Galaxies Lecture 24

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The Winding Problem

  • Winding Problem
    • Our galaxy differentially rotates. If we assume that spiral arms hang around for about a Hubble time (1010yrs), and if spiral arms move with the rotation of the galaxy, then we’d expect arms to have a characteristic angle of 0.15^\circ . However, we measure an angle of \sim 5^\circ .
    • Either spiral arms are short-lived (in which case we should see many fewer spiral galaxies with clear arms–but we see about \frac12), or spirals are density waves kicked up by a precessing bar.
  • Precessing Bar
    • Considering the form of a gravitational potential in a rotating reference frame, there is a potential for an oscillating potential with:
 \kappa ^2=R\frac{d}{dR}{(\Omega ^2)}+4\Omega ^2 \,\!

or written in terms of the Oort constants:

 \kappa ^2=-4B\Omega  \,\!

This results in a pattern which precesses with angular velocity:

 \Omega _ p=\Omega -{n\kappa \over m} \,\!

where n,m are integers representing different harmonics. In practice, the lower harmonics are excited with greatest amplitude.

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