The self-enrichment of galactic halo globular:|
a clue to their formation ?
* Maître de Recherches au Fonds Natrional de la Recherche Scientifique (Belgium)
** Chercheur qualifié au Fonds Natrional de la Recherche Scientifique (Belgium)
We present a model of globular cluster self-enrichment. In the
protogalaxy, cold and dense clouds embedded in the hot
protogalactic medium are assumed to be the progenitors of galactic halo
The massive stars of a first generation of metal-free stars, born in
the central areas of the proto-globular cluster clouds, explode as
Type II supernovae.
The associated blast waves trigger the expansion of a supershell, sweeping
all the material of the cloud, and the heavy elements released by these
massive stars enrich the supershell. A second generation of stars is
born in these compressed and enriched layers of gas. These stars
can recollapse and form a globular cluster.
This work aims at revising the most often encountered argument against
self-enrichment, namely the presumed ability of a small number of
supernovae to disrupt a proto-globular cluster cloud.
We describe a model of the dynamics of the supershell and of its
progressive chemical enrichment.
We show that the minimal mass of the primordial cluster cloud
required to avoid disruption by several tens of Type II supernovae is
compatible with the masses usually assumed for
proto-globular cluster clouds. Furthermore,
the corresponding self-enrichment level is
in agreement with halo globular cluster metallicities.
Key words: globular clusters: general - Galaxy: evolution - supernovæ: general - ISM: bubbles - population III
|Table of contents|
The study of the chemical composition and dynamics of the galactic halo
components, field metal-poor stars and globular clusters (hereafter GCs),
natural way to trace the early phases of the galactic evolution. In an
attempt to get some new insights on the early galactic nucleosynthesis,
accurate relative abundances have been obtained from the analysis of
high resolution and high signal-to-noise spectra for a sample of 21
mildly metal-poor stars (Jehin et al. 1998, 1999).
The correlations between the relative
abundances of 16 elements have been studied, with a special emphasis on the
neutron capture ones. This analysis reveals the existence of two
sub-populations of field metal-poor stars, namely Pop IIa and
Pop IIb. They differ by the behaviour of the s-process
elements versus the and
To explain such correlations, Jehin et al. (1998, 1999) have suggested
a scenario for the formation of metal-poor stars which closely
relates the origin of these stars to the formation and the evolution of
galactic globular clusters.
At present, there is no widely accepted theory of globular cluster formation. According to some scenarios, GC formation represents the high-mass tail of star cluster formation. Bound stellar clusters form in the dense cores of much larger star-forming clouds with an efficiency of the order 10-3 to 10-2 (Larson, 1993). If GCs form in a similar way, the total mass of the protoglobular clouds should therefore be two or three orders of magnitude greater than the current GC masses, leading to a total mass of 108 . Harris and Pudritz (1994) have investigated the GC formation in such clouds which they call SGMC (Super Giant Molecular Clouds). The physical conditions in these SGMC have been further explored by McLaughlin and Pudritz (1996a).
Another type of scenarios rely on a heating-cooling balance to preserve a given temperature (of the order of 104K) and thus a characteristic Jeans Mass at the protogalactic epoch. In this context, Fall and Rees (1985) propose that GCs would form in the collapsing gas of the protogalaxy. During this collapse, a thermal instability triggers the development of a two-phase structure, namely cold clouds in pressure equilibrium with a hot and diffused medium. They assume that the temperature of the cold clouds remains at 104K since the cooling rate drops sharply at this temperature in a primordial gas. This assumption leads to a characteristic mass of order 106 for the cold clouds. However, this temperature, and therefore the characterictic mass, is preserved only if there is a flux of UV or X-ray radiation able to prevent any H2 formation, the main coolant in a metal-free gas below 104K. Provided that this condition is fullfilled, and since the characteristic mass is of the order of GC masses (although a bit larger, but see section 5.2.1), Fall and Rees identify the cold clouds with the progenitors of GCs. Several formation scenarios have included their key idea : cloud-cloud collisions (Murray and Lin 1992), self-enrichment model (Brown, Burkert and Truran 1991, 1995).
According to the scenario suggested by Jehin et al. (1998, 1999), GCs may have undergone a Type II supernovae phase in their early history. This scenario appears therefore to be linked with the self-enrichment model developed by Brown et al. within the context of the Fall and Rees theory. Following Jehin et al., thick disk and field halo stars were born in globular clusters from which they escaped either during an early disruption of the proto-globular cluster (Pop IIa) or through a later disruption or evaporation process of the cluster (Pop IIb). The basic idea is that the chemical evolution of the GCs can be described in two phases. During phase I, a first generation of metal-free stars form in the central regions of proto-globular cluster clouds (hereafter PGCC). The corresponding massive stars evolve, end their lives as Type II supernovae (hereafter SNeII) and eject , r-process and possibly a small amount of light s-process elements into the interstellar medium. A second generation of stars form out of this enriched ISM. If the PGCC get disrupted, those stars form Pop IIa. If it survives and forms a globular cluster, we get to the second phase where intermediate mass stars reach the AGB stage of stellar evolution, ejecting s elements into the ISM through stellar winds or superwind events. The matter released in the ISM by AGB stars will be accreted by lower mass stars, enriching their external layers in s elements. During the subsequent dynamical evolution of the globular cluster, some of the surface-enriched low-mass stars evaporate from the cluster, become field halo stars and form PopIIb.
Others studies have already underlined the two star generations concept : Cayrel (1986) and Brown et al. (1991, 1995) were pioneers in this field. Zhang and Ma (1993) have demonstrated that no single star formation can fit the observations of GCs chemical properties. They show that there must be two distinct stages of star formation : a self-enrichment stage (where the currently observed metallicity is produced by a first generation of stars) and a starburst stage (formation of the second generation stars).
These two generations scenarios were marginal for a long time. Indeed, the major criticism of such globular cluster self-enrichment model is based on the comparison between the energy released by a few supernova explosions and the PGCC gravitational binding energy : they are of the same order of magnitude. It might seem, therefore, that proto-globular cluster clouds (within the context of the Fall and Rees theory) cannot survive a supernova explosion phase and are disrupted (Meylan and Heggie, 1997). Nevertheless, a significant part of the energy released by a supernova explosion is lost by radiative cooling (Falle, 1981) and the kinetic energy fraction interacting with the ISM must be reconsidered.
While Brown et al. (1991, 1995) have mostly focused on the computations of the supershell behaviour through hydrodynamical computations, we revisit some of the ideas that have been used against the hypothesis of GC self-enrichment. In this first paper, we tackle the questions of the supernova energetics and of the narowness of GC red giant branch. Dopita and Smith (1986) have already addressed the first point from a purely dynamical point of view. In their model, they assume the simultaneity of central supernova explosions and they use the Kompaneets (1960) approximation to describe the resulting blast wave motion. During this progression from the central regions to the edge of the PGCC, all the material encountered by the blast wave is swept up into a dense shell. They demonstrate that, when the shell emerges from the cloud, its kinetic energy, based on the number of supernovae that have exploded, is compatible with the gravitational binding energy of a cloud whose mass is more or less 107 . When the kinetic energy of the emerging shell is larger than the binding energy of the initial cloud, this cloud is assumed to be disrupted by the SNeII. There is therefore a relation between the cloud mass and the maximum number of supernovae it can sustain without being disrupted. However, a 107 cloud is more massive than the PGCCs considered within the Fall and Rees theory.
We derive here a similar relation based on the supershell description (Castor, McCray, Weaver, 1975) of the central supernova explosions. Contrary to the Kompaneets approximation, this theory allows us to take into account the existence of a mass spectrum for the massive supernova progenitors and, therefore, the spacing in time of the explosions. In addition to the above dynamical constraint, we also establish a chemical one. For a given mass of primordial gas, we compute the maximum number of supernovae the PGCC can sustain and the corresponding self-enrichment level at the end of the supernova phase. We show that the metallicity reached is compatible with the metallicity observed in galactic halo globular clusters.
The paper is organized as follows. In section 2, we review the observations gathered by Jehin et al.² (1998, 1999) and the scenario proposed to explain them. In section 3, we describe the PGCCs, the first generation of metal-free stars, and the supershell propagation inside PGCCs due to SNeII explosions. In section 4, we show that the disruption criterion proposed by Dopita and Smith (1986), here computed with the supershell theory, gives the correct globular cluster metallicities. In section 5, we discuss the sensitivity of our model to the first generation IMF parameter values and we examine the implications of an important observational constraint, the RGB narrowness noticed in most globular cluster Color Magnitude Diagrams (CMDs). Finally, we present our conclusions in section 6.
|2. The EASE scenario|
|2.1. Observational results|
Jehin et al. (1998, 1999) selected a sample of 21 unevolved metal-poor stars with roughly one tenth of the solar metallicity. This corresponds to the transition between the halo and the disk. All stars are dwarfs or subgiants, at roughly solar effective temperature and covering a narrow metallicity range. High quality data have been obtained and a careful spectroscopic analysis was carried out. The scatter in element abundances reflects genuine cosmic scatter and not observational uncertainties. Abundances of iron-peak elements (V, Cr, Fe, Ni), elements (Mg, Ca, Ti), light s-process elements (Sr, Y, Zr), heavy s-process elements (Ba, La, Ce), an r-process element (Eu) and mixed r-,s-process elements (Nd, Sm) have been determined. Among these data, Jehin et al. (1998, 1999) have found correlations between abundance ratios at a given metallicity. If some elements are correlated, they are likely to have been processed in the same astrophysical sites, giving fruitful information about nucleosynthesis. The following results were obtained (Jehin et al. 1999) :
|2.2. Interpretation: two-phases globular cluster evolution|
We associate the two branches of the diagram with two distinct chemical
evolution phases of globular clusters, namely a SNII phase
(phase I) and an AGB wind phase (phase II).
We assume the formation of a first generation of stars in the central regions, the densest ones, of a proto-globular primordial gas cloud. The most massive stars of this first generation evolve and become supernovae, ejecting and r-process elements into the surrounding ISM. These supernova explosions also trigger the formation of an expanding shell, sweeping all the PGCC material encountered during its expansion and decelerated by the surrounding ISM. In this supershell, the supernova ejecta mix with the ambient ISM, enriching it in and r-process elements. The shell constitutes a dense medium since it contains all the PGCC gas in a very thin layer (a few tenths of parsecs) (Weaver et al., 1977). This favours the birth of a second generation of stars (triggered star formation) with a higher star formation efficiency (hereafter SFE) than the first one (spontaneous star formation). There are today several observational evidence of triggered star formation (Fich, 1986; Walter et al., 1998; Blum et al., 1999). For instance, within the violent interstellar medium of the nearby dwarf galaxy IC2574, Walter et al. (1998) have studied a supergiant HI shell obviously produced by the combined effects of stellar winds and supernova explosions. A major star formation event (equivalent to our first generation) has likely taken place at the center of this supershell and the most massive stars have released energy into the ISM. This one, swept by the blast waves associated with the first supernova explosions, accumulates in the form of an expanding shell surrounding a prominent HI hole. On the rim of the HI shell, H emissions reveal the existence of star forming regions (equivalent to our second generation). Actually, these regions of HI accumulated by the sweeping of the shell have reached densities high enough for a secondary star formation to start via gravitational fragmentation.
In our scenario, the second generation of stars formed in this dense and enriched shell makes up the proto-globular cluster. If the shell doesn't recontract, these stars form PopIIa and they appear somewhere on the slowly varying branch depending on the time at which the second generation formation has occurred. When all stars more massive than 9 have exploded as supernovae, the and r element synthesis stops, leading to a typical value of [/Fe]. Our scenario requires this typical value of [/Fe] to be the maximum value observed in the two-branches diagram: the end of the supernova phase must correspond to the bottom of the vertical branch. If the proto-globular cluster survives the supernova phase, the shell of stars will recontract and form a globular cluster.
After the birth of the second generation, intermediate mass stars evolve until they reach the asymptotic giant branch where they enrich their envelope in s-process elements through dredge-up phases during thermal pulses. These enriched envelopes are ejected into the ISM through stellar winds. Lower mass stars in the globular cluster can accrete this gas (Thoul et al., in preparation) : the s-process element enrichment occurs only in the external layers. With time, some of those stars can be ejected from the globular clusters through various dynamical processes, such as evaporation or disruption, and populate the galactic halo. These stars account for our PopIIb. Theoretically foreseen for a long time (see for example Applegate, 1985; Johnstone, 1992; Meylan and Heggie, 1997), these dynamical processes dislodging stars from globular clusters begin to rely upon observations. De Marchi et al. (1999) have observed the globular cluster NGC 6712 with the ESO-VLT and derived its mass function. Contrary to other globular clusters, NGC 6712 mass function shows a noticeable deficit in stars with masses below 0.75 . Since this object, in its galactic orbit, has recently penetrated very deeply into the Galactic bulge, it has suffered tremendous gravitational shocks. This is an evidence that tidal forces can strip a cluster of a substantial portion of its lower mass stars, easier to eject than the heavier ones.
Our scenario requires that a significant fraction of the field stars now observed in the halo have been evaporated from globular clusters at an earlier epoch. Indeed, Johnston et al. (1999) claim that GC destruction processes are rather efficient : a significant fraction of the GC system could be destroyed within the next Hubble time. However, McLaughlin (1999) and Harris and Pudritz (1994) argue that these various destructive mechanisms are important only for low mass clusters. Therefore, these clusters cannot have contributed much to the total field star population because of their small size. As one can see, the origin of the field halo stars is still a much debated question.
In relation with the different steps proposed above to explain the observations, the scenario was labeled EASE which stands for Evaporation/Accretion/Self-Enrichment (Fig. 2).
|3. Model description|
|3.1. The proto-globular cluster clouds|
According to Fall and Rees (1985), PGCCs are cold
and dense primordial gas clouds in pressure equilibrium with a hot
(Th 2 × 106K) and
diffused protogalactic medium.
As already mentioned in section 1, the PGCCs can be maintained at
a temperature of 104K only if some external heat sources were
present at the protogalactic epoch. Fall and Rees (1988) and Murray and
Lin (1993) have proposed that the UV flux
resulting from the hot protogalactic background could be sufficient to
offset the cooling below 104K in a gas with a metallicity less
than [Fe/H] -2.
As the PGCC is assumed to be made up of primordial gas
(we deal with a self-enrichment model and not a
pre-enrichment one), we will suppose it is indeed the case.
Within the context of this preliminary model,
the following assumptions are made :
|3.2. The formation of the first generation|
It is well known that star formation can only occur in the coolest and
densest regions of the ISM.
We assume that the UV external heating provided by the hot
protogalactic background is shielded by the bulk of the PGCC gas.
Therefore, H2 formation and thermal cooling are assumed
to occur only near the center
of the PGCC : the formation of the star first generation takes
place in the PGCC central area, the densest and the coolest regions
of the cloud. For the value of the SFE, i.e. the
ratio between the mass of gas converted into stars and the total mass of
gas, we refer to Lin and Murray (1992). Their computation shows that the
early star formation in protogalaxies was highly inefficient, leading to a
SFE not higher than one percent. The mass spectrum is described with the
following parameters :
|3.3. Supershell propagation|
The model of Castor et al. (1975) primarily describes the evolution of
a circumstellar shell driven by the wind of an early-type star.
Their study can be extented to multiple supernova shells if the supernova
progenitors (the first generation massive stars) are closely associated.
In this case, all supernova shells will merge into a single supershell
from the center to the edge of the PGCC. Following the remarks of the
previous section, we assume that this is indeed the
The blast waves associated with the first supernova explosions sweep the PGCC material in a thin, cold and dense shell of radius Rs and velocity . This shell surrounds a hot and low-density region, the bubble, whose pressure acts as a piston driving the shell expansion through the unperturbed ISM. The following equations settle the expansion law Rs(t) of the shell during its propagation in a given PGCC (Castor et al., 1975; Brown et al., 1995) :
|4. Level of self-enrichment|
We have assumed that stars form in the central regions of
a given PGCC. This first generation of stars is spontaneous, i.e. not
triggered by any external event, a shock wave for instance. This results
in a low SFE. After a few millions years,
the massive stars
(9 < M ;< 60 )
end their lives as SNeII. The consequences are :
|4.1. Dynamical constraint|
As the energy released by one SNII is typically 1051 ergs
(E51 = 1), the energy of a few supernova explosions
and the gravitational binding energy of a PGCC are of the same order of
magnitude. This is the major argument used against self-enrichment.
Actually, it is often argued that successive supernovae will disrupt the
proto-globular cluster cloud.
To test whether this idea is right or not, we can compare the gravitational
energy of the cloud to the kinetic energy of the expanding shell, supplied
by the supernova explosions, when it reaches the edge of the cloud.
Indeed, taking the following criterion for disruption :
|4.2. Chemical constraint|
The first generation of stars is not triggered by any event (shock wave
for instance) and therefore the SFE is likely to be be very low.
The typical halo metallicity of [Fe/H] ~ -1.6 must however be
reached despite this low first
generation SFE. We now show that this is indeed the case.
We compute the relation between the mass of primordial gas
and the number of first generation supernovae for two different
cases. In the first case, we assume a given SFE
(plain curve in Fig. 3),
while in the second one, we impose the final metallicity (dashed curves in
In what follows, all the masses are in units of one solar mass.
The mass distribution of the first generation of stars obeys the following power-law IMF,
|5.1. The IMF of the first generation|
The first generation of stars forms out of a gas very poor, or even free, in heavy elements. We now examine the consequences for our model.
|5.1.1 The shape of the IMF in a metal deficient medium|
As already mentioned in section 3.2,
we assume that the gas
temperature can decrease significantly below 104K in the
central regions of the PGCC only.
We now focus on what might happen in this central region where
star formation is expected.
According to Larson (1998), the Jeans scale can be identified with an intrinsic scale in the star formation process. It is defined as the minimum mass that a gas clump must have in order for gravity to dominate over thermal pressure (although the thermal Jeans mass is not universally accepted as relevant to the present-day formation of stars in turbulent and magnetized molecular clouds). It scales as
|5.1.2 The star formation efficiency|
The star formation efficiency is an important parameter, since the final mass fraction of heavy elements released in the primordial medium depends linearly on it. How stars are formed out of a gaseous cloud is still poorly known and it is not easy to estimate the value of the SFE. One of the most crucial step in the star formation process is the creation of molecular hydrogen (Lin and Murray 1992). H2 cooling results in a rapid burst of star formation which continues until massive stars have formed in sufficient number to reheat the surrounding gas. The massive stars produce a UV background flux which destroys the molecular hydrogen by photodissociation and shuts down further star formation. Applying this principle of self-regulated star formation by negative feed back to a protogalactic cloud, Lin and Murray (1992) have calculated the UV flux necessary to destroy the molecular hydrogen and the required number of massive stars to produce this UV flux. Finally, the mass and the SFE of this first generation of stars in the protogalaxy are estimated. They find a value of the order of one percent. Under the asumed IMF, an SFE of one per cent corresponds to a metallicity of -1.5 (see Fig. 3).
|5.1.3.The upper limit of the mass spectrum|
In the model we have adopted in section 4, the mass of heavy elements released by a star is proportional to its total mass (see Eq. (20)). However, above a critical mass mBH, a star can form a black hole without ejecting the heavy elements it has processed. This critical mass is given by mBH =50 ± 10 (Tsujimoto et al., 1995). Moreover, Woosley and Weaver (1995) have shown that zero initial metallicity stars have a final structure markedly different from solar metallicity stars of the same mass. The former ones are more compact and larger amounts of matter fall back after ejection of the envelope in the SN explosion. In this case, more heavy elements are locked in the remnant left by the most massive stars. In order to evaluate the consequences for our model, we now define two different upper mass limits for the IMF. The mass of the most massive supernova contributing to the enrichment of the ISM is chosen to be mu1 = 40 . But the more massive stars will have a dynamical impact on the ISM and contribute to the trigger and the early expansion of the supershell, even though they will not contribute to the self-enrichment. All stars with masses between ml2 and mu2 end their lives as supernovae, but only the ones with masses between ml3 and mu1 contribute to the PGCC self-enrichment. We adopt mu2 = 60 as the mass of the most massive supernova progenitor. This value is the same as in section 4.2 and therefore the plain curve in Fig. 3 (given SFE) is not modified. Keeping the same SFE, if we decrease mu1 from 60 to 40 , there is a reduction of ~ 0.2 dex in the final metallicity (Fig. 5). An IMF with a Salpeter slope doesn't favour at all the highest mass stars and these stars are quite rare compared to the less massive supernovae. This explains why the final metallicity is not strongly dependent on the value of mu1.
|5.1.4. The lower limit of the mass spectrum|
We have adopted the point of view of Nakamura and Umemura (1999) who assume that there is a sharp cutoff at the lower mass end of the IMF (ml1 = 3 ). If we consider a pure Salpeter IMF, this parameter is very critical. Indeed, if we take ml1 = 0.1 instead of 3, while keeping the SFE unchanged, the mass of heavy elements ejected by SNeII is decreased by a factor of four, leading to a decrease in metallicity of 0.6 dex. The Larson's modified IMFs provide less sensitive results.
|5.1.5. The slope of the IMF|
Following Larson (1998), we have used the Salpeter value. Changing the slope of the IMF will have the same consequences as changing the value of the lower mass cut off. If we decrease the slope, we will increase the ratio of high mass stars over low mass stars. The same result can be obtained by increasing the lower mass cut off of the mass spectrum.
|5.2. Observational constraint: the RGB narrowness|
With the exception of Cen, and perhaps M22, galactic globular clusters share the common property of a narrow red giant branch, indicative of chemical homogeneity within all stars of a given globular cluster. This observational property is also often used as an argument against self-enrichment. We now show that self-enrichment and a narrow RGB are in fact compatible.
|5.2.1. The mass of the first generation stars|
If we adopt the lower mass limit for the mass spectrum of initially
metal-free stars proposed by Nakamura and Umemura (1999), we get rid of one
of the major arguments against self-enrichment scenarios in globular
the existence of two distinct generations of stars with clearly different
metallicities. Indeed, if the first generation of stars is biased towards
high mass stars as previously suggested, these stars are no more
observed today and the current width of the RGB is not affected.
However, following Larson (1998), we could also allow low mass star formation during the first phase but under a different mass-scale than today. Using the IMF given by equation (26), we have computed the ratio between the currently observed numbers of low-mass (0.1 < M < 0.8 ) stars, which are produced in both generations. According to Brown et al. (1995), the second generation of stars will form a bound globular cluster if its SFE is at least 0.1. We therefore assume a value of 10 for the ratio SFE(2nd generation)/SFE(1st generation). The second generation mass scale m1 (see Eq. (26)) has been fixed to 0.34 to match the solar neighborhood potential peak located at m = 0.25 (see section 5.1.1). The mass peak of the first generation stars is left as a parameter and we allow it to vary between 1 and 3 . The ratio R of the number of second generation low mass stars to the number of first generation low mass stars is shown in Fig. 6. For one metal-free star, the number of second generation stars lies between 100 and 4000 depending on the first generation mass peak. Thus, even if low mass stars were formed in the metal-free PGCC, their relative number observed today is so small that the existence of the first generation is not in contradiction with the RGB narrowness observed on globular cluster CMDs.
|5.2.2. The time of formation of the second generation|
Another controversial point about self-enrichment concerns the ability of
the shell to mix homogeneously the heavy elements with the primordial gas.
If the mixing is not efficient,
inhomogeneities will be imprinted in the second
generation stars formed in the shell and will show up as a broader red
giant branch in CMDs, contrary to observations.
Brown et al. (1991) have established
that the accretion time by the blast wave propagating ahead of the
shell is one to two orders of magnitude larger than the mixing time due to
post-shock turbulence in the shell. In other words, the material swept by
the shell is more quickly mixed
than accreted and the post-shock turbulence insures supershell homogeneity.
But even if the supershell is chemically homogeneous
at a given time, the chemical composition varies with time :
metallicity is increasing as more and more supernova explosions occur
at the center of the bubble. So, one can argue that the second generation
will not be homogeneous : stars which are born early will be more
metal-poor than stars which are born later, when self-enrichment has gone
on. However, shell fragmentation into molecular clouds,
in which second generation stars
will form, cannot take place too early, at least not before the death of
all first generation O stars. Indeed, these ones
are the most important UV flux emitters and, as such, prevent the formation
of molecular hydrogen.
It is very interesting to plot the increase of metallicity versus time when the shell has emerged in the hot protogalactic medium (all the cloud material has been swept in the shell whose mass is now a constant). For simplicity, we have assumed that the ejecta of one supernova mix with all the PGCC gas before the next supernova explosion. In Fig. 7, the parameter values are the same as in section 4 (same IMF, N = 201, Ph = 8 × 10-11 dyne.cm-2) and the relation between the mass of a SNII progenitor and its lifetime on the Main Sequence is given by (Mc Cray, 1987). In this case, the shell reaches the edge of the cloud 2.3 millions years (explosion of the 35 supernovae) after the first explosion. We see in Fig. 7 that after a rapid increase in metallicity, as expected for a metal-free medium, the increase in metallicity slows down and saturates. After 9 millions years, when all stars more massive than 19 have exploded, the further metallicity increase is less than 0.1 dex, the upper limit of the RGB metallicity spread. Therefore, there is no conflict between a self-enrichment scenario and the RGB narrowness if the second generation of stars is born after this time . Even if supernova explosions still occur, the self-enrichment phase has ended. This point was already underlined by Brown et al. (1991) from a dynamical point of view.
We have investigated the possibility that globular clusters have undergone
self-enrichment during their evolution.
In our scenario, massive stars contribute actively
to the chemical enrichment and to the gas dynamics in the early Universe.
When a stellar system is formed, supernovae enrich the remaining gas
in such a way that the next generation of stars is more metal-rich than the
first one. In this paper, we assume the birth of a first generation of
stars in the
central areas of PGCCs. When the massive stars end their lives, the
corresponding SNeII explosions trigger the expansion of a
spherical shell of gas, where the PGCC primordial gas and the heavy
elements ejected by supernovae get mixed. Because of the dynamical impact
of supernova shock waves on the ISM, the gas is compressed into a dense
shell and this high density favours the birth of a second generation of
stars with a higher SFE.
This scenario of triggered star formation is now confirmed by observational
examples in the disk of our Galaxy and in irregular galaxies.
The second generation stars formed in these compressed layers of gas are
we observed today in GCs. Others authors have proposed scenarios where
these stars are also formed in triggered events, namely in gas layers
compressed by shock waves, but the origin of the trigger is different.
For instance, following Vietri and Pesce (1995) and Dinge (1997), the
propagation of shock waves in the cloud could be respectively promoted by
thermal instabilities inside the cloud or cloud-cloud collisions.
Thus, in these
scenarios, there is no first generation massive stars as shock wave
sources: this is the major difference between our scenario and theirs.
It has long been thought that PGCCs were not able to sustain SNeII explosions because of the associated important energetic effects on the surrounding ISM. In this paper, we have shown that this idea may not be true. For this purpose, the criterion for disruption proposed by Dopita and Smith (1986) was used. Nevertheless, we have extended it to more general conditions. Owing to the shell motion description proposed by Castor et al. (1975), the spacing in time of the supernovae explosions was taken into account. Also, we have not considered a tidal-truncated cloud as Dopita and Smith did but a pressure-confined one, which is certainly more suitable to protogalactic conditions. With this model, we have computed the speed of propagation of the shell through the PGCC for a given supernova rate and a given external pressure. We have demonstrated that a PGCC can sustain many supernova explosions. Moreover, the dynamical upper limit on the number of SNeII is compatible with an enrichment of the primordial gas clouds to typical halo globular cluster metallicities. This conclusion is quite robust to changes in IMF parameters. Our result depends on the hot protogalactic pressure confining the PGCC and implies therefore a relationship between the metallicity and the radial location in the protogalaxy. We have also pointed out that a scenario which involves two distinct generations of stars is not in contradiction with the RGB narrowness noticed in CMDs of nearly all galactic globular clusters providing that the birth of the second generation of stars is not triggered before the 19 supernova explosions have occurred. In a forthcoming paper, the correlations expected from this self-enrichment model will be deduced and compared to the observational data of the galactic halo GCs.
We are very grateful to Dean McLaughlin, whose suggestions as referee of this paper have resulted in several improvements over its original version. This work has been supported by contracts ARC 94/99-178 "Action de Recherche Concertée de la Communauté Française de Belgique" and Pôle d'Attraction Interuniversitaire P4/05 (SSTC, Belgium).
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