The Multi-Band Magnification Bias for Gravitational Lenses

Details The Multi-Band Magnification Bias for Gravitational Lenses The Multi-Band Magnification Bias for Gravitational Lenses

2002-08-29

arxiv.org/abs/astro-ph/0208532v1

Astrophys.J. 583 (2003) 58-66

Astronomy and Astrophysics

Astrophysics

20 pages, 4 figures. Submitted to ApJ

Scientific paper

10.1086/345358

We present a generalization of the concept of magnification bias for gravitationally-lensed quasars, in which the quasars are selected by flux in more than one wavelength band. To illustrate the principle, we consider the case of two-band selection, in which the fluxes in the two bands are uncorrelated, perfectly correlated, or correlated with scatter. For uncorrelated fluxes, we show that the previously-held result - that the bias is the product of the single-band biases - is generally false. We demonstrate some important properties of the multi-band magnification bias using model luminosity functions inspired by observed correlations among X-ray, optical, infrared and radio fluxes of quasars. In particular, the bias need not be an increasing function of each flux, and the bias can be extremely large for non-linear correlations. The latter fact may account for the high lensing rates found in some X-ray/optical and infrared/radio selected samples.

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