Open Isopedic Magnetic Field in Composite SIDs

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Open Isopedic Magnetic Field in Composite SIDs

• Wu Yue, THCA, Tsinghua Univ.

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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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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

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M31 The Andromeda Galaxy
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M74 or NGC 628
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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.

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• 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).

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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.

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Two theorems for isopedic magentic field on
razor-thin disk (Shu Li 1997)
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Modified theorems for composite SID

• Shus 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.

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Modified theorems for composite SID

• Its worthy of point out that in single SID
  situation 0lt ? 1 and 1 ? 2 because the
  background equilibrium must be satisfied. In
  composite SIDs, 0lt1?? and 1 ? 2 .

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Basic equations for composite SIDs

• ??(r) is the angular speed at radius r. We
  define two dimensionless parameter

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Linearization Procedure

• ??0?1 ?1/?0ltlt1
• Also we assume
• Other variants also take the form

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Linearization Procedure

• For stationary solution with zero pattern speed,
  we set ?0.

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Some properties for aligned case

• Ds2 declines with ??/?
• Ds2 increases with

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For aligned case
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Unaligned (spiral) case

• When m 2, the properties share many similarity
  with the aligned case
• Also, we can prove that
• Ds2 declines with ?
• Ds2 increases with

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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.

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• 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.

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Main Reference

• Binney, J., Tremaine, S. 1987, Galactic
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• Shu F.H., Laughlin G., Lizano S., Galli D., 2000,
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