Article (Scientific journals)
Use of the Fourier transform to derive the gravitational lens deflection angle
Wertz, Olivier; Surdej, Jean
2013In Monthly Notices of the Royal Astronomical Society, 437, p. 1051-1055
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Keywords :
Gravitational Lensing
Abstract :
[en] Knowing that the gravitational lens deflection angle can be expressed as the convolution product between the dimensionless surface mass density κ(x) and a simple function of the scaled impact parameter vector x, we make use of the Fourier transform to derive its analytical expression for the case of mass distributions presenting a homoeoidal sym- metry. For this family of models, we obtain the expression of the two components of the deflection angle in the form of integrals performed over the radial coordinate ρ. In the limiting case of axially symmetric lenses, we obviously retrieve the well-known relation α(x)∝ M(≤ |x|)x/|x|^2. Furthermore, we derive explicit solutions for the deflection angle characterized by dimensionless surface mass density profiles such as κ ∝ (ρ^2c + ρ^2)^{−ν}; corresponding to the non-singular isothermal ellipsoid (NSIE) model for the particular case ν = 1/2. Let us insist that all these results are obtained without using the complex formal- ism introduced by Bourassa and Kantowski (1973,1975). Further straightforward applica- tions of this Fourier approach are suggested in the conclusions of the present work.
Disciplines :
Space science, astronomy & astrophysics
Author, co-author :
Wertz, Olivier ;  Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Astroph. extragalactique et observations spatiales (AEOS)
Surdej, Jean  ;  Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Astroph. extragalactique et observations spatiales (AEOS)
Language :
English
Title :
Use of the Fourier transform to derive the gravitational lens deflection angle
Publication date :
26 November 2013
Journal title :
Monthly Notices of the Royal Astronomical Society
ISSN :
0035-8711
eISSN :
1365-2966
Publisher :
Blackwell Publishing, Oxford, United Kingdom
Volume :
437
Pages :
1051-1055
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 22 January 2014

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