### Abstract

It has been known for over a decade that many four-image gravitational lenses exhibit anomalous radio flux ratios. These anomalies can be explained by adding a clumpy cold dark matter (CDM) component to the background galactic potential of the lens. As an alternative, Evans & Witt (2003) recently suggested that smooth multipole perturbations provide a reasonable alternative to CDM substructure in some but not all cases. We generalize their method in two ways so as to determine whether multipole models can explain highly anomalous systems. We carry the multipole expansion to higher order, and also include external tidal shear as a free parameter. Fitting for the shear proves crucial to finding a physical (positive-definite density) model. For B1422+231, working to order k_{max} = 5 (and including shear) yields a model that is physical but implausible. Going to higher order (k_{max} ≳ 9) reduces global departures from ellipticity, but at the cost of introducing small-scale wiggles in proximity to the bright images. These localized undulations are more pronounced in B2045+265, where k_{max} ∼ 17 multipoles are required to smooth out large-scale deviations from elliptical symmetry. Such modes surely cannot be taken at face value; they must indicate that the models are trying to reproduce some other sort of structure. Our formalism naturally finds models that fit the data exactly, but we use B0712-1-472 to show that measurement uncertainties have little effect on our results. Finally, we consider the system B1933+503, where two sources are lensed by the same foreground galaxy. The additional constraints provided by the images of the second source render the multipole model unphysical. We conclude that external shear must be taken into account to obtain plausible models, and that a purely smooth angular structure for the lens galaxy does not provide a viable alternative to the prevailing CDM clump hypothesis.

Original language | English (US) |
---|---|

Pages (from-to) | 1459-1466 |

Number of pages | 8 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 364 |

Issue number | 4 |

DOIs | |

State | Published - Dec 21 2005 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

- Dark matter
- Galaxies: haloes
- Galaxies: structure
- Gravitational lensing

### Cite this

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*Monthly Notices of the Royal Astronomical Society*, vol. 364, no. 4, pp. 1459-1466. https://doi.org/10.1111/j.1365-2966.2005.09699.x

**Multipole models of four-image gravitational lenses with anomalous flux ratios.** / Congdon, Arthur B.; Keeton, Charles.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Multipole models of four-image gravitational lenses with anomalous flux ratios

AU - Congdon, Arthur B.

AU - Keeton, Charles

PY - 2005/12/21

Y1 - 2005/12/21

N2 - It has been known for over a decade that many four-image gravitational lenses exhibit anomalous radio flux ratios. These anomalies can be explained by adding a clumpy cold dark matter (CDM) component to the background galactic potential of the lens. As an alternative, Evans & Witt (2003) recently suggested that smooth multipole perturbations provide a reasonable alternative to CDM substructure in some but not all cases. We generalize their method in two ways so as to determine whether multipole models can explain highly anomalous systems. We carry the multipole expansion to higher order, and also include external tidal shear as a free parameter. Fitting for the shear proves crucial to finding a physical (positive-definite density) model. For B1422+231, working to order kmax = 5 (and including shear) yields a model that is physical but implausible. Going to higher order (kmax ≳ 9) reduces global departures from ellipticity, but at the cost of introducing small-scale wiggles in proximity to the bright images. These localized undulations are more pronounced in B2045+265, where kmax ∼ 17 multipoles are required to smooth out large-scale deviations from elliptical symmetry. Such modes surely cannot be taken at face value; they must indicate that the models are trying to reproduce some other sort of structure. Our formalism naturally finds models that fit the data exactly, but we use B0712-1-472 to show that measurement uncertainties have little effect on our results. Finally, we consider the system B1933+503, where two sources are lensed by the same foreground galaxy. The additional constraints provided by the images of the second source render the multipole model unphysical. We conclude that external shear must be taken into account to obtain plausible models, and that a purely smooth angular structure for the lens galaxy does not provide a viable alternative to the prevailing CDM clump hypothesis.

AB - It has been known for over a decade that many four-image gravitational lenses exhibit anomalous radio flux ratios. These anomalies can be explained by adding a clumpy cold dark matter (CDM) component to the background galactic potential of the lens. As an alternative, Evans & Witt (2003) recently suggested that smooth multipole perturbations provide a reasonable alternative to CDM substructure in some but not all cases. We generalize their method in two ways so as to determine whether multipole models can explain highly anomalous systems. We carry the multipole expansion to higher order, and also include external tidal shear as a free parameter. Fitting for the shear proves crucial to finding a physical (positive-definite density) model. For B1422+231, working to order kmax = 5 (and including shear) yields a model that is physical but implausible. Going to higher order (kmax ≳ 9) reduces global departures from ellipticity, but at the cost of introducing small-scale wiggles in proximity to the bright images. These localized undulations are more pronounced in B2045+265, where kmax ∼ 17 multipoles are required to smooth out large-scale deviations from elliptical symmetry. Such modes surely cannot be taken at face value; they must indicate that the models are trying to reproduce some other sort of structure. Our formalism naturally finds models that fit the data exactly, but we use B0712-1-472 to show that measurement uncertainties have little effect on our results. Finally, we consider the system B1933+503, where two sources are lensed by the same foreground galaxy. The additional constraints provided by the images of the second source render the multipole model unphysical. We conclude that external shear must be taken into account to obtain plausible models, and that a purely smooth angular structure for the lens galaxy does not provide a viable alternative to the prevailing CDM clump hypothesis.

KW - Dark matter

KW - Galaxies: haloes

KW - Galaxies: structure

KW - Gravitational lensing

UR - http://www.scopus.com/inward/record.url?scp=29144520469&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29144520469&partnerID=8YFLogxK

U2 - 10.1111/j.1365-2966.2005.09699.x

DO - 10.1111/j.1365-2966.2005.09699.x

M3 - Article

AN - SCOPUS:29144520469

VL - 364

SP - 1459

EP - 1466

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 4

ER -