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Period of radial oscillations

  1. Oct 4, 2015 #1
    • Missing template due to originally being posted in different forum.
    Assuming a neutron star is a uniformly dense sphere of radius 10km and mass =1.4 mass of sun, derive the period of radial oscillations.First use hydrostatic equilibrium to calculate p, then the velocity of sound is $$v= \sqrt{ \gamma p / \rho}$$, so the period of pulsation is time it takes from r=0 to r=R and come back.

    I first used hydrostatic equilibrium:$$ \frac{dp}{dr}=- \frac{GM(r)\rho}{r^2}$$
    and $$M(r)= \frac{4}{3} \pi r^3 \rho$$ so that $$ p(r)=- \frac {2}{3} \pi \rho^2r^2$$,
    so question 1: how does there is a negative value?
    question 2:how do I calculate time from r=0 to r=R and back?
     
  2. jcsd
  3. Oct 5, 2015 #2

    mfb

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    Don't forget the integration constant. What is the boundary condition for pressure?
    That follows from the velocity.
     
  4. Oct 5, 2015 #3
    Thanks for your answer. No the problem doesn't say the boundary condition. How do I know that?
     
    Last edited: Oct 5, 2015
  5. Oct 5, 2015 #4

    mfb

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    What do you expect as pressure at the surface?
     
  6. Oct 5, 2015 #5
    Because P(r) decrease along r it would be 0? so I can derive the constant?
     
  7. Oct 6, 2015 #6

    mfb

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    It is zero, as particles would move outwards otherwise. Yes, this allows to find the constant.
     
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