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Astron. Astrophys. 355, 929-948 (2000)

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7. Summary and conclusions

From the results of static chemical models, PC99 underlined the need to introduce radial flows to explain some features of the Galactic Disc. In fact, static models are unable to reproduce, at the same time, both the metallicity gradient and the radial gas profile; in particular, the peak corresponding to the molecular ring at 4-6 kpc is likely to be a consequence of gas drifts induced by the dynamical influence of the Galactic Bar. Therefore, in the present paper we introduced a new chemical model including radial gas flows, developed as a multi-dimensional generalization of the original static model (Sect. 3). Our model is conceived so as to adapt to any imposed radial velocity profile, describing both inflows and outflows in any part of the disc. The model is carefully tested against instability problems and spatial resolution, by comparing it to suitable exact analytical cases (Appendix B). In this paper we applied the model to the Galactic Disc; more in general, such models allowing for gas drifts are meant to be used as fast and handy interfaces between detailed dynamical galaxy models (predicting the velocity profiles) and parametric chemical and spectro-photometric models.

An overview of the behaviour of chemical models with radial inflows of gas shows that these provide an alternative "dynamical" assumption to the inside-out disc formation scenario to explain the metallicity gradient (Sect. 4). With radial gas flows, the model can reproduce the metallicity gradient even in the case of a Schmidt or an Oort-type SF law, which were excluded in the case of static models (see PC99). In addition, it appears that even low radial flow velocities, well within observational limits and theoretical expectations (see Sect. 2), have non-negligible effects upon model predictions on the metallicity gradient and moreover on the gas distribution. In particular, if radial gas inflows are allowed for, a metallicity gradient can coexist with a high gas fraction in the inner regions, at odds with simple static models. This is indispensable to reproduce the observed gas distribution in the inner Galaxy (see point 2 below). The remarkable effects of even slow radial flows upon observable quantities, mainly upon the gas distribution, should be kept in mind as a caveat when comparing real galaxies to simple analytical models which predict a one-to-one relationship between metallicity and gas fraction (e.g. Tinsley 1980). Our models show that small dynamical effects, like slow gas flows, can easily make real systems depart from the behaviour of simple models.

With our model it is possible to mimic the dynamical influence of the Galactic Bar and reproduce the peak in the gas distribution around 4 kpc (Sect. 6). Two scenarios, related to two different models for the structure of the Bar, are qualitatively suggested.

  • A. With a Schmidt or an Oort-type SF law, slow radial inflows in the disc pile up gas inward down to [FORMULA] kpc. Here, the Bar CR radius is found and the gas is quickly swept inward from CR toward an ILR, which causes the drop in the gas profile at 3.5 kpc.

  • B. With a SF law like that by Dopita & Ryder (1994), smaller inflow rates suffice to reproduce the metallicity gradient, leading to a lower concentration of gas in the inner regions than in the previous case. The peak corresponding to the molecular ring can be reproduced with a Bar CR around 2.5 kpc and its OLR around 4.5 kpc, so that all the gas external to [FORMULA] kpc tends to pile up around the OLR.

Though these models are just qualitative and cannot describe the detailed dynamical process of Bar formation nor the evolution of the related gas flows to form the molecular ring, they provide two interesting indications.

  1. Only when introducing the effects of the Bar, the model is able to reproduce the radial gas profile properly. The only possible exception resides in a particular combination of an Oort-type SF law with a radial inflow pattern whose velocity decreases inward (model O10RFe); this combination may lead to a peak of the gas distribution in the inner Galactic regions, closed to the observed molecular ring. But this particular, fortunate case does not diminish the general conclusions about the role of the Galactic Bar.

  2. In any case (A or B above), overall radial inflows in the disc are indispensable to replenish the inner regions with enough gas that the observed molecular ring can form under the influence of the Bar. This seems to favour disc models with radial inflows, unless one assumes that the gas in the ring has some different origin (gas swept from the Bulge, or accreted later).

To investigate these issues any further, detailed gas-dynamical models are obviously required. Unfortunately, most studies on Bar-induced gas dynamics (see references in Sect. 6) concentrate on the observed features of the very inner regions, such as the nuclear ring, the 3 kpc expanding arm, and so forth. Little discussion can be found about the effects of the Bar on more external regions, and on the formation of the molecular ring in particular: whether it is due to gas depletion inside CR as in our case A, or due to gas accumulation at some resonance (e.g. Binney et al. 1991, Fux 1999) as in our case B, or whether it just consists of two or more tightly wound spiral arms (e.g. Englmaier & Gerhard 1999). Further gas-dynamical studies suggesting detailed scenarios, time-scales, and velocity profiles for the formation of the molecular ring would be welcome, for the sake of including the effects of the Bar in chemical evolution models more consistently.

Further investigation of gas-dynamical models on the influence of the Bar on even larger scales (namely, outside its OLR) should be pursued as well, since this is a clue issue related to a claimed discrepancy between the characteristics of the Galactic Bar and the observed metallicity gradient. It is well known that barred galaxies display systematically shallower gradients than ordinary spirals (e.g. Alloin et al. 1981, Vila-Costas & Edmunds 1992, Martin & Roy 1994). This is likely a consequence of the radial mixing induced by bars; in fact, Martin & Roy (1994) found a correlation for external galaxies between the strength of a bar and the metallicity gradient. Taking this empirical relation at face value, the Galactic Bar with an axial ratio of [FORMULA] should induce a metallicity gradient of -0.03 dex/kpc, much shallower than the observed one of -0.07 dex/kpc, which is typical of a normal Sbc galaxy. To overcome such a puzzle, it has been suggested that the Galactic Bar must be very young ([FORMULA]1 Gyr), so that there was not enough time yet to flatten the gradient (Gummersbach et al. 1998); but this is in conflict with other estimates of the Bar's age (e.g. Sevenster 1997, 1999). Alternatively, we suggest that the discrepancy might be only apparent, since the Galactic Bar is quite small, and the Milky Way cannot be properly considered a barred spiral. It might be unlikely that the Bar can influence the metallicity gradient all over the Disc, as in really barred galaxies: Bar-induced radial drifts and corresponding chemical mixing are expected to occur from CR toward the ILR (inflows) and to the OLR (outflows; e.g. Schwarz 1981, 1984; Friedli et al. 1994). Present understanding of the Galactic Bar sets its OLR between 4.5 and 6 kpc (Sect. 6 and references therein), so in our models we presumed that the Bar induces negligible mixing beyond these radii, regardless of its age (see also Gerhard 1999). If the situation is as in the models we presented here, in fact, the metallicity gradient in the outer regions is unperturbed and just related to intrinsic Disc properties and/or large-scale viscous flows.

However, gas-dynamical simulations dedicated to the effects of the Galactic Bar over the whole Disc would be necessary, so as to investigate the relation between the Bar, radial mixing and the metallicity gradient more consistently. More in general, including the effects of bar-induced radial flows in the picture of the chemical evolution of spiral galaxies might turn out to be of wide interest, since it is likely that all spirals develop at some point, or have developed in the past, some bar-like structure (Binney 1995). Infrared observations indeed reveal that a large fraction of spirals host a barred structure (e.g. Eskridge et al. 1999), and recent numerical simulations suggest that even weak bars or oval distortions may be able to induce radial drifts to form multiple gaseous rings at the corresponding Lindblad resonances (Jungwiert & Palou 1996). Bars could even drive secular evolution of spiral discs from late to early type (e.g. Dutil & Roy 1999). Bar-driven radial gas flows might therefore play a fundamental role in the chemical evolution of spiral discs.

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Online publication: March 21, 2000
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