Magnification bias in galaxy surveys with complex sample selection
  functions
  Gravitational lensing magnification modifies the observed spatial
distribution of galaxies and can severely bias cosmological probes of
large-scale structure if not accurately modelled. Standard approaches to
modelling this magnification bias may not be applicable in practice as many
galaxy samples have complex, often implicit, selection functions. We propose
and test a procedure to quantify the magnification bias induced in clustering
and galaxy-galaxy lensing (GGL) signals in galaxy samples subject to a
selection function beyond a simple flux limit. The method employs realistic
mock data to calibrate an effective luminosity function slope,
$\alpha_{\rm{obs}}$, from observed galaxy counts, which can then be used with
the standard formalism. We demonstrate this method for two galaxy samples
derived from the Baryon Oscillation Spectroscopic Survey (BOSS) in the redshift
ranges $0.2 < z \leq 0.5$ and $0.5 < z \leq 0.75$, complemented by mock data
built from the MICE2 simulation. We obtain $\alpha_{\rm{obs}} = 1.93 \pm 0.05$
and $\alpha_{\rm{obs}} = 2.62 \pm 0.28$ for the two BOSS samples. For BOSS-like
lenses, we forecast a contribution of the magnification bias to the GGL signal
between the multipole moments, $\ell$, of 100 and 4600 with a cumulative
signal-to-noise ratio between 0.1 and 1.1 for sources from the Kilo-Degree
Survey (KiDS), between 0.4 and 2.0 for sources from the Hyper Suprime-Cam
survey (HSC), and between 0.3 and 2.8 for ESA Euclid-like source samples. These
contributions are significant enough to require explicit modelling in future
analyses of these and similar surveys. Our code is publicly available within
the \textsc{MagBEt} module (\url{https://github.com/mwiet/MAGBET}).
