Alice Quillen University of Rochester

in collaboration with

Ivan MinchevObservatoire de Strassbourg

Aug, 2009

Motivation

Hercules stream

Sirius group

Pleiades group

Hyades stream

Coma Berenices group

The Milky Way has only rotated about 40 times (at the Sun’s Galacto-centric radius).

Little time for relaxation!

Diffusive approximations are inappropriate for large and precise data sets

Stellar velocity distribution Dehnen 98

Radial velocity

Tan

gen

tial

vel

oci

tyStructure in the motions of the stars can reveal clues about the evolution and formation of the disk.

Non equilibrium processes• Resonances in the uv plane and Precision Galactic

measurements – Libration timescales are likely to be long so evolution may

be near or in non-adiabatic limit– Resonances are often narrow, so when identified they

give a strong constraint on pattern speed

• Resonant trapping and heating– Constraints on evolution and growth of patterns

• Phase wrapping– Giving clues to ages since disturbances

• Perturbations to the disk caused by mergers– Can we tell the difference between merger remnants and

perturbations to the existing populations?

Interpreting the U,V planeIn terms of resonances

2 22

0

(1 ) ln

2

2

circular orbit epicyclic motionE E E

v uV r

Coma Berenices group

Orbit described by a guiding radius and an epicyclic amplitude

On the (u,v) plane the epicyclic amplitude is set by a2~u2/2+v2

The guiding or mean radius is set by v

Gap due to 2:1 resonance with bar (e.g., Dehnen 2000)

Hercules stream

Near the 4:1 Lindblad resonance. Orbits excited by resonances can cross into the solar neighborhood (Quillen & Minchev 2005)

U

v

Each region on the u,v plane corresponds to a different family of closed/periodic orbits

Hamiltonian including a perturbation

1/ 2

0 1 2 1 2 1 22 21 2 1 2

1 21

0 1 2 2

1 2

( , ; , )

cos[ ( )]

Canonical transformation

( , ; , )

( ) is the resonant anglep

p

H I I I I

aI bI cI I

I m t

H J J

m t

1/ 2

1 2

2 21 2 1 2 1

( )

' ' ' cos[ ]

pJ J

a J b J c J J J

This is time independent, and is conserved.2J

First order Lindblad Resonances with bar or spiral

1/ 221, 1 1 1( ) cos( )H I I I I

Incr

easi

ng r

adiu

s Closed orbits correspond to fixed points

BAR

• Outside OLR only one type of closed orbit.

• Inside OLR two types of closed orbits

Gro

win

g ba

r

Φ angleR=2I1 Radius related to eccentricity

Precision Measurements of the Galactic

Bar

Both pattern speed and angle can be constrained using both streams and simulated Oort function measurements.C functions in hot and cold populations can only be matched for bar pattern speed +- a few %

Bar angle

Oo

rt C

(Minchev et al. 2007)

Why does the hot population have a higher C?

Model hot: dotted Model cold: solid

Bar and Spiral arm Growth• Near resonance there are no circular orbits ---

accounts for deficits of particles in certain regions in uv plane

• Bar/spiral arm growth resonance capture• Depending on whether pattern slows down or

speeds up – causes resonance capture, eccentricity related to

pattern speed change– causes a jump in eccentricity as particles must jump

across the resonance. Jump depends on bar/spiral strength.

Transient structure during and after bar growth

Diversity in morphology in barred galaxies may be explained by recent bar growth (Bagley et al. 09)Explanations for some low velocity streams; Minchev et al. in preparation

During bar growth Long lived R1,R2 rings following bar growth as long as pattern speed and strength does not vary

Bar Evolutionbar sped up R1 destroyed

bar slowed downresonant capture into R2

bar slows down during growth

effect on initially cold test particle population

Heating mechanisms

• Transient spiral arms --- also leads to migration (DeSimone et al. 2004; Sellwood & Binney 2002)

• Resonant and chaotic (e.g., multiple patterns; Quillen 2003; Minchev & Quillen 2006; Chakrabarty 2007)

• Merger induced (e.g., Villalobos & Helmi 2009)

All three leave signatures in phase space

An example of chaotic heating

later times

starting with stars in a circleIf integrable then eventually they would remain in a thin but twisted loop rather than a smooth distribution

heating larger near a separatrix of one resonance and when there is a second perturbation

Minchev & Quillen 2006

Analogy to the forced pendulum

1/ 2 1/ 221 1 1 1cos cos[ ] H I I I I t

Controls center of first resonance and depends on radius

Controls spacing between resonances and also depends on radius

Strength of first perturbation

Strength of second perturbation

A model for chaotic resonant heating

Spiral structure at the BAR’s 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 (Quillen 2003)

2t

1/ 2

1/ 2

2 21 2 1 2 1 2

1 21

1 21

cos[ ( )] from spiral

cos[ ( )] from bar

s s

b b

H I I aI bI cI I

I m t

I m t

Vertical resonances with a bar2

0 3, 3 3 3( ) ( ) cos2H I I I I t

Banana shaped periodic orbits

OR 1:1 anomalous orbits

Incr

easi

ng r

adiu

s

Orbits in the plane

Orbits in the plane

As the bar grows stars are lifted

Resonance trappingG

row

ing

bar

Extent stars are lifted depends on the radius.

An explanation for sharp edge to the peanut in boxy-peanut bulges.

Phase wrapping in the disk

v

u

Semi-analytical model constructed by weighting with radial angle

time

following uneven distribution in epicylic oscillation angle, the thick disk can exhibit streams (Minchev et al. 2009)

Is the Milky Way Ringing?

Proposed model for High Eccentricity Disk StreamsAlternative model to merger remnants for high velocity streams in the disk

Mock Pencil Beam Surveys“getting out of the solar neighborhood’’

mean radial velocity velocity dispersion

mass surface density

galactic longitude

dis

tanc

e fr

om S

un

Ωs=0.6Ω0

Ωs=0.9Ω0

4 arm steady spiral patternMean subtracted(Minchev & Quillen 2008)

Disk perturbed by a low mass satellite passing

through the disk

u

v

streams induced over short timescales as well as heating(Quillen et al. 2009)

Migration and mixing in the outer disk caused by multiple perturbations from a low mass satellite galaxy

After 1 passage After 3 passages

change in mean radius

ecc

ent

rici

ty

Outer disk

Mid disk

Inner disk

Quillen et al. 2009

Summary• Rich dynamics!• Dynamical structures and events

leave signatures in velocity field • Precise measurements will be

made as observations becomes more comprehensive

• Time dependent models could be better explored

• Unveiling current and past structure and evolution of Milky Way will be very exciting