bars, disks and halos j a sellwood photometric decomposition dynamical friction

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

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

Bars, Disks and HalosJ A Sellwood

• Photometric decomposition

• Dynamical Friction

Page 2: Bars, Disks and Halos J 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

Page 3: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 4: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 5: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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)

Page 6: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 7: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 8: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

Same orbit in rotating frames

Page 9: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 10: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 11: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 12: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 13: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 14: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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

Page 15: Bars, Disks and Halos J A Sellwood Photometric decomposition Dynamical Friction

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