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Three-dimensional Global MHD simulations of the Magnetic Loop Structures in our Galactic Center

Galactic Center Workshop 2009,10,19 Shanghai. Three-dimensional Global MHD simulations of the Magnetic Loop Structures in our Galactic Center. MACHIDA Mami (Nagoya Univ.) collaborator

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Three-dimensional Global MHD simulations of the Magnetic Loop Structures in our Galactic Center

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  1. Galactic Center Workshop 2009,10,19 Shanghai Three-dimensional Global MHD simulations of the Magnetic Loop Structures in our Galactic Center MACHIDA Mami (Nagoya Univ.) collaborator MATSUMOTO R.(Chiba Univ.), NOZAWA S.(Ibaraki Univ.), TAKAHASHI K. (JAMSTEC), TORII K., KUDO N., and FUKUI Y. (Nagoya Univ.)

  2. Galactic Center Workshop 2009 Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Magnetic loop structure in the Galactic center 300 pc 220 pc ※Distance from earth:8500pc ※Estimated mass: lower limit (We assume LTE to 13CO) The kinematic energy of lower limit is estimated to be 1051erg. This energy is too large to be explained by a single supernova explosion. -> We considered this structure is formed by the magnetic floatation.

  3. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Magnetic flotation of Parker instability Loop structures observed in the solar corona are produced by the buoyant rise of magnetic loops from below the photosphere. ⇒ Parker (1966) proposed that magnetic loops can be created in galactic gas disks by an MHD instability driven by buoyancy. However, it was hard to observe such galactic magnetic loops. MHD activities of galactic disks Magnetic loop in solar corona (TRACE：191Å)

  4. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion 2D MHD simulations Projected on the sky White curve: magnetic field lines Color : horizontal velocity sliced in the vertical plane. Fukui et al. (2006) Numerical simulations reproduced structures similar to the observed loops.

  5. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion The effect of galactic rotation Ω Chou et al. 1997 Coriolis force Due to the Coriolis force, the magnetic tension becomes larger that in no rotating layer. Due to the magneto-rotational instability, the disk becomes turbulent. Matsumoto, Tajima (1995)

  6. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Purpose of this talk • We study the evolution of galactic gas disk inside 1kpc from the Galactic center. • We try to reproduce of the loop structures by global simulation. Machida + (2009)

  7. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Basic equations Ideal MHD equations

  8. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Galactic gravitational potential Miyamoto & Nagai(1975) Galactic gravitational potential created by disk + bulge star mass Subscription 1: Bulge component Subscription 2: Disk component Nishikori et al. (2006)

  9. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Initial Model Equilibrium gas disk threaded by toroidal magnetic fields　（Okada et al. 1989） ・Angular momentumL∝r0.496 ・Sound velocity cs0= 0.14 v00.05v0 ・Specific heat ratioγ=5/3、1.05 ・Plasmaββ=1, 10 ,100 ◇We simulated warm component of the inter stellar gas (T～104K) because the size of the magnetic loops is determined by the scale height of this warm component. ◇We ignore self-gravity of gas and radiative cooling. Units Lengthr0=1kpc Velocityv0=207km/s MassM0 =1010Msolar TemperatureT0 = 5×106 K

  10. Galactic Center Workshop Introduction: Observations Introduction: Theory ModelsNumerical Results Conclusion Magnetic Loops on the Galactic Corona left）　Blue surface：　volume rendered image of the gas density Curves：　Floating magnetic loops. Color depicts vertical velocity from minus to plus: blue – white –red. right）　Enlarged figure of the left panel. Curves are same on the left panel.

  11. Galactic Center Workshop Introduction: Observations Introduction: Theory ModelsNumerical Results Conclusion Schematic picture showing the formation of magnetic loops

  12. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Summary 1 • NANTEN observations discovered molecular loops in the Galactic center region. • Global 3D MHD simulations of galactic center gas disks showed that magnetic loops with length 1kpc and height several hundred pc can be created. • About 400 magnetic loops are formed in the corona. • Gas temperature became about 105 K by the adiabatic heating. Galactic gases have multiple component, such as cool molecule (10K), warm HI (1000K), and hot plasma (106K). We have to consider the cooling and heating effect. Before including the molecular cooling, we try to calculate an iso-thermal (～104K) model .

  13. Galactic Center Workshop Introduction: Observations Introduction: Theory ModelsNumerical Results Conclusion Density and magnetic structure of iso-thermal model Preliminary • About 20 magnetic loop are formed in the corona. • The size of loop is about 1kpc length, 60pc height. • Smaller loops are emerging below the large loop.

  14. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Conclusion • Magnetic loops with length 1kpc and height several hundred pc can be created by the global 3D MHD simulations. • About 400 magnetic loops are formed in the corona. • Gas temperature became about 105 K by the adiabatic heating. • In the iso-thermal model, about 20 magnetic loops are formed. • Loop size in isothermal model becomes smaller than in the adiabatic model.

  15. HIガスの鉛直方向分布 21cm線の観測により、鉛直方向1kpc以上までHIガスが一様に広がっている事がわかった。(Oosterloo et al 2007) ↓ 暖かいHIガスに対応する　10000Kの等温ガス円盤を仮定した数値実験を行い、その振る舞いを調べる

  16. ガス円盤上のループ構造 • 大きなループ構造の下に多数の浮上途中の構造が形成されている。 • 全長1.5kpc程度の大きな浮上構造の上に小さなループが多数連なっている。小ループの長さは約300pcである。これは、おおよそ円盤のスケールハイトの10倍になっている。 • 高さ50pcまでは弓型の膨張をしているが、50pcを超えると急激に浮上する箇所が見られ、立った構造になる。

  17. Galactic Center Workshop Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Critical wavelength for the Parker instability Buoyancy　（ρ’－ρ）ｇ　＞ Magnetic tension B2 /（４πｒ’） When the buoyancy force created by sliding down the gas along the magnetic field line exceeds the restoring magnetic tension. λ　＞　λｃ　＝　８（１＋１/β） H1/2 Instability grows for long wave length perturbations along the magnetic field lines. The most unstable wave length is about 10 times of the scale height.

  18. EANAM2006. 11.1 Introduction: Observations Introduction: Theory ModelsNumerical Results Conclusion General Properties of Magnetized Disks The initial weak magnetic fields are amplified due to the magneto-rotational instability (MRI). Due to the MRI, the disk becomes turbulent. Averaged plasma β is about 10 inside the disk. Mass accretes to the central region losing the angular momentum. When the magnetic energy comparable to the gas pressure, magnetic pressure driven outflows emerge from the central region. This outflows create a large-scale poloidal magnetic field in the inner most region.

  19. EANAM2006. 11.1 Introduction: Observations Introduction: Theory ModelsNumerical Results Conclusion Histogram of Magnetic Loops Gray shade boxes show the loops whose height exceed over 200pc. (a) Maximum loop height (b) Length between loop foot-points. (c) Distribution of the azimuthal angle (d) Distribution of the radial direction About 180 loops picked up on the upper half of the gaseous disk. Some concentrations appear both in azimuthal range and radial range.

  20. EANAM2006. 11.1 Introduction: Observations Introduction: Theory ModelsNumerical Results Conclusion Relation of the density to magnetic loops left） equatorial density averaged in |z| <0.06. Gray scale indicates the density. Dotted curves show the magnetic loops projected on to the equatorial plane. right） equatorial density normalized by the azimuthally averaged density ρ/<ρ>. Symbols denote the position of the loop tops. Equatorial density shows the m=1 one-armed distribution. Loops are formed in the lower density region because the magnetic energy becomes higher in lower density region.

  21. EANAM2006. 11.1 Introduction: Observations Introduction: Theory ModelsNumerical Results Conclusion Distribution of quantities along the loop Sound speed Vz Loop foot points becomes high density, high plasma β, and loop top is lower density and β=1. It means that this loop is formed by the Parker instability.

  22. EANAM2006. 11.1 Introduction: Observations Introduction: Theory ModelsNumerical Results Conclusion Position – Velocity diaglam This magnetic loop is same as yellow magnetic loop on the density distribution. Foot points show the larger velocity dispersion than the loop top.

  23. 浮上ループの形成（町田ら2009） • 銀河円盤とバルジを考慮した、銀河ガス円盤の磁気流体数値実験を行った。 • 円盤コロナ中にパーカー不安定性による磁気ループ構造が数多く形成される事を示した。 • ループ形成位置には空間的に偏りがある事がわかった。 円盤ガスはおおよそ10万度 　→　10度～1万度のガス＋100万度程度のプラズマ 　低温ガスを考える必要がある

  24. Isothermal disk model • Exponential density distribution • Isothermal　～　10000K 　→We assume that the heating of the magnetic dissipation balance with the cooling. • Kepler rotation • Initial magnetic fields has only azimuthal component and the magnetic pressure is β=100.

  25. Basic equations Resistive MHD equations (isothermal)

  26. Galactic Center Workshop 2009 Introduction: Observations Introduction: Theory Models Numerical Results Conclusion Magnetic loop structure in the Galactic center 300 pc 220 pc ※Distance from earth:8500pc ※Estimated mass: lower limit (We assume LTE to 13CO) ・kinetic energy 　～1.5×1051erg 　→ 100 × SN energy

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