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Disc-like bulges form from inflow of (mainly) gas material to the centre of the galaxy and subsequent star formation. This inflow is due to the torques exerted by a non-axisymmetric component, usually a large-scale bar, as witnessed in hydrodynamic simulations (e.g. Athanassoula 1992; Friedli & Benz 1993; Heller & Shlosman 1994; Wada & Habe 1995). The high density of the gas accumulated in the inner regions triggers very strong star formation. Such inflow, however, is also seen in N-body simulations (AM02; Valenzuela & Klypin 2003), which represent the old stellar population. Thus, this inner region is not only a region of increased density for the gas and the young stars, but also for the older stellar populations. This should lead to the formation of an inner, central component of disc-like shape, whose extent is of the order of a kpc and which is constituted mainly of gas and young stars, but also of older stars. This was named disc-like bulge, or, for short, discy bulge in A05 and is often observed in disc galaxies. Due to its disc-like shape, it often has spirals or inner bars (KK04 and references therein). It stands out very clearly in radial photometric profiles, whose decomposition shows it is well represented by a Sérsic law (Sérsic 1968). Contrary to classical bulges, however, it does not swell out of the galactic plane. This is not the only difference between disc-like and classical bulges. Disc-like bulges have a Sérsic index of the order of 1, i.e. much smaller than the values found for classical bulges (KK04 and references therein). They also have different kinematics, like that of discs, a higher fraction of young stars and a higher gas content. A lot of data on such bulges has been collected over the last few years, but still much work, particularly theoretical, is necessary before we fully understand these objects.

In order to describe adequately the formation and evolution of disc-like bulges, simulations should include gas, star formation and feedback, all in a realistic way. It would, furthermore, be preferable if they started from cosmological or cosmologically-motivated initial conditions, since the properties of pre-existing discs may influence the properties of the disc-like bulges. I will briefly describe here results from simulations following this outline (Athanassoula, Heller & Shlosman, in preparation). For information on the numerical techniques used in these simulations and an initial discussion of some of the results see Heller, Shlosman & Athanassoula (2007a) and (2007b).

Several non-axisymmetric components - such as a triaxial halo, oval disc, inner and outer bar - form during these simulations. Their interactions give very interesting dynamical phenomena (Heller et al. 2007a; b), while they induce considerable inflow and gaseous high density inner discs. As in the sketchy outline in the beginning of this section, the high gas concentration in the central area triggers considerable star formation, resulting in a disc-like central, high-density object, which, seen face-on, is often somewhat oval. It has many properties similar to those of discy-bulges. For example, it has, in many cases, sub-structures, like an inner bar. In order to further assess the properties of the disc galaxy formed in these simulations and to better establish the link with disc-like bulges, I chose a characteristic specific snapshot, i.e. a characteristic specific simulation and time, and examine its mass distribution in order to compare best with the observed light distribution in galaxies. An analysis of the kinematics, together with a statistical treatment, including other times and other simulations, will be given elsewhere. The radial projected surface density profile of the snapshot under consideration is given in Fig. 4, together with a fit by an exponential disc and a Sérsic component. Note that the fit is excellent, all the way to the outer parts of the disc, roughly at 10 kpc. In this example, the disc scale-length is ~ 2.7 kpc, i.e. very realistic, while the Sérsic index is ~ 1, in good agreement with observed discy bulges.

Figure 4a Figure 4b

Figure 4. Properties of a simulated disc-like bulge. Left : Radial projected density profile in arbitrary units. Radii are measured in kpc. The dots give the simulation results and the straight line the fit by an exponential disc and a Sérsic component. Right : Measure of the vertical height of the material near the equatorial plane (see text), as a function of radius, measured in kpc.

Fig. 5 shows the snapshot seen edge-on. The three outer isodensity curves show clearly that the shape and aspect ratio of the disc component is very realistic. The two innermost contours (within 1 kpc) reveal the existence of a small, central, disc-like object, the vertical height of which we need to quantify. Measuring the average thickness would not be useful, since this is due to both the external big disc and the small inner component, so I proceeded differently. I divided the `stars' in the snapshot into circular annuli, according to their distance from the centre and, in each annulus, sorted them as a function of their distance from the equatorial plane (|z|). Since, statistically, the `stars' in the disc-like inner component will have smaller |z| values than the ones in the outer disc, I plot in Fig. 4 the |z| component of the `star' with rank 0.3Nan, where Nan is the total number of `stars' in the annulus. This shows a deep minimum in the central region, as one would expect due to the existence of an inner disc with a shorter vertical extent than the outer one. It also shows that the region where the inner disc is contributing significantly is of the order of 1 kpc, in good agreement with the radial density profile (Fig. 4). Finally, the aspect ratio of the inner and the outer discs are similar.

Figure 5

Figure 5. Edge-on view of the stellar component of the simulation with a disc and a disc-like bulge. The projected density is given by grey-scale and also by five isocontours whose level is picked so as to show best the features under consideration.

To summarise, in our fiducial simulation, as well as in several others, we witness inflow of mainly gas material to the central regions and strong subsequent star formation. Thus, an inner disc is formed, composed of both stars and gas. Its radial extent is of the order of a kpc and its vertical extent much smaller than that of the outer disc. This disc can harbour spiral structure, or an inner bar. Its contribution to the radial projected density profile is well fitted by a Sérsic law with Sérsic index ~ 1. It is thus very likely that this simulation describes correctly the formation of discy-like bulges in galaxies.

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