Transient Spiral Waves in Disk Galaxies by J A Sellwood

1
Transient Spiral Wavesin Disk Galaxiesby J A
Sellwood
2
Sellwood Carlberg (1984)
3
Transient Spiral Wavesin Disk Galaxiesby J A
Sellwood

• Easy to observe in N-body simulations
• But what causes them?
• Does it work the same way in nature?
• Mixture of evidence from real data and simulations

4
Indirect evidence for transients

• Age-velocity dispersion relation
• Geneva-Copenhagen survey (Nordström et al 2004)
• scattering by GMCs inadequate (L84, L91)
• heating by transient spirals (CS86)
• hint of evolution in velocity ellipsoid shape
  (IKM93)

5
Indirect evidence for transients

• Age-velocity dispersion relation
• Metallicity spread of stars in the solar
  neighbourhood (EA93)
• spirals cause radial mixing of stars (SB02)
• also must drive large-scale turbulence in gas

6
Indirect evidence for transients

• Age-velocity dispersion relation
• Metallicity spread of stars in the solar
  neighbourhood
• Importance of dissipation (gas)
• if spiral activity is to continue (SC84)

7
A linearly stable disk

• Mestel disk ? ? 1/r, Vc const
• Toomre Zang introduced central cutout and an
  outer taper in active density
• both replaced by rigid mass
• Carried through a global stability analysis of
  warm disks with a smooth DF
• confirmed by N-body simulation (SE01)
• Halve the active mass, in order to suppress a
  lop-sided instability, and set Q1.5
• They proved this disk is globally stable

8
Simulations of the ½-mass Mestel disk

• m2 spiral analysis
• upper tight leading
• lower tight trailing
• 50K ? N ? 500M
• No steady rise for the largest N
• confirms stability
• Otherwise saturation amplitude is independent of
  N
• Characteristic of true instabilities
• Non-linear feedback?

9
No single coherent wave

• Several separate frequencies as the amplitude
  rises i.e. not a single mode

10
Groove modes

• Any sharp feature in the DF is destabilizing
• Groove yields a vigorous mode (SK91)
• enthusiastic support from the surrounding disk
• Amplitude limited by onset of horseshoe orbits at
  corotation (SB02)

11
Angular Momentumand Resonances

• Lindblad diagram for a logarithmic potential
• slope of all vectors ?p
• Wave action absorbed at LRs ? scattering
• Lines show loci of resonances for eccentric orbits

12
Pick out one wave

• Coherent frequency for significant time
• Best fit shape
• peak near corotation
• extends to LRs
• But it decays
• CR peak disperses
• wave action drains to LRs

13
Scattering at ILR

• Particle distribution after wave decays
• No free parameters!
• solid lines are LRs
• dashed lines scattering trajectories
• Large Erand because ILR particles stay on
  resonance

14
Recurrent cycle?

• Each coherent wave leaves behind a damaged DF
• Apparently creating the conditions for a new
  instability
• Exactly how this works is still unclear
• maybe just a horrible artifact of the
  simulations!
• Can I find evidence that anything similar occurs
  in nature?

15
Geneva-Copenhagen survey(Nordström et al. 2004)

• Known distances, full space motions and ages of
  13,240 local F G dwarfs

• DF not at all smooth (DB98)
• Not dissolved clusters (FP06)
• Hard to interpret the structure in velocity space

16
Project into integral space

• Scaled by R0 and V0 assuming a locally flat RC
• Lower boundary selection effect
• L-R bias asymmetric drift
• Look at features
• adjust ?p ? slide L-R
• Scattering or trapping?

scattering trajectories dot-dash LRs dotted
CR dashed
17
Bootstrap analysis

• Assuming scattering at
• ILR (above) real data are highly significant
  (confidence gtgt 99) at one frequency
• or OLR (below) nothing really credible
• But it could also be trapping at any resonance

18
Phases of these stars

• Action-angle variables
• radius shows ?( 2 ? radial action)
• azimuth is 2w? wr
• Concentration of stars at one phase
• No other simple combination of phases does this
• Exactly the stars (red) I identified before

19
Implications

• Evidence for an ILR is strong
• What the heck is an inner LR doing out here?
  (AT) notwithstanding!
• Support for the picture I have been developing
  from the simulations
• spirals are transient
• decay of one pattern seeds the growth of another
• each is true instability of a non-smooth DF
• Needs more work

20
Conclusions

• Simulations display recurrent transient spirals
• result may even be right!
• each wave is a true instability of a non-smooth
  DF
• mechanism for recurrence yet to be understood
• gravitationally driven turbulence
• Seems to be what is going on in solar
  neighbourhood and perhaps elsewhere
• strong evidence for a recent ILR in the local
  Geneva-Copenhagen survey data
• three strands of supporting evidence for
  transients