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

4. Effects of radial inflows on the disc

After presenting our new model with radial flows, we investigate their general effects on the chemical evolution of the disc. Here we first analyse how the predicted metallicity gradient and gas and total surface density profiles of a static model are altered by a superimposed uniform gas inflow, while in Sect. 5 we will suitably combine radial flows with various SF laws to match the observed radial profile of the Disc. The characteristics and parameters of the various models presented in this and in the next section are summarized in Table 1.

Table 1. Parameter values and resulting metallicity gradients for models S15RF , O10RF and DRRF

To gain a qualitative understanding of the effects of radial gas inflows on chemical evolution, we impose a uniform inflow pattern  km sec^-1 upon a static chemical model and compare the new outcome with the original static case. Radial flows over the disc are expected to be mainly inflows, with velocities from 0.1 to 1 km sec^-1 (see Sect. 2); imposing a uniform inflow of 1 km sec^-1 is therefore a sort of "extreme case", considered here for the sake of qualitative analysis. Anyways, previous studies in literature suggest that the effects of radial flows saturate for much higher velocities (Köppen 1994). We will consider both the case of inflow from the outer gaseous disc and not ( or 0, respectively).

All models with radial flows are rescaled so that the final surface density at the Solar ring ( kpc) corresponds to 50  pc^-2. Namely, with radial flows and it cannot be imposed as an input datum (see Sect. 3), but the zero-point of the exponential accretion profile (3)

can be rescaled so that at the end of the simulation   pc^-2. This zero-point does not influence the profile, nor the chemical evolution, so it can always be rescaled a posteriori .

For our example, we take as the reference static case a model adopting a Schmidt SF law with (Kennicutt 1998) and a uniform infall time-scale of 3 Gyr (model S15a of PC99, see also Table 1).

4.1. Models with inflow from the outer disc

In model S15RFa a uniform radial inflow pattern with  km sec^-1 and inflow from the outer disc is imposed upon the static model S15a , with no further change in the model parameters (Table 1). Fig. 2 shows the effects of inflow on the total surface density and gas density distribution, and on the oxygen gradient (details on the observational data in the plots can be found in PC99). By comparing the solid line and the dashed line, we notice the following main effects.

• Since matter flows inward and accumulates toward the Galactic Centre, the density profile gets steeper in the inner parts, while in the outer parts it remains rather flat because gas is continuously poured in by the flat outer gaseous disc. The gas density distribution shows a similar behaviour.

• The overall metallicity gets much lower because of the dilution by primordial gas inflowing from the outer disc. The gradient becomes steeper, especially in the outermost shells, since the discontinuity in metallicity between the star-forming disc and the outer gaseous layer is smeared inward by radial inflows.

Fig. 2. Left panels : final profiles of the total surface density from models S15RF with inflow from the outer disc, in linear (upper panel) or logarithmic (lower panel) plot; the reference observed profile of models with scale length 4 kpc, as adopted in models with no flows (PC99), is shown as a thick solid line. Upper right panel : radial gas density profiles compared to the observed one. Lower right panel : predicted radial metallicity profiles compared to the observational data (data and symbols as in PC99).

To compensate for the steepening of the density distribution induced by radial inflows, we must adopt a shallower initial accretion profile; our simulations show that a scale length  kpc for the infall profile reduces in the end to a density profile matching the desired scale length of 4 kpc at the Solar Neighbourhood. At the same time, the chemical enrichment must get more efficient for the overall metallicity to increase to the observed levels; the predicted metallicity is improved by adopting an IMF more weighted towards massive stars, i.e. by increasing the "IMF scaling fraction" (see PCB98 and PC99 for a description of our model parameters). Together with the SF efficiency , is re-calibrated to match the observed gas surface density and metallicity at the Solar Neighbourhood (as for the models of PC99). In this way we calibrate model S15RFb with respect to the Solar Neighbourhood; see Table 1 for details on the adopted parameters. Comparing now this re-calibrated model with radial flows (dotted line) to the original model S15a , the metallicity gradient is increased with respect to the static case, but still a bit flat with respect to observations. The gas density distribution peaks in the inner regions, as expected, and remains quite high (much higher than observed) in the outer regions due to substantial replenishment from the outer disc.

4.2. Models with no inflow from the outer disc

Let us now consider the case when radial flows are limited within the star forming disc and there is no inflow from the external gaseous disc (). If radial flows are mainly driven by shocks in spiral arms, for instance, they might indeed occur only within the stellar disc, while the outer gas layer remains unperturbed.

Fig. 3 (left panels) shows how the final density profile becomes much steeper than the reference accretion profile (model S15RFc , dashed line), as expected since matter is efficiently drifting inward with no replenishment from the outer disc. For the final density profile to match the observed one, we must assume a much shallower initial accretion profile ( kpc). Then the resulting local density profile is close to the observed one, while in the outer parts the profile remains steeper (model S15RFd , dotted line).

Fig. 3. Same as Fig. 2, but for models S15RF with no inflow from the outer disc edge.

The gas density profile shows a similar behaviour, strongly peaked toward the centre while dropping quickly (much more quickly than observed) outside the Solar ring (upper right panel).

The overall metallicity is reduced with respect to the original model S15a (lower right panel, model S15RFc) and again we need to increase the IMF scaling fraction to raise the chemical enrichment to the observed values (model S15RFd). The resulting gradient is roughly comparable to the observed one.

4.3. Concluding remarks

We can summarize the general effects of radial flows as follows.

• Since matter flows inward and accumulates toward the Galactic Centre, the density profile in the inner parts gets steeper. A shallower intrinsic accretion profile is to be adopted, in order to recover the observed local scale-length at the end of the simulation.

• In the outer parts, the profile declines more or less sharply, depending on whether the inflow occurs only within the star-forming disc or there is also substantial inflow from the outer, purely gaseous disc.

• The gas distribution shows a similar behaviour: it remains quite flat in the outer regions if gas is poured in by the flat outer gas disc, while it tends to drop sharply (more than observed) otherwise.

• The inner gas profile is very steep in the case of a Schmidt SF law (models S15RF) - while with other SF laws with radially decaying efficiency (see PC99 and Sect. 5) the effect would be somewhat compensated by a larger gas consumption by SF in the inner regions.

• The overall metallicity gets much lower because of the dilution by gas inflowing from metal poor outer shells (and possibly the primordial outer disc). A higher fraction of stars contributing to the chemical enrichment is needed in the model to match the observed metallicity.

• The metallicity gradient tends to steepen, in agreement with results by other authors (see references in Sect. 2).

© European Southern Observatory (ESO) 2000

Online publication: March 21, 2000
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