Galactic angular velocity of interstellar cloud

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SUMMARY

The discussion centers on the relationship between Galactic angular velocity (\Omega) and the stability of interstellar clouds. It establishes that if \Omega exceeds the threshold of sqrt(4piG\rho/3), the cloud cannot collapse radially. Participants are encouraged to estimate \Omega and compare it to the Galaxy's rotation rate, emphasizing the conceptual understanding of how increased angular velocity contributes to cloud stability and equilibrium conditions.

PREREQUISITES
  • Understanding of Galactic dynamics and angular momentum
  • Familiarity with gravitational physics, specifically the equation sqrt(4piG\rho/3)
  • Knowledge of interstellar medium properties and behavior
  • Basic concepts of equilibrium in astrophysical contexts
NEXT STEPS
  • Research the calculation of Galactic angular velocity using current astronomical data
  • Explore the implications of angular momentum on the stability of astrophysical structures
  • Study the conditions for equilibrium in rotating systems in astrophysics
  • Investigate the role of density (\rho) in the collapse of interstellar clouds
USEFUL FOR

Astronomers, astrophysicists, and students studying Galactic dynamics and the behavior of interstellar clouds will benefit from this discussion.

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I've got a question that I am stumped on right now

Show that if the Galactic angular velocity [tex]\Omega[/tex]
of an interstellar cloud is > sqrt(4piG[tex]\rho[/tex]/3), the cloud can not collapse in the radial direction. Estimate [tex]\Omega[/tex] and compare it to the rotation rate of the Galaxy.
 
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What is stumping you?
Start out conceptually, why would a higher angular velocity prevent a cloud from collapsing?---It might help to think about extremal cases.

Under what conditions would the cloud be in equilibrium?---I.e. if it collapses at zero angular velocity, and won't collapse at very high velocities... where will it be in equilibrium (in the radial direction).
 

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