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Strong Lensing by Galaxies

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Principles of Gravitational Lensing

Part of the book series: Springer Praxis Books ((ASTRONOMY))

Abstract

The remainder of this book is concerned with applications of gravitational lensing of cosmological relevance. We proceed by considering ever larger mass and distance scales, starting with galaxy-scale strong lensing in the present chapter. The background sources in this context are point-like quasars or extended galaxies. As we will see in Sect. 6.1, the axisymmetric models of Chap. 2 can be readily adapted to the more general setting of Chap. 4. Only such non-axisymmetric mass distributions can be expected to describe observed lens systems. We noted in Chap. 2 that actual galaxies have finite density everywhere and offered the nonsingular isothermal sphere as an example. We extend that discussion to more general lenses in Sect. 6.2. Even all of these refinements are insufficient for understanding the full variety of observed galaxy lenses. For example, we must account for extended sources (Sect. 6.3) and for lenses that cannot be described by smooth density profiles (Sect. 6.4). Using the properties of observed images to infer the mass distribution of the lens is the subject of Sect. 6.5. Applications of the models and methods described in this chapter are outlined in Sect. 6.6.

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Notes

  1. 1.

    For a source on the negative u-axis, we let (x, y) → (−x, y) in Eq. (6.5a) while leaving the sign of u unchanged.

  2. 2.

    For a source on the negative v-axis, we let (x, y) → (x, −y) in Eq. (6.9a) while leaving the sign of v unchanged.

  3. 3.

    Same as Footnote 1, but for Eq. (6.17a).

  4. 4.

    Same as Footnote 2, but for Eq. (6.18a).

  5. 5.

    The isothermal model does not have any radial magnification.

  6. 6.

    Another model for subhalos is the NFW model that we will encounter in Sect. 7.1.1.

  7. 7.

    In some literature, especially for cluster lensing, this model is referred to as a pseudo-isothermal elliptical mass distribution, or PIEMD, after Kassiola and Kovner (1993). It has also been called a pseudo-Jaffe model (Keeton et al. 2000a).

  8. 8.

    This local region needs to be defined with some care because the deflection can be non-negligible even at many times the star’s Einstein radius (see, e.g., Wambsganss 1999).

  9. 9.

    This is a generalization of the Chang-Refsdal lens mentioned in Problem 5.2 to multiple stars.

  10. 10.

    If the images are blurred together, \(\chi ^2_{\mathrm {pos}}\) can be generalized to account for covariances between different images.

  11. 11.

    The exception is radio wavelengths, where observations usually use interferometry. The modeling methods discussed here can be generalized to handle interferometric data.

  12. 12.

    Section 6.5.1 shows that the inferred Einstein radius does depend on the choice of model, but the quantitative difference between results from various models is typically no more than a few percent.

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Authors and Affiliations

  1. Monrovia, CA, USA

    Arthur B. Congdon

  2. Physics & Astronomy Department, Rutgers University, Piscataway, NJ, USA

    Charles R. Keeton

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Congdon, A.B., Keeton, C.R. (2018). Strong Lensing by Galaxies. In: Principles of Gravitational Lensing. Springer Praxis Books(). Springer, Cham. https://doi.org/10.1007/978-3-030-02122-1_6

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