Inversion of the Amplification Bias and the Number Excess of Foreground Galaxies around High Redshift QSOS

Details Inversion of the Amplification Bias and the Number Excess of Foreground Galaxies around High Redshift QSOS Inversion of the Amplification Bias and the Number Excess of Foreground Galaxies around High Redshift QSOS

Feb 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992a%26a...254...14s&link_type=abstract

Astronomy and Astrophysics, Vol.254, NO. FEB(I), P. 14, 1992

Astronomy and Astrophysics

Astrophysics

16

Scientific paper

In an inhomogeneous universe, where gravitational light deflection caused by matter clumps can affect the apparent brightness of distant sources, the relation between the intrinsic luminosity function and the observed source counts (at fixed redshift) is no longer simple. Rather, the source counts are determined by convolving the intrinsic luminosity function with a magnification probability distribution, an effect called amplification bias. Given the observed source counts, and assuming a magnification probability distribution, the intrinsic luminosity function can in principle be obtained by deconvolution. Here, a method for this deconvolution is described and applied to high-redshift QSO source counts, using a parametrized form for the magnification probability. It is shown that the amplification bias can in fact be considerable, and we present an explicit example in some detail. In particular, from that example we can expect that the QSOs in bright flux- limited samples have a fairly broad magnification distribution, a conclusion supported by recent results from gravitational lens surveys. The observed number excess of (foreground) galaxies around high- redshift QSOs has been interpreted as being due to gravitational lensing by matter associated with the foreground galaxy, thereby causing a `local' amplification bias. Under the assumption that the overall (i.e., sky-averaged) source counts are unaffected by amplification bias, this interpretation is in quantitative disagreement with the number excess obtained observationally. This paper investigates the question whether by dropping the assumption of unaffected overall QSO counts, the quantitative agreement between a lens theory and the observed number excess can be improved, concentrating on the sample by Webster et al. (1988). As it turns out, the discrepancy decreases, but not to a sufficiently low level; in fact, QSO-galaxy associations are not a strong indicator for an overall amplification bias. However, this effect is very sensitive to the flux threshold of the QSO sample, relative to the flux at which the source counts show a break. By increasing the magnitude difference between break and flux threshold of the Webster et al. sample, a satisfactory quantitative agreement can be achieved.

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