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 halfinteger index. We then present formulae describing the gravitational lensing effects due to smoothlytruncated 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 nondivergent total mass. We show how the observables predicted by this profile differ from that of the original infinitemass 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):
 SLACPUB12497
Journal ID: ISSN 00358711; MNRAA4; arXiv:0705.0682; TRN: US200719%%121
 DOE Contract Number:
 AC0276SF00515
 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 halfinteger index. We then present formulae describing the gravitational lensing effects due to smoothlytruncated 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 nondivergent total mass. We show how the observables predicted by this profile differ from that of the original infinitemass 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 raytracing simulations, and the need for readilycalculable 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}
}

Gravitational lenses on galaxy scales are plausibly modelled 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. Emphasising 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 halfintegermore »

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