Magnification Probability Distribution Functions of Standard Candles in a Clumpy Universe

TL;DR

This study uses Monte Carlo simulations to analyze how gravitational lensing by clumpy matter affects the brightness of standard candles like Type Ia supernovae, revealing potential insights into dark matter halo profiles.

Contribution

It introduces a detailed simulation approach to model lensing effects in a clumpy universe and identifies conditions under which gamma distributions fit magnification probabilities.

Findings

Gamma distributions fit well for certain lens models with larger-than-Einstein-radius lenses.

The fit depends on the density profile slope, with steeper profiles fitting less well.

Lensing effects can provide information about dark matter halo density slopes.

Abstract

Lensing effects on light rays from point light sources, such like Type Ia supernovae, are simulated in a clumpy universe model. In our universe model, it is assumed that all matter in the universe takes the form of randomly distributed objects each of which has finite size and is transparent for light rays. Monte-Carlo simulations are performed for several lens models, and we compute probability distribution functions of magnification. In the case of the lens models that have a smooth density profile or the same degree of density concentration as the spherical NFW (Navarro-Frenk-White) lens model at the center, the so-called gamma distributions fit well the magnification probability distribution functions if the size of lenses is sufficiently larger than the Einstein radius. In contrast, the gamma distributions do not fit the magnification probability distribution functions in the case of the SIS (Singular Isothermal Sphere) lens model. We find, by using the power law cusp model, that the magnification probability distribution function is fitted well using the gamma distribution only when the slope of the central density profile is not very steep. These results suggest that we may obtain information about the slope of the central density profiles of dark matter halo from the lensing effect of Type Ia supernovae.