Testing the Convergence of the Multiple Lens Plane Algorithm

Details Testing the Convergence of the Multiple Lens Plane Algorithm Testing the Convergence of the Multiple Lens Plane Algorithm

Jul 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000apj...537...28m&link_type=abstract

The Astrophysical Journal, Volume 537, Issue 1, pp. 28-36.

Astronomy and Astrophysics

Astronomy

6

Cosmology: Theory, Cosmology: Gravitational Lensing, Cosmology: Large-Scale Structure Of Universe, Methods: Numerical

Scientific paper

We perform a series of ray-tracing experiments to test the convergence of the multiple lens plane algorithm. We consider six COBE-normalized cold dark matter (CDM) models with various values of the density parameter, Ω0, cosmological constant, λ0, Hubble constant, H0, and rms density fluctuation, σ8. For each model, we choose one ray-tracing experiment and perform that experiment six times, with six different numbers of lens planes. We study how the results of these experiments depend upon the number of planes used. For each experiment, we compute the magnification distribution, the magnification probability, and the location of the beam on the source plane. We also compute a stringent pointwise cross-correlation between the magnification maps generated for the same model with different numbers of planes. The cross-correlations converge as the number of planes is increased, but only for relatively large numbers of planes, ~100-200 planes, because the magnification maps suffer shifts in position due to small shifts in ray position in examples with different numbers of planes. Other results, such as the magnification distribution, are quite reliable even with only one experiment per model. We find that all the results converge as the number of planes increases, and that, for sources at redshifts zs~2.5, 14 planes are sufficient to obtain reliable results for all cosmological models. This is significantly smaller than the number of planes typically used in such experiments.

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