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trying to understand gas cloud collapse ? constant rate of contraction ? Rate Topic: -----

#1 25 January 2012 - 10:29 PM Widdekind 


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From the Virial Theorem,

K = -\frac{1}{2} U

\frac{M k_B T}{\mu} \approx \frac{3}{10} \frac{G M^2}{R}

\therefore R \; T = \frac{3}{10} \frac{G \mu}{k_B} M

Now, the Luminosity, radiated away as heat:

L = 4 \pi \sigma R^2 T^4 = \frac{4 \pi \sigma}{R^2} \left( R \; T \right)^4

is balanced by the release, of GPE:

L = -\frac{dU}{dt} = \frac{3}{5} \frac{G M^2}{R^2}\dot{R}

Er go,

\frac{4 \pi \sigma}{R^2} \left( R \; T \right)^4 = \frac{3}{5} \frac{G M^2}{R^2}\dot{R}

4 \pi \sigma \left( \frac{3}{10} \frac{G \mu}{k_B} M \right)^4 = \frac{3}{5} G M^2 \dot{R}

\frac{2 \pi \sigma}{G} \left( \frac{3}{10} \right)^3 \left( \frac{G \mu}{k_B} \right)^4 M^2 = \dot{R}

Assuming primordial gas composition (X = 3/4, Y = 1/4), so that the average particle mass is ~0.6 mH, w.h.t.:

\dot{R} \approx 100 km/s \times \left( \frac{M}{M_{\odot}} \right)^2

\approx \frac{1}{3} 10^{-3} c \times \left( \frac{M}{M_{\odot}} \right)^2

If so, then the "implosion speed" of collapse \dot{R} \rightarrow c near M \rightarrow 50 M_{\odot}. Are such speeds plausible ?

Such massive proto-stars collapse, on the MS, in ~104yrs:

Posted Image

And, Molecular Cloud 'cores' are typically <1 lyr across ; however, cloud collapse occurs isothermally (Sterzik 2003, Sterzik 2003). Perhaps isothermal collapse accounts for the slower observed collapse speeds ?
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#2 4 February 2012 - 07:24 PM homie12 


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I thought neutral gases in a vacuum do not coelesce?
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#3 4 February 2012 - 08:21 PM User is online  swansont 


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View Posthomie12, on 4 February 2012 - 07:24 PM, said:

I thought neutral gases in a vacuum do not coelesce?


Not chemically, but they would gravitationally.
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#4 4 February 2012 - 09:47 PM ajb 


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Virial Theorem, I am getting flashbacks to my undergraduate lectures in astrophysics.
"In physics you don't have to go around making trouble for yourself - nature does it for you" Frank Wilczek.

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