Esferas transparentes como lentes gravitacionales
DOI:
https://doi.org/10.15517/3fczkg02Palabras clave:
Lentes gravitacionales, Simulaciones numéricas, Relatividad generalResumen
En esta contribución, presentamos un estudio conciso y educativo de lentes gravitacionales debido a distribuciones de masa transparentes. Nos enfocamos en los cálculos de las propiedades de la imagen para perfiles de masa idealizados, incluyendo la esfera transparente uniforme, la esfera de gas isotérmico, la esfera de gas isotérmino no singular, y el perfil de King transparente. Utilizando técnicas numéricas y el software XFGLenses, se calculan y se visualizan las imágenes resultantes, junto con las curvas críticas y cáusticas asociadas. Los resultados son consistentes con las predicciones teóricas de los lentes transparentes, como lo son un número impar de imágenes, y la reducción del número de imágenes en dos cuando la fuente atraviesa la cáustica. Las geometrías que presentan las curvas cáusticas encontradas incluyen la forma de diamante, forma elíptica, y tipo lemniscata. Entre las curvas críticas, formas elípticas fueron las más encontradas, y la forma tipo lemniscata aparecieron específicamente en el case de la esfera isotérmica no singular, lo cual es esperado de lo conocido de lentes gravitacionales debido a distribuciones ideales.
Descargas
Referencias
[1] R. J. Adler, W. C. Barber, M. E. Redar, Gravitational lenses and plastic simulators. American Journal of Physics 63(1995), no. 6, 536–541. doi: 10.1119/1.17865 DOI: https://doi.org/10.1119/1.17865
[2] A. Barnacka, Gravitational lenses as high-resolution telescopes. Physics Reports 778-779(2018). Gravitational lenses as high-resolution telescopes, 1–46. doi: 10.1016/j.physrep.2018.10.001 DOI: https://doi.org/10.1016/j.physrep.2018.10.001
[3] R. R. Bourassa, R. Kantowski, The theory of transparent gravitational lenses. The Astrophysical Journal 195(1975), 13. doi: 10.1086/153300 DOI: https://doi.org/10.1086/153300
[4] R. R. Bourassa, R. Kantowski, T. D. Norton, The Spheroidal Gravitational Lens. The Astrophysical Journal 185(1973), 747. doi: 10.1086/152452 DOI: https://doi.org/10.1086/152452
[5] I. Bray, Spheroidal gravitational lenses. Monthly Notices of the Royal Astronomical Society 208(1984), 511–516. doi: 10.1093/mnras/208.3.511 DOI: https://doi.org/10.1093/mnras/208.3.511
[6] O. Chwolson, Über eine mögliche Form fiktiver Doppelsterne. Astronomische Nachrichten 221(1924), no. 20, 329–330. doi: 10.1002/asna.19242212003 DOI: https://doi.org/10.1002/asna.19242212003
[7] E. E. Clark, The Uniform Transparent Gravitational Lens. Monthly Notices of the Royal Astronomical Society 158(1972), no. 2, 233–243. doi: 10.1093/mnras/158.2.233 DOI: https://doi.org/10.1093/mnras/158.2.233
[8] J. P. Coles, J. I. Read, P. Saha, Gravitational lens recovery with glass: measuring the mass profile and shape of a lens. Monthly Notices of the Royal Astronomical Society 445(2014), no. 3, 2181–2197. doi: 10.1093/mnras/stu1781 DOI: https://doi.org/10.1093/mnras/stu1781
[9] C. C. Dyer, R. C. Roeder, Possible multiple imaging by spherical galaxies. The Astrophysical Journal 238(1980), L67. doi: 10.1086/183260 DOI: https://doi.org/10.1086/183260
[10] M. Falbo-Kenkel, J. Lohre, Simple gravitational lens demonstrations. The Physics Teacher 34(1996), no. 9, 555–557. doi: 10.1119/1.2344566 DOI: https://doi.org/10.1119/1.2344566
[11] F. Frutos-Alfaro, A computer program to visualize gravitational lenses. American Journal of Physics 69(2001), no. 2, 218–222. doi: 10.1119/1.1290251 DOI: https://doi.org/10.1119/1.1290251
[12] F. Frutos-Alfaro, Reduction of the gravitational lens equation to a one-dimensional non-linear form for the tilted Plummer model family.Monthly Notices of the Royal Astronomical Society: Letters 376(2007), no. 1, L72–L75. doi: 10.1111/j.1745-3933.2007.00289.x DOI: https://doi.org/10.1111/j.1745-3933.2007.00289.x
[13] D. H. Gottlieb, A gravitational lens need not produce an odd number of images. Journal of Mathematical Physics 35(1994), no. 10, 5507–5510. doi: 10.1063/1.530762 DOI: https://doi.org/10.1063/1.530762
[14] J. Higbie, Gravitational lens. American Journal of Physics 49(1981), no. 7, 652–655. doi: 10.1119/1.12440 DOI: https://doi.org/10.1119/1.12440
[15] G. Hinshaw, L. M. Krauss, Gravitational Lensing by Isothermal Spheres with Finite Core Radii: Galaxies and Dark Matter. Astrophysical Journal 320(1987), 468. doi: 10.1086/165564 DOI: https://doi.org/10.1086/165564
[16] V. Icke, Construction of a gravitational lens. American Journal of Physics 48(1980), no. 10, 883–886. doi: 10.1119/1.12284 DOI: https://doi.org/10.1119/1.12284
[17] C. Jacobs et al., An Extended Catalog of Galaxy–Galaxy Strong Gravitational Lenses Discovered in DES Using Convolutional Neural Networks. The Astrophysical Journal Supplement Series 243(2019), no. 1, 17. doi:10.3847/1538-4365/ab26b6 DOI: https://doi.org/10.3847/1538-4365/ab26b6
[18] R. Kantowski, B. Chen, X. Dai, Fermat’s least-time principle and the embedded transparent lens. Phys. Rev. D 88(2013) 8, 083001. doi: 10.1103/ PhysRevD.88.083001 DOI: https://doi.org/10.1103/PhysRevD.88.083001
[19] H. Karttunen et al., Fundamental astronomy. Springer, 2007. doi: 10.1007/ 978-3-540-34144-4
[20] R. Kayser, P. Helbig, T. Schramm, A general and practical method for calculating cosmological distances. 1997. doi: 10.48550/arXiv.astro-ph/9603028
[21] I. R. King, Density Data and Emission Measure for a Model of the Coma Cluster. The Astrophysical Journal 174(1972), L123. doi: 10.1086/180963 DOI: https://doi.org/10.1086/180963
[22] S. Liebes, Gravitational Lenses. Physical Review 133(1964), no. 3B, B835–B844. doi: 10.1103/physrev.133.b835 DOI: https://doi.org/10.1103/PhysRev.133.B835
[23] S. Liebes, Gravitational Lens Simulator. American Journal of Physics 37(1969), no. 1, 103–104. doi: 10.1119/1.1975345 DOI: https://doi.org/10.1119/1.1975345
[24] R. H. McKenzie, A gravitational lens produces an odd number of images. Journal of Mathematical Physics 26(1985), no. 7, 1592–1596. doi: 10.1063/ 1.526923 DOI: https://doi.org/10.1063/1.526923
[25] M. J. Nandor, T. M. Helliwell, Fermat’s principle and multiple imaging by gravitational lenses. American Journal of Physics 64(1996), 45–49. doi: 10.1119/1.18291 DOI: https://doi.org/10.1119/1.18291
26] P. R. Newbury, R. J. Spiteri, Inverting Gravitational Lenses. SIAM Review 44(2002), no. 1, 111–130. doi: 10.1137/S0036144500380934 DOI: https://doi.org/10.1137/S0036144500380934
[27] B. Patla, R. J. Nemiroff, Gravitational Lensing Characteristics of the Transparent Sun. The Astrophysical Journal 685(2008), no. 2, 1297. doi: 10.1086/588805 DOI: https://doi.org/10.1086/588805
[28] M. Quirós-Rojas et al., ALMA follow-up of 3000 red-Herschel galaxies: the nature of extreme submillimetre galaxies. Monthly Notices of the Royal Astronomical Society 533(2024), no. 3, 2966–2979. doi: 10.1093/mnras /stae1974 DOI: https://doi.org/10.1093/mnras/stae1974
[29] T. Sauer, Nova Geminorum 1912 and the Origin of the Idea of Gravitational Lensing. Archive for History of Exact Sciences 62(2008), 1–22. doi: 10.1007/ s00407-007-0008-4 DOI: https://doi.org/10.1007/s00407-007-0008-4
[30] P. Schneider, J. Ehlers, E. E. Falco, Gravitational Lenses. Springer Berlin Heidelberg, 1992. doi: 10.1007/978-3-662-03758-4 DOI: https://doi.org/10.1007/978-3-662-03758-4
[31] M. Selmke, An optical n-body gravitational lens analogy. American Journal of Physics 89(2021), no. 1, 11–20. doi: 10.1119/10.0002117 DOI: https://doi.org/10.1119/10.0002117
[32] A. Sonnenfeld et al., Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). I. Automatic search for galaxy-scale strong lenses. Publications of the Astronomical Society of Japan 70(2017), no. SP1, S29. doi:10.1093/pasj/psx062 DOI: https://doi.org/10.1093/pasj/psx062
[33] B. Szafraniec, J. F. Harford, A simple model of a gravitational lens from geometric optics. American Journal of Physics 92(2024), no. 11, 878–884. doi: 10.1119/5.0157513 DOI: https://doi.org/10.1119/5.0157513
[34] H. Thuruthipilly, A. Zadrozny, A. Pollo, M. Biesiada, Finding strong gravitational lenses through self-attention - Study based on the Bologna Lens Challenge. A&A 664(2022), A4. doi: 10.1051/0004-6361/202142463 DOI: https://doi.org/10.1051/0004-6361/202142463
[35] E. L. Turner, J. P. Ostriker, J. R. Gott III, The statistics of gravitational lenses : the distributions of image angular separations and lens redshifts. Astrophysical Journal 284(1984), 1–22. doi: 10.1086/162379 DOI: https://doi.org/10.1086/162379
[36] P. van Dokkum et al., A massive compact quiescent galaxy at z=2 with a complete Einstein ring in JWST imaging. Nature Astronomy 8(2024), 119. doi: 10.1038/s41550-023-02103-9 DOI: https://doi.org/10.1038/s41550-023-02103-9
[37] D. Walsh, R. Carswell, R. Weymann, 0957+561 A, B: Twin quasi-stellar objects or gravitational lens? Nature 279(1979), 381–384. doi: 10.1038 /279381a0 DOI: https://doi.org/10.1038/279381a0
[38] S. Xu, G. Su, Y. Zhang, Y. Liu, Mimicking gravitational lens on a thin elastic plate. Applied Physics Letters 120(2022), no. 3, 031106. doi: 10.1063/5.0075683 DOI: https://doi.org/10.1063/5.0075683
[39] P. Young et al., The double quasar Q0957+561 A, B: a gravitational lens image formed by a galaxy at z=0.39. Astrophysical Journal 241(1980), 507–520. doi: 10.1086/158365 DOI: https://doi.org/10.1086/158365
Descargas
Publicado
Número
Sección
Licencia
Derechos de autor 2025 Edwin Santiago-Leandro, Alexander Mora-Chaverri, Francisco Frutos-Alfaro (Autor/a)
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
Revista de Matemática: Teoría y aplicaciones por Universidad de Costa Rica se distribuye bajo una Licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional.
Cómo citar
