9'1'2 Noncircular motion

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9.1.2 Non-circular motion the (l, v) plot

• by Nari Jeong 2007. 10. 2

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Non-circular motion

• Observed plots deviate significantly from naive
  (l, v) plot
• more complex motion
• Possibilities
• 1. Axisymmetric radial expansion
• 2. Oval distortions
• 3. Spiral structures
• 4. Random motion

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Axisymmetric radial expansion

• Ring expand radially as well as rotating
• expansion perpendicular to line of sight at
  tangent point
• v unaffected
• Line of sight through Galactic center
• expansion parallel
• section of sine curve open up into curve loops

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Oval distortion

• Ellipticity of rings changes the angle it
  subtends on the sky
• changes in velocity
• Dynamical theory needed to predict changes
• Weak bar theory

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Oval distortion

• - Gravitational potential F (R, f)
• in which object orbit is the sum of 2 terms
• - F (R) and weaker bar
• - where F is the force of the bar and O pattern
  speed of the bar
• (angular velocity of bar in rotation like
  solid body)
• - Orbit is compound of clockwise motion around
  a circle and anti clockwise motion about epicycle
  centered on guiding center and has principal axes
  aligned with local radial and tangential
  directions
• - Orbit is at pericenter (closest to Galactic
  center) when epicycle displaces object inwards
  and at apocenter (furthest from Galactic center)
  when epicycle displaces the object outwards.
• - Contribution to vf from circle and epicycle
  add at pericenter and subtract at apocenter.

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Oval distortion

• - Effect of epicycle upon (l, v) plot depends on
  f
• - angle between sun center line and major axis
  of orbit
• - in general traces becomes closed curve
  reminiscent of cross section through aerofoil

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Spiral structure

• - Spiral form if stars and gas clouds move on
  elliptical orbits whose major axis position vary
  smoothly as a function of radius
• Disk made of number of ovals each oval
  uniformly populated with gas clouds because long
  axes of ovals rotate more than 540o from smallest
  to largest ovals
• oval in some places are closer together
• surface density of clouds higher in these regions
  
• crowded parts form 2 spiral arms

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Spiral structure

• - Observed plot of MW
• - crowded regions
• identified to spiral arms
• - transformation
• to real space
• - needed to be
• modeled dynamically

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Random motion

• clouds do not move on perfectly symmetric orbits
• at any given position velocities spread
  over a few km/s
• Within clouds spread in velocities of
  individual atoms
• Effect on plot smoothing