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Title: 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 » 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.« less

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}
}
  • 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 half-integermore » 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 modelled, 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.« less
  • Upcoming gravitational wave (GW) detectors might detect a stochastic background of GWs potentially arising from many possible sources, including bubble collisions from a strongly first-order electroweak phase transition. We investigate whether it is possible to connect, via a semi-analytical approximation to the tunneling rate of scalar fields with quartic potentials, the GW signal through detonations with the parameters entering the potential that drives the electroweak phase transition. To this end, we consider a finite temperature effective potential similar in form to the Higgs potential in the Standard Model (SM). In the context of a semi-analytic approximation to the three dimensionalmore » Euclidean action, we derive a general approximate form for the tunneling temperature and the relevant GW parameters. We explore the GW signal across the parameter space describing the potential which drives the phase transition. We comment on the potential detectability of a GW signal with future experiments, and physical relevance of the associated potential parameters in the context of theories which have effective potentials similar in form to that of the SM. In particular we consider singlet, triplet, higher dimensional operators, and top-flavor extensions to the Higgs sector of the SM. We find that the addition of a temperature independent cubic term in the potential, arising from a gauge singlet for instance, can greatly enhance the GW power. The other parameters have milder, but potentially noticeable, effects.« less
  • Images of the gravitational lens 2237+0305 acquired in good seeing have resolved the system into at least five components within the central few arsec of the object: the galaxy nucleus and four point sources in a ringlike formation approximately centered on the galaxy. It is found that the four point sources are distinctly bluer than the galaxy, but that they do not have identical colors. The observed configuration is well reproduced by a simple model that assumes that the four objects are images of the quasar and that the lens is a constant mass-to-light ratio, elliptical, de Vaucouleurs bulge. 29more » references.« less
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  • It is noted that observations of gravitational lens systems can yield useful estimates for characteristics of the lenses and for cosmological parameters. However, the nature of these observations restricts the types of characteristics that can be determined. This paper demonstrates some of these inherent restrictions (i.e., degeneracies in parameter estimation) through an analysis of the effects of prismatic, similarity, magnification, and combined transformations. These transformations show that changes over continuous ranges in the values of parameters describing the source and the lens models can leave unchanged the predicted values of observable properties (relative positions, luminosities, magnifications, and time delays) ofmore » gravitational images. 32 references.« less