Properties of the Structuresformed by

Parker-Jeans Instability

Y.M. Seo1, S.S. Hong1, S.M. Lee2 and J. Kim3

1 ASTRONOMY, SEOUL NATIONAL UNIVERSITY2 SUPERCOMPUTING CENTER , KiSTI

3 KOREA ASTRONOMY & SPACE SCIENCE INSTITUTE

Previous Works of Parker Instability

Results Summary

Under Uniform External Gravity

→ convective motion everywhere in the disk.

Under Non-uniformExternal Gravity[ Kim & Hong 1998; Kim, et al. 2004 ]

Under Self-gravity [ Lee & Hong 2006, accepted ]

→ ISM turned into thin sheets due to interchange mode

→ compatible with HI super-clouds, but not with GMCs.

This workIsothermal, magnetized, and self gravitating disk under influence of external gravity

1. Giant Molecular Cloud [Blitz 1993, PP III]

2x105 ~1x106 MSUN ; ~50 H2 cm-3 ; separation 0.4~0.6 Kpc

Star forming rate → Gas consumption rate

→ Need about 33 Myrs [Larson 1994]

2. HI Super-cloud [Elmegreen & Elmegreen in 1981]

1x106 ~4x107MSUN ; ~10 H cm-3 ; separation 1~4 Kpc

mean separation of 106Msun clouds 1.2Kpc

[Alfaro, Cabrear-Cano, Delgado 1992]

Arm Crossing time → about 120 Myrs

- All HI super-clouds have GMCs inside ; not all GMCs are

located inside HI super-clouds.

Observations

Dispersion Relation : Undular Mode

ΩJEANS < ΩPARKER

ΩJEANS > ΩPARKER

ΩJEANS ≈ ΩPARKER

Self Gravity + External Gravity

Solar Neighborhood

Code: Isothermal MHD TVD

MHD + Poisson

(Nx, Ny, Nz) = (256, 512, 256)

→ (1Kpc, 2Kpc, 1Kpc) , with 4pc pixel resolution

o = 2mHcm-3 , = 0.3 , cs = 5.0 km/s

H = 156pc , h = 0.94Kpc , b = 20, 15, 10

Time is in units of [H/cs] , which is 28.3 Myr.

Cs is observed velocity dispersion of cloudlets.

Non Linear Simulations

Non Linear Simulations• ΩPARKER > ΩJEANS

78 Myrs after transient phase 210 Myrs after transient phase

AzimuthMagnetic Field

Radial

Cylinder-like structure perpendicular to B

(Parker Cylinder)

Non-linear Simulations• ΩJEANS > ΩPARKER

130 Myrs after transient phase170 Myrs after transient phase

AzimuthMagnetic Field

Radial

Parker cylinders form first. Parker cylinders merge witheach other.

Fourier Analysis

ΩJEANS > ΩPARKERΩPARKER > ΩJEANS

• ΩPARKER > ΩJEANS : Several peaks

• λy ≈ 2 kpc → HI super-cloud scale structure

λy ≈ 705 pc, λy ≈ 445 pc → GMCs scale structure• ΩPARKER < ΩJEANS : A broad peak

Properties of Clumps

Clump Identification code [Jonathan P. Williams, Eugene J. De Geus, & Leo Blitz]

AzimuthalMagnetic Field

Radial

93 Myrs after transient phase

Mass Distribution

Mean SeparationΩParker > Ω Jean

Projected distance of the peaks

→ 500pc & 1140pc

Averaged distances between all of each clumpsin three dimension

dl 3/2

Mean density → a little lower than GMCs

Radius → a little larger than GMCs

The clumps are precursorsof GMCs

Properties of Clumps

Parker instability dominates in the early stage of clump formation.

Principle Axis of Clumps

Total 22 Clumps at t = 9.8

Longest axis

Shortest Axis

Radialdirection

15 1

Azimuthaldirection

7 0

Verticaldirection

0 21

Clumps are made by the Parker instability

Energies of Clumps

dVw

dVcs 2

2

3

dVuT 2

Clumps are in the virial equilibrium.

Surface energy ≈ Internal energy

Cs is NOT thermal sound speed

[unit in erg]

dVB

M8

2

dSxPE surfp

,

dSxB

E surfm

8

2

,

ID W Π T M Ep,surf Em,surf

1 1.02E+50 2.23E+50 3.70E+48 3.15E+49 3.33E+50 5.33E+49

11 2.85E+47 6.87E+48 2.58E+47 6.91E+47 1.29E+49 1.37E+48

22 1.92E+43 2.69E+46 5.21E+44 1.96E+45 5.37E+46 4.13E+45

Fourier Analysis

Slope: -5

Kolmogorov’s slope : -5/3

Slope : -3

Discussion & Summary

2. Parker - Jeans instability tends to steepen the power spectrum.

1. Structures & Formation Time Scales ΩPARKER > ΩJEANS

→Formation of HI superclouds scale structures and GMCs scale structures within 130Myrs

Parker cylinders and GMCs form first.This Work

HI super-clouds

Fragmentation

GMCs & HI super-clouds

Parker cylinder & GMCs

Collect Parker cylinder and GMCs

GMCs in HI-superclouds

Initial Equilibrium Configuration• (1 + ) cs

2 ism(z) = - ism(z) tot

► 2 ism = 4G ism(z), ext = tot-ism

ism(z) = osech2 (z/ H) sech2b (z/ h)

► o= 2mHcm-3, = 0.3, cs = 5.0 km/s H = 156pc, b = 20, h = 0.94Kpc

• In Simulations

► b = 20, 15, 10 The other parameters are fixed.

tot [Bienayme, Robin, & Creze 1987, A.Ap., 180, 94.]

Observational Facts

ρ [Boulares, A. & Cox, D.P. 1990, ApJ, 365, 544.]

B = 4 ±1 μG (local regular field) [Rainer Beck, 2001, Sp Rev. 99: 243-260]

Synthesized HI Profiles

• < σV(x,y,z) >x,y ≈ 5.0 km/s BUT FWHM ≈ 2.5 km/s < Cs

→ Clump velocity is much too small compared to observed cloud velocity.

Time vs

< Vx(x,y,z) >xy /Cs

Cs = 5.0 km/s < Vx(z) > ≈ 0.0 km/s < σVx(z) > ≈ 5.0 km/s

Time vs

< σVx (x,y,z) >xy /Cs

Slop :0.75

Magnetic to Gas Pressure

P

B

8

2

2scP ,

Velocity dispersion of cloudlets