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Astron. Astrophys. 337, 338-348 (1998)

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4. Model results

Our study of the evolution of BCG and DIG starts from the results obtained by Marconi et al. (1994): i) the star formation is assumed to proceed in short and intense bursts of activity, which may induce galactic winds; ii) metal enriched and normal winds have been considered. In particular, for the metal enriched winds the assumption is made that galactic winds carry mostly the nucleosynthesis products of supernovae of type II, with the consequence of removing elements such as oxygen but not elements such as helium and nitrogen which are mainly produced in low and intermediate mass stars, and ejected through stellar winds.

The novelty is that i) galactic winds are powered both by supernova explosions (SNII and SNIa) and stellar winds from massive stars, and that ii) we consider the presence of dark matter halos in these galaxies.

In order to understand the observed distribution of N/O, C/O versus O/H, and of [O/Fe] versus [Fe/H], we computed different galaxy models by varying some parameters such as the number of bursts, the duration of each burst, the star formation efficiency, the galactic wind efficiency, the dark matter mass and distribution, and finally, the IMF exponent.

We first considered three sets of standard models characterized by 1, 3, 5, 7 and 10 bursts of a duration of 20, 60 and 100 Myr, whereas the other parameters were fixed by the results presented in Marconi et al. (1994). In particular, the IMF is the Salpeter one, and the star formation efficiency is [FORMULA]. The galactic wind is differential, namely [FORMULA] is different from zero only for the [FORMULA]-elements ejected through type II supernova explosions. In particular, for the elements studied here, [FORMULA] is zero for N and He, whereas it is [FORMULA] for O, Ne, Na, Mg and Si, is [FORMULA] for C, since carbon is partly produced and ejected by low and intermediate mass stars through stellar winds, and is [FORMULA] for Fe since only [FORMULA] of this element is produced by SNe II. The ratio between dark and luminous matter is assumed to be 10 and that between the luminous and dark core radius is [FORMULA] for the three sets of standard models. Normal galactic winds instead require [FORMULA] to be the same for all the chemical elements. From now on we will indicate the models with differential winds by a capital D, (e.g. [FORMULA] indicating the value for the [FORMULA]-elements).

Among our standard models, those with burst duration [FORMULA] never developed galactic winds, and those with [FORMULA] predicted the destruction of the galaxy (i.e. when the thermal energy of gas is larger than the binding energy of the galaxy) when a large number of bursts was assumed (in particular when [FORMULA]); on the contrary, models with [FORMULA] never predicted galaxy destruction and developed galactic winds for [FORMULA]. As a consequence of this, we chose to examine only models with [FORMULA].

We started then from our standard models and varied several parameters such as the star formation efficiency, the wind efficiency, the amount and distribution of dark matter. We found that in order to reproduce the observed spread of [FORMULA] and [FORMULA] and [FORMULA], the most important parameter is the star formation efficiency. We computed two series of models characterized by two different IMF: the Salpeter (1955) and the Scalo (1986) function. To reproduce the observed spread in all three diagrams, we needed a star formation efficiency ([FORMULA]) between 0.1 and 7 [FORMULA] when using the Salpeter IMF, and between 1 and 10 [FORMULA] when using the Scalo IMF. The best value for the wind parameter was [FORMULA].

Consider first the Salpeter IMF case: we computed models with 1, 2, 3, 5 and 7 bursts, and tested the importance of the presence of the dark matter. Greater is the amount of dark matter, deeper is the galaxy potential and higher the gas binding energy. Therefore, the thermal energy required to develop the galactic wind has also to be higher. We found that if the amount of dark matter is the same as that of the luminous matter ([FORMULA]) any model predicts galaxy destruction during the first starburst if the star formation efficiency is high ([FORMULA]). This upper limit of [FORMULA] depends of course on the number of bursts: models with many bursts, are characterized by a great consume of gas through star formation activity, so they must have lower star formation rates to keep bound than models with just one or two bursts. We previously said that we need [FORMULA] to explain the observed spread of the abundances ratios. So, let us consider the presence of a greater amount of dark matter: ten times the luminous matter ([FORMULA]). In this case none of the models characterized by 1 or 2 bursts and [FORMULA] predicts galaxy destruction during starbursts, whereas those with 3 or more bursts sometimes do. Considering an even greater amount of dark matter, fifty times the luminous matter ([FORMULA]), none of the models predicts galaxy destruction for any value of the star formation efficiency [FORMULA].

In Table 1 we summarize the range of variation of the star formation efficiency and the occurrence of the galactic wind for different values of the number of bursts and different amounts of dark matter for stable models (i.e. the galaxy never blows up). In column 1 is presented the number of bursts ([FORMULA] 1, 2, 3, 5, 7), in column 2 the range of variation of the star formation efficiency ([FORMULA]) and in column 3 we indicate if models develop the galactic wind or not. This same scheme is reproduced three times, for [FORMULA] and 50.


[TABLE]

Table 1. Salpeter IMF models characterized by [FORMULA], [FORMULA]: we indicate the range of variation of the star formation efficiency ([FORMULA], expressed in [FORMULA]) for different values of R and [FORMULA], and the development of the galactic wind (GW).


Therefore, one interesting result of our study is the fact that the presence of dark matter halos around dwarf irregulars and blue compact galaxies seems to be required in order to avoid total destruction due to the energy injected by supernova explosion and stellar winds during starbursts, especially in objects which suffered more than one starburst. In particular, we find that in models characterized by one or two bursts the quantity of dark matter should vary between one and ten times the amount of the luminous matter, according to the assumed star formation efficiency. This is in agreement with the amount of dark matter derived observationally (Skillman 1996). On the other hand, models with a number of bursts between 3 and 7 require an amount of dark matter which could be even 50 times the luminous matter. Moreover, the distribution of dark matter in our formulation, is described by the parameter [FORMULA], and we find that S can vary between 0.1 and 0.4.

Fig. 1 shows the range of variation of the star formation efficiency for standard models characterized by two 0.06 Gyr bursts (occurring at [FORMULA] and 5 Gyr), [FORMULA], [FORMULA], [FORMULA] and the Salpeter IMF. We notice the peculiar sawtooth behaviour, indicating the alternation of the active star formation periods (during the bursts) and the quiescent periods (during the interbursts). During the starbursts, the star formation rate is high, and the SNe of type II dominate in the chemical enrichement of O, Fe, N and C, while during the interbursts, when the star formation is not acting, only the elements like C, N, or Fe, are produced mostly by low and intermediate mass stars. In this case the abundance of these elements increases relative to the oxygen abundance, and this is exactly what we observe in all the figures presented here. The observed spread of N/O abundance ratio, reported in Fig. 1, is quite well reproduced if [FORMULA].

[FIGURE] Fig. 1. Two 0.06 [FORMULA] burst models: Salpeter IMF, [FORMULA], [FORMULA], [FORMULA]. We present the observed distribution of [FORMULA] and the variation range of the star formation efficiency of our models: [FORMULA]. The data points are from Kobulnicky and Skillman (1996), the error bars are also indicated.

Figs. 2 and 3 show the C/O and the [O/Fe] abundance ratios relative to the same models, respectively. In these cases we can notice how the observed spreads are quite well reproduced if [FORMULA] for C/O and if [FORMULA] for [O/Fe]. These differences are probably due to the few data available in literature for C and Fe abundances and to uncertainties present in the nucleosynthesis calculations.

[FIGURE] Fig. 2. Two 0.06 Gyr burst models: Salpeter IMF, [FORMULA], [FORMULA], [FORMULA]. We present the observed distribution of [FORMULA] and the variation range of the star formation efficiency of our models: [FORMULA]. The data points are from Garnett et al. 1995) (filled symbols) and Garnett et al. (1997) (open symbols). The error bars are also indicated.

[FIGURE] Fig. 3. Two 0.06 Gyr burst models: Salpeter IMF, [FORMULA], [FORMULA], [FORMULA]. We present the observed distribution of [FORMULA] and the variation range of the star formation efficiency of our models: [FORMULA]. The data points are from Thuan et al. (1995) and the error bars are also indicated.

On the other hand, Figs. 4, 5 and 6 show the same models but with the Scalo IMF, reproducing the N/O, C/O and [O/Fe] abundance ratios. In this case the best results are obtained with [FORMULA]. However, while the [O/Fe] observed spread is quite well reproduced (Fig. 6), the C/O and in particular the N/O abundance ratios are worsely reproduced than by the Salpeter IMF models (Figs. 2 and 1).

[FIGURE] Fig. 4. Two 0.06 Gyr burst models: Scalo IMF, [FORMULA], [FORMULA], [FORMULA]. We present the observed distribution of [FORMULA] and the variation range of the star formation efficiency of our models: [FORMULA]. The data points are the same as in Fig. 1.

[FIGURE] Fig. 5. Two 0.06 Gyr burst models: Scalo IMF, [FORMULA], [FORMULA], [FORMULA]. We present the observed distribution of [FORMULA] and the variation range of the star formation efficiency of our models: [FORMULA]. The data points are the same as in Fig. 2.

[FIGURE] Fig. 6. Two 0.06 Gyr burst models: Scalo IMF, [FORMULA], [FORMULA], [FORMULA]. We present the observed distribution of [FORMULA] and the variation range of the star formation efficiency of our models: [FORMULA]. The data points are the same as in Fig. 3.

On the basis of our study we can conclude that models with the Salpeter IMF are favoured relative to those adopting the Scalo one, since these latter do not explain all the spread present in the N/O vs O/H diagram. The models with the Salpeter IMF require a star formation efficiency [FORMULA] and a dark to luminous matter ratio [FORMULA].

In our analysis of the best model we have also considered the relation between metallicity (Z) and the gas mass fraction ([FORMULA] with [FORMULA]). Matteucci and Chiosi (1983) discussed the problem of reproducing the observed spread existing in the [FORMULA] diagram and suggested that different wind rates, different infall rates and different IMF from galaxy to galaxy could equally well explain the spread. However, they did not consider the role played by the dark matter. On the other hand, Kumai and Tosa (1992) suggested that the observed spread could be explained with the presence of variable amounts of dark matter: they proposed that the dark matter fraction should vary from galaxy to galaxy as [FORMULA]. Our results agree with Kumai and Tosa (1992) and, as one can see in Fig. 7, where it is shown that the dark matter can vary between 1 and 50 times the luminous matter ([FORMULA]) in order to reproduce the spread. This means that the parameter [FORMULA] should vary in the range [FORMULA].

[FIGURE] Fig. 7. Two 0.06 Gyr burst models: Salpeter IMF, [FORMULA][FORMULA], [FORMULA]. We present the observed distribution of Z versus [FORMULA] ([FORMULA]). The models are characterized by a different amount of dark matter: [FORMULA]. The data points are from Matteucci and Chiosi (1983).

The second main result of our study concerns the energetics of interstellar gas: the ISM receives energy from both supernova explosions and stellar winds from massive stars. In Fig. 8 we can notice the interstellar gas thermal energy relative to its binding energy and the total galaxy binding energy. When the thermal energy equates the gas binding energy, the galaxy develops the galactic wind. When a supernova explodes it injects almost [FORMULA] into the ISM, but just some percents (see paragraph 3.) of this energy are transformed into thermal energy of the gas. The question about stellar winds from massive stars is still under debate. As already discussed, we considered here a typical massive star ([FORMULA]) and assumed that it may inject into the ISM something like [FORMULA] through stellar winds during all of its life, and our results in this case suggest that the total thermal energy due to stellar winds from massive stars, is negligible if compared to the component due to supernovae of type II and Ia. Supernovae of type Ia also do not contribute significantly, as shown in Fig. 9 where the different contributions to the thermal energy due to the SNeII, the SNeIa and the stellar winds are presented. This would mean that both stellar winds and SNeIa play a negligible role in the evolution of these systems.

[FIGURE] Fig. 8. Three 0.06 Gyr burst model, characterized by: Salpeter IMF, [FORMULA], [FORMULA], [FORMULA], [FORMULA]. The bursts occur at [FORMULA] and 11 Gyr. We present the galaxy binding energy ([FORMULA]), the interstellar gas binding energy ([FORMULA]) and the interstellar gas thermal energy ([FORMULA]). The time of occurence of the galactic wind correspond to the time at which [FORMULA].

[FIGURE] Fig. 9. Three 0.06 Gyr burst model, characterized by: Salpeter IMF, [FORMULA], [FORMULA], [FORMULA], [FORMULA]. The bursts occur at [FORMULA] and 11 Gyr. We present the SNIa and the stellar winds contributions to the total thermal energy relative to the SNeII contribution: note that the stellar winds contribution is smaller than the one due to the SNeIa.

In agreement with the Marconi et al. (1994) results, our results also favour differential galactic winds, but we find that the wind efficiency parameter [FORMULA] has to be lower ([FORMULA]) than in Marconi et al. (1994).

Finally in Fig. 10 is reported the characteristic behaviour of type II supernova rates: each peak corresponds to a burst of star formation. In Fig. 11 instead typical type Ia supernova rates are presented and we can notice how type Ia supernovae explode also during the interbursts periods. Considering Salpeter models characterized by [FORMULA], [FORMULA], and [FORMULA], we find that the present value of SNeIa rate varies between [FORMULA] and [FORMULA], depending on the values of both the star formation efficiency and the number of bursts. In particular, in Table 2 we indicate the range of variation of the present value of type Ia SNe rate ([FORMULA]) for different values of the number of bursts ([FORMULA]) and [FORMULA].

[FIGURE] Fig. 10. Three 0.06 Gyr burst model, characterized by: Salpeter IMF, [FORMULA], [FORMULA], [FORMULA], [FORMULA]. The bursts occur at [FORMULA] and 11 Gyr. We present the rate of type II supernova explosion as a function of time. The units of the SN rate are [FORMULA]

[FIGURE] Fig. 11. Three 0.06 Gyr burst model, characterized by: Salpeter IMF, [FORMULA], [FORMULA], [FORMULA], [FORMULA]. The bursts occur at [FORMULA] and 11 Gyr. We present the rate of type Ia supernova explosion as a function of time. The units of the SN rate are [FORMULA]


[TABLE]

Table 2. Range of variation of type Ia supernova rates ([FORMULA]) for different values of the number of bursts ([FORMULA]). The star formation efficiency is [FORMULA].


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© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998
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