Doppler shift produced by galactic differential rotation by material at different locations along a given line of sight. (a) The locations of five test particles in an overhead view.Arrows for each particle indicate the velocity (magnitude and direction). For each particle the Doppler shift will depend on the relative radial velocity of that particle and the Sun. (b) For each particle, the position of the arrow shows the amount of Doppler shift.
measured around the galactic plane, starting in the direction of the galactic center.
We also define a convenient reference frame for measuring velocities, called the local standard of rest, LSR. If the only motion the Sun had were its orbital motion about the galactic center, then the local standard of rest would coincide with the Sun's motion. That is, we could simply measure motions with respect to the Sun (so-called heliocentric velocities). However, because of gravitational interactions with its nearest neighbors, the Sun has a small motion superimposed on its circular orbital motion, so it is not a convenient reference point for velocities. There are actually two ways of defining the LSR:
(1) Dynamical. The origin of the coordinate system orbits at a distance R0 from the galactic center, and R0 is the distance of the Sun from the galactic center. The coordinate system moves with a velocity v(R0) = v0, or fl(R0) = O0, appropriate for circular motion at R0. Defined
slower than us. We are therefore overtaking it, so there is a Doppler shift to shorter wavelength (blueshift).
In determining the rotation curve for our galaxy, it is convenient to introduce a set of coordinates, known as galactic coordinates, measured from our viewing point at the Sun. They are shown in Fig. 16.5. The galactic latitude, b, measures the angle above or below the galactic plane of an object. The galactic longitude, /, is an angle
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