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Article: Statistics of gravitational microlensing magnification. I. Two-dimensional lens distribution

TitleStatistics of gravitational microlensing magnification. I. Two-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. 508-521 How to Cite?
AbstractThe propagation of light from distant sources through a distribution of clumpy matter, acting as point-mass lenses, produces multiple images that contribute to the total brightness of the observed macroimages. In this paper, we refine the theory of gravitational microlensing for a planar distribution of point masses. In an accompanying paper, we extend the analysis to a three-dimensional lens distribution. In the two-dimensional case, we derive the probability distribution of macroimage magnification, P(A), at A -1 ≫ τ 2 for a low optical depth lens distribution by modeling the illumination pattern as a superposition of the patterns due to individual "point-mass plus weak-shear" lenses. A point-mass lens perturbed by weak shear S produces an astroid-shaped caustic. We show that the magnification cross section σ(A / S) of the point-mass plus weak-shear lens obeys a simple scaling property, and we provide a useful analytic approximation for the cross section. By convolving this cross section with the probability distribution of the shear due to the neighboring point masses, we obtain a caustic-induced feature in P(A) that also exhibits a simple scaling property. This feature results in a 20% enhancement in P(A) at A ≈ 2/τ. In the low-magnification (A - 1 ≪ 1) limit, the macroimage consists of a single bright primary image and a large number of faint secondary images formed close to each of the point masses. The magnifications of the primary and the secondary images can be strongly correlated. Taking into account the correlations, we derive P(A) for low magnification and find that P(A) has a peak of amplitude ≈0.16/τ 2 at A - 1 ≈ 0.84τ 2. The low-magnification distribution matches smoothly the distribution for A - 1 ≫ τ 2 in the overlapping regimes A - 1 ≫ τ 2 and A ≪ 1/τ. Finally, after a discussion of the correct normalization for P(A), we combine the results and obtain a practical semianalytic expression for the macroimage magnification distribution P(A). This semianalytic distribution is in qualitative agreement with the results of previous numerical simulations, but the latter show stronger caustic-induced features at moderate A (1.5 ≲ A ≲ 10) for τ as small as 0.1. We resolve this discrepancy by reexamining the criterion for low optical depth. A simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is approximately 1 - exp (-8τ). For τ = 0.1, the fraction is surprisingly high: ≈ 55%. A simple criterion for the low optical depth analysis to be valid is τ ≪1/8, though the comparison with numerical simulations indicates that the semianalytic distribution is a reasonable fit to P(A) for τ up to 0.05. © 1997. The American Astronomical Society. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/151157
ISSN
2015 Impact Factor: 5.487
2015 SCImago Journal Rankings: 3.369
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorKofman, Len_US
dc.contributor.authorKaiser, Nen_US
dc.contributor.authorLee, MHen_US
dc.contributor.authorBabul, Aen_US
dc.date.accessioned2012-06-26T06:17:54Z-
dc.date.available2012-06-26T06:17:54Z-
dc.date.issued1997en_US
dc.identifier.citationAstrophysical Journal Letters, 1997, v. 489 n. 2 PART I, p. 508-521en_US
dc.identifier.issn2041-8205en_US
dc.identifier.urihttp://hdl.handle.net/10722/151157-
dc.description.abstractThe propagation of light from distant sources through a distribution of clumpy matter, acting as point-mass lenses, produces multiple images that contribute to the total brightness of the observed macroimages. In this paper, we refine the theory of gravitational microlensing for a planar distribution of point masses. In an accompanying paper, we extend the analysis to a three-dimensional lens distribution. In the two-dimensional case, we derive the probability distribution of macroimage magnification, P(A), at A -1 ≫ τ 2 for a low optical depth lens distribution by modeling the illumination pattern as a superposition of the patterns due to individual "point-mass plus weak-shear" lenses. A point-mass lens perturbed by weak shear S produces an astroid-shaped caustic. We show that the magnification cross section σ(A / S) of the point-mass plus weak-shear lens obeys a simple scaling property, and we provide a useful analytic approximation for the cross section. By convolving this cross section with the probability distribution of the shear due to the neighboring point masses, we obtain a caustic-induced feature in P(A) that also exhibits a simple scaling property. This feature results in a 20% enhancement in P(A) at A ≈ 2/τ. In the low-magnification (A - 1 ≪ 1) limit, the macroimage consists of a single bright primary image and a large number of faint secondary images formed close to each of the point masses. The magnifications of the primary and the secondary images can be strongly correlated. Taking into account the correlations, we derive P(A) for low magnification and find that P(A) has a peak of amplitude ≈0.16/τ 2 at A - 1 ≈ 0.84τ 2. The low-magnification distribution matches smoothly the distribution for A - 1 ≫ τ 2 in the overlapping regimes A - 1 ≫ τ 2 and A ≪ 1/τ. Finally, after a discussion of the correct normalization for P(A), we combine the results and obtain a practical semianalytic expression for the macroimage magnification distribution P(A). This semianalytic distribution is in qualitative agreement with the results of previous numerical simulations, but the latter show stronger caustic-induced features at moderate A (1.5 ≲ A ≲ 10) for τ as small as 0.1. We resolve this discrepancy by reexamining the criterion for low optical depth. A simple argument shows that the fraction of caustics of individual lenses that merge with those of their neighbors is approximately 1 - exp (-8τ). For τ = 0.1, the fraction is surprisingly high: ≈ 55%. A simple criterion for the low optical depth analysis to be valid is τ ≪1/8, though the comparison with numerical simulations indicates that the semianalytic distribution is a reasonable fit to P(A) for τ up to 0.05. © 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. I. Two-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.doi10.1086/304791en_US
dc.identifier.scopuseid_2-s2.0-21944448834en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-21944448834&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume489en_US
dc.identifier.issue2 PART Ien_US
dc.identifier.spage508en_US
dc.identifier.epage521en_US
dc.identifier.isiWOS:A1997YF30000007-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridKofman, L=35299507100en_US
dc.identifier.scopusauthoridKaiser, N=7103118947en_US
dc.identifier.scopusauthoridLee, MH=7409119699en_US
dc.identifier.scopusauthoridBabul, A=35228472900en_US

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