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Astro 346, Spring Semester 2006 Homework, 2nd set, solutions. Problem 1: Radiation transport a) The optical depth is increased at the line frequency, because the line adds its emission and absorption coeFcient to those of the continuum radiation processes. Any increase in the absorption coeFcient implies an increase in the optical depth. b) We are dealing with a thermal gas, so LTE applies and the source function S ν , is a Planckian. Consider the general solution to the radiation transport equation I ν ( τ ) = I ν (0) exp( - τ ) + Z τ 0 dτ 0 S ν ( τ 0 ) exp( - τ + τ 0 ) (8 . 9) If the source function is a constant and LTE applies (thermal particle distribution!), then S ν = B ν ( T ) and I ν ( τ ) = I ν (0) exp( - τ ) + B ν ( T ) [1 - exp( - τ )] ’ ± I ν (0) + j ν s for τ ¿ 1 B ν ( T ) for τ À 1 (8 . 10) You can distinguish three cases: – The continuum optical depth is À 1 . One observes a Planckian. – The continuum optical depth is
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