Dynamics of Galaxies Bars & AGN fueling

1. Dynamics of GalaxiesBars & AGN fueling Françoise Combes Observatoire de Paris

2. Barred Galaxies The majority of galaxies are barred (2/3) About 1/3 have strong bars SB, and 1/3 intermediate (SAB) Bars are also a way to generate Grand design spiral structure Environmnt Type Stochastic Global Percentage SA 15 7 32% Isolated SAB 7 16 70% SB 4 11 73% SA 3 4 57% Binaries SAB 1 16 94% SB 1 11 92% SA 15 32 68% Group SAB 21 38 64% SB 12 45 79%

3. N2442 N613 N3351 N5850

4. Spiral Galaxies should be viewed as accretion disks • Galaxies disks in perpetual evolution/ reformation • Tend to concentrate mass (tend to a least energy state) • Gravity is the principal engine • But rotation prevents mass to concentrate more •  Angular momentum should flow away • Energy dissipation (gas) reduces random motions, but viscous • torques insufficient • Formation of spirals and bars to get rid of angular momentum

5. Bar Formation Bars are density waves, and can be considered as the combination of leading & trailing wave paquets They are more stationnary than spirals (no torque, if purely stellar) quasi mode The first numerical N-body simulations (Hohl 1971, Miller et al 1970) do not show spirals, but only bars robust over a Hubble time, since only made of stars, dissipationless

6. Orbits in a barred potential Bisymmetric m=2 (Fourier component) In the rotating frame, at the bar pattern speed Ωb Φ eq = Φ (r, θ, z) - Ωb2 r2/2 Integral of motion (Jacobian) Energy in this referential frame: EJ = v2/2 + Φ (r, θ, z) - Ωb2 r2/2 Lz not conserved of course, since potential is non-axisymmetric  torques

7. Shape of the equivalent potential, in the rotating frame Bar parallel to Ox Lagrange points: stationnary points L4 & L5 maxima, L1 & L2 saddle points (max in x, min in y) Around corotation The orbits have been computed precisely (cf Contopoulos & Papayannopoulos 1980)

8. Orbit families The periodic orbits are the squeleton; they attract and trap all other orbits (except chaotic orbits) (1) Very near the centre, orbits are // bar, family x1 (there exists also retrograde orbits x4, low population) (2) Between the two ILR, if they exist, are the orbits of family x2, perpendicular to the bar, direct and stable (also x3 unstable) x2 disappears if the bar strength is too large (ILR suppressed) (3) between ILR and corotation, again family x1, // bar with secondary lobes (4) at CR, around L4 and L5, stable orbits (5) after CR, again orbits change orientation (quasi circular, however)

9. When getting near CR, resonances of higher level Families x1 et x2 After corotation Contopoulos & Papayannopoulos 1980

10. Obvioulsy x1 orbits support the bar, while X2 orbits weaken it, and can even destroy it Auto-regulation The presence of ILR triggers the processus The orbits no longer support the Bar, beyond corotation A bar ends in general at a radius just inner its corotation  excellent diagnostic to determine Ωb

11. N-body simulations: bars Analytic calculations, based on density wave theory WKB  tightly wound waves At the opposite of bars! Surprise of the 1st numerical simulations (1970) Self-gravity, collective effects, interactions in N2 N = 1011 Clues: fast Fourier Transforms FFT The potential is the convolution of 1/r by the density At each dt, one computes the TF of the density, then multiplies in Fourier space, the FT(1/r) and the FT(ρ) ==> inverse FT Softening 1/(r2 + a2), to avoid 2-body relaxation  gives an idea of the spatial resolution

12. Methods: Tree-code Approx: monopole + quadrupole, according opening criterion Advantage: no grid Variable resolution Barnes & Hut (83)

13. Methods: collisions or SPH For gas hydrodynamics, the essential is a weak dissipation Collisions between particules ("sticky-particules") or finite differences (fluid code) Or variable spatial resolution: SPH "Smoothed Particules Hydrodynamics" (Lucy & Monaghan 77) Principle: kernel function(or weight W( r )) with a variable size, which contains a fixed number of neighbors Density is computed by averaging over neigbors (30-50) And all other quantities & derivatives similarly

14. Technique SPH convolution With W( r ) normalised to 1, and finite support Evaluation of all quantity: Or derivative Symmetrisation of pressure terms

15. Bar formation stars gas

16. Total time: 1.2 Gyr Formation of rings at resonances

17. Formation of a bar

18. Bar pattern speed • The bar pattern speed is such that the bar radius < corotation • During its growth, the bar slows down • The transient stellar spiral arms take away angular momentum • The bar grows, the orbits are more elongated • The equivalent precession is lower This neglects the dynamical friction effects on the halo Debattista & Sellwood (1999) Since bars are rotating fast, the centre of galaxies is not dominated by DM

19. Vertical profile: peanuts Resonance in z (Combes & Sanders 81 Combes et al 90) The bar in the vertical direction always develops a "peanut" after a few Gyr Box shape in the other orientation

20. NGC 128 The peanut galaxy COBE, DIRBE Milky Way

21. Peanut bulge formation

22. Periodic orbits in 3D: Lindblad resonance in z explains the formation of peanuts

23. Gas response to a bar potential The gas tends to follow the periodic orbits But gas orbits cannot cross, because of collisions, dissipation  the gas response rotates gradually at each resonance spirals

24. Sanders & Huntley 1976 The number of windings of the spiral is related To the number of resonances According to the nature of the gas, its response changes in morphology Schock waves, if fluid gas Athanassoula 1992 bar at 45° The presence of resonances ILR ==> orbits x2  shocks

25. Torques exerted by the bar on the gas Torques change sign at each resonance, and can be deduced by simple geometrical arguments The gas inside corotation loses its angular momentum and inflows Outside CR, on the contrary the gas accumulates at the OLR

26. Formation of rings Ωb = 16km/s/kpc Ωb = 13km/s/kpc Ωb = 10km/s/kpc ILR Combes & Gerin 1985 Formation of an outer ring at OLR Schwarz, 1981

27. N1433 N3081 N6300 Formation of rings at resonances (Schwarz 1984) Give an idea of Vsound low viscosity Gravity torques from the bar Change sign At each resonance  Relative equilibrium Buta & Combes 2000

28. Phenomenon observed since a long time, but explained since a few years Nuclear bars NGC 4314 NGC 5850 Erwin 2004 Contours + B-V colors

29. NGC 5728 DSS +CFH Adaptive Optics NIR Embedded bars can form, like russian dolls Here a nuclear bar (at right, field of 36") inside the primary bar (at left, field of 108"). Note the star above the nuclear bar, giving the scale The secondary bar rotates faster than the primary (Combes et al. 2001).

30. NGC4314 Star formation in the ring around the nuclear bar The nuclear bars are mainly visibles in NIR, not perturbed By extinction

31. Decoupling of nuclear bars The natural evolution of a barred disk, with gas Accumulation of mass towards the centre, gravity torques Formation of 2 Lindblad resonances, that weaken the bar The rotation curve (Ω) rises more and more in the centre, and also the precession rate of elongated orbits (Ω - κ/2) The central matter can no longer follow the rest of the disk decoupling To avoid the chaos, there is a common resonance between the 2 bars primary & secondary Ex: CR of the 2nd = ILR of the primary

32. Friedli & Martinet 93 Respective positions of the ring and the bar Formation of a secondary bar In the N-body + gas simulations

33. Secondary bars Stars Gas t N body + SPH (D. Friedli)

34. Bars and double bars

35. Angular velocities compared for the 2 bars Non linear coupling between two waves Ω= ω/m Maintenance by exchange of energy? ω1, ω2 Product ξ1ξ2* with V grad V Or ρ grad Φ, etc… Beating mb = m1 + m2 ωb = ω1+ ω2

36. Amplitude spectrum for the mode m=2 (Masset & Tagger 97) 2 Ω- κ versus r Gives the location of resonance Lindblad ILR 2 Ω- κ versus r OLR at t=8 Gyr Spectrum m=4 The curves 4 Ω- κ versus r 4 Ω+ κ Beating wave m=4 Obtained at the right frequency ωb + ωs 31.8 + 13.9 =45.7 km/s/kpc

37. density potential Bar and spiral at different speeds (Sellwood & Sparke 1988)

38. All stars with small epicycles CR DL OLR ILR Migrations of stars and gas Resonant scattering at resonances Sellwood & Binney 2002

39. DL exchange without heating Invariant: the Jacobian EJ= E- Wp L  DE = WpDL DJR = (Wp-W)/kDL If steady spiral, exchange at resonance only In fact, spiral waves are transient The orbits which are almost circular will be preferentially scattered Sellwood & Binney 2002

40. Chemical evolution with migration O/H, and O/Fe Thick disk is both a-enriched and low Z Churning = Change in L, without heating Blurring= Increase of epicyclic amplitude, through heating Gas contributes to churning, and is also radially driven inwards Shoenrich & Binney 2009

41. Transfert of L, and migrations Bars and spirals can tranfer L at Corotation Transfer multiplied if several patterns with resonances in common Much accelerated migrations Bar Spiral Minchev & Famaey 2010

42. Effect of coupled patterns Time evolution of the L transfer with bar and 4-arm spiral, in the MW Top: spiral CR at the Sun Bottom: near 4:1 ILR Minchev et al 2010

43. Migration extent Time evolution of the L transfer with bar and 4-arm spiral Explains absence of AMR Age Metallicity Relation +AVR relation Initial position of stars ending in the green interval after 15 and 30 Rotations Black: almost circular s = 5km/s Minchev et al 2010

44. Bar+spiral migrations Overlap of resonances Minchev et al 2010

45. Active nuclei fueling Bars are the way to drive the gas towards the centre To fuel starbursts, but also AGN Yet, in a first step, matter is trapped in resonant rings at ILR The secondary bar allows to go farther, and takes over What are the orbits inside the secondary bar ? Nuclear spiral? Third bar? How many resonances?

46. Periodic orbits in a potential in cos 2θ The gas tends to follow these orbits, but rotates gradually by 90° at each resonance A) without BH, leading B) with BH, trailing

47. Destruction of bars Bars self-destroy, by driving mass towards the centre (gas) With a central concentration of mass (concentrated nuclear disk, black hole) Less and less regular x1 orbits, more and more chaotic orbits, deflection due to the central mass Evolution: destruction of periodic orbits, if rapid evolution And radial shift of resonances Creation of "lenses", diffusion of chaotic orbits limited only by their energy in the rotating frame Φ( r ) -1/2 Ω2 r2 Outside corotation: no more limit (abrupt boundary)

48. Fraction of phase space occupied by x1 orbits supporting the bar Surfaces of section for a BH of 3% in mass for a particule of max distance a) 0.25 a b) 0.65a a = size of the bar

49. Surfaces of section for the orbits in the plane of the galaxy, for various energies (y, dy/dt) at the crossing point of Oy, with dx/dt > 0 The invariant curves of the X1 families disappear at H~-0.3 Hasan et al (1993)

50. Formation of lenses, and of "ansae" During the destruction of the bar The first orbits to become chaotic are between ILR and CR Near the central black hole, the potential becomes axisymmetric and regular The lenses in galaxies can be detected by their radial profile, characteristic and steep (Kormendy 1982)