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5.3 Magnitudes (fluxes)

5.3.1 Effects due to space curvature

The global effect is the geometrical dilution of light along the light path (see Fig. 25) from light emission (scale factor R1) to light reception (scale factor R1). The global effect depends on z and the cosmological parameters and applies to the total amount of light, measured e.g. as bolometric magnitude.

Light is generally measured in limited frequency intervals, e.g. the blue wavelength region (B-magnitude). Due to the redshift, different wavelength regions are moved into the frequency range measured, and a K-correction has to be applied. The correction is a function of the spectral energy distribution.

Local distortions of the light path may lead to considerable changes of magnitude, e.g. enhancement through gravitational lensing.

Local effects of particle motion due to the presence of mass concentrations influence magnitude measurements in the same way as the global effects. This holds for both the motion of the object and the motion of the observer. In the special relativistic approximation, dimming or brightening due to local motion can be described as aberration: the change in the amount of light received because of the concentration of radiation into a cone extending into the direction of particle motion. For peculiar galaxy velocities, which are generally much smaller than c, the effect can be neglected.

A (1 + z) correction to the magnitude was introduced by Hubble and Humason (1931):

``A redshift, by redistributing the radiation to correspond with a lower temperature and hence with a later spectral type, introduces an increment to the photographic magnitude . . .''

In a paper by Hubble and Tolman (1935) the correct (1 + z)2 correction is used:

``. . . it has been derived in such a way as to make proper allowance, first, for the double effect of nebular recession in reducing both the individual energy and the rate of arrival of the photons, and then for the further circumstance that a change in spectral distribution of the energy that does arrive will lead to changes in its photographic effectiveness.''

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