Other
Scientific paper
Jul 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977apj...215..417g&link_type=abstract
Astrophysical Journal, Part 1, vol. 215, July 15, 1977, p. 417-426.
Other
6
Doppler Effect, Galactic Clusters, Intergalactic Media, Red Shift, Velocity Distribution, Astrodynamics, Cosmology, Hubble Diagram, Radial Velocity
Scientific paper
For an isotropic Maxwellian distribution of velocities with an arbitrary mean motion with respect to the fundamental frame, the distribution of redshifts that would be measured by a distant observer in an isotropic homogeneous universe is derived to second order in the peculiar velocities as a function of the relative Hubble velocity, the dispersion of the velocity distribution, and the peculiar mean motion. The mean of the redshift distribution and the next three higher-order moments about this mean are obtained explicitly as a function of the Hubble expansion parameter, the velocity dispersion, and a parameter that is a function of the mean peculiar velocity. In general, it is found that the redshift distribution is not a Gaussian, but has a measure of asymmetry expressed by the nonvanishing of the third moment about the mean. Consideration is given to the problem of trying to solve for the relevant parameters for a particular cluster of galaxies from the moments of the observed redshift distribution on the assumption that the velocity distribution of the galaxies in the cluster is isothermal.
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