Statistics of redshift periodicities

208 Current Issues in Cosmology
where the observed radial velocities (presumably virialized) have a dispersion of
1000 km s −1 .Asecond major claim, made by Tifft and Cocke (1984), was that there
exists a global, galactocentric quantization of redshifts. For galaxies with narrow
HI profiles a periodicity of 24.2 km s −1 was claimed, while for broad HI profiles
the claimed periodicity was 36.2 km s −1 .Tosee these latter periodicities it was
necessary to correct for a solar motion of
V ⊙ = 233.6kms −1 , l ⊙ = 98.6 ◦ , b ⊙ = 0.2 ◦
close to the galactocentric solar motion.
Subsequently, a series of progressively higher periodic frequencies have been
claimed by Tifft, some of which lie on the wrong side of the Nyquist frequency. The
current study is concerned only with these initial claims, however. An immediate
problem arises from the fact that, in correcting for the vectorial solar motion, three
free parameters have been introduced. Thus a Hubble flow of, say, 72 km s −1 in
a system of galaxies with characteristic projected separation 0.5 megaparsec, has
a characteristic velocity separation 36 km s −1 and we can imagine that this might
be made to appear periodic with some “parameter tweaking,” in essence hunting
for periodicity. The way to handle this problem is to construct synthetic data sets,
identical in all respects to the real one except for the periodicity under test, and to
operate on them all, real and synthetic, in identical fashion.
The 72 km s −1 claim was tested by Guthrie and Napier (1990) using 48 spiral
galaxies in the Virgo cluster, which avoided the core and which had well-determined
redshifts (formal accuracies σ ≤ 10 km s −1 ). This is the nearest rich cluster of
galaxies, and had not previously been used to test for redshift periodicity claims,
and so is an unbiased sample. Guthrie and Napier (1990) attempted to correct these
redshifts for infall towards the Virgo cluster and found that there was indeed a
strong periodicity of 71 km s −1 , essentially identical to that claimed for the Coma
cluster.
In Fig. 17.1 the differential redshifts of the 48 spirals are plotted in the fixed,
galactocentric frame of reference. For this plot the latter was taken to be the IAUapproved
V ⊙ = 220 km s −1 , l ⊙ = 90.0 ◦ , b ⊙ = 0.0 ◦
where (V ⊙ , l ⊙ , b ⊙ ) are respectively the speed, galactic longitude, and galactic
latitude of the Sun’s velocity vector around the nucleus of the Galaxy. The data in
Fig. 17.1 have been smoothed by a standard procedure: The data set is converted
from the velocity to the frequency domain, high frequencies are chopped off, and the
remaining signal is reconverted back to the original velocity domain. It is assumed
that the high frequencies so removed correspond to noise and measurement error