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1.3.1 Doppler Shift

If a source of light moves with velocity v relative to the observer so that the velocity vector makes an angle theta with respect to the radial vector from the observer to the source, the spectral shift of the light from the source measured by the observer will be given by

Equation 1.1 (1.1)

where v = |v| and c is the speed of light. For small velocities, this formula reduces to the Newtonian limit z = v / c for radially outward motion.

For stellar motion in our galaxy it is common to find small Doppler shifts both positive and negative and these are interpreted in terms of stars moving away from or towards us. James Terrell in 1966 interpreted the quasar redshifts as arising from fast ejection of quasars from the galactic centre. The problem with this concept was that it endowed the galactic centre with violent activity, which was not consistent with the undisrupted motions of stars in the area. This idea was taken further by Hoyle and Burbidge (1966), who suggested that, unlike the case for our galaxy, ejection from a galactic nucleus that shows violent activity would appear normal. in particular, they suggested NGC 5128 as a likely site for ejection.

The Doppler hypothesis thus delinks redshift from distance: that is, a large redshift does not imply that the source is very distant. This eases the energy budget of a typical source. However, if several such sources are to be ejected from a single site (such as NGC 5128) the energetics of that site becomes problematical. Moreover, there is the problem of blueshifts.

The problem was first highlighted by P. Strittmatter in 1966 (unpublished). A site of explosion will eject quasars in all directions. Thus, unless the explosion occurred a long time ago, some quasars would still be travelling towards the observer and these should show blueshifts. Moreover, these quasars would appear brighter due to the blueshift effect and would tend to dominate in a sample that is complete with respect to all quasars brighter than a specified flux level. Detailed calculations based on isotropic ejection of all such quasars show that the ratio of blueshifted (N-) quasars to redshifted (N+) quasars in a flux-limited sample is

Equation 1.2 (1.2)

where zm is the maximum redshift in the sample, and alpha is the spectral index of a typical source. Thus, for a maximum redshift of 2, say, and a spectral index unity, we may expect 81 times as many blueshifted sources as redshifted ones!

We will return to this problem in Chapter 15. For the time being we leave the topic of Doppler shifts as it was perceived in the early sixties, and move on to the next alternative.

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