# The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters

## Abstract

Time delays of gravitationally lensed sources can be used to constrain the mass model of a deflector and determine cosmological parameters. We here present an analysis of the time-delay distribution of multiply imaged sources behind 17 strong lensing galaxy clusters with well-calibrated mass models. We find that for time delays less than 1000 days, at z = 3.0, their logarithmic probability distribution functions are well represented by P(log Δt) = 5.3 × 10{sup −4}Δt{sup β-tilde}/M{sub 250}{sup 2β-tilde}, with β-tilde = 0.77, where M{sub 250} is the projected cluster mass inside 250 kpc (in 10{sup 14}M{sub ☉}), and β-tilde is the power-law slope of the distribution. The resultant probability distribution function enables us to estimate the time-delay distribution in a lensing cluster of known mass. For a cluster with M{sub 250} = 2 × 10{sup 14}M{sub ☉}, the fraction of time delays less than 1000 days is approximately 3%. Taking Abell 1689 as an example, its dark halo and brightest galaxies, with central velocity dispersions σ≥500kms{sup −1}, mainly produce large time delays, while galaxy-scale mass clumps are responsible for generating smaller time delays. We estimate the probability of observing multiple images of a supernova in the known images of Abell 1689.more »

- Authors:

- Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100, Copenhagen (Denmark)
- CRAL, Observatoire de Lyon, Université Lyon 1, 9 Avenue Ch. André, 69561 Saint Genis Laval Cedex (France)

- Publication Date:

- OSTI Identifier:
- 22279684

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2012; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ASTROPHYSICS; COSMOLOGY; DISTRIBUTION FUNCTIONS; GALAXIES; GALAXY CLUSTERS; GRAVITATIONAL COLLAPSE; GRAVITATIONAL LENSES; MASS; PROBABILITY; SUPERNOVAE; TIME DELAY; VELOCITY

### Citation Formats

```
Li, Xue, Hjorth, Jens, and Richard, Johan, E-mail: lixue@dark-cosmology.dk, E-mail: jens@dark-cosmology.dk, E-mail: johan.richard@univ-lyon1.fr.
```*The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters*. United States: N. p., 2012.
Web. doi:10.1088/1475-7516/2012/11/015.

```
Li, Xue, Hjorth, Jens, & Richard, Johan, E-mail: lixue@dark-cosmology.dk, E-mail: jens@dark-cosmology.dk, E-mail: johan.richard@univ-lyon1.fr.
```*The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters*. United States. doi:10.1088/1475-7516/2012/11/015.

```
Li, Xue, Hjorth, Jens, and Richard, Johan, E-mail: lixue@dark-cosmology.dk, E-mail: jens@dark-cosmology.dk, E-mail: johan.richard@univ-lyon1.fr. Thu .
"The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters". United States. doi:10.1088/1475-7516/2012/11/015.
```

```
@article{osti_22279684,
```

title = {The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters},

author = {Li, Xue and Hjorth, Jens and Richard, Johan, E-mail: lixue@dark-cosmology.dk, E-mail: jens@dark-cosmology.dk, E-mail: johan.richard@univ-lyon1.fr},

abstractNote = {Time delays of gravitationally lensed sources can be used to constrain the mass model of a deflector and determine cosmological parameters. We here present an analysis of the time-delay distribution of multiply imaged sources behind 17 strong lensing galaxy clusters with well-calibrated mass models. We find that for time delays less than 1000 days, at z = 3.0, their logarithmic probability distribution functions are well represented by P(log Δt) = 5.3 × 10{sup −4}Δt{sup β-tilde}/M{sub 250}{sup 2β-tilde}, with β-tilde = 0.77, where M{sub 250} is the projected cluster mass inside 250 kpc (in 10{sup 14}M{sub ☉}), and β-tilde is the power-law slope of the distribution. The resultant probability distribution function enables us to estimate the time-delay distribution in a lensing cluster of known mass. For a cluster with M{sub 250} = 2 × 10{sup 14}M{sub ☉}, the fraction of time delays less than 1000 days is approximately 3%. Taking Abell 1689 as an example, its dark halo and brightest galaxies, with central velocity dispersions σ≥500kms{sup −1}, mainly produce large time delays, while galaxy-scale mass clumps are responsible for generating smaller time delays. We estimate the probability of observing multiple images of a supernova in the known images of Abell 1689. A two-component model of estimating the supernova rate is applied in this work. For a magnitude threshold of m{sub AB} = 26.5, the yearly rate of Type Ia (core-collapse) supernovae with time delays less than 1000 days is 0.004±0.002 (0.029±0.001). If the magnitude threshold is lowered to m{sub AB} ∼ 27.0, the rate of core-collapse supernovae suitable for time delay observation is 0.044±0.015 per year.},

doi = {10.1088/1475-7516/2012/11/015},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 11,

volume = 2012,

place = {United States},

year = {2012},

month = {11}

}