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Open Isopedic Magnetic Field in Composite SIDs

Open Isopedic Magnetic Field in Composite SIDs. Wu Yue, THCA, Tsinghua Univ. Contents. Basic model description: SID model, isopedic magnetic field, Some results for aligned case and unaligned(spiral) case The futher applications.

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Open Isopedic Magnetic Field in Composite SIDs

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  1. Open Isopedic Magnetic Field in Composite SIDs Wu Yue, THCA, Tsinghua Univ.

  2. Contents • Basic model description: SID model, isopedic magnetic field, • Some results for aligned case and unaligned(spiral) case • The futher applications

  3. SID model Singular Isothermal Disk • Singular the surface mass density is inversely proportional to the radius • Isothermal we treat the material in the disk as ideal gas and it has an effective “thermal” pressure

  4. M31: The Andromeda Galaxy

  5. M74 or NGC 628

  6. Composite SIDs • In the evolutionary history of the galaxies, the early-type galaxies are made of mainly gas. The late-type galaxies are mainly made of stars. Composite SIDs means there are two SIDs, one is gaseous disk g and the other is stellar disk s.

  7. Galaxy M 83. The upper panel shows a picture in visible light (VLT, FORS team), the lower panle shows an X-ray image taken by the Chandra X-ray telescope (R.Soria & K.Wu).

  8. Isopedic Magnetic Field • Originate in the external (interstellar) medium. • Disks have dimensionless ratios  of the mass to flux that are spatially constant, a condition that we term isopedic.

  9. Two theorems for isopedic magentic field on razor-thin disk (Shu & Li 1997)

  10. Modified theorems for composite SID • Shu’s two theorems are made for Single SID. For composite SIDs, they has to be changed slightly. Here we have the assumption that the isopedic magnetic field ONLY interact with the gaseous SID. • For the first theorem, we just ignore the existence of the stellar SID and follow the procedure to get the same result. • For the second theorem, because of the gravitational coupling, it take a different but similar form.

  11. Modified theorems for composite SID • It’s worthy of point out that in single SID situation 0< · 1 and 1·· 2 because the background equilibrium must be satisfied. In composite SIDs, 0<1+ and 1·· 2 .

  12. Basic equations for composite SIDs • =(r)is the angular speed at radius r. We define two dimensionless parameter

  13. Linearization Procedure • =0+1 |1/0|<<1 • Also we assume • Other variants also take the form

  14. Linearization Procedure • For stationary solution with zero pattern speed, we set =0.

  15. Some properties for aligned case • Ds2declines with =/ • Ds2increases with

  16. For aligned case

  17. Unaligned (spiral) case • When m¸ 2, the properties share many similarity with the aligned case • Also, we can prove that • Ds2declines with  • Ds2increases with

  18. Galactic winds & isopedic magnetic field • Isopedic magnetic field is open • Comparing with the coplanar magnetic field, the isopedic one will be easier to allow the material to go out and may also amplify this procedure.

  19. Many galaxies have spiral structure. According to the density-wave theory (C.C.Lin and Frank H. Shu), the spiral arms have higher density and consequently have higher vertical magnetic field in our model. • Apart from the central outflows of the galaxies (it may concern the AGN and so on), the spiral arms may have stronger material escaping due to stronger magnetic field. We can called it Spiral Arm Winds.

  20. Main Reference • Binney, J., & Tremaine, S. 1987, Galactic Dynamics (Princeton : Princeton Univ. Press) • Frick P. et al., 2000, MNRAS, 318, 925 • Goldreich, P., & Tremaine, S. 1979, ApJ, 233, 857 • Kalnajs A.J., 1971, ApJ, 166,275 • Lin C.C., Shu F.H. , 1964, ApJ, 140, 646 • Lou Y.-Q., Shen Y., 2003, MNRAS • Ostriker J.P., Peebles P.J.E.,1973, ApJ, 186, 467 • Shu F.H., Laughlin G., Lizano S., Galli D., 2000, ApJ, 535, 190 • Shu F.H., &Li, Z.-Y 1997, ApJ, 475, 251 • Toomre A., 1964, ApJ, 139, 1217

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