Aspects of Spiral Structure Theory J. A. Sellwood and R. Carlberg - - PowerPoint PPT Presentation

Aspects of Spiral Structure Theory

• J. A. Sellwood
• and R. Carlberg
• Seoul National university,

October 21, 2013

Why spirals matter

• Present structure of a galaxy is not simply the

consequence of its formation

• Spirals are major drivers of secular evolution:

– angular momentum transport (esp. in the gas) – age-velocity dispersion relation – radial mixing reduces abundance gradients – smoothing rotation curves – galactic dynamos – etc.

• How do they work?

M51 & Hubble Heritage NGC 1300

• Some spirals are clearly tidally driven, others

may be bar-driven – clear driving mechanism

Self-excited patterns

• Spirals are ubiquitous in galaxies with gas
• They also appear spontaneously in simulations
• f cool, isolated, unbarred galaxies
• Argues that

many spiral patterns in galaxies are self-excited

As SC84 but 2M particles

• rot  25 or

250 Myr

Heating rate?

• Test of N-dependence in 2D

Heating rate?

• Test of N-dependence in 2D
• Shift in time

– 20K heats rather more rapidly, but N=200K seems OK – except for an increasingly delayed heating – later

• SC84 essentially correct – spirals still fade quickly

What about 3D?

• Weak dependence on N
• Without cooling the disk heats and spirals fade

– except again heating is increasingly delayed as N rises

Why do

• thers

disagree?

• 2M particles in both cases
• A lower active mass fraction causes less

heating – lower Q

• Spirals are more multi-armed

Low- mass disk

Spiral activity lasts much longer

Lindblad diagram

• Jacobi integral

conserved IJ = E - pLz

• so E = pLz
• Slope is parallel

to circular orbit curve at CR

• Random motion

created at LRs

• less when they

are close to CR, as for high m

Low-mass disk

• Most

power is at m>4

• LRs are

close to CR

• Slow

heating

Disk twice as massive

• Little

power for m>4

• LRs

farther from CR

• More

rapid heating

Two superposed steady waves

• inner wave has the higher

pattern speed

Heavy disk model

• Lifetime of each

pattern is several galactic rotations

• Inner disk heats first

and patterns fade

• Thus apparent shearing transient spiral

patterns result from the superposition of a small number of coherent, longer lived waves

– quite a few recent papers have stressed the apparent shear instead

• They have also suggested that spirals corotate

with the stars everywhere so that radial migration is affected

– Not so!

Disk churning by spirals

(SB02)

• Changes at CR of a single spiral

and multiple transient spirals

Low-mass disk

• Multi-arm patterns

just as others find

• Radial migration still

works well

• Characteristic pattern
• f scattering at

corotation by waves

• f fixed frequency

Multiple waves

• Responses away from resonances can be

calculated by perturbation theory (BT08)

• Each pattern causes an independent response

at least in linear theory

– calculations by Comparetta & Quillen needlessly complicated

• The response at each resonance is also

independent – except where they overlap

Transient spiral modes

• The underlying waves seem to be genuine

modes

– i.e. standing-wave oscillations that have fixed pattern speed and shape – unstable modes also grow exponentially

• Each pattern lasts a few (5-10) galaxy rotations

– each mode grows, saturates, then decays

Modes

• Standing wave oscillations familiar from guitar

strings, organ pipes, etc.

Swing amplification

• NOT a mode

– shape changes

• ver time

– non-constant growth rate

• Vigorous

response to a perturbation

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 independently (Evans & Read, S & Evans)

• Halve the active mass, in order to suppress

a lop-sided instability, and set Q = 1.5

• They proved this disk is globally stable

Simulations of the ½-mass Mestel disk

• Linear theory predicts

it should be stable

• Peak  = / from

m = 2 with different N

• Amplified shot noise

at first

• Always runaway

growth of spiral activity

rot = 50 in these units

Simulations of the ½-mass Mestel disk

• Rapid growth is more

and more delayed as N is increased

• Surges once max > 2%

– non-linear effect

• Since real galaxies are

not as smooth as N = 500M, non-linear behavior must happen all the time

No single coherent wave

• Several separate

frequencies as the amplitude rises – i.e. not a single mode

Action-angle variables

• Rosette orbit

– uniform angular speed – plus a retrograde epicycle

• Actions are

Lz  J & JR

• Angles

w & wR

A true instability

• f the perturbed disk
• Restart N=50M case

from time 1400 with reshuffled phases

– green: w only – blue: both wR and w

• No visible spiral by

t=1400

• Yet the model now

possesses a vigorous instability

A true instability

• f the perturbed disk
• Vigorously growing mode

– fixed shape and frequency

• Best fit shape

– peak near corotation – extends to LRs

• Decays after it saturates

– CR peak disperses – “wave action” drains to LRs

Lindblad diagram again

• Notice that stars scattered at ILR stay close

to resonance

– allows large changes to build up

• Does not happen at OLR

Recurrence mechanism

• Each coherent wave

scatters stars at the resonances (S12)

– especially strong at the inner Lindblad resonance

• Scattering changes the dynamical structure of

the disk

• and creates the conditions for a new instability

Feature put in “by hand”

• Demonstrates that ILR

scattering really does provoke the new instability

– Mode is vigorous – probably of cavity-type with a “hard” reflection near the ILR

Emerging picture

• Spiral patterns are unstable

modes that grow rapidly,

saturate, and decay on time scales of several (5-10) galactic rotations

• New instabilities develop in rapid succession

that are neither

a) long-lived quasi-steady modes (Bertin & Lin), nor b) responses to noise (Toomre, Kalnajs, ...)

• Does this happen in nature?

Geneva-Copenhagen survey (Nordström et al. 2004)

• Known distances, full

space motions and ages

• f 13,240 local F &G

dwarfs

• DF not at all smooth

(Dehnen 98)

– Not dissolved clusters

(Famaey et al.; Bensby et al.; Bovy & Hogg; Pompéia et al.)

• Hard to interpret the

structure in velocity space

Project into action space

• Scaled by R0 and V0

assuming a locally flat RC

– Lower boundary: selection effect – L-R bias: asymmetric drift

• One strong feature

– (bootstrap analysis)

• Scattering or

trapping?

Phases of these stars

• Action-angle variables

– radius shows epicycle size – ( 2  JR) – azimuth is 2w – wR

• Concentration of stars

at one phase

– m > 2 disturbances are also supported, – suggests an ILR

• Exactly the stars (red)

in scattering tongue

Resonant stars

• S10 – red stars have been

scattered by an ILR

• Resonant stars are the

“Hyades” stream

• Far more than just the

Hyades cluster

• Distributed pretty

uniformly around the sky

• Hyades cluster (age ~ 650

Myr) is in this resonance

Implications

• Evidence for an LR

– probably an ILR of an m = 4 spiral

• 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

Gas seems to be essential for spirals

• NGC 1533 – Hubble image
• Misled the community for many years

Recurrent transients

• Random motion rises

and patterns fade

Recurrent transients

• Random motion rises

and patterns fade

• Add “gas dissipation”

and patterns recur “indefinitely” (SC84)

• A natural explanation for

the importance of gas

Galaxy formation simulations

• Agertz et al. (2010) – barely a remark!

Age-vely dispersion relation

• Data from Holmberg et al. (2009)

– cloud scattering is inadequate – transient spirals required (Binney & Lacey, Hänninen & Flynn)

Aumer & Binney

• Ages disputed – use color as a proxy for age
• Hipparcos data

3D shape of ellipsoid

• Ida et al. (1993) showed that cloud scattering

sets the ellipsoid flattening: z = 0.6R (V=const)

• But GMCs redirect peculiar velocities more

efficiently than they increase them

• Spirals increase in-plane motions only and most

3D simulations do not include GMCs

• Any thickening people report is due to 2-body

relaxation!

2-body relaxation in 3D disks

• Demonstrates spirals cause in-plane heating only
• Thickening (and segregation) by relaxation

Other work

• Quinn et al. (1993) worried that disks

thickened without an obvious mechanism

• McMillan & Dehnen (2007) also worried

– scrambling test suppressed collisions too – concluded (wrongly) that vertical heating was caused by spirals

• In fact, every thin disk simulation with

N < 2M thickens by relaxation

– House et al. (2012) compared their model with MW data – not really meaningful

Conclusions

• Spiral patterns are short-lived (a few rotations)

unstable modes

– superposition can lead to apparently continuously shearing patterns – low-mass disks manifest multi-arm patterns that cause slower heating – radial migration is alive and well – gas still needed to prolong activity

• Non-linear effects cause the recurring cycle

– larger amplitude delayed with increasing N – supporting evidence for the recurrence mechanism from nearby stars