Figure 8.9. A 1-m2 column through an emitting cloud along the line of sight. The total radiation from a column of cross section 1 m2 and length A is simply the product of the average power emitted per unit volume and the length, jav A (W m-2 Hz-1). The detected specific intensity I turns out to be equal to this product divided by 4n.

The atoms that actually contribute to the radiation detected by an observer do not come from a simple column of the cloud as sketched in Fig. 9, but rather from a much larger area and from a cone of angles as shown in Fig. 8. However, the simple view in Fig. 9 is an easy way to visualize the meaning of the expression (50) or (53) for I. The additional factor 1/(4n) tells us that only radiation emitted into one steradian from each element of the column contributes, in effect, to the specific intensity. Many measurable quantities in astrophysics are similarly proportional to a source function (like j) integrated along the line of sight.

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