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Cusps and Cores in the presence of galactic bulges

In this paper, we study how the presence of bulge formation in galaxies influence their inner density profile, by means of an extended version of the Del Popolo (2009) semi-analytical model. As in Del Popolo (2009), the model takes into account the effect of baryons adiabatic contraction, ordered and random angular momentum, dynamical friction, and adds to the previous the effect of gas cooling, star formation, supernova feedback, and reionization. Our model shows that dwarf galaxies are bulgeless, in agreement with observations showing that the large majority of them has no stellar bulges, and are characterized by a flat profile well described by a Burkert profile. {We then studied the effect of a bulge, added to the {cored} DM halo, on the density profile}. In the case of a galaxy having a mass $10^{11} M_{\odot}$ the inner density profile has a slope $α\simeq 0.65$, for a bulge of $4.5 \times 10^{9} M_{\odot}$, while if bulge formation is not considered, the slope would be $α\simeq 0.55$. If the bulge is larger, $6.5 \times 10^{9} M_{\odot}$ the slope is $α\simeq 0.7$. In the case of a larger galaxy with $10^{12} M_{\odot}$ the slope is $α\simeq 0.85$, while in absence of bulge it is $α\simeq 0.75$. We finally study how the inner slope $α$ changes with the bulge mass, and we find a correlation among the two quantities. The result shows that bulge formation has an important role in shaping the inner DM density profile in agreement with Inoue & Saitoh (2011) result. The result implies that going from Sc to SO Hubble type the slope is slightly steepening due to the bulge formation, and due to the fact that early type galaxies have larger bulges.