Paper detail

Intrinsic properties of the bars formed by the bar instability in flat stellar discs

The properties of the bars formed by the bar instability are examined for flat stellar discs. The initial mass models chosen are Kuzmin--Toomre discs, for which two types of exact equilibrium distribution function (DF) are employed in order to realize different distributions of Toomre's $Q$ values along the radius. First, the most linearly unstable, global two-armed modes (MLUGTAMs) of these disc models are determined by numerically solving the linearized collisionless Boltzmann equation. Next, we carry out $N$-body simulations whose models are constructed from the DFs adopted above. The latter simulations unravel that the MLUGTAMs corresponding to those obtained from the former modal calculations are excited in the early phases of evolution, finally being deformed into bars in the nonlinear regime by the bar instability. We show that for simulated bars, the length increases and the axis ratio, in essence, decreases as the amplitude increases. These correlations are almost similar to those of the observed bars. In addition, we find that these bar properties are tightly correlated with the initial typical $Q$ value, irrespective of the DF. In conclusion, a disc with a smaller typical $Q$ value produces a bar which is smaller in amplitude, shorter in length and rounder in shape. This finding might suggest that the Hubble sequence for barred galaxies is the sequence of decreasing $Q$ from SBa to SBc or SBd. The implied correlations between the initial typical $Q$ value and each of the bar properties are discussed on the basis of the characteristics of the MLUGTAMs.