What does strong gravitational lensing? The mass and redshift
  distribution of high-magnification lenses
  Many distant objects can only be detected, or become more scientifically
valuable, if they have been highly magnified by strong gravitational lensing.
We use EAGLE and BAHAMAS, two recent cosmological hydrodynamical simulations,
to predict the probability distribution for both the lens mass and lens
redshift when point sources are highly magnified by gravitational lensing. For
sources at a redshift of two, we find the distribution of lens redshifts to be
broad, peaking at z=0.6. The contribution of different lens masses is also
fairly broad, with most high-magnification lensing due to lenses with halo
masses between 10^12 and 10^14 solar masses. Lower mass haloes are inefficient
lenses, while more massive haloes are rare. We find that a simple model in
which all haloes have singular isothermal sphere density profiles can
approximately reproduce the simulation predictions, although such a model
over-predicts the importance of haloes with mass <10^12 solar masses for
lensing. We also calculate the probability that point sources at different
redshifts are strongly lensed. At low redshift, high magnifications are
extremely unlikely. Each z=0.5 source produces, on average, 5x10^-7 images with
magnification greater than ten; for z =2 this increases to about 2x10^-5. Our
results imply that searches for strongly lensed optical transients, including
the optical counterparts to strongly lensed gravitational waves, can be
optimized by monitoring massive galaxies, groups and clusters rather than
concentrating on an individual population of lenses.
