Characterizing the best cosmic telescopes with the millennium simulations

Certain configurations of massive structures projected along the line of sight (LOS) maximize the number of detections of gravitationally lensed z ∼ 10 galaxies. We characterize such LOSs with the étendue σ_μ, the area in the source plane magnified over some threshold μ. We use the Millennium I and Millennium XXL cosmological simulations to determine the frequency of high σ_μ beams on the sky, their properties, and efficient selection criteria. We define the best beams as having σ_μ > 3 > 2000 arcsec², for a z ∼ 10 source plane, and predict 477 ± 21 such beams on the sky. The total mass in the beam and σ_μ > 3 are strongly correlated. After controlling for total mass, we find a significant residual correlation between σ_μ > 3 and the number of cluster-scale halos (>10¹⁴ M _⊙ h ^-1) in the beam. Beams with σ_μ > 3 > 2000 arcsec ², which should be best at lensing z ∼ 10 galaxies, are 10 times more likely to contain multiple cluster-scale halos than a single cluster-scale halo. Beams containing an A1689-like massive cluster halo often have additional structures along the LOS, including at least one additional cluster-scale (M ₂₀₀ > 10¹⁴ M _⊙ h ^-1) halo 28% of the time. Selecting beams with multiple, massive structures will lead to enhanced detection of the most distant and intrinsically faint galaxies.