8 Primary nitrogen production

8.1 Brief recalls on the nitrogen synthesis

Nitrogen is mainly produced in the CN branch of the CNO cycles within H-burning stellar zones (see Clayton 1983; Arnett 1996). More precisely, three reactions occur to transform ¹²C to ¹⁴N: ¹²C $(p,\gamma)^{13}$N $(\beta^+,\nu)^{13}$C $(p,\gamma)^{14}$N. Nitrogen can also be produced in the ON cycle by transformation of ¹⁶O, but at a much slower rate. The reaction ¹⁴N $(p,\gamma)^{15}$O which depletes nitrogen has a relatively low cross section enabling ¹⁴N to accumulate with time. Thus, ¹⁴N is usually the daughter element, hence a secondary element, of the CNO initially present in stars.

Nitrogen is said to be primary (Talbot & Arnett 1974), if it is formed in a star not from the initial CNO elements, but from the hydrogen and helium. Of course, the reactions forming primary nitrogen are those mentioned above, but the sequence of events is different: the formation of primary nitrogen implies firstly the synthesis of some ¹²C by the 3$\alpha$-reaction in a helium burning region, then this new ¹²C needs to be transported in an hydrogen burning region, where the CNO cycle will convert it to nitrogen. Thus, primary nitrogen is likely to be formed in stars with a He-burning core and a CNO burning shell, provided there is some transport mechanism between the two. The absence of such transport is the main reason why current models do not produce in general any primary nitrogen.

If ¹⁴N is of primary origin, the ¹⁴N-abundance is proportional to that of the other primary heavy elements. While if nitrogen is secondary, the increase in the abundance of ¹⁴N is proportional to the initial CNO content and thus in the chemical history of a galaxy the ¹⁴N-content will be proportional to the square of the CNO and metal content. These different behaviors provide the basic test for ascertain the primary or secondary origin of nitrogen.

The observations point toward the need of primary nitrogen sources at low metallicities (see below). The main problem is that the stellar models, unless ad hoc hypothesis are made, do not currently predict any primary nitrogen. This suggests that some physical process may be missing in the stellar models.

There are two other related problems. At solar metallicities, the observations do not suggest the production of primary nitrogen. Thus, a global question is how is changing the respective efficiencies of the primary and secondary ¹⁴N productions during the evolution of galaxies. The other question concerns the relative importance of massive and intermediate mass stars in the production of primary and secondary nitrogen. This point is important in relation for the interpretation in terms of the star formation history the N/O ratios observed at high redshifts (Pettini et al. 1995; Lu et al. 1998). Nitrogen, primary and secondary, is produced in the longest and main evolutionary phases. As long as its production is not well understood, we may doubt of the correctness of the models for these main phases of stellar evolution.

8.2 The observations of the N/O ratio

There are several kinds of evidences in favour of primary nitrogen in the early phases of the evolution of galaxies.

1) An indication of primary nitrogen is provided by the study of the N/O ratio in low metallicity stars of the galactic halo. The "discovery'' of primary nitrogen was made by Edmunds & Pagel (1978) in a study of the N/O ratio in such stars and in some external galaxies. Following this work, others authors (Barbuy 1983; Tomkin & Lambert 1984; Matteucci 1986; Carbon et al. 1987; Henry et al. 2000) have shown that the ratio N/O of nitrogen to oxygen remains constant with a plateau at $\log~\rm N/O \simeq -1.7$ in the early evolution of the Galaxy, thus implying a primary origin of nitrogen. The limit in metallicity above which secondary production of nitrogen becomes important is difficult to fix with precision, since the transition is progressive. It is around $12+ \log$ O/H = 7.8 to 8.2 according to Henry et al. (2000; cf. also Izotov & Thuan 1999). Since for the Sun one has $12+ \log~\rm O/H =8.9$, this means at a metallicity Z equal to $Z_{\odot}/12$ to $Z_{\odot}/5$. Above this limit, the N/C and N/O ratios grow rapidly, implying that nitrogen is essentially a secondary element. It is not known whether the primary production stops completely for Z values higher than the above limit. A good way to check it would be to measure the sum of CNO elements in planetary nebulae of the SMC, LMC and Galaxy, to see whether this sum is higher than the initial local CNO content of these galaxies. 2) A very compelling evidence for primary ¹⁴N is provided by the study of the N/O ratios in ionized HII regions of blue compact dwarf galaxies (Thuan & Izotov 1995; Kobulnicky & Skillman 1996; Izotov & Thuan 1999; Izotov & Thuan 2000). These HII regions also show a plateau of N/O at $\log~\rm N/O \simeq -1.7$below $12+ \log {\rm O/H} \simeq 8.0$, while above this limit the N/O ratio is a steeply growing function of O/H, as due to the secondary production of nitrogen. An example of a low metallicity galaxy is IZw 18, which has the lowest known metallicity (1/50 of solar), and which shows indications of primary nitrogen (Kunth et al. 1995; Izotov & Thuan 1999). The study of the N/O ratio in spiral galaxies by van Zee et al. (1998) well confirms the same result, with the difference that the authors find a plateau below $12+ \log~\rm O/H = 8.45$, i.e. for abundance of heavy elements less than 1/3 solar.

A problem was that some low Z damped Ly$\alpha$ systems have N/O ratios lower than those observed in the HII regions of blue compact dwarf galaxies of the same Z (Pettini et al. 1995). However, the apparent discrepancy has been resolved by models of damped Ly$\alpha$ systems which account for both ionized and neutral regions (Izotov et al. 2001).

3) Another argument for primary nitrogen production comes from the observed gradient of N/O in spiral galaxies. If nitrogen is purely a secondary element, the N/O gradient should be identical to that of O/H. In general, the N/O gradients tend to be shallower than the O/H gradients (Vilchez & Esteban 1996). The various data on the galactic gradients of N/O (Rudolph et al. 1997; Garnett et al. 1997; Ferguson et al. 1998; Henry & Worthey 1999) generally show that the N/O gradient is relatively flat at low metallicity Z, which supports the conclusion that the production of nitrogen is dominated by primary processes at low Z, while at solar or higher Zthe similarity of the N/O and O/H gradients support the view that nitrogen is secondary.

The situation is rather confused concerning the masses of the stars responsible for the injection of primary nitrogen. There are authors supporting the origin of primary nitrogen in massive stars (Matteucci 1986; Thuan & Izotov 1995; Izotov & Thuan 1999; Izotov & Thuan 2000). Their main argument is the low scatter of the observed N/O ratios at low Z. Indeed, if nitrogen is synthesized in massive stars, there is no time delay between the injection of nitrogen and oxygen and thus a rather small scatter would result. On the contrary, if the primary nitrogen is made in intermediate mass stars, the N/O ratio increases with time, since these stars release their nitrogen much later than massive stars do eject their oxygen. This would lead to a larger scatter in the observations, because galaxies are observed at various stages of their evolution. Izotov & Thuan (1999) suggest also that because of the intermediate mass star delay, the faster evolving massive stars must be a significant source of primary nitrogen in order to raise the $\log$(N/O) ratio to the observed plateau at $12+\lg({\rm O/H}) \sim 7.2$, a metallicity they assume to correspond to a galactic age too short to allow nitrogen ejection by the intermediate masses.

The situation may be not so clear, because some studies found that a significant scatter does exist (Garnett 1990; Skillman et al. 1997). Also, Henry et al. (2000) have calculated chemical evolution models which support the view that intermediate mass stars between 4 and 8 $M_\odot$, with an age of about 250 Myr, are likely to dominate the nitrogen production.

What can we deduce if we accept the fact that the N/O values show a great scatter at fixed value of O/H? A possibility might be that the observed scatter occurs because we are observing a large sample of HII regions in various stages of oxygen and nitrogen enrichments. This picture implies that most observed data should have relatively high N/O values with fewer points, representing those objects experiencing sudden oxygen enrichment, located below the bulk of data, since presumably bursts are followed by relatively long periods of quiescence, with relatively higher N/O ratios.

The reality looks different. The distribution of points in N/O vs. O/H plane reveals that most points seem to be clustered at relatively low values. This suggests that the "equilibrium'' or unperturbed locus where most HII regions reside is the low N/O envelope. Thus, this suggests that the excursions caused by sudden injections of material are actually upward, toward the region of fewer points. This picture seems consistent with the lack of evidence for localized oxygen contamination from massive stars in H II regions (Kobulnicky & Skillman 1997). The falloff in points above the N/O envelope is more consistent with injections of nitrogen rather than oxygen. In this case, the nitrogen source might be WR stars or luminous blue variable stars, both of which were considered by Kobulnicky et al. (1997) in their study of nitrogen-enriched H II regions in NGC 5253. They expect also a simultaneous enrichment in helium, and thus H II regions exhibiting high values of N/O should also be checked for evidence of helium enrichment.

Figure 13: Variations as a function of the langrangian mass coordinate Mr of the abundances of various elements inside a non-rotating 3 $M_\odot$ model at the metallicity Z = 10-5. Panel a) shows the chemical structure at the end of the core H-burning phase. Panels b) and c) at the middle and at the end of the core He-burning phase. The structure after one pulse along the Thermal Pulse-AGB phase is shown on panel d).

Figure 14: Same as Fig. 13 for a rotating 3 $M_\odot$ model at the metallicity Z = 10-5. The initial velocity on the ZAMS is 300 km s-1, which corresponds to an average surface equatorial velocity during the Main Sequence equal to $\sim$230 km s-1. Panel a) shows the chemical structure at the end of the core H-burning phase. Panels b) and c) at the middle and at the end of the core He-burning phase. The structure after the first five pulses along the Thermal Pulse-AGB phase is shown on panel d).

8.3 The existing stellar models

For massive stars, there is at present no model producing primary nitrogen unless some ad hoc assumptions are made in order to reproduce the observed N/O ratio at low metallicity (Timmes et al. 1995). In these ad hoc models, some mixing is permitted between the helium- and hydrogen-burning zones. Some primary nitrogen may also be produced in low-metallicity massive stars via some adjusted convective overshoot (Woosley & Weaver 1995). Without any physical explanation, it is difficult to understand why the production of primary nitrogen only occurs at low metallicities. Models of metal free Population III stars (Umeda et al. 2000) produce some primary nitrogen, but in too low quantities to reproduce the observed plateau (see also Heger et al. 2000b).

There is an extensive literature on AGB star models (see for example Forestini & Charbonnel 1997; Boothroyd & Sackmann 1999; Marigo 1998, 2001). Up to the phase of thermal pulses on the AGB branch, the intermediate mass star models predict no primary nitrogen production. Only when the star enters the phase of thermal pulses, some He-burning products may be transported into the H-burning shell, thus producing some primary nitrogen. These models are complex and require a lot of computing time. This is why the AGB models (Renzini & Voli 1981; Marigo 1998) are "synthetic'' models, which means that the model parameters follow some analytical relations that have generally been fitted to the observations (this is the case for example for the minimum stellar mass experiencing the third dredge-up). In addition the dependence of this minimum mass on metallicity is based on observation. The same kind of adjustments are made for the occurrence of the hot bottom burning. While this may be useful for some purposes, it cannot be claimed that it represents consistent physics leading to primary nitrogen production. The published stellar yields for intermediate mass stars are generally based on such synthetic models. According to the models of Marigo (2001), the primary nitrogen production depends heavily on the parameters describing the hot bottom burning and the third dredge-up, both processes which are not adequately described in complete stellar models. This means that for intermediate mass stars the primary nitrogen production is not a fully consistent output.

For completness, we also mention here that some explanations of the N/O ratios advocates galactic processes, such as differential outflows of the chemical elements produced by galactic winds (Edmunds 1990). Oxygen is predominantly made in high-mass stars that undergo more violent explosions than intermediate mass stars, thus is more likely to be removed from the galaxy. This differential outflow results in a decrease in the effective yield for oxygen with a corresponding increase in the N/O ratio. By observing massive spiral galaxies, van Zee et al. (1998) tried to minimize the complicating effects of gas outflow/inflow. They performed nitrogen and oxygen abundance measurements for 185 H II regions spanning a range of radii in 13 spiral galaxies and obtained for the N/O ratios the same behavior as in low-metallicity dwarf galaxies. This result suggests that the observed trend in dwarf galaxies is not due to the outflow of enriched material in a shallow gravitational potential. They conclude that low-metallicity H II regions in all types of galaxies do show evidence of primary nitrogen production.

8.4 The physics of the production of primary nitrogen in low Z rotating models

We need to look with some details the physics which determines the synthesis of primary nitrogen and more generally the particular yields at low Z. Some effects have already been examined by Meynet & Maeder (2002). We organize the discussion in a systematic way:

1)

effects of rotation in a 3 $M_\odot$ model at Z = 10^-5;

2)

same problem at Z = 0.004 and 0.02;

3)

effects of rotation in a 20 $M_\odot$ at Z= 10^-5, 0.004 and 0.020.

1) Figures 13 and 14 compare the variations of the abundances inside a non-rotating and a rotating 3 $M_\odot$ model with Z =10^-5 at various evolutionary stages. At the end of the H-burning phase (panels a), we notice the milder $\mu$-gradient at the very edge of the core, this contributes to make slightly larger He-cores in rotating models. This characteristic is generally larger in larger masses, it also persists and increases in further stages. We notice a significant diffusion of He and N throughout the star in the rotating models. At the middle and at the end of the He-burning phase (panels b and c), the differences in the chemical profiles are striking. In the non-rotating case, there is no new ¹²C outside the convective core, and therefore there is no primary ¹⁴N produced. While in the rotating model, ¹²C (together with some ¹⁶O) is diffusing out the He-burning core and when it reaches the H-burning shell, it is turned by the CNO-cycle into primary ¹⁴N, producing a big bump of ¹⁴N and a smaller one in ¹³C. As the H-shell migrates toward the exterior, the bumps of primary ¹⁴N and ¹³C also progressively extends toward the exterior. The height of these two bumps is growing during the He-burning phase, since diffusion is bringing more and more ¹²C which is turned to ¹⁴N, this explains the growth of the peak in ¹⁴N at the outer edge of the intershell region. The abundance of ¹⁴N in the rest of the intershell region is also growing with time and this is likely due to the inward diffusion of nitrogen from the peak. Typically, at the end of the He-burning phase, the ¹⁴N-abundance in the intershell zone has increased by 3 orders of a magnitude with respect to ¹⁴N in the corresponding non-rotating model. At this stage, the integrated quantity of new nitrogen synthesized is $3.22 \times 10^{-3}~M_\odot$, while it is only $3.22 \times 10^{-5}~M_\odot$ in the non-rotating model.

In further stages, the He-burning shell progresses outwards, letting a degenerate CO core behind it and transforming the ¹⁴N into ²²Ne (panels d in Figs. 13 and 14). Also in the TP-AGB phase, the content in nitrogen of the outer convective zone increases a lot, due to both the facts that the outer convection zone deepens in mass and that the diffusion at the base of the convective zone continues to proceed. This is saving from destruction a large fraction of the primary nitrogen produced earlier. At the stage shown in Fig. 14 nearly the whole quantity of ¹⁴N is in the outer convective envelope. The integrated quantity of primary ¹⁴N at this stage is $1.58\times 10^{-3}$ $M_\odot$, i.e. about 50% of what was present in panel c) at the end of the He-burning phase. This fraction of 50% does not change very much during the end of the TP-AGB phase, because the edge of the CO-core and the outer envelope stay very close in lagrangian coordinates. This nitrogen will be ejected by the AGB star either by the superwinds or in the planetary nebula.

In the corresponding non-rotating model (see Fig. 13, panel d), we notice a very similar final structure with a large CO core surrounded by a convective envelope and two thin shells at the basis of it. As only differences, we notice the much smaller ¹⁴N and ¹⁶O abundances in the envelope. Also, because central degeneracy is higher and thus there is more cooling by neutrinos, the nuclear reaction ¹²C( $\alpha,\gamma)^{16}$O proceeds farther in the outer core regions than in the inner regions, leading to a kick in ¹²C and a bump in ¹⁶O as observed in panel d of Fig. 13.

The production of ¹³C in the outer half of the zone between the He-core and the H-burning shell during the He-burning phase is relevant for the nucleosynthesis of "s-process'' elements, since ¹³C is an efficient neutron source. The "s-elements'' are produced when ¹³C is reached by the outer progression of the He-burning shell. Clearly, the formation of "s-elements'' is strongly favoured in rotating stars (see also Langer et al. 1999). Amazingly, in the convective envelope, the mass fraction of the CNO elements is about 100 times the initial mass fraction of the heavy elements!

Figure 15: Variation of the abundances of some elements in the intershell region of 3 $M_\odot$ models at the end of the He-burning phase for the metallicities Z = 0.004 and 0.020. The initial velocities $v_{\rm ini}$ are indicated.

Figure 16: Variation of the abundances of some elements inside 20 $M_\odot$models at various stages during the core and shell He-burning phases. The initial metallicity is Z=10-5. The upper panels refer to non-rotating models. Panel a) corresponds to the beginning of the core He-burning phase, panel b) shows the situation at the middle of the He-burning phase ( $Y_{\rm c} \sim$0.50) and panel c) at the end of the C-burning phase. Panels d) to f) show the same stages for the corresponding rotating models with $v_{\rm ini} = 400$ km s-1.

2) It is interesting to compare the above results with those of models of a 3 $M_\odot$ at higher metallicities. Figure 15 shows models with and without rotation for Z = 0.004 and 0.020 at the end of the helium burning phase, i.e. corresponding to panel c in Figs. 13 and  14. As usual, the models with zero rotation show flat curves separated by steep transitions due to intermediate convective zones. The models with rotation at Z = 0.004 and 0.020 show both the typical internal diffusion profile for ¹²C and ¹⁶O outside the core and noticeably the distributions of ¹⁴N are rather similar to that observed for the models at Z = 10^-5. There is still some quantity of primary nitrogen in the intershell model of the Z = 0.004 model, but it is relatively negligible in the Z = 0.02 model. The maximum values of ¹⁴N in the interior are similar in the three 3 $M_\odot$ models considered, independently of Z.

What are the reasons of this relative constancy? For the models illustrated, the central T are about the same, as normal for He, C, O cores of about the same mass at the middle of the He-burning phase in rotating models. However, the temperatures at the basis of the H-burning shells are different: $\log T = 7.573$ at Z = 10^-5 and 7.446 at Z = 0.02. This is consistent with the fact that the Z = 10^-5 model is much brighter ( $\log ~L/L_{\odot} = 2.787$ compared to 2.013 at Z = 0.02), because of its much lower opacity. The nuclear energy production (mainly of the H-shell) necessary to supply the stellar luminosity is adjusted, as usual, by the temperature of the shell and not by the content in ¹⁴N. The similarity of the distributions of ¹⁴N at low metallicity essentially results from the rotational transport of material from the core. We have seen in Sect. 3 that the $\Omega$-distribution during the MS evolutionary phase is different for different Z. However, in later phases the $\mu$-contrast between the dense core and the surrounding layers is about the same and this contrast determines the $\Omega$-gradient and in turn the importance of the diffusion. Thus, the diffusion of ¹²C outside the core is not very different in models of same mass and rotation, and as a consequence the same is true for ¹⁴N.

At Z = 10^-5 the gradient of ¹⁴N between the H-shell and the envelope is much larger than at Z = 0.02, because the difference between the peak of ¹⁴N in the intershell region and the cosmic abundance in the envelope is also much larger. This has two consequences: firstly, the inward progression of the outer convective zone will bring relatively much more ¹⁴N in the envelope; secondly there is also more diffusion of ¹⁴N in the envelope at very low Z.

Finally, we also emphasize (cf. Meynet & Maeder 2002) that in the TP-AGB phase the distance between the He- and the H-burning shells is much smaller in lower Z models. This effect will certainly influence considerably the occurrence and properties of the relaxation oscillations. Also, this effect makes the transport of ¹²C from the He-burning shell to the H-burning shell much shorter, since the timescale for diffusion varies with the square of the distance. In this respect, the smaller intershell region in lower Z models also favours the increase of the abundance of primary nitrogen in the envelope.

In summary, the higher production of primary ¹⁴N in very low Z models results mainly from the relatively stronger peak of primary ¹⁴N built by rotational mixing in the intershell region during the He-burning phase, a part of which is entering the envelope during its inward migration and another part is brought to the envelope by the diffusion, which is favoured by the smaller intershell region during the TP-AGB phase.

3) Let us examine the 20 $M_\odot$ models at Z = 10^-5, 0.004 and 0.020. In Fig. 16 for Z = 10^-5, we see for the rotating model at the middle of the He-burning phase (panel e) the same kind of diffusion profile of ¹²C and ¹⁶O outside the core, as in the corresponding 3 $M_\odot$ model. A similar, although slightly smaller peak of primary ¹⁴N is built between the core and the H-shell. Contrarily to smaller masses, where there is no central C-burning, the intershell region remains large. The mainly primary ¹⁴N in this region will of course contribute to the yield, as well as that in the outer envelope. The abundance of ¹⁴N is increasing in the envelope during He-burning and later phases. Since here, contrarily to the low mass models, there is no inward migration of the envelope, the increase of ¹⁴N in the envelope is only due to the diffusion from the ¹⁴N gradient in the H-burning shell. As in smaller masses, most of the ¹⁴N in the envelope is primary.

When we do a similar study in the 20 $M_\odot$ models at Z = 0.004, we notice that there is only a negligible amount of primary ¹⁴N produced and the abundance of ¹⁴N in the envelope of the final models is within a few percents the same in the rotating and non-rotating cases.

In conclusion, we see that there is still some primary nitrogen produced at Z = 0.004 in intermediate mass models, as shown by the 3 $M_\odot$ case, but nothing in the high mass stars.