1. Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

2. What fraction of light is in a bar? Does fraction vary with luminosity, early-late types, etc.? –Important if we are to understand the origin of bars Many people have tried to be quantitative –bar-interbar contrast (Elmegreens) –Fourier analysis (Ohta) –bar ellipticity (Martin) –gravitational torque (Buta et al.) –bar axis ratio (Abraham & Merrifield) –etc. All measure something useful –but not easy to convert to light fraction

3. New approach Generalization of Barnes & S Least-squares fitting of components Assume –1) disk is round and flat, fixed i and  –2) bar is straight and elliptical with a diff  and  both components have arbitrary intensity profiles non-parametric –3) spheroidal Sersic bulge, disk i and 

4. Work by Adam Reese I-band images Still in progress –About 60 galaxies –magnitude limited sample –known redshifts Method works 14/45 (so far) seem to have no bar at all

5. Preliminary Results For those with bars –bar light fraction has a broad spread around 20% –varies from 1% to 43% Fits are too new to say much else Most bars are not elliptical –need a better shape Apply to larger samples –possibly MGC survey of Liske & Allen (but near IR would be better)

6. Bar-halo friction A bar rotating in a halo loses angular momentum through dynamical friction Important for 2 reasons: –Offers a constraint on the density of the DM halo (Debattista & S) –May flatten the density cusp (Weinberg & Katz) Both have been challenged –Realistic bars in cuspy halos produce mild density changes at most –Valenzuela & Klypin claim little friction on a bar in a dense halo

7. Frictional torque Tremaine & Weinberg – classic paper 2 non-zero actions in a spherical potential: L ≡ J φ and J r and two separate frequencies: Ω and κ Bar perturbation rotates at Ω p LBK torque  (m∂f/ ∂L + k ∂f/ ∂J r )  Φ mnk  2 /(n Ω + k κ – m Ω p ) notice the resonant denominator

8. Same orbit in rotating frames

9. Resonances The unperturbed orbit can be regarded as a closed figure that precesses at the rate Ω = Ω + k κ / m The orbit is close to a resonance when Ω s  (Ω  Ω p )  Ω p where the “fast action” is conserved and the “slow action” can suffer a large change Orbits are highly eccentric, so resonances are not localized spatially

10. What happens in simulations? Restricted method: –rigid bar + test particle halo At some time, t=800 say –Compute Ω = Ω + k κ / m for every particle –Find F  density of particles as a function Ω and plot against L for a circular orbit –Find that corotation (m = 2, k = 0) is the most important resonance

11. Corotation resonance Large changes in F –Negative slope implies an excess of gainers over losers  friction –but resonance keeps moving as Ω p declines OLR dominates if the bar is unreasonably fast Minor changes at ILR when the bar is very slow

12. Suppose Ω p rises Resonance can move to the other side of the hump Gradient then adverse for friction –balance between gainers and losers soon established Bar can rotate in a dense halo with little friction – “metastable” state Ω p declines slowly because of friction at other resonances Normal friction resumes when the slope of F at the main resonance changes

13. Valenzuela & Klypin Pattern speed in their simulation rose causing friction to stop for a while Ω p can rise because – an interaction between the bar and a spiral in the disk (rare), or –gravity becomes stronger when the grid is refined Their anomalous result is an artifact of their adaptive code

14. Metastable state is fragile 1% mass satellite flew by at 30kpc (dashed curve) Minor kick to the bar (dotted curve) Unlikely to survive in nature

15. Conclusions Dynamical friction dominated by a single resonance at most times Corotation is most important for a realistic bar Gradients in phase space density usually favorable for friction If the pattern speed rises, gradient may change and friction cease for a while “Metastable” state is fragile Absence of friction in VK03 now clearly an artifact of their code Conclusion of Debattista & S still stands: –A strong bar in a dense halo will quickly become unacceptably slow through dynamical friction