Statistics of weak gravitational lensing in cold dark matter models: Magnification bias on quasar luminosity functions

Takashi Hamana, Hugo Martel, Toshifumi Futamase

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


We compute statistical properties of weak gravitational lensing by large-scale structure in three cold dark matter (CDM) models: two flat models with (Ω0, γ0) = (1, 0) and (0.3, 0.7) and one open model with (Ω0, γ0) = (0.3, 0), where Ω0 and γ0 are the density parameter and cosmological constant, respectively. We use a particle-particle/particle-mesh (P3M) N-body code to simulate the formation and evolution of large-scale structure in the universe. We perform 1.1 × 107 ray-tracing experiments for each model, by computing the Jacobian matrix along random lines of sight, using the multiple lens-plane algorithm. From the results of these experiments, we calculate the probability distribution functions of the convergences, shears, and magnifications, and their rms values. We find that the rms values of the convergence and shear agree with the predictions of a nonlinear analytical model. We also find that the probability distribution functions of the magnifications μ have a peak at values slightly smaller than μ = 1 and are strongly skewed toward large magnifications. In particular, for the high-density (Ω0 = 1) model, a power-law tail appears in the distribution function at large magnifications for sources at redshifts zs > 2. The rms values of the magnifications essentially agree with the nonlinear analytical predictions for sources at low redshift but exceed these predictions for high redshift sources, once the power-law tail appears. We study the effect of magnification bias on the luminosity functions of high-redshift quasars, using the calculated probability distribution functions of the magnifications. We show that the magnification bias is moderate in the absence of the power-law tail in the magnification distribution but depends strongly on the value of the density parameter Ω0. In presence of the power-law tail, the bias becomes considerable, especially at the bright end of the luminosity functions where its logarithmic slope steepens. We present a specific example that demonstrates that the bias flattens the bright-side logarithmic slope of a double power-law luminosity function.

Original languageEnglish
Pages (from-to)56-68
Number of pages13
JournalAstrophysical Journal
Issue number1 PART 1
Publication statusPublished - 2000 Jan 20


  • Cosmology: observations
  • Cosmology: theory
  • Dark matter
  • Gravitational lensing
  • Large-scale structure of universe
  • Quasars: general

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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