Amplification bias by gravitational lensing on observed number counts of quasars - effects of a finite source size

The statistical effects on the observed number counts of quasars due to amplification by gravitational light deflection are investigated. It is shown that the approximation of point sources, hitherto made in most studies of this effect, can cause misleading results: whereas for point sources any amplification-dominated source count necessarily has the canonical integral (logarithmic) slope of d log N/d log S = -2, this ceases to be true if a finite source extent is taken into account. It is demonstrated explicitly by considering a distribution of masses for the deflectors that lensing can account for slopes of source counts which lie between the canonical value of -2 and the intrinsic (unlensed) one, provided the latter is steeper than -2. The implications of this effect are briefly discussed. 21 references