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Astron. Astrophys. 358, 869-885 (2000)

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5. Comparison with other constraints

5.1. The SFH driving the chemical enrichment of the disk

On theoretical grounds, there should be a correlation between the SFH and the age-metallicity relation (hereafter AMR). The increase in the star formation leads to an increase in the rate at which new metals are produced and ejected into the interstellar medium. The correlation is not a one-to-one, since the presence of infall and radial flows can also affect the enrichment rate of the system. Moreover, the enrichment rate is constrained by the amount of gas into which the new metals will be diluted. Nevertheless, it is interesting to see whether the AMR we have found in Paper I is consistent with the SFH derived from the same sample, especially because, to our knowledge, this was never tried before.

From the basic chemical evolution equations (Tinsley 1980), for a closed box model (i.e., no infall), the link between the AMR and the SFH can be written as


where [FORMULA] gives the AMR, expressed by absolute metallicity, [FORMULA] is the SFH as in Eq. (1), and [FORMULA] is the total gas mass of the system, in units of [FORMULA] pc-2.

According to this equation, bursts in the SFH are echoed through an increase of the metal-enrichment rate. Certainly, this is particularly true when the metallicity is measured by an element produced mostly in type II supernovae, like O. The gas mass can dilute more or less the enrichment, changing the proportionality between it and the SFH, at each age, but will not destroy the relationship. On the other hand, the intrinsic metallicity dispersion of the interstellar medium can certainly somewhat obscure this proportionality, especially if it were as big as the AMR by Edvardsson et al. (1993, hereafter Edv93) suggests.

In Fig. 16, we show a comparison between the metal-enrichment rate (top panel) with the SFH (bottom panel). The enrichment rate increases substantially in the last 2 Gyr, which could be a suggestion for a recent burst of SFH. However, the agreement between both functions seems very poor. There is a peculiar bump in the enrichment rate between 4 and 6 Gyr, which is coeval to a feature in the SFH, but most probably this is mere coincidence.

[FIGURE] Fig. 16. Comparison between the metal-enrichment rate (defined as the derivate in time of the AMR, expressed by absolute metallicity Z), and the SFH. On theoretical grounds both quantities should be correlated, and it should give a test to the reliability of the SFH. In practice, the magnitude of the errors in both functions still hinders the application of this test.

Although we have used iron as a metallicity indicator, which invalidates Eq. (11), due to non recycling effects, we are not sure whether the situation would be improved by using O. The errors in both the AMR and SFH are still big enough to render such a comparison extremely uncertain. However, it can be a test to be done with improved data. The more important result for chemical evolution studies is that, provided that we know accurately both functions, the empirical AMR and SFH will allow an estimate of the variation of the gas mass with time, which could lead to an estimate of the evolution of the infall rate. Future studies should attempt to explore this tool.

5.2. Scale length of the SFH

The stars in our sample are all presently situated within a small volume of about 100 pc radius around the Sun. The star formation history derived from these stars is nevertheless applicable to a quite wide section of the Galactic disk, since the stars which are presently in the Solar neighbourhood have mostly arrived at their present positions from a torus in the disk concentric with the Solar circle.

We have investigated how wide this section of disk is by integrating the equations of motion for 361 stars of the `kinematic sample' (see Paper I) within a model of the Galactic potential. The potential consists of a thin exponential disk, a spherical bulge and a dark halo, and is described in detail in Flynn et al. (1996). For each star we determine the orbit by numerical integration, and measure the peri- and apogalactic distances, [FORMULA] and [FORMULA] and the mean Galactocentric radius, [FORMULA] for the orbit (cf. Edvardsson et al. 1993).

The distribution of [FORMULA] is shown in Fig. 17. Most of the stellar orbits have mean Galactocentric radii within 2 kpc of the Sun (here taken to be at [FORMULA] kpc), i.e. [FORMULA] kpc. Very few stars in the sample are presently moving along orbits with mean radii beyond these limits.

[FIGURE] Fig. 17. The histogram presents the mean galactocentric radius for the orbits of 361 stars presently located near the Sun. According to Binney & Sellwood (2000), these mean galactocentric radii indicate with good confidence the stellar birthplace radii. This shows that the SFH here derived is not a local history, but the average history over a significant part of the Milky Way disk.

As discussed by Wielen, Fuchs and Dettbarn (1996), due to irregularities in the Galactic potential caused by (for example) giant molecular clouds and spiral arms, the present mean Galactocentric radius of a stellar orbit [FORMULA] at time t does not bear a simple relationship to the mean Galactocentric radius of the orbit on which the star was born [FORMULA]. Wielen, Fuchs and Dettbarn describe the process by which stars are scattered by these irregularities as orbital diffusion, and show that over time scales of several Gyr, that one cannot reconstruct from [FORMULA] the radius at which any particular star was born to better than a few kpc. This is of the same order as the width of the distribution of [FORMULA] seen in Fig. 17. We therefore conclude that our stars fairly represent the star formation history within a few kpc of the present Solar radius, [FORMULA], or the "middle distance" regions of the Galactic disc. The SFH of the inner-disk/bulge, and the outer disk are not sampled.

However, Binney & Sellwood (2000) have criticized this conclusion. They show that during the lifetime of a star, the guiding-center of its orbit can change generally by no more than 5%. In this scenario, the value of [FORMULA] that we have calculated is close to the galactocentric radius of the star birthplace, and our star formation history would still be representative of a considerable fraction of the galactic disk, [FORMULA].

Another important conclusion of kinematic studies it that the older is a feature in the SFH, the more damped it is recovered from the data, related to its original amplitude (see, for example, Meusinger 1991b), since the stars formed by the burst will be scattered through a larger region. Hence, the younger bursts in our SFH are the most local features. This does not mean that they are most probably `local irregularities'. In time scales of 1-2 Gyr, the diffusion of stellar orbits homogenize any irregularities in the azimutal direction, so that the bursts would apply to the whole solar galactocentric annulus.

5.3. The Galaxy and the Magellanic Clouds

When evidences for an intermittent SFH in the Galaxy were first discovered, Scalo (1987) proposed that they could have originated from interactions between the Galaxy and the Magellanic Clouds. Indeed, the Magellanic Clouds are known to have probably experienced some episodes of strong star formation for a long time. Butcher (1977) first proposed that the bulk of star formation in the Large Magellanic Cloud (LMC) has occurred from 3-5 Gyr ago, by the analysis of the luminosity function of field stars. Stryker et al. (1981) and Stryker (1983) subsequently confirmed this result. In the last few years, additional studies have arrived almost at the same conclusions (Bertelli et al. 1992; Vallenari et al. 1996a,b). Westerlund (1990) also remarked that the star formation in the LMC seems to have been very small from 0.7 to 2 Gyr ago. A very recent burst of star formation (around 150 Myr ago) was also found by the MACHO team (Alcock et al. 1999) from the study of the period distribution of 1800 LMC cepheids. Their analysis present compeling arguments favouring this hypothesis, as well as for the propagation of the star formation to neighbour regions.

However, these results have more recently been questioned, on the basis of colour-magnitude diagram synthesis. Some authors claim that important information on the SFH are provided by the part of the colour-magnitude diagram below the turnoff-mass, which could only be resolved with the most recent observations (Holtzman et al. 1999, 1997, and references therein; Olsen 1999). These papers conclude that star formation in the LMC has been a continuous process over much of its lifetime.

Note that continuity in the SFH does not means constancy . Holtzman et al. (1997) points that their method cannot constrain accurately the burstiness of the SFH in the LMC on small time scales, particularly for ages greater than 4 Gyr. Nevertheless, they show evidence for an increase in the star formation rate in the last 2.5 Gyr. Dolphin (2000) arrives to the same conclusion studying two different fields of the LMC, separated by around 2 kpc one from the other. The author recognizes that some large environment alteration must have triggered an era of star formation in our neighbour galaxy.

In spite of the controversy, it is impossible not to verify that some results on the SFH of the LMC are in apparently synchronism with some SFH events in the Milky Way disk. But this should be not really surprising. The Magellanic Clouds are satellites of our Galaxy, and past interactions between them were a rule, not an exception. Byrd & Howard (1992) showed that a companion satellite, whose mass is larger than 1% of the primary galaxy, could excite large-scale tidal arms in the disk of the primary, and we know that spiral arms do induce, or at least organize, star formation. This number is to be compared with the mass ratio between our Galaxy and the Clouds which is 0.20 (Byrd et al. 1994). Besides direct tidal effects, the Clouds can produce a dynamical wake in the halo that distorts the disk (Weinberg 1999). It is quite possible that such an effect could also enhance the star formation in the disk (M. Weinberg, private communication).

Additional evidence comes from dynamical studies of the Magellanic Clouds. Several groups have worked on the derivation of their orbits around the Galaxy. The full orbit of the Magellanic Clouds are still unknown, but there is some agreement in the published works. The most important is that all of these works conclude that the most recent close encounter between the Clouds and the Milky Way has occurred 0.2-0.5 Gyr ago, which was the closest encounter through the entire history of the system (however, Holtzman et al. 1997mention an unpublished work by Zhao in which the last perigalacticon occurred 2.5 Gyr ago). Murai & Fujimoto (1980) calculated that other close encounters have occurred 1.5, 2.6 and 7.5 Gyr ago. Gardiner et al. (1994) revisited Murai & Fujimoto (1980)'s model and recalculated the epochs of the close encounters as around 1.6, 3.4, 5.5, 7.6 and 10 Gyr ago. However, Lin et al. (1995) have found different values: 2.6, 5.3, 8.4 and 11.8 Gyr ago.

From these results we can tentatively assume that, in the last 12 Gyr, the Clouds have had at most six close encounters with the Milky Way occurring more or less at 0.2-0.5, 1.4-1.5, 2.6-3.4, 5.3-5.5, 7.5-8.4 and 10-11.8 Gyr ago. Some of these encounters are not predicted by all the authors, while some are in good agreement. For the sake of simplicity, we will refer to these encounters as I, II, III, IV, V and VI, respectively.

There are similarities between the time of close encounters and the events of our derived SFH. In Fig. 18 we show the epoch of these encounters superimposed over our SFH. We can associate burst A with encounter I, peak B1 with encounter III, and peak C1 with encounter V. It is not unlikely that peak B2 could also be associated with encounter IV. On the other hand, encounter VI probably cannot be responsible for any of the features found beyond 9 Gyr, since it occurs in an age range where the SFH is highly uncertain and subject to random fluctuations.

[FIGURE] Fig. 18. Star formation history compared with the times of close encounters between the Galaxy and the Magellanic Clouds.

A significant exception to the rule is encounter II. It is thought to have happened in the middle of the AB gap. It seems strange to think that a close encounter between interacting galaxies could suppress the star formation. Other mechanism should be responsible for the gap. On the other hand, Lin et al. (1995) have not found such an encounter. In fact, these authors predict that by this time, the Clouds would be located in their apogalacticon, more than 100 kpc away.

Although the comparison is very premature, we conclude that the data on the age distribution and orbits of the Magellanic Clouds present some agreement with the Miky Way SFH. Have the bursts of star formation in the Milky Way been produced by interaction with its satellite galaxies? The comparison above certainly points to this possibility, that deserves more investigations to be properly answered, since there is still much uncertainty in the Magellanic Clouds close encounters, as well as on the chronologic scale of the chromospheric ages.

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© European Southern Observatory (ESO) 2000

Online publication: June 20, 2000