9 The stellar yields

9.1 M$_\alpha$, M $_\mathsf{CO}$ and the mass of the remnants, M $_\mathsf{rem}$

   

Table 3: Masses of the helium cores, of the carbon-oxygen cores and of the remnants for different initial mass star models with and without rotation at Z = 10^-5and 0.004. The masses are in solar mass and the velocities in km s^-1.

		Z = 10-5			Z = 0.004
M	$v_{\rm ini}$	$M_\alpha$	$M_{\rm CO}$	$M_{\rm rem}$	$M_\alpha$	$M_{\rm CO}$	$M_{\rm rem}$
60	0	23.18	18.44	5.68	25.09	20.32	6.26
	300	31.52	26.26	8.03
40	0	14.05	10.50	3.50	14.61	10.86	3.59
	300	15.38	11.54	3.75	17.87	14.52	4.49
25	0				8.44	5.35	2.25
	300				9.95	7.07	2.69
20	0	5.50	3.35	1.75	6.21	3.57	1.80
	200	7.00	4.66	2.08	7.28	4.64	2.07
	300	6.58	3.92	1.89	7.46	4.80	2.11
	400	5.66	3.45	1.77	7.60	4.94	2.15
15	0	4.15	2.25	1.46	4.45	2.27	1.46
	300	4.99	2.87	1.62	5.01	2.84	1.62
12	0				3.48	1.78	1.34
	300				3.74	1.78	1.34
9	0	2.29	1.12	1.08	2.36	0.87	0.87
	200	2.70	1.40	1.24
	300	2.53	1.28	1.17	2.85	1.23	1.14
	400	2.51	1.31	1.19
7	0	1.74	0.90	0.90
	300	1.07	1.02	1.02
5	0	1.23	0.75	0.75
	300	0.88	0.86	0.86
3	0	0.74	0.73	0.73	0.66	0.46	0.46
	300	0.77	0.76	0.76	0.72	0.66	0.66
2	0	0.62	0.53	0.53
	300	0.64	0.56	0.56

   

Table 4: Stellar yields for helium, carbon, nitrogen, oxygen and the heavy elements from different initial mass stars at Z=10^-5 with and without rotation. The initial stellar masses are in solar units. The stellar yields are in solar mass and the velocities in km s^-1. The contributions of the stellar winds have been accounted for and are indicated in parenthesis when they exceed one percent of the total yield.

		Z=10-5
M	$v_{\rm ini}$	$mp_{\rm He4}$	$mp_{\rm C12}$	$mp_{\rm N14}$	$mp_{\rm O16}$	$mp_{\rm Z}$
60	0	1.1e+1	8.4e-1	1.6e-4	1.1e+1	1.3e+1
	300	1.0e+1	6.1e-1	7.0e-4	1.6e+1	1.9e+1
		(0.2e+1)		(0.4e-4)
40	0	6.9e+0	6.3e-1	1.0e-4	5.0e+0	7.3e+0
	300	8.0e+0	5.8e-1	7.6e-4	5.8e+0	8.2e+0
20	0	3.1e+0	2.2e-1	4.6e-5	5.6e-1	1.7e+0
	200	2.5e+0	2.8e-1	4.2e-5	1.2e+0	2.8e+0
	300	3.3e+0	2.9e-1	3.6e-4	9.9e-1	2.3e+0
	400	3.5e+0	2.9e-1	7.7e-3	6.2e-1	2.0e+0
15	0	2.0e+0	1.2e-1	3.5e-5	1.9e-1	8.6e-1
	300	1.9e+0	1.9e-1	4.1e-4	3.9e-1	1.4e+0
9	0	1.0e+0	1.1e-2	2.2e-5	4.0e-3	5.1e-2
	200	1.1e+0	3.2e-2	7.7e-4	4.0e-3	2.0e-1
	300	1.1e+0	3.6e-2	3.5e-3	4.0e-3	1.6e-1
	400	1.1e+0	4.8e-2	9.2e-3	4.0e-3	2.0e-1
7	0	6.9e-1	1.3e-2	1.6e-5	1.2e-3	1.4e-2
	300	8.0e-1	1.8e-2	4.2e-3	5.6e-3	2.8e-2
5	0	4.1e-1	6.9e-3	1.0e-5	5.6e-4	7.7e-3
	300	4.5e-1	4.5e-3	4.3e-3	1.8e-3	1.1e-2
3	0	9.0e-2	4.7e-4	3.3e-6	8.0e-6	7.0e-4
	300	1.4e-1	2.5e-3	1.6e-3	7.0e-4	5.1e-3
2	0	9.8e-2	1.5e-3	1.7e-6	1.9e-5	1.8e-3
	300	1.2e-1	7.7e-3	6.4e-4	1.1e-3	1.0e-2

   

Table 5: Same as Table 4 for the metallicity Z = 0.004.

		Z = 0.004
M	$v_{\rm ini}$	$mp_{\rm He4}$	$mp_{\rm C12}$	$mp_{\rm N14}$	$mp_{\rm O16}$	$mp_{\rm Z}$
60	0	9.3e+0	6.7e-1	6.8e-2	1.2e+1	1.4e+1
		(2.1e+0)		(1.5e-2)
40	0	6.3e+0	4.0e-1	4.3e-2	5.3e+0	7.3e+0
		(0.2e+0)		(0.2e-2)
	300	5.2e+0	4.9e-1	3.9e-2	7.3e+0	1.0e+1
		(4.1e+0)		(2.6e-2)
25	0	3.7e+0	1.1e-1	2.1e-2	1.9e+0	3.1e+0
	300	3.1e+0	2.4e-1	2.2e-2	2.6e+0	4.7e+0
		(0.1e+0)		(0.2e-2)
20	0	3.0e+0	8.6e-2	1.6e-2	8.5e-1	1.8e+0
	200	2.7e+0	1.5e-1	1.7e-2	1.3e+0	2.7e+0
	300	2.5e+0	2.1e-1	1.7e-2	1.4e+0	2.9e+0
				(0.1e-2)
	400	2.5e+0	2.8e-1	1.7e-2	1.4e+0	3.2e+0
				(0.1e-2)
15	0	2.0e+0	3.5e-2	1.0e-2	2.5e-1	8.0e-1
	300	2.0e+0	1.9e-1	1.4e-2	3.9e-1	1.4e+0
12	0	1.4e+0	8.3e-2	6.8e-3	2.7e-2	4.9e-1
	300	1.8e+0	9.3e-2	1.6e-2	7.0e-2	6.0e-1
9	0	1.2e+0	1.4e-2	5.4e-3	4.0e-3	1.6e-2
	300	1.3e+0	4.6e-2	1.6e-2	4.0e-3	1.8e-1
3	0	1.6e-1	8.8e-3	1.1e-3	6.5e-4	1.1e-2
	300	1.3e-1	7.6e-4	2.4e-3	-2.7e-4	3.6e-3

The computation of the stellar yields, i.e. the quantities of an element newly produced by a star, necessitates, as a first step, the estimate of the masses $M_\alpha$ of the helium cores, $M_{\rm CO}$ of the carbon-oxygen cores, and of the masses $M_{\rm rem}$ of the remnants. These quantities are used for two purposes: 1) To obtain the oxygen yields using the relation between $M_\alpha$ and the oxygen yields by Arnett (1991). Our models only give an upper limit of the oxygen yields, since they are stopped at the end of the carbon or helium burning phase, i.e. at phases where oxygen has not yet been depleted in the inner regions. 2) To obtain the mass of the remnants using a relation between  $M_{\rm CO}$ and  $M_{\rm rem}$. The knowledge of this quantity allows us to calculate the mass of the elements expelled by the supernova. In this work we use the same $M_{\rm rem}$ vs. $M_{\rm CO}$ relation as Maeder (1992). For the intermediate mass stars, we have taken as remnant masses, the mass $M_{\rm CO}$ of the CO core.

Both relations, $M_\alpha$ versus the oxygen yields and $M_{\rm CO}$ versus $M_{\rm rem}$are deduced from non-rotating models. Ideally one should have used relations obtained from rotating models and more precisely from rotating models treating the effects of rotation as we did. If such computations would have been available, would the stellar yields be the same? For what concern helium, nitrogen and carbon (although to less extent) the answer is yes. Indeed the parts of the stars which contribute the most to the yields in helium, nitrogen and carbon are in too far out portions of the star for being affected by the $M_{\rm CO}$ versus $M_{\rm rem}$ relation. For the oxygen and heavy element yields, the situation is more complicated. For the moment, we can say that, unless strong and very rapid mixing episodes take place after the end of the carbon burning phase, it is likely that the yields in oxygen and heavy elements obtained here are good estimates of the yields one would have obtained from rotating presupernovae models.

In Table 3, $M_\alpha$, $M_{\rm CO}$and $M_{\rm rem}$, are indicated for different initial mass stars with various metallicities and initial rotation velocities. For initial masses inferior or equal to 7 $M_\odot$, the core masses are estimated after the end of the He-burning phase, during the TP-AGB phase. For higher initial mass models, $M_\alpha$ and $M_{\rm CO}$are evaluated at the end of the C-burning phase at Z = 10^-5, except for the 9 $M_\odot$ models with $v_{\rm ini} = 0$, 200 and 400 km s^-1for which the core masses are estimated at the beginning of the C-burning phase. For the models at Z = 0.004 (Maeder & Meynet 2001), the core masses are estimated at the end of the He-burning phase. We define $M_\alpha$ as the mass interior to the shell where the mass fraction of helium becomes superior to 0.75. For the rotating 40 and 60 $M_\odot$ models at Z = 10^-5, the diffusion of helium outside the He-core is so great that the above definition yields an unrealistic high value for the helium core. For these models, we choose to fix the outer border of the He-core at the position where the hydrogen mass fraction goes to zero. Let us note that for the other initial masses this alternative definition of the He-core does not change the results presented in Table 3. The mass of the carbon-oxygen core $M_{\rm CO}$ is the mass interior to the shell where the sum of the mass fractions of ¹²C and ¹⁶O is superior to 0.75.

From Table 3, we note, that rotation in general increases the masses of the helium and CO cores for the massive stars. The reason is that for higher rotation, the intermediate convective zone, associated to the H-burning shell, disappears more quickly. Since the H-burning shell is not replenished in hydrogen, it can more quickly migrate outwards and thus produces the general increase of the He-core mass. However, for the models at Z = 10^-5 we notice a saturation effect in the increase of M$_\alpha$ for higher rotation and even a decrease for a very high rotation (see the 9 and 20 $M_\odot$ models in Table 3). This behaviour results from the following opposite effect: when rotation increases, the diffusion becomes so efficient that large amounts of hydrogen are brought from the radiative envelope into the H-burning shell. This slows down its outward progression and thus does not produce the growth of the He-core mass in the He-burning phase. As to $M_{\rm CO}$, we see that the variations of $M_{\rm CO}$ with $v_{\rm ini}$ follows those of $M_\alpha$.

In conclusion, we find that fast rotation in general increases  $M_{\rm CO}$ and thus will also increase the yields in $\alpha$-elements. This is true at very low Z, but not necessarily at solar metallicity, because there fast rotating massive stars will experience high mass loss.

For the intermediate mass stars, the situation is more complicated, since in addition to the effects just mentioned above, the mass of the helium core also results from the inward progression in mass of the outer convective zone during the AGB phase. The deeper this inward extension, the smaller is $M_\alpha$.

9.2 The stellar yields

Figure 17: Variation as a function of the initial mass of the stellar yields in 14N for different metallicities and rotational velocities. The continuous lines refer to the models at Z =10-5 of the present paper, the dotted lines show the yields from the models at Z = 0.004 from Maeder & Meynet (2001), the dashed lines present the yields for two solar metallicity models (present work). The filled squares and circles indicate the cases without and with rotation respectively. In this last case $v_{\rm ini}$ = 300 km s-1. The crosses are for the models of Woosley and Weaver (1995) at $Z=0.1~{Z}_\odot$, the empty squares for the yields from van den Hoek & Groenewegen (1997) at Z=0.004, the empty triangles are for solar metallicity models of van den Hoek & Groenewegen (1997) up to 8 $M_\odot$ and of Woosley and Weaver (1995) above.

In Tables 4 and 5, the stellar yields for helium, carbon, nitrogen, oxygen and for the heavy elements are given for different initial stellar masses with various initial metallicities and rotational velocities. Except for oxygen in massive stars, our models have reached a sufficiently advanced evolutionary stage for the above yields to be directly deduced from our models. The quantity of an element x, newly produced by a star of initial mass m, i.e. the stellar yields in x, is given by

$$mp_{x}=\int_{M_{\rm rem}}^{M_{\rm fin}} [X_{x}(m_r)-X^0_{ x}] {\rm d}m_r,$$

where $M_{\rm fin}$ is the mass of the star at the end of its evolution, X_x(m_r)is the mass fraction of element x at the langrangian mass coordinate m_r inside the star and X⁰_x is the initial abundance of element x. We consider that the SN ejecta in carbon consist of the C-distribution in the star as it is at the end of the C-burning phase, but we count only the layers which are external to the mass, where carbon is not depleted by the further nuclear burning stages (see Maeder 1992).

We also accounted for the effects of the stellar winds on the yields as is done in Maeder (1992). In Tables 4 and 5, we have indicated in parenthesis the contribution of the winds when it exceeds one percent of the total stellar yields. For the metallicities considered here, the effects of the winds are small and only modify the yields in helium and nitrogen.

Figure 18: Variation as a function of the mean velocity during the Main Sequence, $\overline v$, of the stellar yields in 14N for a 9 and a 20 $M_\odot$ model at Z = 10-5.

In Fig. 17, the stellar yields in ¹⁴N are plotted as a function of the initial mass for different metallicities and rotation velocities. Our non-rotating models (filled squares along the continuous lines) show very small yields at Z = 10^-5, as expected from a pure secondary origin of ¹⁴N. When the effects of rotation are included (filled circles along the continuous lines), the yields for the intermediate mass star models at Z =10^-5 become of the same order of magnitude as the yields for the corresponding models at Z = 0.004. In this mass range, the yields present thus a very weak metallicity dependence. At solar metallicity, the yields given by the rotating and non-rotating models are identical, this well illustrates the smaller effects of rotation on the nitrogen yields for the higher metallicities.

Figure 19: Variation of the stellar yields in oxygen and carbon as a function of the initial mass, at three different metallicities. The black triangles are for the present non-rotating models, the black circles are for the present rotating models. The empty squares and pentagons are for the stellar yields of Maeder (1992) at the metallicity Z = 0.001 and 0.020 respectively.

Figure 18 shows that the ¹⁴N stellar yields at Z=10^-5 strongly depend on the rotational velocity. Starting from the point at $\overline v$ = 230 km s^-1 for the 9 $M_\odot$, an increase of 20% of the mean velocity on the MS, already suffices to double the yield in nitrogen. One notes also the strong increase obtained for the 20 $M_\odot$ when $\overline v$ passes from 240 to 325 km s^-1. This means that if massive stars have sufficiently high initial velocities at low Z, they might also play a role in the production of primary nitrogen (see below).

Figure 19 shows the yields in carbon and oxygen for Z= 10^-5, 0.004 and 0.020 for models with and without rotation. We notice that the yields of carbon and oxygen (and other heavy elements) are much less affected by rotation than the yields in nitrogen. In general, the yields in carbon, oxygen (and heavy elements) are increased by rotation (cf. Heger 1998), this is a result of the generally bigger value of M $_{{\rm CO}}$ when rotation is included, as shown above. At solar metallicity, rotation decreases the yield in oxygen because of the higher mass loss, which also produces an increase in the amount of carbon ejected.

How the present stellar yields compare with the yields from other authors? The situation for nitrogen can be seen in Fig. 17, where yields of van den Hoek & Groenewegen (1997, see their Tables 9 and 17) and of Woosley & Weaver (1995, see their models S and P) are plotted. The yields at Z=0.004 of van den Hoek & Groenewegen (1997) for the masses between 5 and 8 $M_\odot$ are higher by about an order of magnitude than the yields of their lower initial mass models. They are nearly at the same level as the yields obtained from the solar metallicity models. This huge enhancement of their ¹⁴N stellar yields in this mass range is a consequence of accounting, in a parameterized way, for the effects of the third dredge-up and of the hot bottom burning, which enable the production of primary nitrogen. The values of the parameters (minimum core mass for the third dredge-up, third dredge-up efficiency, scaling law for mass loss on the AGB, core mass at which the hot bottom burning is assumed to operate) have been chosen in order to reproduce various observational constraints, as e.g. the luminosity function of carbon stars or the abundances observed in planetary nebulae (see van den Hoek & Groenewegen 1997). Interestingly, our rotating models are well in the range of these parameterized yields. Thus rotation, not only naturally leads to the production of primary nitrogen, but also predicts yields in primary nitrogen at a level compatible with those deduced from previous parameterized studies.

 

 

Table 6: Integrated yields in helium, carbon, nitrogen, oxygen and heavy elements (see text).

Z	12+log( ${{\rm O} \over {\rm H}}$)	$m_{\rm d}$	$m_{\rm u}$	$v_{\rm ini}$	$P_{\rm He}$	$P_{\rm C}$	$P_{\rm N}$	$P_{\rm O}$	$P_{\rm Z}$	Log ${P_{\rm C} \over P_{\rm O}}$	Log ${P_{\rm N} \over P_{\rm O}}$
10-5	5.74	20	120	0	4.9E-3	3.8E-4	7.4E-8	4.1E-3	5.1E-3	-1.034	-4.743
		8	120	0	7.8E-3	4.9E-4	1.3E-7	4.2E-3	5.8E-3	-0.936	-4.515
		2	120	0	1.1E-2	5.3E-4	2.1E-7	4.2E-3	5.9E-3	-0.900	-4.303
		2	60	0	9.2E-3	4.2E-4	1.8E-7	1.9E-3	3.7E-3	-0.659	-4.013
0.004a	8.35	20	120	0	4.3E-3	2.5E-4	2.9E-5	4.7E-3	5.6E-3	-1.269	-2.205
		8	120	0	7.3E-3	3.3E-4	4.4E-5	4.9E-3	6.4E-3	-1.175	-2.050
		2	120	0	1.1E-2	4.6E-4	6.5E-5	4.9E-3	6.6E-3	-1.024	-1.878
		2	60	0	9.5E-3	3.6E-4	5.5E-5	2.4E-3	4.0E-3	-0.824	-1.638
0.020b	8.93	2	120	0	8.9E-3	4.4E-4	3.6E-4	3.3E-3	5.9E-3	-0.881	-0.963
10-5	5.74	20	120	300	4.8E-3	3.3E-4	4.1E-7	6.4E-3	7.7E-3	-1.286	-4.200
		8	120	300	7.7E-3	5.3E-4	3.8E-6	6.8E-3	9.0E-3	-1.106	-3.245
		2	120	300	1.0E-2	6.2E-4	1.1E-4	7.4E-3	9.5E-3	-1.080	-1.833
		2	60	300	1.0E-2	5.4E-4	3.4E-5	2.7E-3	5.0E-3	-0.698	-1.898
0.004a	8.35	20	120	300	3.7E-3	3.8E-4	2.8E-5	7.0E-3	7.8E-3	-1.265	-2.396
		8	120	300	6.9E-3	5.7E-4	5.8E-5	7.4E-3	9.3E-3	-1.112	-2.109
		2	120	300	1.0E-2	6.2E-4	1.1E-4	7.4E-3	9.5E-3	-1.080	-1.833
		2	60	300	8.8E-3	4.6E-4	9.9E-5	3.4E-3	6.0E-3	-0.871	-1.536
0.020b	8.93	2	120	300	1.1E-2	1.2E-3	3.9E-4	2.7E-3	6.5E-3	-0.370	-0.844

^a Models of Maeder & Meynet (2001).
^b Models of Meynet & Maeder (2000).

One also notes that our yields at Z=0.004 (both from rotating and non-rotating models) are inbetween the yields at Z=0.004 and Z=0.020 of van den Hoek & Groenewegen (1997) and between those of Woosley and Weaver (1995) at $Z \sim 0.002$ and 0.020. This indicates that at higher metallicity, the present yields in nitrogen seem to be in agreement with the yields of other authors. Similar conclusion are reached when comparisons are made between our yields in carbon and oxygen with those of these authors. Our carbon and oxygen yields also compare well with those obatined by Maeder (1992) (see Fig. 19).

9.3 Net yields and comparison with the observations

Figure 20: Simplified model for the galactic evolution of the C/O ratio as a function of the O/H ratio (in number). The dashed and continuous lines show the results deduced from the non-rotating and the rotating models respectively (see text). The range of the initial masses used for computing the integrated yields are indicated. The empty symbols show the results when only stars more massive than 8 $M_\odot$ are considered. The initial velocity is indicated. The shaded area shows the region where most of the observations of extragalactic HII regions and stars are located (see e.g. Gustafsson et al 1999; Henry et al. 2000).

Figure 21: Same as Fig. 20 for the N/O ratio.

In order to evaluate the impact of these new yields (see Tables 4 and 5) on a galactic scale, we use them in a very simple model of galactic chemical evolution making use of the closed box, instantaneous recycling approximations and supposing a constant star formation rate. We are of course fully aware of the roughness of these approximations, but our intention here is just to estimate the relative effects of rotation on the chemical yields.

In the conditions of this simplified chemical evolution model, the ratio x_i/x_j of the mass fractions of the elements x_i and x_j in the interstellar medium are given by ${x_i \over x_j}= {\widetilde{y_{i}}\over \widetilde{y_{j}}}$, where $\widetilde{y_{i}}$ and $\widetilde{y_{j}}$ are representative time-independent approximations of the integrated yields of the elements i and j from a stellar generation. The integrated yield of an element x, P_x, is defined as the mass fraction of all stars formed, which is eventually expelled under the form of the newly synthesized element x:

$$P_{x}=\int_{m_{\rm d}}^{m_{\rm u}} mp_x(m) \Phi(m) {\rm d}m,$$

where $\Phi(m)$ is the Initial Mass Function (IMF). Here we choose a Salpeter IMF, normalized so that

$$\int_{0.1{M}_\odot}^{120{M}_\odot} \Phi(m) {\rm d}m = 1.$$

The masses $m_{\rm d}$ and $m_{\rm u}$ limit the mass range of the stars having contributed to the chemical evolution of the interstellar medium at the epoch considered.

In Table 6, the integrated yields are given for various metallicities, initial rotational velocities and values of $m_{\rm d}$ and $m_{\rm u}$. The integrated yields for the solar metallicity have been deduced from the models of Meynet & Maeder (2000). These models have been computed with a different shear diffusion coefficient, and for a different prescription of the mass loss rate than the present models. Therefore they do not belong to the homogeneous set of data constituted by the models at Z=10^-5and 0.004. Despite these differences in the physical ingredients, their properties are well in the lines of the results obtained at lower metallicity. This is the reason why, we have complemented the data of Table 6 with the integrated yields obtained from these models at solar metallicity.

In Figs. 20 and 21, the C/O and N/O ratios, obtained by simply taking the ratios of the corresponding integrated yields, are plotted as a function of O/H. To disentangle the still controversial role of the intermediate mass stars and the effects of rotation, we have taken several values of the upper and lower mass limits. We have considered at Z = 10^-5 the 20 to 120 $M_\odot$ interval, that of 8 to 120 $M_\odot$ and that of 2 to 60 $M_\odot$. In each case, the models without rotation and with an initial rotation of 300 km s^-1 (i.e. an average of 230 km s^-1 during the MS phase) have been considered. In addition, for the case of 8 to 120 $M_\odot$ an initial rotation of 400 km s^-1 has also been considered. At Z=10^-5, we notice that rotation only slightly decreases the C/O ratio, the effect is a bit larger when only massive stars are considered. This behaviour is due to the growth of $M_{\rm CO}$with rotation, which favours the production of O more than that of C. However, we emphasize that the effect of the mass interval is more important than rotation. When the intermediate mass stars are included, the C/O ratio is as expected much larger. In summary, at low Z, the diagram C/O vs. O/H is particularly sensitive to the mass interval.

Between Z=0.004 and 0.02, the main effect influencing the C/O ratio is no longer the value of $M_{\rm CO}$ as above, but the effects of stellar winds and their enhancement by rotation. Rotation favours a large C/O ratio, because rotating models enter at an earlier stage into the Wolf-Rayet phase than their non-rotating counterparts. As a consequence, in rotating models at Z=0.02, great quantities of carbon are ejected by the massive stars through their stellar winds, when they become a Wolf-Rayet star of the WC type. This is quite in agreement with the results by Maeder (1992) who showed that when the mass loss rates are high, most of the carbon is produced and ejected by massive stars through their stellar winds. In non-rotating models, the new mass loss rates used here are much lower than those used in 1992 because now the mass loss rates account for the clumping effects in the Wolf-Rayet stellar winds.

The diagram N/O vs. O/H (Fig. 21) has a different sensitivity to the mass interval and rotation. At very low Z, we notice a very high sensitivity to rotation when the lowest mass limit is at 2 or 8 $M_\odot$; this is due to the production of primary nitrogen. The increase in the N/O ratio may reach more than 2 orders of a magnitude. Contrarily to the previous diagram, the N/O ratio is not sensitive at all to the mass interval for models without rotation. Thus, the combination of the diagrams C/O vs O/H, more sensitive to the mass interval, and of the diagram N/O vs. O/H, more sensitive to rotation, may be particularly powerful to disentangle the two effects of rotation and mass interval, and to precise the properties of the star populations responsible for the early chemical evolution of galaxies.

At the present stage, when we compare our results to the observations we may derive the following tentative conclusions, which could change if the data further improve. The C/O vs O/H diagram does not seem favorable to enrichments by only very massive stars in the range 20 to 120 $M_\odot$; contributions from stars down to 8 or 2 $M_\odot$ may be needed, depending on the exact slope observed at low Z in Fig. 20. As to the N/O vs. O/H diagram, no model without rotation is able to account for the observed plateau, moreover contributions from only stars above 20 $M_\odot$ seem difficult. The observed plateau at $\log~\rm N/O = -1.7$ strongly supports rotating models including the large contribution from intermediate mass stars down to, either 2 $M_\odot$ if these stars have the same average rotation as in Pop. I stars, or down to only 8 $M_\odot$ if the rotations are faster as suggested by Maeder et al. (1999). In this respect, it would be sufficient that the average rotational velocities during the MS phase are larger by about 80 km s^-1.

We must temper these conclusions by the following remark (cf. also Meynet & Maeder 2002), related to a current problem in the chemical evolution of galaxies. Nitrogen is ejected mainly by AGB stars with ejection velocities of a few 100 km s^-1, while oxygen is ejected by supernovae at much higher velocities of 10⁴ km s^-1 or more. Thus, a fraction of the oxygen produced may escape from the parent galaxy, leading to a higher N/O ratio than in the simple estimate made here.