Interpretation 2: At fixed
Keywords: class-spectral-axis-v12

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Interpretation 2: At fixed

Let's assume that the measured spectrum is made of a line centered around in the observatory frame. The associated rest frame frequency, i.e., the frequency of the line at rest, will be . The observation is naturally set up so that the source frame is also the rest frame. This implies that , and are linked through

| (6)

The modeller will use the Doppler effect to interpret the observed frequency difference as a local velocity difference (projected along the line of sight direction) around the systemic velocity of the source. Let's write ( ) the velocity associated to ( ). The velocity difference will be noted

| (7)

In order to derive this velocity difference, we associate the velocity to each observed frequency through the Doppler effect, i.e.,

| (8)

It is easy to deduce that

| (9)

i.e., the local velocity difference is proportional to the observed frequency difference. We can define a linear velocity axis associated to the set of brightnesses, as

| (10)

This velocity scale is only meaningful locally, i.e., as long as the brightnesses can be associated to the line rest frequency under consideration.

Next: Heterodyne receivers and signal/image Up: Introduction Previous: Interpretation 1: At fixed Contents