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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

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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. 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 work Isothermal, magnetized, and self gravitating disk under influence of external gravity

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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

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Dispersion Relation : Undular Mode Ω JEANS < Ω PARKER Ω JEANS > Ω PARKER Ω JEANS ≈ Ω PARKER Self Gravity + External Gravity Solar Neighborhood

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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

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

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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.

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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

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

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Mass Distribution

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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

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Properties of Clumps Parker instability dominates in the early stage of clump formation.

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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

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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+502.23E+503.70E+483.15E+493.33E+505.33E+49 112.85E+476.87E+482.58E+476.91E+471.29E+491.37E+48 221.92E+432.69E+465.21E+441.96E+455.37E+464.13E+45

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Fourier Analysis Slope: -5 Kolmogorov’s slope : -5/3 Slope : -3

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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

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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.

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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 ]

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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.

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

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Slop :0.75

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Magnetic to Gas Pressure, Velocity dispersion of cloudlets

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