Boxy/Peanut/X-Shaped Bulges: Steep Inner Rotation Curve Leads to Barlens Face-on Morphology

We use stellar dynamical bulge/disk/halo simulations to study whether barlenses (lens-like structures embedded in the narrow bar component) are only the face-on counterparts of Boxy/Peanut/X-shapes (B/P/X) seen in edge-on bars, or if some additional physical parameter affects that morphology. A range of bulge-to-disk mass and size ratios are explored: our nominal parameters (B/D = 0.08, r(eff)/h(r) = 0.07, disk comprising. two-thirds of total force at 2.2h(r)) correspond to typical Milky Way mass galaxies. In all models, a bar with pronounced B/P/X forms in a few Gyr, visible. in the edge-on view. However, the pure barlens morphology forms only in models with sufficiently steep inner rotation curves, dV(cir)/dr greater than or similar to 5V(max)/h(r), achieved when including a small classical bulge with B/D greater than or similar to 0.02 and r(eff)/h(r) less than or similar to 0.1. For shallower slopes, the central structure still resembles a barlens, but shows a clear X signature even in low inclinations. A similar result holds for bulge-less simulations, where the central slope is modified by changing the halo concentration. The predicted sensitivity on the inner rotation curve is consistent with the slopes that are estimated from gravitational potentials calculated from the 3.6 mu m images, for the observed barlens and X-shaped galaxies in the Spitzer Survey of Stellar Structure in Galaxies (S(4)G). For inclinations <60 degrees the galaxies with barlenses have on average twice steeper inner rotation curves than galaxies with X shapes: the limiting slope is similar to 250 km s(-1) kpc(-1). Among barred galaxies, those with barlenses have both the strongest bars and the largest relative excess of inner surface density, both in barlens regions (less than or similar to 0.5h(r)) and near the center (less than or similar to 0.1h(r)); this provides evidence for bar-driven secular evolution in galaxies.