the dominant producers of nitrogen. In fact, the IMF could have been different in the past. Terlevich and Melnik (1983) suggested a power law for the IMF with a slope
VARIABLE YIELDS AND THE PROBLEM OF NITROGEN PRODUCTION
TABLE
131
I
M o d e l s f o r t h e g a l a c t i c d i s k a t t h e p r e s e n t age Radius Mass
6
7
8
9
10
11
12
t83.00
144.00
110.00
84.0
62.50
34.00
12.90
1.9
2.4
3.0
3.8
4.5
5.0
0.263
1.5
C a s e A : c o n s t a n t y i e l d s ; Z = 0.02, r / = 0.333 GAS
0.022
0.034
0.053
0.078
0.112
0.167
[O/H]
9.137
9.064
8.985
8.913
8.846
8.784
8.697
[N/O]
- 1.051
- 1.080
- 1.108
- 1.133
- 1.157
- 1.186
- 1.225
[NflO]
- 1.357
- 1.413
- 1.473
- 1.529
- 1.588
- 1.665
- 1.785
IN/O]
- 1.348
- 1.352
- 1.354
- 1.357
- 1.359
- 1.362
- 1.365
0.264
C a s e B : c o n s t a n t y i e l d s ; Z = 0.02, , / = 0.667 GAS
0.022
0.034
0.053
0.079
0.112
0.168
[O/H]
9.135
9.062
8.985
8.912
8.846
8.784
8.697
[N/O]
- 1.133
- 1.166
- 1.200
- 1.229
- 1.260
- 1.295
- 1.343
[Ns/O ]
- 1.363
- 1.419
- 1.480
- 1.534
- 1.595
- 1.672
- 1.792
[N/O]
- 1.519
- 1.522
- 1.524
- 1.526
- 1.529
- 1.531
- 1.534
0.263
C a s e C : c o n s t a n t y i e l d s ; Z = 0.04 GAS
0.022
0.034
0.053
0.078
0.112
0.167
[O/H]
9.131
9.056
8.973
8.903
8.837
8.776
8.690
[N/O]
- 0.888
- 0.910
- 0.929
- 0.950
- 0.969
- 0.992
- 1.022
[Ns/O ]
- 1.303
- 1.358
- t.412
- 1.469
- 1.528
- 1.605
- 1.725
[Np/O]
- 1.098
- 1.102
- 1.104
- 1.106
- 1.110
- 1.114
- 1.118
C a s e D : v a r i a b l e y i e l d s ; Z = 0.004, Z = 0.02, ~/= 0.333 GAS
0.022
0.034
0.053
0.078
0.111
0.167
[O/H]
9.137
9.062
8.982
8.907
8.840
8.779
0.263 8.691
[N/O]
- 1.019
- 1.029
- 1.036
- 1.036
- 1.043
- 1.048
- 1.055
[NflO]
- 1.363
- 1.409
- 1.459
- 1.503
- 1.557
- 1.628
- 1.740
[Np/O]
- 1.280
- 1.263
- 1.241
- 1.217
- 1.201
- 1.181
- 1.156
C a s e E : v a r i a b l e y i e l d s ; Z = 0.004, Z = 0.02, r / = 0.333 GAS
0.022
0.034
0.053
0.078
0.112
0.167
[O/H]
9.134
9.061
8.982
8.907
8.840
8.779
0.263 8.691
[N/O]
- 1.071
- 1.077
- 1.079
- 1.071
- 1.073
- 1.071
- 1.069
[NJO]
- 1.365
- 1.411
- 1.462
- 1.506
- 1.559
- 1.629
- 1.741
[Np/O]
- 1.379
- 1.347
- 1.311
- 1.271
- 1.245
- 1.212
- 1.173
dependent on the metallicity. Here we have adopted the relation below for the exponent of the IMF x = logZ
+ 3.05.
This is slightly different from the original formulation of Terlevich and Melnick (1983) as we required the IMF with variable x to match also the slope determined by Garmany et al. (1982) for young stars in the solar vicinity. Both the case of constant yields (Z--0.02, ~ = 0.333) and metal-dependent stellar nucleosynthesis, the relation [O/H]-[N/O] does not differ very much from the case of constant IMF.
132
c. FORIERI
However, there are several new results in the proposed stellar evolution that might improve upon the agreement with observations. Among other, the new rate for the reaction 12C(~, 7)160 given by Kettner et al. (1982) which implies a decrease in the N/O ratio. The lack of a complete grid of stellar models with the above new rate makes it impossible to properly evaluate its effect on the yields. Furthermore, the stellar model of Bertelli etal. (1984) with overshooting offers another possibility. They find that due to the larger CO cores in presence of overshooting the maximum mass for C, explosion is down to 6 M o. Although we cannot quantify the variation in the yields brought about by Bertelli et al. (1984) models, we expect a lower production of N. 7. Conclusions The aim of this paper has been to verify whether the variability of the nitrogen yield, caused by the dependence of stellar evolution on the initial metal content, might affect its abundance in the Galaxy. An interesting preliminary result has been obtained: namely, that a metal-dependent efficiency in the nitrogen production, as predicted by the current models of stellar evolution, would imply a N yield decreasing with increasing total metal content. This fact should balance the growth of secondary nitrogen synthesis; therefore, the relation between oxygen and nitrogen abundances should be in relatively good agreement with the empirical data for galactic H II region. The same agreement with the data of the Galaxy cannot easily be obtained for other galaxies. A suitable variation in the IMF could explain the abundances observed in irregular and blue compact systems. Acknowledgement The author is deeply indebted to Prof. C. Chiosi for his useful suggestions and comments during all the stages of this work. References Abbott, D. C.: 1982, Astrophys. J. 259, 282. Alcock, C. and Paczynski, B.: 1978, Astrophys. J. 223, 244. Alloin, D., Collin-Souffrin, S., Joly, M., and Vigroux, L.: 1979, Astron. Astrophys. 78, 200. Arnett, W. D.: 1978, Astrophys. J. 219, 1008. Barbuy, B.: 1983, Astron. Astrophys. 123, 1. Bertelli, G., Bressan, A. G., and Chiosi, C.: 1984, Astron. Astrophys. (in press). Bessel, M. and Norris, J.: 1982, Astrophys. J. 263, L29. Binette, L., Dopita, M. A., D'Odorico, S., and Benvenuti, P.: 1982, Astron. Astrophys. 115, 315. Bond, H.: 1981, Astrophys. J. 248, 606. Caldwell, J. A. R. and Ostriker, J. P.: 1982, Astrophys. J. 251, 61. Castor, J. I., Abbott, O. C., and Klein, R. I.: 1975, Astrophys. J. 195, 157. Chiosi, C.: 1977, fAU Colloq. 45, 61. Chiosi, C.: 1980, Astron. Astrophys. 83, 206. Chiosi, C.: 1981, Astron. Astrophys. 93, 163.
VARIABLEYIELDS AND THE PROBLEMOF NITROGENPRODUCTION
133
Chiosi, C. and Matteucci, F.: 1982, preprint. Clegg, R. E. S.: 1977, Monthly Notices Roy. Astron. Soc. 181, 1. Edmunds, M. G. and Pagel, B. E. J.: 1978, Monthly Notices Roy. Astron. Soc. 185, 779. Edmunds, M. G. and Pagel, B. E. J.: 1984, in C. Chiosi and A, Renzini (eds.), Stellar Nucleosynthesis, D. Reidel Publ. Co., Dordrecht, Holland, p. 341. Forieri, C.: 1982, Thesis Magister Philosophiae. Garmany, C., Conti, P. S., and Chiosi, C.: 1982, Astrophys. J. 263, 777. Harmen, D. and Pagel, B. E. J.: 1970, Nature 225, 349. Hawley, S. A.: 1978, Astrophys. J. 22,4, 417. Iben, I. and Renzini, A.: 1983, Ann. Rev. Astron. Astrophys. 21,271. Iben, I. and Renzini, A.: 1984, Physics Rep. 105, 329. Kettner, K. U., Becker, H. W., Buchmann, L., Clayton, D. D., Macklin, R. L., and Ward, R. A.: 1982, Astrophys. J. 257, 821. Larson, R. B.: 1972, Nature Phys. Sci. 236, 7. Larson, R. B.: 1976, Monthly Notices Roy, Astron. Soc. 176, 31. Lynden-Bell, D.: 1975, Vistas Astron. 19, 229. Maeder, A.: 1981, Astron. Astrophys. 101,385. Miller, G. E. and Scalo, J. M.: 1979, Astrophys. J. Suppl. 41, 513. Pagel, B. E. J. and Edmunds, M. G.: 1981, Ann. Rev. Astron. Astrophys. 19, 77. Peimbert, M. and Serrano, A.: 1979, Rev. Mex. Astron. Astrof. 5, 9. Peimbert, M., Torres-Peimbert, S., and Rayo, J. F.: 1978, Astrophys. J. 220, 516. Rayo, J. F., Peimbert, M., and Torres-Peimbert, S.: 1982, Astrophys. J. 255, 382. Renzini, A.: 1984, in C. Chiosi and A. Renzini (eds.), StellarNucleosynthesis, D. Reidel Publ. Co., Dordrecht, Holland, p. 99. Renzini, A. and Voli, M.: 1981, Astron. Astrophys. 94, 175. Salpeter, E. E.: 1955, Astrophys. J. 121, 161. Serrano, A.: 1983, Rev. Mex. Astron. Astrof. 8, 131. Serrano, A. and Peimbert, M.: 1983, Rev. Mex. Astron. Astrof. 8, 117. Shaver, P. A., McGee, R. X., Newton, L. M., Danks, A. C., and Pottash, S. R.: 1982, ESO Sci. Prep., No. 210. Sneeden, C.: 1974, Astrophys. J. 189, 493. Talbot, R. J. and Arnett, W. D.: 1971, Astrophys. J. 170, 409. Talbot, R. J. and Arnett, W. D.: 1973, Astrophys. J. 186, 69. Talent, D. L. and Dufour, R. J.: 1979, Astrophys. J. 190, 605. Terlevich, R. and Melnik, J.: 1983, ESO Sci. Prep., No. 264. Tinsley, B. M.: 1980, Fundamentals Cosmic Phys. 5, 287. Torres-Peimbert, S. and Peimbert, M.: 1977, Rev. Mex. Astron. Astrof. 2, 181. Vanbeveren, D. and Conti, P. S.: 1980, Astron. Astrophys. 88, 230. Weaver, T. A. and Woosley, S. E.: 1980, Proc. N.Y. Acad. Sci. 336, 335. Weaver, T. A., Zimmerman, G. B., and Woosley, S. E.: 1978, Astrophys. J. 225, 1021. White, J. D. and Audouze, J.: 1983, Monthly Notices Roy. Astron. Soc. 203, 603. William, R. E.: 1982, Astrophys. J. 261, L77. Willis, A. J. and Wilson, R.: 1978, Monthly Notices Roy. Astron. Soc. 182, 559. Woosley, S. E. and Weaver, T. A.: 1982, in C. Barnes, D. Clayton, and D. Schramm (eds.), Nuclear Astrophysics, Cambridge University Press, Cambridge - London - New York - New Rochelle - Melbourne - Sydney, p. 377.