Wednesday, November 26, 2014

tidal stretching of Palomar 5

the globular cluster Palomar 5 orbits the Milky Way and is stretched by tidal forces. on what time-scale would the tidal arms reach all around the Milky Way?

2 comments:

  1. the equilibrium condition would be $\upsilon^2=GM/R$ with the distance $R$ from the Milky Way centre to Palomar 5 and with the mass $M$ of the Milky Way. the variation in velocity between the close and far edges of Palomar 5 would be
    \begin{equation}
    \Delta\upsilon= \left|\frac{\partial\upsilon}{\partial R}\right|\Delta r = \frac{1}{2}\sqrt{\frac{GM}{R^3}}\Delta r
    \end{equation}
    and therefore, the time scale $t$ needed for the slower moving far edge to circle the Milky way at the velocity $\Delta\upsilon$ results as
    \begin{equation}
    t = \frac{2\pi R}{\Delta\upsilon} = 10^{18}\mathrm{sec} = 10^{11}\mathrm{years}
    \end{equation}
    with the distance $R=23~\mathrm{kpc}=10^{21}m$, the mass $M=10^{12}M_\odot$ and the size $\Delta r = 10^{19}m$ of Palomar 5. comparing this to the orbital time $T = 2\pi R/\upsilon=10^9\mathrm{yr}$ shows that the arms will reach all around the Milky Way after 100 orbits.

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    1. thinking about this it seems to me that this puts a bound on the age of Palomar 5, luckily that's less that the inverse Hubble constant. I'd be curious how old the stars in Palomar 5 are: aren't they very old because there's no star formation there?

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