bars, disks and halos j a sellwood photometric decomposition dynamical friction
TRANSCRIPT
Bars, Disks and HalosJ A Sellwood
• Photometric decomposition
• Dynamical Friction
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
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
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
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)
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
Frictional torque
• Tremaine & Weinberg – classic paper
• 2 non-zero actions in a spherical potential: L ≡ Jφ and Jr
• and two separate frequencies: Ω and κ
• Bar perturbation rotates at Ωp
• LBK torque (m∂f/ ∂L + k ∂f/ ∂Jr)Φmnk2
/(n Ω + k κ – m Ωp)
• notice the resonant denominator
Same orbit in rotating frames
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
Ωs (Ω Ωp) Ωp
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
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
Corotation resonance
• Large changes in F – Negative slope implies an excess of gainers over losers
friction
– but resonance keeps moving as Ωp declines
• OLR dominates if the bar is unreasonably fast
• Minor changes at ILR when the bar is very slow
Suppose Ωp 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
• Ωp declines slowly because of friction at other resonances
• Normal friction resumes when the slope of F at the main resonance changes
Valenzuela & Klypin• Pattern speed in their
simulation rose causing friction to stop for a while
• Ωp 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
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
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