# Analytic Models of Plausible Gravitational Lens Potentials

## Abstract

Gravitational lenses on galaxy scales are plausibly modeled as having ellipsoidal symmetry and a universal dark matter density profile, with a Sersic profile to describe the distribution of baryonic matter. Predicting all lensing effects requires knowledge of the total lens potential: in this work we give analytic forms for that of the above hybrid model. Emphasizing that complex lens potentials can be constructed from simpler components in linear combination, we provide a recipe for attaining elliptical symmetry in either projected mass or lens potential.We also provide analytic formulae for the lens potentials of Sersic profiles for integer and half-integer index. We then present formulae describing the gravitational lensing effects due to smoothly-truncated universal density profiles in cold dark matter model. For our isolated haloes the density profile falls off as radius to the minus fifth or seventh power beyond the tidal radius, functional forms that allow all orders of lens potential derivatives to be calculated analytically, while ensuring a non-divergent total mass. We show how the observables predicted by this profile differ from that of the original infinite-mass NFW profile. Expressions for the gravitational flexion are highlighted. We show how decreasing the tidal radius allows stripped haloes to be modeled,more »

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center (SLAC)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 903002

- Report Number(s):
- SLAC-PUB-12497

Journal ID: ISSN 0035-8711; MNRAA4; arXiv:0705.0682; TRN: US200719%%121

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Monthly Notices of the Royal Astronomical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GALAXIES; GRAVITATIONAL LENSES; NONLUMINOUS MATTER; MATHEMATICAL MODELS; Astrophysics,ASTRO

### Citation Formats

```
Baltz, Edward A., Marshall, Phil, and Oguri, Masamune.
```*Analytic Models of Plausible Gravitational Lens Potentials*. United States: N. p., 2007.
Web.

```
Baltz, Edward A., Marshall, Phil, & Oguri, Masamune.
```*Analytic Models of Plausible Gravitational Lens Potentials*. United States.

```
Baltz, Edward A., Marshall, Phil, and Oguri, Masamune. Fri .
"Analytic Models of Plausible Gravitational Lens Potentials". United States.
doi:. https://www.osti.gov/servlets/purl/903002.
```

```
@article{osti_903002,
```

title = {Analytic Models of Plausible Gravitational Lens Potentials},

author = {Baltz, Edward A. and Marshall, Phil and Oguri, Masamune},

abstractNote = {Gravitational lenses on galaxy scales are plausibly modeled as having ellipsoidal symmetry and a universal dark matter density profile, with a Sersic profile to describe the distribution of baryonic matter. Predicting all lensing effects requires knowledge of the total lens potential: in this work we give analytic forms for that of the above hybrid model. Emphasizing that complex lens potentials can be constructed from simpler components in linear combination, we provide a recipe for attaining elliptical symmetry in either projected mass or lens potential.We also provide analytic formulae for the lens potentials of Sersic profiles for integer and half-integer index. We then present formulae describing the gravitational lensing effects due to smoothly-truncated universal density profiles in cold dark matter model. For our isolated haloes the density profile falls off as radius to the minus fifth or seventh power beyond the tidal radius, functional forms that allow all orders of lens potential derivatives to be calculated analytically, while ensuring a non-divergent total mass. We show how the observables predicted by this profile differ from that of the original infinite-mass NFW profile. Expressions for the gravitational flexion are highlighted. We show how decreasing the tidal radius allows stripped haloes to be modeled, providing a framework for a fuller investigation of dark matter substructure in galaxies and clusters. Finally we remark on the need for finite mass halo profiles when doing cosmological ray-tracing simulations, and the need for readily-calculable higher order derivatives of the lens potential when studying catastrophes in strong lenses.},

doi = {},

journal = {Monthly Notices of the Royal Astronomical Society},

number = ,

volume = ,

place = {United States},

year = {Fri May 04 00:00:00 EDT 2007},

month = {Fri May 04 00:00:00 EDT 2007}

}