SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


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

Previous Section Next Section Title Page Table of Contents

3. Theoretical prescriptions

To calculate the chemical evolution of the star forming region of DIG and BCG, we used an improved version of the model presented in Marconi et al. (1994). The main features of our chemical evolution model are the following:

  1. one-zone, with instantaneous and complete mixing of gas inside this zone;

  2. no instantaneous recycling approximation, i.e. the stellar lifetimes are taken into account;

  3. the evolution of several chemical elements (He, C, N, O, Fe) due to stellar nucleosynthesis, stellar mass ejection, galactic wind powered by supernovae and stellar wind and infall of primordial gas, is followed in details.

If [FORMULA] is the fractional mass of the element i in the gas, its evolution is given by the equations:

[EQUATION]

where [FORMULA] is the gas mass in the form of an element i normalized to a total luminous mass [FORMULA] and [FORMULA] is the present time.
The quantity [FORMULA] represents the abundance by mass of an element i and by definition the summation over all the elements present in the gas mixture is equal to unity. The quantity [FORMULA] is the total fractional mass of gas.

The star formation rate we assume during a burst, [FORMULA], is defined as:

[EQUATION]

where [FORMULA] is the star formation efficiency (expressed in units of [FORMULA]), and represents the inverse of the timescale of star formation, namely the timescale necessary to consume all the gas in the star forming region.

The rate of gas loss via galactic winds for each element is assumed to be simply proportional to the amount of gas present at the time t:

[EQUATION]

where [FORMULA] is the abundance of the element i in the wind and in the interstellar medium (ISM); [FORMULA] is a free parameter describing the efficiency of the galactic wind and expressed in [FORMULA]. We have considered normal and differential winds: in the first case, all the elements are lost at the same efficiency ([FORMULA]). In the second case, the value of [FORMULA] has been assumed to be different for different elements: in particular, the assumption has been made that only the elements produced by type II SNe (mostly [FORMULA]-elements and one third of the iron) can escape the star forming region. We have made this choice following the conclusions of Marconi et al. (1994), who showed that models with differential winds can better explain the observational constraints of blue compact galaxies in general. The conditions for the onset of the galactic wind are studied in detail and described in paragraph 3.2.

The chemical evolution equations include also an accretion term:

[EQUATION]

where [FORMULA] is the abundance of the element i in the infalling gas, assumed to be primordial, [FORMULA] is the time scale of mass accretion [FORMULA] is the galactic lifetime, and C is a constant obtained by imposing to reproduce [FORMULA] at the present time [FORMULA]. The parameter [FORMULA] has been assumed to be the same for all dwarf irregulars and short enough to avoid unlikely high infall rates at the present time ([FORMULA] years). The presence of infalling gas in these systems can be justified by the existence of large HI halos.

Finally, the initial mass function (IMF) by mass, [FORMULA], is expressed as a power law:

[EQUATION]

We considered two cases for the IMF:

  1. the exponent [FORMULA] over the mass range [FORMULA] (Salpeter 1955 IMF), and

  2. [FORMULA] over the mass range [FORMULA], and [FORMULA] over the mass range [FORMULA] (Scalo 1986 IMF).

A is the normalisation constant, obtained with the following condition:

[EQUATION]

3.1. Nucleosynthesis prescriptions

The [FORMULA] term of the Eq. (1) represents the stellar contribution to the enrichment of the ISM, i.e. the rate at which the element i is restored into the ISM from a stellar generation (see Marconi et al. 1994). This term contains all the nucleosynthesis prescriptions:

  1. for low and intermediate mass stars ([FORMULA]) we have used Renzini and Voli's (1981) nucleosynthesis calculations for a value of the mass loss parameter [FORMULA] (Reimers 1975), and the mixing length [FORMULA]. The standard value for [FORMULA] is 8 [FORMULA];

  2. for massive stars ([FORMULA]) we have used Woosley's (1987) nucleosynthesis computations but adopting the relationship between the initial mass M and the He-core mass [FORMULA], from Maeder and Meynet (1989). It is worth noting that the adopted [FORMULA]) relationship does not substantially differ from the original relationship given by Arnett (1978) and from the new one by Maeder (1992) based on models with overshooting and [FORMULA]. These new models show instead a very different behaviour of [FORMULA]) for stars more massive than 25 [FORMULA] and [FORMULA], but our galaxies never reach such a high metallicity;

  3. for the explosive nucleosynthesis products, we have adopted the prescriptions by Nomoto et al. (1984) and Thielemann et al. (1993), model W7, for type Ia SNe, which we assume to originate from C-O white dwarfs in binary systems (see again Marconi et al. 1994 for details).

As already said, nitrogen is a key element to understand the evolution of galaxies with few star forming events since it needs relatively long timescales as well as a relatively high underlying metallicity to be produced. The reason is that N is believed to be mostly a secondary element (secondary elements are those synthesized from metals originally present in the star and not produced in situ , while primary elements are those synthesized directly from H and He). Up to now N has been considered secondary in massive stars and mostly secondary and probably partly primary in low and intermediate mass stars (Renzini and Voli 1981). However, some doubts exist at the moment on the amount of primary nitrogen which can be produced in intermediate mass stars due to the uncertanties related to the occurrence of the third dredge-up in asymptotic giant branch stars (AGB). In fact, if Blöcker and Schoenberner (1991) calculations are correct, the third dredge-up in massive AGB stars should not occur and therefore the amount of primary N produced in AGB stars should be strongly reduced (Renzini, private communication).

As a consequence, the only way left to produce a reasonable quantity of N during a short burst (no longer than 20 Myr) is to require that massive stars produce a substantial amount of primary nitrogen. This claim was already made by Matteucci (1986) in order to explain the [N/O] abundances in the solar neighbourhood. Recently, Woosley and Weaver (1995) have indicated that massive stars can indeed produce primary nitrogen, and Marconi et al. (1994) and Kunth et al. (1995) have taken into account this possibility. In this paper we also have considered this possibility and, since quantitative predictions are not yet available, we have used the same parametrization adopted by Marconi et al. (1994) and Kunth et al. (1995).

3.2. Energetics

We define as "galactic wind" any gas flow carrying material outside the galaxy. Such flows, which are not necessarily hot, have been recently detected in several blue compact galaxies (Kunth et al. 1998).

Our model presents a new formulation of galactic winds relative to previous published models of this type (Matteucci and Tosi 1985 and Marconi et al. 1994). In particular, we adopted the prescriptions developed for elliptical galaxies (Matteucci and Tornambé 1987; Gibson 1994, 1997): galaxies develop galactic winds when the gas thermal energy [FORMULA], exceeds its binding energy [FORMULA], i.e. when:

[EQUATION]

A detailed treatment of the energetics of the ISM is considered, in order to compute the gas thermal energy:

[EQUATION]

we calculated the energy fraction deposited in the gas by stellar winds from massive stars [FORMULA], and by supernova explosions [FORMULA]. Here the supernova contribution is given by:

[EQUATION]

where:

[EQUATION]

[EQUATION]

[EQUATION]

[FORMULA] and [FORMULA] are the rates of supernova (II and Ia) explosion, [FORMULA] is the IMF and [FORMULA] is the star formation rate. The type Ia and II SN rates are calculated according to Matteucci and Greggio (1986). The energy injected and effectively thermalized into the ISM from supernova explosions ([FORMULA]) and stellar winds from massive stars ([FORMULA]), are given by the following formulas:

[EQUATION]

[EQUATION]

where [FORMULA] is the total energy released by a supernova explosion, [FORMULA] is the energy injected into the ISM by a typical massive star through stellar winds during all its lifetime, and [FORMULA] and [FORMULA] are the efficiencies of energy transfer from supernova and stellar winds into the ISM, respectively. We adopted a formulation for [FORMULA] and [FORMULA] which is described in detail in appendix.

Our formulation refers to an ideal case characterized by an uniform ISM, and no interaction with other supernova explosions or interstellar clouds. When a supernova explodes the stellar material is violently ejected into the ISM and its expansion is gradually slowed down by the ISM. The energy released by the supernova explosion is assumed to be [FORMULA], while the energy effectively transferred and thermalized into the ISM is given by Eq. (13) and depends on the assumed value for [FORMULA]. The main parameters used to derive [FORMULA], as described in the appendix, are: the initial blast wave energy [FORMULA], the interstellar gas density [FORMULA], and the isothermal sound speed in the ISM [FORMULA].

For typical values of these parameters [FORMULA], [FORMULA] and [FORMULA] we obtained the following range of possible values for [FORMULA]:

[EQUATION]

In particular, we have adopted an intermediate value of [FORMULA] which we assume to be the typical SN energy transfer efficiency.

The energy injected into the ISM by a typical massive star through stellar winds during all its lifetime is estimated to be:

[EQUATION]

where [FORMULA] is the time the star spends in Main Sequence and [FORMULA] is the stellar wind luminosity. By using the arguments developed in the appendix, we obtained:

[EQUATION]

if we assume a 20[FORMULA] star as a typical massive star contributing to the stellar winds then [FORMULA], [FORMULA] with [FORMULA] and [FORMULA], we obtain:

[EQUATION]

Therefore, in our formulation we adopted:

[EQUATION]

and

[EQUATION]

It is worth noting that the assumed value for [FORMULA] is in agreement with that calculated by Gibson (1994) for a star of initial mass [FORMULA].

The introduction of dark matter halos with variable amounts and concentrations of dark matter is considered when we compute the binding energy of interstellar gas, [FORMULA]:

[EQUATION]

The two terms on the right of the equation take in account the gravitational interaction between the gas mass [FORMULA], and the total luminous mass of the galaxy [FORMULA], and between the gas mass and the dark matter [FORMULA]:

[EQUATION]

[EQUATION]

where [FORMULA].

G is the gravitational constant, and [FORMULA] is the ratio between the effective radius of luminous matter and the effective radius of dark matter. These equations are taken from Bertin et al. (1991) and are valid for S defined in the range [FORMULA].
It is worth noting that the original formulation of Bertin et al. (1991) was thought for massive elliptical galaxies, and that it is not necessarily the right one for dwarf irregulars. However, we used such a formulation since theoretical formulations for the binding energy of dwarf irregulars are not available.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1998

Online publication: August 17, 1998
helpdesk.link@springer.de