Pattern Speed and Galaxy Morphology

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Pattern Speed and Galaxy Morphology

• Ron Buta
• University of Alabama

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The diversity of galaxy morphology.
De Vaucouleurs sketch circa 1962
To what extent does it depend on pattern speed(s)?
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Many factors can influence the morphology of a
given galaxy, such as - gas content - frequency
of past interactions/mergers - basic state
characteristics (star/gas surface densities,
velocity dispersion, rotation curve) - strength
of internal perturbations and secular evolution -
rotation rate of patterns etc
Pattern speed is just one factor influencing
morphology! However, it is not arbitrary but
should come with the mode that spontaneously
arises out of the basic state.
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Pattern speed is relevant to galaxy morphology
because it - determines the location of all
resonances, and resonances can limit the extent
of patterns (e.g., Contopoulos 1980) and
influence angular momentum transfer to the outer
regions (Lynden-Bell Kalnajs 1972 Athanassoula
2003) - affects the properties of periodic
orbits, which can affect the morphology of
features such as rings (Contopoulos 1979 Buta
Combes 1996) - determines rate at which bars and
spirals influence galaxy evolution (Zhang 1996,
1998, 1999 Zimmer et al. 2004). - can determine
the lifetime of a pattern (Merrifield et al.
2006).
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Density wave theory led to discussions of the
role of pattern speed on spiral
structure. Roberts, Roberts, and Shu 1975 the
value of Omega_p should affect the radial extent
of three tracers 1. The prominent spiral
structure 2. The easily visible disk 3. The
distribution of HII regions These result because
pattern speed and the rotation curve determine
the speed at which stars and gas clouds encounter
the pattern.
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To understand connections between pattern speed
and morphology, one can - directly measure
pattern speeds or resonance locations and connect
observed features to resonances - compare
sequences of numerical simulations with actual
galaxies, either through generic modeling or
modeling of a specific galaxy
Garcia-Burillo et al. 1993 modeling of M51 The
gas response is very sensitive to pattern
speed we obtain a spiral structure similar to
what is observed only for a narrow range of
Omega_p.
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Rings are believed to be direct tracers of the
pattern speed.
Buta Combes 1996 Rings are a precious tool to
measure the pattern speed, when the rotation
curve is known. Examine models of ringed
galaxies to see how pattern speed might affect
what we see.
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• Types of models (or interpretations)
• test particles, analytic, rigidly rotating bars
  (e.g., Schwarz 1981 Byrd et al 1994)
• Similar, but bar potential from near-IR image
  (e.g., Salo et al. 1999)
• N-body allowing multiple modes, plus gas test
  particles (e.g., Rautiainen Salo 2000)
• Hydrodynamical (e.g., Lindblad et al. 1996 L.-H.
  Lin, C. Yuan, et al. 2008)
• Invariant manifolds around equilibrium points of
  barred galaxy (Romero-Gomez et al. 2006, rR1
  rings)
• Deceased 24 August 2008

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R1
R1R2
R2
These simulated patterns were discovered in high
pattern speed models by Schwarz 1981. CR and OLR
are the main resonances. The outer spirals extend
to the OLR.
UGC 12646
ESO 577-3
ESO 509-98
The outer spirals of these galaxies show
similarities to the above models. R1, R1R2, and
R2 are called OLR subclasses.
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Do some galaxies wear their resonances like
crowns
Background-disk-subtracted B-band image of NGC
3081 can you eyeball corotation in this galaxy?
OLR orbits
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This low pattern speed model from Simkin, Su, and
Schwarz 1980 shows how inner and nuclear rings
might develop when the inner resonances (ILR,
I/41)exist.
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IC 5240
NGC 7098
NGC 6782
NGC 1433
The alignment between these inner rings and their
bars depends on pattern speed. If the
ring/spirals did not share the same pattern speed
with the bar, misalignment would likely be the
rule.
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high
medium
Sequences of simulations for different pattern
speeds of a barred galaxy, from Byrd et al. 1994.
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Low pattern speed simulations from Byrd et al.
1994.
Use the Catalogue of Southern Ringed Galaxies
(CSRG, Buta 1995) to evaluate these simulations.
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Pattern speed domains (Byrd et al. 1994) could
these really exist?
ILR Omega_pOmega-kappa/2 I/41
Omega_pOmega-kappa/4 OLR Omega_pOmegakappa/2
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Comparison of Byrd et al. (1994) high pattern
speed models with observed (CSRG) deprojected
galaxies. Models have CR and OLR only.
Omega_b0.27
NGC 3358
ESO 509-98
These galaxies lack inner and nuclear rings.
Could this mean they lack the required resonances?
Omega_b0.22
ESO 365-35
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Omega_b0.10
ESO 575-47
ESO 426-2
ESO 577-3
Medium pattern speed models of Byrd et al. 1994
compared with observed galaxies. The models have
an inner 41 resonance as well as OLR and CR.
The three galaxies all have red nuclei, which
could imply the lack of an ILR.
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Omega_b0.06
ESO 437-67
ESO 325-28
Low pattern speed sequence having OLR, inner 41,
CR, and barely an ILR. The two galaxies have blue
nuclei. Does this imply that they have an ILR?
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At Omega_b0.05 in the Byrd et al. 1994 models,
x1 orbits in the vicinity of ILR produce a highly
elongated ring inside the bar. Is this the nature
of the feature, seen in NGC 6012?
NGC 6012
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NGC 1566
This frame in the lowest pattern speed
(Omega_b0.03) Byrd et al 1994 sequence shows
some features that might explain galaxies like
NGC 1566 where a bright spiral dominates an
extended oval zone, from which the faint arms of
an R1 outer pseudoring emerge.
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The Rautiainen and Salo (2000) models focused on
the impact of Toomre Q-parameter and the
background stellar components. Frames showed the
response of gas test particles to an n-body bar.
Evolution of a misaligned bar-ring model. The
reason for the misalignment is that the spiral is
a slower mode than the bar.
Evidence for multiple pattern speeds in a single
galaxy?
ESO 565-11 - a misaligned bar/inner ring galaxy
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ESO 566-24
Comparison between a four-armed barred galaxy
model (Rautiainen et al. 2004) and a very rare
but real symmetric m4 barred spiral. The
pattern is confined between the inner and outer
41 resonances. Bar potential from near-IR image.
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Sticky-particle models of NGC 1433, type
(R1)SB(r )ab, for different pattern speeds
(Treuthardt et al. 2008). The appearance of the
secondary arcs is sensitive to pattern speed. Bar
potential from near-IR image.
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CR is far from the ends of the bar in a
hydrodynamical model of NGC 6782 by L.H. Lin et
al. (2008). This galaxy is also an rR1 example,
but the R1 does not reach OLR in this model.
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Strong, two-armed logarithmic spiral modes extend
to the inner 41 resonance
N-body model from Patsis Kaufmann 1999
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The Potential-Density Phase-Shift Method for
Locating Corotation Radii
Xiaolei Zhang and Ron Buta
A method that uses the expected phase difference
between the density and the potential implied by
that density to locate corotation radii in
galaxies. The method was conceived by Zhang
(1996, 1998, 1999) and first applied to real
galaxies by Zhang and Buta (2007).
Zhang 1996, ApJ, 457, 125 Zhang 1998, ApJ, 499,
93 Zhang 1999, ApJ, 518, 613 Zhang Buta, 2007,
AJ, 133, 2584
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The density spiral is ahead of the potential
spiral inside CR and behind outside CR. This
leads to a positive to negative phase difference
crossing at CR which can be inferred using
near-IR images.
The torque applied by the spiral potential on the
disk density in an annulus at r is
density spiral
potential Spiral
where ?is the disk surface density, V is the
disk potential, m is the number of arms, ?1 is
spiral density perturbation amplitude, V1 is
spiral potential perturbation amplitude, L is the
angular momentum in the annulus, ?0 is the
potential/density phase-shift.
rco
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• Physical basis of method
• -global self-consistency requirement of wave
  modes
• -working assumption spontaneously-formed density
  wave patterns that have reached a quasi-steady
  state
• corotations are positive-to- negative crossings
  in phase-shift versus radius
• negative-to-positive crossings show extent of
  modes

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Phase-shift analysis of NGC 1530 - Ks-band image
A case of a bar-driven spiral? This means the
bar and spiral are corotating and are likely to
have emerged from the same global mode. Another
pattern may be decoupling from the bar at r4kpc.
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Ks-band Image of NGC 613
The phase-shift plot suggests decoupling of the
bar from the spiral is in progress.
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Ks-band image of NGC 175
In this case, the bar and the spiral are likely
fully decoupled and may have different pattern
speeds.
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Ks-band Image of NGC 1300
Not a case of a bar-driven spiral? Inner part of
bar has CR halfway out in bar radius. Bar mode
ends at the green circle which is the strong
negative-to-positive crossing near r/ro(25)0.5,
where ro(25)Do/2 half the extinction-corrected
isophotal diameter from RC3.
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Do phase-shift distributions for ringed galaxies
provide any support to the implications from
test-particle and other numerical models?
NGC 1350, type (R1)SAB(r )ab - CR of main oval
could support OLR interpretation of R1.
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NGC 1433, type (R1)SB(r )ab
Treuthardt et al. 2008 sticky particle model
resonances I/41, CR, O/41, R1 not OLR!
Rautiainen Salo 1999 CR-I/41 coupling
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UGC 12646, type (R1)SB(r )ab with dimpled R1.
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In this grand-design spiral, the phase-shift
method places the main CR in the middle of the
pattern.
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What does the phase-shift method have to say
about fast and slow bars? Debattista
Sellwood 2000 r(CR)/r(bar)lt1.4 fast bars,
gt1.4slow bars
lt---1.4
Phase-shift corotation radius to bar radius for
100 OSUBGS galaxies versus RC3 stage index. Over
all types, ltr(CR)/r(bar)gt1.17 /-0.36. Bar radii
are from Laurikainen et al. 2004. Sbc and earlier
(Tlt4) have fast bars on average, Sc and later
(Tgt4) have slow bars on average.
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How well do phase-shift CR radii agree with
values from other methods?
Comparison of bar CR radii from phase-shift
method with CR radii determined from the
numerical simulation method (Rautiainen et al.
2005).
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• Conclusions
• - numerical simulations can shed a lot of light
  on the way pattern speed affects morphology.
• - different pattern speed domains may exist
• the phase-shift method suggests that multiple
  pattern speeds are common in spiral and barred
  galaxies.
• Both bar-driven and non-bar-driven spirals are
  detected,

I thank Drs. X. Zhang, E.Laurikainen, and H. Salo
for their input in this work. This work was also
supported by NSF grant AST050-7140.