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We show by numerical simulations that a purely stellar dynamical modelcomposed of an exponential disc, a cuspy bulge, and an NFW halo with parametersrelevant to the Milky Way Galaxy is subject to bar formation. Taking intoaccount the finite disc thickness, the bar formation can be explained by theusual bar instability, in spite of the presence of an inner Lindblad resonance,that is believed to damp any global modes. The effect of replacing the livehalo and bulge by a fixed external axisymmetric potential (rigid models) isstudied. It is shown that while the e-folding time of bar instability increasessignificantly (from 250 to 500 Myr), the bar pattern speed remains almost thesame. For the latter, our average value of 55 km/s/kpc agrees with theassumption that the Hercules stream in the solar neighbourhood is an imprint ofthe bar--disc interaction at the outer Lindblad resonance of the bar. Verticalaveraging of the radial force in the central disc region comparable to thecharacteristic scale length allows us to reproduce the bar pattern speed andthe growth rate of the rigid models, using normal mode analysis of linearperturbation theory in a razor thin disc. The strong increase of the e-foldingtime with decreasing disc mass predicted by the mode analysis suggests thatbars in galaxies similar to the Milky Way have formed only recently.

On the bar formation mechanism in galaxies with cuspy bulges