Bar Formation and Evolution in N-Body Simulations

The main idea here is to verify whether or not the current scenario for bar formation (i.e., the global dynamical disk instability) is able to account for the observed bars in galaxies as early-type as lenticulars (S0s). This scenario possibly may not hold in these cases, since we know it to be effective only in dynamically cool stellar systems, which is not the case for S0s. Moreover, the absence of gas, as well as the prominent central bulge in this type of galaxy, certainly make the disks of these galaxies less unstable to the bar mode instability. The following animations are a representative sample of those simulations I performed in my Ph.D. thesis to tackle this issue.

All experiments were performed within the NEMO package with the widely used tree code for the force calculation. They contain around ~ 105 particles each and a softening parameter epsilon of 0.05. Energy is conserved to better than ~ 0.3%, typically. The disks are isothermal with an exponential mass density profile, while bulges are described by a Plummer sphere. The halos are rigid and described by a logarithmic potential. The parameters which constrain each of these components were chosen as to simulate real galaxies with different morphological types. Each simulation runs for ~ 2 Gyr.

In each animation you'll find three frames. One corresponds to a face-on view while the others are edge-on views.

Bars form naturally in pure stellar disks!

Which are also dynamically cool. This is what shows this simulation (exp14) which may be considered a realization of a very late-type (Sd) spiral galaxy. This is exactly the disk global dynamical instability, which is now our best answer to the question of how bars develop in galaxies.

But bulges stabilize disks against bar formation! (This was written before Lia Athanassoula changed the way we see the interaction between bulges and haloes with bars.)

However, when we want to mimic a galaxy with a bulge (even if it is not a big one!), it gets harder to see a bar develop, as you can see here (exp9).

A solution is to force an unstable disk . . .

We can account for the existence of barred galaxies as early-type as Sa/Sb if we consider disks with Toomre parameters Q as low as 0.5, as I did in this experiment (exp18).

How can we develop bars in S0s ? ? ?

If we tackle the problem of explaining the existence of barred S0s, then the disk instability seems not to work anymore. The prominent bulge and the hot dynamics of these stellar systems render the common answer useless... I was only able to develop a bar in a S0 galaxy by unrealistically lowering the Q parameter to 0.25 and raising the softening parameter to 0.25 (exp34).

One alternate solution: eccentric halos.

What if the dark matter halos are not spherical? Indeed, we have reasons to believe that many halos have a non negligible eccentricity and some may be very eccentric, reaching an axis ratio of ~ 2-3. The dynamical influence of such an outer structure will certainly affect the orbits of stars in the inner galaxy. When they accommodate themselves in the potential of the halo we can find a structure which very much resembles a bar. Such a process can be seen in this simulation (plum12). Thus, eccentric halos may be a possible explanation  for the existence of bars in stellar systems as dynamically hot as SO galaxies.