Statistics of redshift periodicities

214 Current Issues in Cosmology
0.6
Count
0.45
0.3
0.15
0
−211.2 −70.4 70.4 211.2 352 492.8
velocity (km/sec)
Figure 17.5 Velocities of 103 KM galaxies relative to a fixed solar apex as described
in the text. Smoothed with a cut-off at 15 km s −1 . There is a best-fit periodicity of
35.2 km s −1 .
4 The QSO periodicity claim
The third anomalous redshift claim tested so far is that QSOs in the neighborhood
of bright, nearby, active spirals show a periodicity of 0.089 in log 10 (1 + z). There is
some imprecision in the formulation of this hypothesis (what do we mean by close?
By active? What phase should we associate with this periodicity, and with what
standard errors?). The hypothesis was tightened up somewhat by bootstrap sampling
of 116 QSOs used by Karlsson (1990)totest it, and fresh data were then employed
as described in Burbidge and Napier (2001), alias BN: These comprised 57 QSO
pairs with separations less than 10 arcseconds, 39 X-ray QSOs near active galaxies
(comprising a complete sample), and 78 3C(R) radio QSOs, again comprising a
virtually complete sample. Figure 17.6 is a histogram of the combined Karlsson and
BN data sets: The periodicity is clearly present and seems to extend three cycles
beyond that originally claimed. Monte Carlo trials yield a formal significance level
of a few parts in 100 000, whether the null hypothesis is defined through smoothing
of the given data or the z-distribution of QSOs as a whole.
It has often been argued that the QSO periodicity is an artefact of observational
selection effects (see the discussion in BN). However the data employed here
were selected precisely to avoid such effects. It was also claimed that the result is
a statistical artefact caused by edge effects (Hawkins et al. 2002), but this has been
shown to be erroneous (Napier and Burbidge 2003): inter alia, edge effects were
automatically allowed for in the procedures employed, and the periodicity is easily
seen by eye, without any statistical analysis (Fig. 17.6). Again, however, although
the periodicity is clear, the circumstances under which it arises are not. For example,