M74 (NGC628)

Woong-Tae Kim (Seoul National University, Korea) Eve Ostriker (University of Maryland, USA)Chang-Goo Kim (Seoul National University, Korea)

EANAM Nov. 2, 2006

What Generate ISM Turbulence?• ISM turbulence is highly supersonic and thus, in the

absence of driving sources, decays rapidly on a timescale comparable to flow crossing times (Stone et al. 1998, Mac Low 1999, Padoan & Nordlund 1999).

• Stellar sources– Supernova explosions (Cappellaro et al. 1999; Avillez 2000)– Expansion of HII regions, stellar winds, radiation, outflows

from young stars, etc. (Mac Low & Klessen 2004; McKee 1989)

• Non-stellar sources– Magnetorotational instability (Sellwood & Balbus 1999) – Thermal instability & MRI (Piontek & Ostriker 2004, 2005) – Gravitational instability (Wada & Norman 1999)– Swing amplification in star+gas systems (Kim & Ostriker, ApJ

submitted)– Galactic spiral shocks (Bonnell et al. 2006; Kim et al. 2006)– …

Local Shearing Periodic Box

• In local models, we consider a small patch of the disk, neglecting the curvature of the coordinates.– This takes into account the effect of galactic differential

rotation.

• Magnetic fields parallel to the y-directions are included.

Model with Qg=1.4

• With Qg=1.4, swing amplification puts the combined disk into a moderately self-gravitating state that is unable to form bound condensations.

• When disks are unstable or at least marginally unstable, the induced velocity dispersions become comparable to the effective speed of sound.– ~4-5 times larger than those resulting from the gas-only counterparts.– Unlikely to explain turbulence seen in extended HI disks of external face-

on galaxies.

gas stars

Σg=13 M pc-2

cg=7 km s-1

Hg=180 pc

Σs=35 M pc-2

σs=30 km s-1

Hs=330 pc

Spiral Arm Coordinates• Transfer to a frame corotating at p=0/2 with an arm, and erect a

local “spiral coordinate system” (Roberts 1969).

• External spiral potential arising from stellar density waves ext0 cos(2x/Lx)

F 2|0|/(02R0

2sini )

(cf. Shu et al 1973)

1D Galactic Spiral Shocks• Isothermal equation of

state is assumed.• Imposed sinusoidal spiral

potential perturbation rapidly sets up one-dimensional spiral shock profiles that are readily stationary (e.g., Roberts 1969; Woodward 1974).

• The conservation of potential vorticity requires the Toomre parameter Q and shear rate q– Q=Q0(Σ/Σ0)-1/2 – q=2-(Σ/Σ0)

for flat disk rotation.

Vertical Disk Stratification

• Real galaxies are vertically stratified.

• Gas has a scale height (Hg ~ 160-180 pc) that is about twice smaller than the scale height of stars.

• It is interesting to see what changes the consideration of the vertical degree of freedom will make.

Effect of Disk Stratification• Spiral shocks in a stratified disk are in general non-

stationary, swaying loosely back and forth in the direction perpendicular to the arm.– In sharp contrast to 1D cases where spiral shocks are

readily stationary.– The fundamental vertical oscillation period is

incommensurable to the arm-to-arm flow period, causing XZ flapping motions of spiral shocks.

Kim, Kim, & Ostriker (2006) F = 10%, Q = 2.0, = 10x

z

Turbulence Inside Spiral Shocks• The shock flapping motions

taps the kinetic energy in galactic rotation, feeding random gas motions on the scale of the vertical disk thickness, which cascade to smaller scales.

• Despite dissipation in shocks and through cascades, the induced δv exceeds the sonic value for a range of shock strengths.

Spiral shocks can be an important source of turbulence in disk galaxies.

• Both swing amplification and the shock flapping motions taps the kinetic energy in galactic rotation and feed random gas motions on a large scale, which cascade to smaller scales.– λ ~ λJ in swing amplification – λ ~ H in vertical spiral shocks

• What effects will turbulent spiral shocks make to the formation of spiral-arm substructures?

Jan. 2005; M51 & NGC 5195

F658N Hα [NII]F814W IF555W VF435W B

• Spiral arm substructures include OB star complexes, gaseous spurs (feathers), and giant clouds.

Aalto et al. (1999)CO 1-0 over Hα

• Giant Molecular Associations– Typically, ~107 M in mass – ~1 kpc in separations

• Also called HI superclouds in atomic forms

Giant Clouds• Perhaps constitute a upper

end of the GMC mass spectrum (when atomic envelopes are included).

• La Vigne, Vogel, & Ostriker (2006) examined 223 HST galaxies and found that– Of 35 good images , 29 (83%) possess gaseous spurs.– gaseous spurs are common in Sb and Sc galaxies.– Sb-Sc galaxies without clear evidence for spurs either

have poorer quality images, or flocculent or complex structure.

Spurs are Ubiquitous!

NGC 1241 NGC 4321

Self-gravitating MechanismsSwing Amplifier

Goldreich & Lynden-Bell (1965); Julian & Toomre

(1966)

Magneto-JeansInstability (MJI)

Lynden-Bell (1966); Elmegreen (1987); Kim & Ostriker (2001)

Conspiracy among shear, Coriolis force,

and self-gravity

Physicalmechanism

Tension force from B-fields removes the stabilizing effect of Coriolis force.

required Self-gravity required

strong Velocity shear weak

stabilizing B-fields de-stabilizing

clouds (~ 107 M ) outcomes spurs + clouds (107 M)

3-4 orbits Growth time ~ 1 orbits

Magneto-Jeans Instability (MJI)• A hurdle to overcome for self-gravitating modes to grow is Coriolis

forces that cause epicyclic motions of gas in a rotating disk.

• Embedded toroidal magnetic field breaks the constraint of potential vorticity conservation, allowing condensation to grow (Lynden-Bell 1966; Elmegreen 1987; Kim & Ostriker 2001).

• Material is gathered mainly along the direction parallel to the magnetic fields.

• For strong B, dispersion relation (no stabilizing effect from rotation) is

2 = 2 + k2cs2 2Gk

• Not present under high shear condition.

An Example of MJI (with no feature)• If unmagnetized, a low-shear thin disk with Q=1.5 would be

stable to gravitational instability.• With embedded magnetic fields, MJI operates vigorously to

form self-gravitating clouds (within 1 orbital time).• Masses of clumps are typically 1 Jeans mass; MJ = cs

4 /G2 ~ 107 M (cs/ 7 km s-1)4(/13Mpc-2)-1

• Mass collection is achieved mainly along the direction parallel to B.

Q 1.5q0.1 1 Log10(0)

Kim & Ostriker (2001)

Magnetized Spiral Arm in Thin Disk

F = 3%, Q= 1.5, = 1

Log10(0)

• Small net velocity shear inside spiral arms provides a favorable condition for the magneto-Jeans instability to develop.

• Separation of gaseous spurs:– L ~ (2-3) λJ,sp in a razor thin disk.

– L ~ 10 λJ,sp in a vertically extended disk.

• Masses of bound clumps:– M ~ 4x106 M in a razor thin disk

– M ~ (1-3)x107 M in an extended disk

Similar to the masses of giant clouds

Kim & Ostriker (2002, 2006)

x

y

Wiggle Instability

• Wada & Koda (2004) proposed wiggle instability may be another mechanism to form gaseous spurs.

• Does the wiggle instability also exist in fully 3D models?

• Wiggle instability ?– potentially Kelvin-Helmholtz instability or shear instability,

occurring at a spiral shock, requiring perturbed velocity structures to remain coherent during its growth.

– Needs strong spiral shocks.– Identified in a 2D, razor-thin disk.– Requires neither magnetic fields nor self-gravity.– Appears to be suppressed by the presence of magnetic

fields with equi-partition strength ( =1) (Shetty & Ostriker 2006).

Absence of the Wiggle Instability

in 3D Models

• But, spiral shocks in a stratified disk are in general non-stationary, causing shock flapping motions and strong vertical shear of the in-plane velocities.

• In fully 3D models, the wiggle instability disappears because any coherent vortical structures are quickly disrupted by these turbulent motions

• For the wiggle instability to develop, nonaxisymmetic vortical structures should remain coherent during its growth.

MJI in a 3D Spiral Arm Model

F = 5%, Q0 = 1.5, 0 = 10Kim & Ostriker (2006)

Magnetized 3D Spiral Arm• Clumps are magnetically supercritical with Mc/ Φ ~(1-3) G-1/2, ,

and have masses similar to those in 2D, thick-disk models.• Spur spacing (λspur ~ 10 λJ, arm) is consistent with 2D, thick-disk

models and also with observations (La Vigne et al. 2006).

Parker Instability Inside Spiral Arm?

• No apparent contribution of the Parker instability to spur formation in 3D models.– No sign of the characteristic correlation of magnetic valley/hills with

overdense/underdense regions.– No sign of sinusoidal variations in the vertical velocities with azimuth.

• Stabilized in part by strong vertical shear of the in-plane velocities and in part by the curved nature of the spiral shock front in the XZ plane.

Conclusions• Swing amplification (in marginally unstable disks)

and galactic spiral shocks (in vertically stratified disks) can be efficient means of turbulence generation in the ISM.– Spiral shocks in the XZ plane is in general non stationary,

efficiently transforming some of the bulk rotational energy into random supersonic gas motions.

See poster #P-11 by Kim, Kim, & Ostriker for details.

• Self-gravity is the key in forming spiral-arm substructures. – Gaseous spurs (feathers) naturally form as a consequence of

Magneto-Jeans Instability inside spiral arms. • With reduced shear and enhanced magnetic fields, MJI is very

efficient inside spiral arms (λspur ~ 10 λJ, arm).– In the nonlinear stage, spurs form bound clumps.

• Typical mass ~ (1-3)107 M in 3D disks.• Could evolve into bright H II regions in both arm and interarm

regions.– Parker and wiggle instabilities are unlikely to play an

important role in forming giant clouds.