Alice Quillen

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Sculpting Galactic Disks

• Alice Quillen
• University of Rochester
• Department of
• Physics and Astronomy

May, 2005
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MotivationThe Galactic Disk

• The Milky Way has only rotated about 40 times (at
  the Suns Galacto-centric radius).
• ? No time for relaxation!
• Structure in the motions of the stars can reveal
  clues about the evolution and formation of the
  disk.
• Little is known about the shape of the Galaxy disk

Coma Berenices group
Stellar velocity distribution Dehnen 98

• We can study our Galaxy star by star.
• Prospect of radial velocity, proper motion,
  spectroscopic surveys of hundreds of millions of
  Galactic stars.

Sirius group
Pleiades group
Tangential velocity
Hercules stream
Hyades stream
Radial velocity
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Low Perturbation Strengths

• Spiral arms give a tangential force perturbation
  that is only 5 of the axisymmetric component.
  Resonances allow a strong affect in only a few
  rotation periods
• Jupiter is the Mass of the Sun
• ? resonant effects or long timescales
  (secular) required

Outline of Talk

• Resonances in the Solar neighborhood
• Explaining moving groups
• Chaos in the Solar neighborhood due to resonance
  overlap
• Resonant trapping models for peanut shaped bulges
• Structure in circumstellar disks
• Disk Edges, CoKuTau/4
• Spiral arms HD141569A, HD100546

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The amplitude of a pendulum will increase if
resonantly forced
The planet goes around the sun J
times. The asteroid goes around K
times. JK mean motion resonance Perturbat
ions add up only if they are in phase. Even small
perturbations can add up over a long period of
time.
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The Galactic Disk Interpreting the U,V plane

Orbit described by a guiding radius and an
epicyclic amplitude
Coma Berenices group
u -radial velocity?
Stellar velocity distribution Dehnen 98
On the (u,v) plane the epicyclic amplitude is set
by a2u2/2v2 The guiding or mean radius is set
by v
v tangential velocity ?
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Orbits associated with Lindblad resonances from
a bar or spiral mode
Location of Lindblad resonances is determined
from the mean angular rotation rate ? by the
guiding or mean radius. On the (u,v) plane, as v
changes, we expect to cross Lindblad resonances
Closer to corotation
Figure from Fux (2001)
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Simple Hamiltonian systems
Harmonic oscillator
I
?
p
q
Stable fixed point Libration Oscillation
Pendulum
p
Separatrix
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Different pattern speeds 2-armed log spirals
The effect of different spiral waves on the local
velocity distribution
Weighting by the distance from closed orbits ---
similar to making a surface of section but this
provides a weight on the u,v plane. Structure set
primarily by v
Different angle offsets w.r.t the Sun
V?
U?
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Each region on the u,v plane corresponds to a
different family of closed/periodic orbits
Near the 41 Lindblad resonance. Orbits excited
by resonances can cross into the solar
neighborhood
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A model consistent with Galactic structure
Explains structure in the u,v plane
Coma Berenices
Pleiades group
Hyades group
Pleiades/Hyades moving groups support the spiral
arms. Coma Berenices stars are out of phase.
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A model consistent with Galactic structure
Explains structure in the u,v plane
Two dominant stellar arms consistent with
COBE/DIRBE model by Drimmel Spergel
(2001) Excites a 4 armed response locally We are
at the 41 Inner Lindblad resonance This is a
second order perturbation
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Disk heating andother consequences
Kink in shape of spiral arms predicted Flocculent
structure past Sun In between resonances, the
possibility of heating Oorts constant and V_LSR
mismeasured
Nearing corotation ?
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Epicyclic motion
Zeroth order axi-symmetric Hamiltonian
Higher order terms
For discussion on action angle variables
Contopoulos 1979, Dehnen 1999, and Lynden-Bell
(1979)
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Adding a perturbation from a bar or spiral arm
Perturbation to gravitational potential
Expand and take the dominant term
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Hamiltonian including a perturbation
This is time independent, and is
conserved.
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In phase space Bar Mode
Closed orbits correspond to fixed points

• Outside OLR only one type of closed orbit.
• Inside OLR two types of closed orbits

Increasing radius
BAR
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In phase space Spiral-Mode
Closed orbits correspond to fixed points

• Inside ILR only one type of closed orbit.
• Outside ILR two types of closed orbits

Increasing radius
Spiral arm supporting
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An additional perturbation can cause chaotic
dynamics near a separatrix
No separatrix Bifurcation of fixed point A
separatrix exists
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Analogy to the forced pendulum
Strength of first perturbation
Strength of second perturbation
Controls center of first resonance and depends on
radius
Controls spacing between resonances and also
depends on radius
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Spiral structure at the BARs Outer Lindblad
Resonance

• Oscillating primarily with spiral structure
• Perpendicular to spiral structure
• Oscillating primarily with the bar
• Perpendicular to the bar

Poincare map used to look at stability. Plot
every Orbits are either oscillating with both
perturbations or are chaotic? heating.
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Barred galaxies when seen edge-on display
boxy/peanut shaped bulges
Boxy/peanut bulge

• Bureau et al. (1997) found that all boxy/peanut
  shaped bulges had evidence of non-circular orbits
  in their spectra.
• No counter-examples of
• barred galaxies lacking boxy/peanut shaped bulges
  
• non-barred galaxies displaying boxy/peanut
  shaped bulges.

NGC 5746
From Bureau and Freeman 1997, PASA
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Previous Boxy/Peanut bulge formation mechanisms

• Galaxy accretion (Binney Petrou 1985)
• Bar buckling (e.g., Raha et al 1991) also known
  as the fire-hose instability.
• Diffusion about orbits associated with the 221
  resonance (banana shaped orbit families) (e.g.,
  Pfenniger Friedli 1992, Combes et al. 1991)

NGC 7582 1.6 µm
Young bar
From Quillen et al. 1995
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A resonant trapping mechanismfor lifting stars
Resulting Hamiltonian model
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Vertical resonances with a bar
Orbits in the plane
Increasing radius

Banana shaped periodic orbits OR 11 anomalous
orbits
Orbits in the plane
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As the bar grows stars are liftedResonance
trapping
Growing bar
Extent stars are lifted depends on the radius. A
natural explanation for sharp edge to the peanut
in boxy-peanut bulges.
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Starting from a stellar velocity distribution
centered about planar circular orbits. Growing
the perturbation in 3 rotation periods, resonance
traps orbits (even though non-adiabatic growth).
Extent of lifting is high enough to
theoretically account for peanut thicknesses.
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Capture into vertical resonances

• This new model suggests that peanuts grow
  simultaneously with bars (differing from other
  models).
• We dont know which resonance is dominant, but if
  we figure it out we may learn about the vertical
  shapes of galaxy bulges.
• We used a symmetrical bar, however warp modes may
  be important during bar formation.
• Formulism can also be used to address situations
  where the pattern speeds are changing, but are
  not well suited towards finding self-consistent
  solutions.

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In Summary Galactic Disks
Lindblad Resonances with a two-armed spiral
density wave are a possible model for structure
in the solar neighborhood velocity
distribution. The pattern speed is Uncertainty
mostly because of that in Oorts
constants. Interplay of different waves can cause
localized heating, something to look for in
observations. Constraints on properties of waves
are possible.
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In Summary Galactic Disks

• Growth of structure can cause resonant trapping.
  A good way to constrain vertical structure of
  galaxy bulges...
• So far no exploration of past history of galaxy!
  The way spiral waves grow should lead to
  different heating and capture and so different
  velocity distributions in different locations in
  the Galaxy.
• Better tools coupled with forthcoming large
  Galactic surveys should tell us about growth and
  evolution of the Galactic disk.

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Spiral structure driven by a close passage of the
binary HD 141569B,C
Disk is truncated and spiral structure drawn out
as the binary passes pericenter
Quillen, Varniere, Minchev, Frank 2005
STIS image Clampin et al. 2003
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Spiral structure in HD100546?
? Flyby Pertruber Mass
Time?
The mass of the perturber affects the amplitude
of the spiral pattern and the asymmetry. If the
perturber is very low mass, only one arm is
driven. The winding of the pattern is dependent
on the timescale since the perturber reached
pericenter.
STIS image of HD 100546 (Grady et al 2001)
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• Flybys and HD100546
• Morphology depends on how long since the flyby
  occurred.
• However there is no candidate nearby star that
  could have been in the vicinity of HD100546 in
  the past few thousand years.
• Furthermore, the probability that a star passed
  within a few hundred AU of HD 100546 is currently
  extremely low, presenting a problem for this
  scenario.
• Differences between flybys and a external bound
  perturber (binary)
• Both stellar flybys and external planets can
  produce spiral structure. However external
  perturbers truncate disks and flybys tend to
  scatter the outer disk rather than truncate it.
  Long wavelength SEDs should be sensitive to the
  difference!
• Both induce spiral structure that is more open
  with increasing radius and with increasing
  amplitude with increasing radius. In contrast to
  spiral density waves driven by an internal planet
  which becomes more tightly wound as a function of
  distance from the planet.

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Explaining spiral structure in HD100546 with a
warped disk
If viewed edge on would resemble Beta
Pictorus Warps are long lasting vary on secular
timescales rather than rotation timescales Twist
caused by precession of an initially tilted disk
induced by a planet? Initial tilt caused by an
interaction? Disk is too twisted to be explained
with a single planet in the inner disk -gt could
be a Jupiter mass of bodies outside of 50AU