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Article: Statistics of gravitational microlensing magnification. II. Three-dimensional lens distribution

TitleStatistics of gravitational microlensing magnification. II. Three-dimensional lens distribution
Authors
KeywordsGravitational Lensing
Methods: Statistical
Issue Date1997
PublisherInstitute of Physics Publishing Ltd. The Journal's web site is located at http://iopscience.iop.org/2041-8205
Citation
Astrophysical Journal Letters, 1997, v. 489 n. 2 PART I, p. 522-542 How to Cite?
AbstractIn the first paper of this series, we studied the theory of gravitational microlensing for a planar distribution of point masses. In this second paper, we extend the analysis to a three-dimensional lens distribution. First we study the lensing properties of three-dimensional lens distributions by considering in detail the critical curves, the caustics, the illumination patterns, and the magnification cross sections σ(A) of multiplane configurations with two, three, and four point masses. For N* point masses that are widely separated in Lagrangian space (i.e., in projection), we find that there are ∼2 N* -1 critical curves in total, but that only ∼N* of these produce prominent caustic-induced features in σ(A) at moderate to high magnifications (A ≳ 2). In the case of a random distribution of point masses at low optical depth, we show that the multiplane lens equation near a point mass can be reduced to the single-plane equation of a point mass perturbed by weak shear. This allows us to calculate the caustic-induced feature in the macroimage magnification distribution P(A) as a weighted sum of the semianalytic feature derived in Paper I for a planar lens distribution. The resulting semianalytic caustic-induced feature is similar to the feature in the planar case, but it does not have any simple scaling properties, and it is shifted to higher magnification. The semianalytic distribution is compared with the results of previous numerical simulations for optical depth τ ≈0.1, and they are in better agreement than a similar comparison in the planar case. We explain this by estimating the fraction of caustics of individual lenses that merge with those of their neighbors. For τ = 0.1, the fraction is ≈20%, much less than the ≈55% for the planar case. In the three-dimensional case, a simple criterion for the low optical depth analysis to be valid is τ ≪ 0.4, though the comparison with numerical simulations indicates that the semianalytic distribution is a reasonable fit to P(A) for τ up to 0.2. © 1997. The American Astronomical Society. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/151103
ISSN
2015 Impact Factor: 5.487
2015 SCImago Journal Rankings: 3.369
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLee, MHen_US
dc.contributor.authorBabul, Aen_US
dc.contributor.authorKofman, Len_US
dc.contributor.authorKaiser, Nen_US
dc.date.accessioned2012-06-26T06:17:06Z-
dc.date.available2012-06-26T06:17:06Z-
dc.date.issued1997en_US
dc.identifier.citationAstrophysical Journal Letters, 1997, v. 489 n. 2 PART I, p. 522-542en_US
dc.identifier.issn2041-8205en_US
dc.identifier.urihttp://hdl.handle.net/10722/151103-
dc.description.abstractIn the first paper of this series, we studied the theory of gravitational microlensing for a planar distribution of point masses. In this second paper, we extend the analysis to a three-dimensional lens distribution. First we study the lensing properties of three-dimensional lens distributions by considering in detail the critical curves, the caustics, the illumination patterns, and the magnification cross sections σ(A) of multiplane configurations with two, three, and four point masses. For N* point masses that are widely separated in Lagrangian space (i.e., in projection), we find that there are ∼2 N* -1 critical curves in total, but that only ∼N* of these produce prominent caustic-induced features in σ(A) at moderate to high magnifications (A ≳ 2). In the case of a random distribution of point masses at low optical depth, we show that the multiplane lens equation near a point mass can be reduced to the single-plane equation of a point mass perturbed by weak shear. This allows us to calculate the caustic-induced feature in the macroimage magnification distribution P(A) as a weighted sum of the semianalytic feature derived in Paper I for a planar lens distribution. The resulting semianalytic caustic-induced feature is similar to the feature in the planar case, but it does not have any simple scaling properties, and it is shifted to higher magnification. The semianalytic distribution is compared with the results of previous numerical simulations for optical depth τ ≈0.1, and they are in better agreement than a similar comparison in the planar case. We explain this by estimating the fraction of caustics of individual lenses that merge with those of their neighbors. For τ = 0.1, the fraction is ≈20%, much less than the ≈55% for the planar case. In the three-dimensional case, a simple criterion for the low optical depth analysis to be valid is τ ≪ 0.4, though the comparison with numerical simulations indicates that the semianalytic distribution is a reasonable fit to P(A) for τ up to 0.2. © 1997. The American Astronomical Society. All rights reserved.en_US
dc.languageengen_US
dc.publisherInstitute of Physics Publishing Ltd. The Journal's web site is located at http://iopscience.iop.org/2041-8205en_US
dc.relation.ispartofAstrophysical Journal Lettersen_US
dc.subjectGravitational Lensingen_US
dc.subjectMethods: Statisticalen_US
dc.titleStatistics of gravitational microlensing magnification. II. Three-dimensional lens distributionen_US
dc.typeArticleen_US
dc.identifier.emailLee, MH:mhlee@hku.hken_US
dc.identifier.authorityLee, MH=rp00724en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1086/304792en_US
dc.identifier.scopuseid_2-s2.0-0040459739en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0040459739&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume489en_US
dc.identifier.issue2 PART Ien_US
dc.identifier.spage522en_US
dc.identifier.epage542en_US
dc.identifier.isiWOS:A1997YF30000008-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridLee, MH=7409119699en_US
dc.identifier.scopusauthoridBabul, A=35228472900en_US
dc.identifier.scopusauthoridKofman, L=35299507100en_US
dc.identifier.scopusauthoridKaiser, N=7103118947en_US

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