set3-f5 - In the absence of energy exchange with the...

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Astro 405/505, fall semester 2005 Homework, 3rd set, return before Friday, October 21, 4pm. Don’t forget to give your name. Problem 5: Gravitational collapse Consider a homogeneous and spherical gas cloud of mass M that is gravitationally unstable. Neglecting pressure and cooling derive an estimate for the duration of the collapse from the initial radius r 0 to a radius r ¿ r 0 . Start with explaining what physics principle would govern the collapse. Then use that physics principle to determine how the collapse timescale depends on the average mass density of the gas cloud. Estimate the time it takes to form stars out of a cloud of cold interstellar gas with number density n = 100 H - atoms / cm 3 . Estimate the time it takes to form galaxies out of diFuse interstellar gas with number density n = 10 - 4 H - atoms / cm 3 . Problem 6: Jeans criterion
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Unformatted text preview: In the absence of energy exchange with the environment a gas is said to evolve adiabatically and the pressure P ∝ ρ γ , where γ is the adiabatic index (=5/3 for a monatomic gas). Consider a spherically symmetric gas cloud under adiabatic conditions. Use the ideal gas law to derive a relation between central pressure and the radius of the cloud, that delineates the boundary between gravitationally stable and unstable situations. ±or simplicity assume the external pressure to be negligible. Gas in star-forming regions in the Galaxy typically has a density n = 10-4 H-atoms / cm 3 and a temperature T ’ 10 K. What is the size of a typical star-forming region? Calculate the mass of unstable gas clouds and compare with the mass of the sun....
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