H4 - density given in chapter 1 of the text Make sure the mass of the isothermal singular sphere is the same as that of the Bonner-Ebert critical

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Homework # 4, due 3 Mar 1. In this problem, you are asked to calculate the expected extinction from a cool cloud. Assume it is spherical and located at a distance of 100 pc from the Earth. Assume the cloud is isothermal with a temperature of 10 K. Assume it is embedded in a warm diFuse ISM with temperature 10,000 K and a density of 1 cm - 3 . Use the Bonner-Ebert critical spherical con±guration to esti- mate the total cloud mass. What is the mass? (You do not have to solve the diFerential equations, use the known expression.) Assuming the density pro±le in the cloud has the form of the isothermal singular sphere, compute an expression for the visual extinction as a function of angular distance from the cloud cen- ter from stars located behind the cloud as seen from the Earth. You may use the relation between visual extinction and column
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Unformatted text preview: density given in chapter 1 of the text. Make sure the mass of the isothermal singular sphere is the same as that of the Bonner-Ebert critical sphere. Hint: what is the radius of the cloud with this density pro±le? Now, instead, assume the density pro±le in the cloud has the form ρ = ρ o b 1 + 13 ( r/R ) 2 B-1 . Re-compute the visual extinction as a function of angular dis-tance from the cloud center. Compare the two predicted extinction cuves to data for Barnard 68 (a ±gure is included in the course notes) and comment. 2. Show that the gravitational potential at a distance r from a point mass m is the same as that as that inside an isothermal singular sphere at the radius r where the enclosed mass is M ( r ) = m ....
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This note was uploaded on 01/25/2012 for the course AST 346 taught by Professor Lattimer during the Spring '11 term at SUNY Stony Brook.

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