Properties of the Structures formed by Parker-Jeans Instability Y.M. Seo 1, S.S. Hong 1, S.M. Lee 2 and J. Kim 3 1 ASTRONOMY, SEOUL NATIONAL UNIVERSITY 2 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-uniform External Gravity [ Kim & Hong 1998; Kim, et al ] 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 work Isothermal, magnetized, and self gravitating disk under influence of external gravity

1. Giant Molecular Cloud [ Blitz 1993, PP III ] 2x10 5 ~1x10 6 M SUN ; ~50 H 2 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 ] 1x10 6 ~4x10 7 M SUN ; ~10 H cm -3 ; separation 1~4 Kpc mean separation of 10 6 M sun 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 Ω JEANS < Ω PARKER Ω JEANS > Ω PARKER Ω JEANS ≈ Ω PARKER Self Gravity + External Gravity Solar Neighborhood

Code: Isothermal MHD TVD MHD + Poisson (N x, N y, N z ) = (256, 512, 256) → (1Kpc, 2Kpc, 1Kpc), with 4pc pixel resolution  o = 2m H cm -3,  = 0.3, c s = 5.0 km/s H = 156pc, h = 0.94Kpc, b = 20, 15, 10 Time is in units of [H/c s ], which is 28.3 Myr. C s is observed velocity dispersion of cloudlets. Non Linear Simulations

Ω PARKER > Ω JEANS 78 Myrs after transient phase210 Myrs after transient phase Azimuth Magnetic Field Radial Cylinder-like structure perpendicular to (Parker Cylinder)

Non-linear Simulations Ω JEANS > Ω PARKER 130 Myrs after transient phase 170 Myrs after transient phase Azimuth Magnetic Field Radial Parker cylinders form first. Parker cylinders merge with each other.

Fourier Analysis Ω JEANS > Ω PARKER Ω PARKER > Ω JEANS Ω PARKER > Ω JEANS : Several peaks λ y ≈ 2 kpc → HI super-cloud scale structure λ y ≈ 705 pc, λ y ≈ 445 pc → GMCs scale structure Ω PARKER < Ω JEANS : A broad peak

Properties of Clumps Clump Identification code [ Jonathan P. Williams, Eugene J. De Geus, & Leo Blitz ] Azimuthal Magnetic Field Radial 93 Myrs after transient phase

Mass Distribution

Mean Separation Ω Parker > Ω Jean Projected distance of the peaks → 500pc & 1140pc Averaged distances between all of each clumps in three dimension Mean density → a little lower than GMCs Radius → a little larger than GMCs The clumps are precursors of 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 Radial direction 151 Azimuthal direction 70 Vertical direction 021 Clumps are made by the Parker instability

Energies of Clumps Clumps are in the virial equilibrium. Surface energy ≈ Internal energy C s is NOT thermal sound speed [unit in erg] IDWΠTME p,surf E m,surf 11.02E E E E E E E E E E E E E E E E E E+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 Ω PARKER > Ω JEANS → 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 +  ) c s 2  ism (z) = -  ism (z)  tot ►  2  ism = 4  G  ism (z),  ext =  tot -  ism  ism (z) =  o sech 2 (z/ H) sech 2b (z/ h) ►  o = 2m H cm -3,  = 0.3, c s = 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: ]

Synthesized HI Profiles x,y ≈ 5.0 km/s BUT FWHM ≈ 2.5 km/s < C s → Clump velocity is much too small compared to observed cloud velocity.

Time vs xy /C s C s = 5.0 km/s ≈ 0.0 km/s ≈ 5.0 km/s Time vs xy /C s

Slop :0.75

Magnetic to Gas Pressure, Velocity dispersion of cloudlets