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Unformatted text preview: Exam # 1 Solutions Lots of partial credit given, so give at least a qualitative answer to each item. Some useful constants are given at the end of the exam. 1. Extensive spectral observations often show two peaks in high excitation emis- sion molecular line profiles from star-forming molecular globules, and the blue peak is usually stronger than the red peak. 1.1. With equations or diagrams, indicate how a double-line spectral line could be formed in this situation. In a star-forming globule, material is infalling. A double line profile could be formed only if a given radial velocity could originate from two different parts of the cloud. If the infalling velocity and density both varied inversely with radius, you would get a situation that a line-of-sight through the cloud, off-center, would traverse first a red-shifted region of low intensity, then a red-shifted region of high intensity, then a blue-shifted region of high intensity and finally a blue-shifted region of low intensity. At the cloud’s midpoint, there is no Doppler shift because there is no component of the cloud’s velocity along the line-of-sight. This could produce a line with two peaks: one red-shifted and one blue-shifted. 1.2. In order to obtain double-line spectral lines, how should the infall velocity behave with radius? A necessary condition is that the infall velocity vary inversely with radius. In this case, a line of sight contains two points with the same radial velocity from the observers viewpoint. Example: v ( r ) = v /r . If R is the distance from the cloud center to the line-of-sight through r , and z from the line θ = 0 to r , a point in the cloud at position r,θ satisfies z = r sin θ . Then the component of the cloud’s velocity along the line-of-sight is v r = v ( r )sin θ . Solving for r = ( v /v r )sin θ which is double-valued as θ goes between 0 and π/ 2....
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- Spring '11