Comparison of bar formation mechanisms I: does a tidally-induced bar rotate slower than an internally-induced bar?

Galactic bars can form via the internal bar instability or external tidal perturbations by other galaxies. We systematically compare the properties of bars formed through the two mechanisms with a series of controlled $N$-body simulations that form bars through internal or external mechanisms. We create three disk galaxy models with different dynamical ``hotness'' and evolve them in isolation and under flyby interactions. In the cold and warm disk models, where bars can form spontaneously in isolation, tidally-induced bars are promoted to a more ``advanced'' evolutionary stage. However, these bars have similar pattern speeds to those formed spontaneously within the same disk. Bars formed from both mechanisms have similar distributions in pattern speed--bar strength ($\Omega_p-A_2$) space and exhibit comparable ratios of co-rotation radius to bar length (${\cal R}={R_{\mathrm {CR}}}/{R_{\mathrm {bar}}}$). Dynamical analyses suggest that the inner stellar disk loses the same amount of angular momentum, irrespective of the presence or intensity of the perturbation, which possibly explains the resemblance between tidally and spontaneously formed bars. In the hot disk model, which avoids the internal bar instability in isolation, a bar forms only under perturbations and rotates more slowly than those in the cold and warm disks. Thus, if ``tidally-induced bars'' refer exclusively to those in galaxies that are otherwise stable against bar instability, they indeed rotate slower than internally-induced ones. However, the pattern speed difference is due to the difference in the internal properties of the bar host galaxies, not the different formation mechanisms.