• PHYSICAL PROBLEM: How bars form in galaxies, what is their role in the galaxy evolution, and in the active galaxy nucleus (AGN) and supermassive central black holes

 
• OBSERVATIONS: Barred galaxies (with AGN, or Seyfert), showing rings.

 
• EQUATIONS: Newton's equations for N "particles" (clouds and stars) in their own gravitational field, with inelastic collisions for the gas, and no collisions for stars

 
• NUMERICAL EXPERIMENTS: integration of the equations during a dozen rotations of the "galaxy" starting from a quasi-homogeneous axisymmetric disk

 
• CONCLUSION: Bars form by gravitational instability of the galactic disk. The gas plays an essential rôle, because it forms again and again the spiral arms. The action of the bar on the spiral arms gives rise to gas transfer towards the center, and to the formation of rings at Lindblad's resonances. Bars play a central role in feeding the massive black holes in the galaxy cores.

 
• REFERENCE: Bar-driven Galaxy Evolution and Time-scales to Feed AGN, F. Combes, in "Galaxy Dynamics: from the Early Universe to the Present", ASP Conf Series, ed. F. Combes, G. Mamon, V. Charmandaris

The FILM (mpg, 65 Mb; gif, 5,1 Mb) shows separately stars LEFT and gas RIGHT.

It shows how, starting from an initially relatively homogeneous state (flat disk with axial symmetry), the gaz clouds and stars moving along their orbits generate instabilitiess which lead to spiral arms.

Stars form only transient spirals, because instabilities heat them, which stops the instability.

The bar in the center is robust however (there is no gravitational couple from the bar on itself, because the potential is in phase with the density, which is not the case of the spiral arms).

The gas is dissipative, cools and is always unstable, so it forms spirals again and again.

Lindblad's resonance (ring formation) is the same as the one which gives rise to Saturn's rings. The resonance occurs between the movements of the stars (or of the clouds) and that of the perturbation (bar or spiral): when the frequencies are in a rational ratio.

There are in general two arms in a galaxy, so the relevant resonances are: Omega_b = Omega-kappa/2 et externe Omega_b=Omega+kappa/2
(Omega is the frequency of the star's rotation, Omega_b is the frequency of rotation of the bar, kappa: epicyclic frequency)