Magnification Cross Sections for the Elliptic Umbilic Caustic Surface
In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as <inline-formula> <math display="inl...
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MDPI AG
2019-07-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/5/7/161 |
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| author | Amir B. Aazami Charles R. Keeton Arlie O. Petters |
| author_facet | Amir B. Aazami Charles R. Keeton Arlie O. Petters |
| author_sort | Amir B. Aazami |
| collection | DOAJ |
| description | In gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as <inline-formula> <math display="inline"> <semantics> <msup> <mi>μ</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics> </math> </inline-formula> for fold caustics and <inline-formula> <math display="inline"> <semantics> <msup> <mi>μ</mi> <mrow> <mo>−</mo> <mn>2.5</mn> </mrow> </msup> </semantics> </math> </inline-formula> for cusp caustics. We aim to extend the results to higher-order caustic singularities, focusing on the elliptic umbilic, which can be manifested in lensing systems with two or three galaxies. The elliptic umbilic has a caustic surface, and we show that the volume cross section scales as <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi>μ</mi> </mrow> <mrow> <mo>−</mo> <mn>2.5</mn> </mrow> </msup> </semantics> </math> </inline-formula> in the two-image region and <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi>μ</mi> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics> </math> </inline-formula> in the four-image region, where <inline-formula> <math display="inline"> <semantics> <mi>μ</mi> </semantics> </math> </inline-formula> is the total unsigned magnification. In both cases our results are supported both numerically and analytically. |
| first_indexed | 2024-04-11T12:32:18Z |
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| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-04-11T12:32:18Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-6b04df3328a34aac8c20355022ecb37c2022-12-22T04:23:43ZengMDPI AGUniverse2218-19972019-07-015716110.3390/universe5070161universe5070161Magnification Cross Sections for the Elliptic Umbilic Caustic SurfaceAmir B. Aazami0Charles R. Keeton1Arlie O. Petters2Department of Mathematics and Computer Science, Clark University, Worcester, MA 01610, USADepartment of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854-8019, USADepartments of Mathematics and Physics, Duke University, Science Drive, Durham, NC 27708-0320, USAIn gravitational lensing, magnification cross sections characterize the probability that a light source will have magnification greater than some fixed value, which is useful in a variety of applications. The (area) cross section is known to scale as <inline-formula> <math display="inline"> <semantics> <msup> <mi>μ</mi> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics> </math> </inline-formula> for fold caustics and <inline-formula> <math display="inline"> <semantics> <msup> <mi>μ</mi> <mrow> <mo>−</mo> <mn>2.5</mn> </mrow> </msup> </semantics> </math> </inline-formula> for cusp caustics. We aim to extend the results to higher-order caustic singularities, focusing on the elliptic umbilic, which can be manifested in lensing systems with two or three galaxies. The elliptic umbilic has a caustic surface, and we show that the volume cross section scales as <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi>μ</mi> </mrow> <mrow> <mo>−</mo> <mn>2.5</mn> </mrow> </msup> </semantics> </math> </inline-formula> in the two-image region and <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi>μ</mi> </mrow> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics> </math> </inline-formula> in the four-image region, where <inline-formula> <math display="inline"> <semantics> <mi>μ</mi> </semantics> </math> </inline-formula> is the total unsigned magnification. In both cases our results are supported both numerically and analytically.https://www.mdpi.com/2218-1997/5/7/161strong gravitational lensingmagnification cross sectionscaustics |
| spellingShingle | Amir B. Aazami Charles R. Keeton Arlie O. Petters Magnification Cross Sections for the Elliptic Umbilic Caustic Surface Universe strong gravitational lensing magnification cross sections caustics |
| title | Magnification Cross Sections for the Elliptic Umbilic Caustic Surface |
| title_full | Magnification Cross Sections for the Elliptic Umbilic Caustic Surface |
| title_fullStr | Magnification Cross Sections for the Elliptic Umbilic Caustic Surface |
| title_full_unstemmed | Magnification Cross Sections for the Elliptic Umbilic Caustic Surface |
| title_short | Magnification Cross Sections for the Elliptic Umbilic Caustic Surface |
| title_sort | magnification cross sections for the elliptic umbilic caustic surface |
| topic | strong gravitational lensing magnification cross sections caustics |
| url | https://www.mdpi.com/2218-1997/5/7/161 |
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