2. The observational data and probability calculations
Data on all four pairs of QSOs with very different redshifts are shown in Table 1.
Table 1. Very close pairs of QSOs
Thus two of the four close pairs involve radio-emitting QSOs which are very rare in comparison with radio-quiet QSOs. It is usually assumed that only 1% of QSOs are strong radio emitters.
Also in three of the four pairs there is, in addition to the very different emission redshifts, an absorption redshift which has the same value as one of the emission redshifts. In AO 0235+164 an absorption redshift of 0.524 in A is almost identical with the emission redshift of B. In 1009+025 A there is an absorption redshift at 1.62 which is the emission redshift of C, and in 1548+114 the emission redshift of A, 0.436, is almost identical with the galaxy redshifts of 0.434.
On the assumption that QSOs have cosmological redshifts and are randomly distributed we can use equation (1) to estimate n for each pair. Provided , then , the probability to find one QSO within in a sample of N `primary' QSOs. We discuss the four pairs in turn.
AO 0235+164 was originally described as a BL Lac object. However the recent work has shown that AO 0235+164 A is a rapidly variable QSO with an emission redshift and AO 0235+164B is an adjacent QSO or AGN. Thus the system should be removed from the BL Lac category. The number of QSOs which are known to be rapidly variable is very small, so that we put N = 100. Thus we find that the probability that one member of this sample has a second QSO closer than and brighter than is . A much more conservative approach is to take all 515 sources from the 1-Jansky catalog (Kühr et al. 1981) as the parent population; then this probability increases to .
The two QSO pairs 1009-025 and 1148+055 were found in an optical survey for gravitational lenses by Surdej et al. (1994). In recent years, there have been four such optical surveys performed, all of which took basically the same strategy: to look for companions around high-luminosity QSOs, since for those the magnification bias should increase the observed fraction of lensed sources. Kochanek (1993) lists the surveys and the number of QSOs in each of them; there is a considerable overlap of targets among the four surveys. The total number of QSOs imaged in these surveys is . The expected number of pairs, where the second QSO is brighter than and lies within of the primary QSO, is . Similarly, the expected number of QSOs within of the primary QSOs brighter than is . Even a most conservative estimate yields very low probabilities: The probability to find two (or more) QSO companions brighter than (where we assume the surface density of QSOs to be about 50 per square degree) within of the 648 high-luminosity QSOs in these lens surveys is .
QSO 1548+114 was selected out of a sample of 280 radio sources from the 4C catalog. Not all these sources are QSOs, so that . As reported in Hazard et al. (1973), only 53 of the 280 radio sources had a blue stellar object within the positional error box on the POSS. Hence we take . The fainter of the QSOs in this pair has ; the number density of QSOs up to this magnitude is estimated to be about (e.g., Hartwick & Schade 1990). Hence the expectation value of the number of pairs with separation in the sample investigated by Hazard et al. (1973) is .
We are aware of the fact that these probabilities have been calculated a posteriori and they should be interpreted with care. The object in the 0235+164 system is extended and relatively faint (Burbidge et al. 1996) and would not necessarily be called a QSO. Nevertheless, for all three surveys discussed, the probability for close pairs is small. In order to evaluate an `overall' probability, one would like to combine these samples. If we do so, the total number in the sample is . If we then put and (corresponding to close companions brighter than , then as compared with the four pairs which are found, the probability of which is .
However, this consideration overlooks that there are many QSO samples, and results on near companions are more like to be published if a close pair is found (there is a negative `publication bias'). However, only a small fraction of QSOs are imaged to sufficient detail to allow for the identification of close companions and subsequent spectroscopic identification - note that the overwhelming fraction of point-like companions are Galactic stars (Kochanek 1993). Thus, as a conservative estimate one might assume that a total of QSOs have been investigated for a close companion QSO with magnitude brighter than (companions as faint as that will not be readily identified on the POSS!); then the probability of finding four (or more) companions within of the primary QSOs is
and the expected number of pairs is .
In the following section we consider ways of explaining the existence of these pairs.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998