SAMPLE INCOMPLETENESS IN THE STUDY OF THE QUASAR-GALAXY ASSOCIATIONS AS A RESULT OF GRAVITATIONAL LENSING

For decades, the angular associations between faint galaxies and high redshift quasars have remained to be a well-known puzzle, which is oft en cited as an evidence for the noncosmological origin of quasar redsh ifts. This happens because the attempt at interpreting the phenomenon as being due to gravitational lensing fails in producing the reported high amplitude of the quasar-galaxy associations unless some unconvent ional hypotheses are made such as an extremely large velocity dispersi on for galaxies, a serious contamination of the overall quasar number counts or a strong matter clustering on galaxy scale. While there are good reasons to believe that the magnification bias should be a natura l cause for the quasar-galaxy associations, we re-address the question by taking into account an important factor that has been overlooked i n previous studies: The expected amplitude of the association in the f ramework of gravitational lensing depends sensitively on the quasar li miting magnitude, whereas none of the quasar samples in the measuremen ts is actually complete. Taking this correction into account our predi ctions of the galaxy enhancement factors based on a simple lensing mod el are essentially consistent with observations, thus providing a help ful clue to eventually resolving the longstanding puzzle in astrophysi cs.