Gravitational Lensing by Spherical Lenses

Affiliation(s)

Observatorio Astronómico Nacional, Universidad Nacional de Colombia, Bogotá, Colombia.

Observatorio Astronómico Nacional, Universidad Nacional de Colombia, Bogotá, Colombia.

ABSTRACT

In this work we introduced
a new proposal to study the gravitational lensing theory by spherical lenses,
starting from its surface mass density ∑(x) written
in terms of a decreasing function *f* of
a dimensionless coordinate x on
the lens plane. The main result is the use of the function *f*(x) to find directly the lens
properties, at the same time that the lens problem is described by a first
order differential equation which encodes all information about the lens. SIS
and NIS profiles are used as examples to find their functions *f*(x). Using the Poisson equation we find
that the deflection angle is directly proportional to *f*(x), and therefore the lens
equation can be written in terms of the function and the parameters of the
lens. The critical and caustic curves, as well as image formation and
magnification generated by the lens are analyzed. As an example of this method,
the properties of a lens modeled by a NFW profile are determined. Although the
puntual mass is spherically symmetric, its mass density is not continuous so
that its *f*(x) function is discussed
in Appendix 1.

Cite this paper

Hurtado, R. , Castañeda, L. and Tejeiro, J. (2014) Gravitational Lensing by Spherical Lenses.*International Journal of Astronomy and Astrophysics*, **4**, 340-352. doi: 10.4236/ijaa.2014.42028.

Hurtado, R. , Castañeda, L. and Tejeiro, J. (2014) Gravitational Lensing by Spherical Lenses.

References

[1] Blandford, R.D. and Narayan, R. (1992) Cosmological Applications of Gravitational Lensing. ARA&A, 30, 311-358. http://dx.doi.org/10.1146/annurev.aa.30.090192.001523

[2] Yu-Chung, N. and Cheng, L. (1999) Krauss, Gravitational Lensing and Dark Structures. The Astrophysical Journal, 514, 25-32. http://dx.doi.org/10.1086/306914

[3] Brouzakis, N., Tetradis, N. and Tzavara, E. (2008) Light Propagation and Large-Scale Inhomogeneities. Journal of Cosmology and Astroparticle Physics, 4, 8.

[4] Shuo, C., Yu, P., Biesiada, M., Godlowski, W. and Zong-Hong, Z. (2012) Constraints on Cosmological Models from Strong Gravitational Lensing Systems. Journal of Cosmology and Astroparticle Physics, 3, 16.

[5] Cohn, J.D. and Kochanek, C.S. (2014) The Effects of Massive Substructures on Image Multiplicities in Gravitational Lenses. The Astrophysical Journal, 608, 25-35. http://dx.doi.org/10.1086/392491

[6] Kaiser, N. and Squires, G. (1993) Mapping the Dark Matter with Weak Gravitational Lensing. The Astrophysical Journal, 404, 441-450. http://dx.doi.org/10.1086/172297

[7] Knudson, A., Ratnatunga, K.U. and Griffiths, R.E. (2001) Investigation of Gravitational Lens Mass Models. The Astronomical Journal, 122, 103-112.

[8] Halkola, A., Seitz, S. and Pannella, M. (2006) Parametric Strong Gravitational Lensing Analysis of Abell 1689. Monthly Notices of the Royal Astronomical Society, 372, 1425-1462.

http://dx.doi.org/10.1111/j.1365-2966.2006.10948.x

[9] Navarro, J., Frenk, C. and White, S. (1996) The Structure of Cold Dark Matter Halos. The Astrophysical Journal, 462, 563-575. http://dx.doi.org/10.1086/177173

[10] Schneider, P., Ehlers, J. and Falco, E.E. (1992) Gravitational Lenses. Springer-Verlag, Berlin.

[11] Wambsganss, J. (1998) Gravitational Lensing in Astronomy. Living Reviews in Relativity, 1, 12.

http://www.livingreviews.org/lrr-1998-12

[12] Wright, C.O. and Brainerd, T.G. (2000) Gravitational Lensing by NFW Halos. The Astrophysical Journal, 534, 34-40. http://dx.doi.org/10.1086/308744

[13] Golse, G. and Kneib, J.P. (2002) Pseudo Elliptical Lensing Mass Model: Application to the NFW Mass Distribution. Astronomy & Astrophysics, 390, 821-827.

[14] Narikawa, T. and Yamamoto, K. (2012) Testing Gravity with Halo Density Profiles Observed through Gravitational Lensing. Journal of Cosmology and Astroparticle Physics, 5, 16.

[15] Bartelmann, M. (1996) Arcs from a Universal Dark-Matter Halo Profile. The Astronomical Journal, 313, 697-702.

[1] Blandford, R.D. and Narayan, R. (1992) Cosmological Applications of Gravitational Lensing. ARA&A, 30, 311-358. http://dx.doi.org/10.1146/annurev.aa.30.090192.001523

[2] Yu-Chung, N. and Cheng, L. (1999) Krauss, Gravitational Lensing and Dark Structures. The Astrophysical Journal, 514, 25-32. http://dx.doi.org/10.1086/306914

[3] Brouzakis, N., Tetradis, N. and Tzavara, E. (2008) Light Propagation and Large-Scale Inhomogeneities. Journal of Cosmology and Astroparticle Physics, 4, 8.

[4] Shuo, C., Yu, P., Biesiada, M., Godlowski, W. and Zong-Hong, Z. (2012) Constraints on Cosmological Models from Strong Gravitational Lensing Systems. Journal of Cosmology and Astroparticle Physics, 3, 16.

[5] Cohn, J.D. and Kochanek, C.S. (2014) The Effects of Massive Substructures on Image Multiplicities in Gravitational Lenses. The Astrophysical Journal, 608, 25-35. http://dx.doi.org/10.1086/392491

[6] Kaiser, N. and Squires, G. (1993) Mapping the Dark Matter with Weak Gravitational Lensing. The Astrophysical Journal, 404, 441-450. http://dx.doi.org/10.1086/172297

[7] Knudson, A., Ratnatunga, K.U. and Griffiths, R.E. (2001) Investigation of Gravitational Lens Mass Models. The Astronomical Journal, 122, 103-112.

[8] Halkola, A., Seitz, S. and Pannella, M. (2006) Parametric Strong Gravitational Lensing Analysis of Abell 1689. Monthly Notices of the Royal Astronomical Society, 372, 1425-1462.

http://dx.doi.org/10.1111/j.1365-2966.2006.10948.x

[9] Navarro, J., Frenk, C. and White, S. (1996) The Structure of Cold Dark Matter Halos. The Astrophysical Journal, 462, 563-575. http://dx.doi.org/10.1086/177173

[10] Schneider, P., Ehlers, J. and Falco, E.E. (1992) Gravitational Lenses. Springer-Verlag, Berlin.

[11] Wambsganss, J. (1998) Gravitational Lensing in Astronomy. Living Reviews in Relativity, 1, 12.

http://www.livingreviews.org/lrr-1998-12

[12] Wright, C.O. and Brainerd, T.G. (2000) Gravitational Lensing by NFW Halos. The Astrophysical Journal, 534, 34-40. http://dx.doi.org/10.1086/308744

[13] Golse, G. and Kneib, J.P. (2002) Pseudo Elliptical Lensing Mass Model: Application to the NFW Mass Distribution. Astronomy & Astrophysics, 390, 821-827.

[14] Narikawa, T. and Yamamoto, K. (2012) Testing Gravity with Halo Density Profiles Observed through Gravitational Lensing. Journal of Cosmology and Astroparticle Physics, 5, 16.

[15] Bartelmann, M. (1996) Arcs from a Universal Dark-Matter Halo Profile. The Astronomical Journal, 313, 697-702.