Here's a direct rebuttal of the Tang and Zhang study that everyone loves to quote from wikipedia.
I read the paper when it came out - and it suffers from the same failing as a test of Arp's model that every test that has been done using SDSS and 2dF data suffers from - an incorrect understanding of what is being proposed in Arp's model. The assumptions they build into the study undermine its value as a test of Arp's model.
In searching for potential galaxies associated with QSO's they consider active galaxies within the redshift range of z=0.01 to z=0.2. It is good that they are looking at AGN as opposed to just any galaxies.
For their periodicity test they select all QSO-galaxy pairs in which the QSO's are within 200 kpc projected distance from the galaxy at the redshift distance of the galaxy. Here is the major problem that undermines this study. The assumption that redshift distances apply to the galaxies nearest the quasars is a serious flaw.
Its easier to understand why if I illustrate with a couple of examples. lets take NGC 5985 . This is a galaxy that has a number of QSO's aligned along its minor axis. The Tully-Fisher distance to NGC 5985 is 42 Mpc. At that distance the z=0.807 QSO has a projected distance from NGC 5985 of ~ 475 kpc. This is consistent with the projected distances of other examples brought forward by Arp for QSO galaxy associations within the local supercluster.
So if we set an upper limit of 500 kpc as a search distance for QSO's associated with AGN, we can predict at any given distance to the parent galaxy, what angular separation is appropriate for searching for QSO's. Now the authors of this Tang and Zhang study did that using a smaller 200kpc projected distance. But again they assumed Hubble distances to the galaxies.
What must be understood is that in Arp's model the ejected objects are expected to pass through a stage where they themselves may be ejecting objects (secondary ejections). But since the primary ejected objects have a sizeable intrinsic redshift when they produce secondary ejections, the redshift distances will be incorrect for those objects.
An illustration is the Seyfert 1 galaxy ESO 359-19(z=.056). On page 180 of Seeing Red Arp discusses the pair of quasars PKS0405-385 (z=1.285) and PKS0402-362(z=1.417) that are paired across ESO 359-19. These happen to be bright quasars with magnitudes of 18 and 17.2 and both are very active in X-rays.
PKS0405-385 has a greater angular separation from ESO 359-19 of slightly less than 80 arc min. Now using H0=70, the redshift distance of ESO 359-19 is ~240 Mpc. At that distance an angular separation of 80 arc min translates to a projected distance of ~5.6 Mpc. Clearly this is much farther from the proposed parent galaxy than is found in local samples. I think Arp would say that such a projected distance for a pairing is impossible in his model.
But this projected distance depends upon the accuracy of the redshift distance. If the parent galaxy is closer, then the projected distance is smaller. Now it turns out that ESO 359-19 is on the outskirts of the Fornax cluster for which Tonry et al (2001) find a SBF distance of 19.9 Mpc. In fact this is the same distance given by two galaxies in the Fornax cluster with Cepheid distances (NGC 1365 and NGC 1425). In Arp's model the Seyfert ESO 359-19 may be a galaxy ejected from a parent galaxy in the Fornax cluster. Thus its distance would be ~20 Mpc. At 20 Mpc an 80 arc min separation leads to a projected distance of ~465 kpc - which clearly falls within the distance range expected in Arp's empirical model. It should also be noted that the bright magnitudes of the QSO's are consistent with what would be expected for QSO's Arp claims are within the local supercluster.
But Tang and Zhang assume redshift distances are accurate for teh parent galaxies. At 240 Mpc, in order for a QSO to be within 500 kpc projected distance of a galaxy it must have an angular separation of < 7.2 arc min. To have a QSO fall within 200 kpc projected distance the angular separation would have to be
arc min. So in the Tang and Zhang study, they would never have identified the QSO pair across the Seyfert ESO 359-19 because they would not be looking for pairs at angular distances of 80 arc min.
I would expect this is a major problem with their study in general. As the redshift of the proposed parent galaxy increases, it becomes increasingly likely in Arp's model that the parent galaxy itself is an ejected object with a sizable intrinsic redshift. For example, the QSO/Sy1 PG 1211+143 has a redshift of z=0.081 and is proposed to be an object ejected by the Active galaxy M-87 in the Virgo cluster. PG 1211+143 lies along the ejection direction of the M-87 jet and has a magnitude of ~14 thus making it one of the brightest quasars. There are at least 2 pairs of quasars aligned across PG 1211+143. These quasars would be secondary ejections in Arp's model. The most distant of these has an angular distance of 28 arc min from PG1211+143. Assuming the current cosmological paradigm the redshift distance of PG1211 is 336 Mpc. That gives a separation of 2.7 Mpc for the farthest secondary quasar. At a Virgo distance of ~17 Mpc that would translate to a projected distance of ~140 kpc - well within the expectations of the model.
So to sum up - the problem with any of these SDSS/2dF studies that attempt to test Arp's model is that they assume the associated galaxies have no intrinsic redshift and they attempt to apply a purely statistical model to objects that must in fact be looked at on a case-by-case basis. It is not shocking under those assumptions that they end up finding no evidence supporting Arp's model.