Bayesian constraints on dark matter halo properties using gravitationally-lensed supernovae

Abstract

A hierarchical Bayesian method is applied to the analysis of Type-Ia supernovae (SNIa) observations to constrain the properties of the dark matter haloes of galaxies along the SNIa lines-of-sight via their gravitational lensing effect. The full joint posterior distribution of the dark matter halo parameters is explored using the nested sampling algorithm {\sc MultiNest}, which also efficiently calculates the Bayesian evidence, thereby facilitating robust model comparison. We first demonstrate the capabilities of the method by applying it to realistic simulated SNIa data, based on the real 3-year data release from the Supernova Legacy Survey (SNLS3). Assuming typical values for the halo parameters in our simulations, we find that a catalogue analogous to the existing SNLS3 data set is incapable of detecting the lensing signal, but a catalogue containing approximately three times as many SNIa does produce robust and accurate parameter constraints and model selection results for two halo models: a truncated singular isothermal sphere (SIS) and a Navarro--Frenk--White (NFW) profile, thereby validating our analysis methodology. In the analysis of the real SNLS3 data, contrary to previous studies, we obtain only a very marginal detection of a lensing signal and weak constraints on the halo parameters for the truncated SIS model, although these constraints are tighter than those obtained from the equivalent simulated SNIa data set. This difference is driven by a preferred value of $\eta \approx 1$ in the assumed scaling-law $\sigma \propto L^{\eta }$ between velocity dispersion and luminosity, which is somewhat higher than the canonical values of $\eta =\frac{1}{4}$ and $\eta =\frac{1}{3}$ for early and late-type galaxies, respectively, and leads to a stronger lensing effect by the halo. No detection of a lensing signal is made for the NFW model.

Revised version matches manuscript accepted by MNRAS: Manuscript ID: MN-12-1716-MJ.R2

References in corpus (8)

• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• Improved Dark Energy Constraints from ~100 New CfA Supernova Type Ia Light Curves
• Supernova Constraints and Systematic Uncertainties from the First 3 Years of the Supernova Legacy Survey
• Improved Distances to Type Ia Supernovae with Multicolor Light Curve Shapes: MLCS2k2
• Rates and properties of type Ia supernovae as a function of mass and star-formation in their host galaxies
• Type Ia Supernova Light Curve Inference: Hierarchical Bayesian Analysis in the Near Infrared
• SNLS Spectroscopy: Testing for Evolution in Type Ia Supernovae
• Lensing and Supernovae: Quantifying The Bias on the Dark Energy Equation of State

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