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answerhappygod
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wrong or incomplete solution gets a downvote.
wrong or incomplete solution gets a downvote.
[6] [4] 3. (a) Two molecular self-gravitating clouds have just started to collapse. Cloud A has a mean density Pa = 10²PB, where pe is the mean density of cloud B. Which of the clouds will collapse first, and how much faster than the other? What can be deduced about the cloud A and B temperatures if their masses are the same? Finally, assuming that their collapse is isothermal, what can be said about the luminosity of the cloud A during its collapse compared with that of cloud B? (b) A dense molecular cloud of temperature Tc = 10 K finds itself inside a Stromgren zone with gas density ps. Assuming that the cloud self-shields against the UV radiation and remains at temperature Tc, what process sets the minimum molecular cloud density Pc inside the zone? Express pe in terms of ps. (c) Assuming the typical interstellar dust abundance within the cloud, and that all dust particles have size a = 0.1 microns, calculate the minimum radius of the cloud, Re, at which it is able to self-shield against the UV. Hint: Use the approximate Mie theory, and assume cloud density p= pe. What would the optical depth of such a cloud be to the optical radiation from the Sun? Hint: What is the wavelength of that radiation? (d) The massive star that ionised the Stromgren zone is very bright, with its luminosity very close to the Eddington limit. Assuming that all of the stellar radiation incident on the cloud is absorbed by it, find the radiation pressure force experienced by the cloud. Derive a condition on the cloud properties for it to be driven away by the star's radiation pressure. [6] [4]
[6] [4] 3. (a) Two molecular self-gravitating clouds have just started to collapse. Cloud A has a mean density Pa = 10²PB, where pe is the mean density of cloud B. Which of the clouds will collapse first, and how much faster than the other? What can be deduced about the cloud A and B temperatures if their masses are the same? Finally, assuming that their collapse is isothermal, what can be said about the luminosity of the cloud A during its collapse compared with that of cloud B? (b) A dense molecular cloud of temperature Tc = 10 K finds itself inside a Stromgren zone with gas density ps. Assuming that the cloud self-shields against the UV radiation and remains at temperature Tc, what process sets the minimum molecular cloud density Pc inside the zone? Express pe in terms of ps. (c) Assuming the typical interstellar dust abundance within the cloud, and that all dust particles have size a = 0.1 microns, calculate the minimum radius of the cloud, Re, at which it is able to self-shield against the UV. Hint: Use the approximate Mie theory, and assume cloud density p= pe. What would the optical depth of such a cloud be to the optical radiation from the Sun? Hint: What is the wavelength of that radiation? (d) The massive star that ionised the Stromgren zone is very bright, with its luminosity very close to the Eddington limit. Assuming that all of the stellar radiation incident on the cloud is absorbed by it, find the radiation pressure force experienced by the cloud. Derive a condition on the cloud properties for it to be driven away by the star's radiation pressure. [6] [4]