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 2, 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 10¹² and 10¹⁴M_⊙⁠. 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 overpredicts the importance of haloes with mass <10¹²M_⊙ 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, 5 × 10⁻⁷ images with magnification greater than 10; for z = 2, this increases to about 2 × 10⁻⁵. 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.