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Register a new userRobust modeling of quadruply lensed quasars (and random quartets) using Witts hyperbola
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We develop a robust method to model quadruply lensed quasars, relying heavily on the work of Witt (1996), who showed that for elliptical potentials, the four image positions, the source, and the lensing galaxy lie on a right hyperbola. For the singular isothermal elliptical potential, there exists a complementary ellipse centered on the source which also maps through the four images, with the same axis ratio as the potential but perpendicular to it. We first solve for Witts hyperbola, reducing the allowable space of models to three dimensions. We then obtain the best fitting complementary ellipse. The simplest models of quadruple lenses require seven parameters to reproduce the observed image configurations, while the four positions give eight constraints. This leaves us one degree of freedom to use as a figure of merit. We applied our model to 29 known lenses, and include their figures of merit. We then modeled 100 random quartets. A selection criterion that sacrifices 20% of the known lenses can exclude 98% of the random quartets.
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Witt (1996) has shown that for an elliptical potential, the four images of a quadruply lensed quasar lie on a rectangular hyperbola that passes through the unlensed quasar position and the center of the potential as well. Wynne and Schechter (2018) have shown that, for the singular isothermal elliptical potential (SIEP), the four images also lie on an `amplitude ellipse centered on the quasar position with axes parallel to the hyperbolas asymptotes. Witts hyperbola arises from equating the directions of both sides of the lens equation. The amplitude ellipse derives from equating the magnitudes. One can model any four points as an SIEP in three steps. 1. Find the rectangular hyperbola that passes through the points. 2. Find the aligned ellipse that also passes through them. 3. Find the hyperbola with asymptotes parallel to those of the first that passes through the center of the ellipse and the pair of images closest to each other. The second hyperbola and the ellipse give an SIEP that predicts the positions of the two remaining images where the curves intersect. Pinning the model to the closest pair guarantees a four image model. Such models permit rapid discrimination between gravitationally lensed quasars and random quartets of stars.
Among known strongly lensed quasar systems, ~25% have gravitational potentials sufficiently flat (and sources sufficiently well aligned) to produce four images rather than two. The projected flattening of the lensing galaxy and tides from neighboring galaxies both contribute to the potentials quadrupole. Witts hyperbola and Wynnes ellipse permit determination of the overall quadrupole from the positions of the quasar images. The position of the lensing galaxy resolves the distinct contributions of intrinsic ellipticity and tidal shear to that quadrupole. Among 31 quadruply lensed quasars systems with statistically significant decompositions, 15 are either reliably ($2sigma$) or provisionally ($1sigma$) shear-dominated and 11 are either reliably or provisionally ellipticity-dominated. For the remaining 8, the two effects make roughly equal contributions to the combined cross section (newly derived here) for quadruple lensing. This observational result is strongly at variance with the ellipticity-dominated forecast of Oguri & Marshall (2010).
Combining the exquisite angular resolution of Gaia with optical light curves and WISE photometry, the Gaia Gravitational Lenses group (GraL) uses machine learning techniques to identify candidate strongly lensed quasars, and has confirmed over two dozen new strongly lensed quasars from the Gaia Data Release 2. This paper reports on the 12 quadruply-imaged quasars identified by this effort to date, which is approximately a 20% increase in the total number of confirmed quadruply-imaged quasars. We discuss the candidate selection, spectroscopic follow-up, and lens modeling. We also report our spectroscopic failures as an aid for future investigations.
We present new measurements of the time delays of WFI2033-4723. The data sets used in this work include 14 years of data taken at the 1.2m Leonhard Euler Swiss telescope, 13 years of data from the SMARTS 1.3m telescope at Las Campanas Observatory and a single year of high-cadence and high-precision monitoring at the MPIA 2.2m telescope. The time delays measured from these different data sets, all taken in the R-band, are in good agreement with each other and with previous measurements from the literature. Combining all the time-delay estimates from our data sets results in Dt_AB = 36.2-0.8+0.7 days (2.1% precision), Dt_AC = -23.3-1.4+1.2 days (5.6%) and Dt_BC = -59.4-1.3+1.3 days (2.2%). In addition, the close image pair A1-A2 of the lensed quasars can be resolved in the MPIA 2.2m data. We measure a time delay consistent with zero in this pair of images. We also explore the prior distributions of microlensing time-delay potentially affecting the cosmological time-delay measurements of WFI2033-4723. There is however no strong indication in our measurements that microlensing time delay is neither present nor absent. This work is part of a H0LiCOW series focusing on measuring the Hubble constant from WFI2033-4723.
Gravitational lensing of point sources located inside the lens caustic is known to produce four images in a configuration closely related to the source position. We study this relation in the particular case of a sample of quadruply-imaged quasars observed by the Hubble Space Telescope (HST). Strong correlations between the parameters defining the image configuration are revealed. The relation between the image configuration and the source position is studied. Some simple features of the selected data sample are exposed and commented upon. In particular, evidence is found for the selected sample to be biased in favour of large magnification systems. While having no direct impact on practical analyses of specific systems, the results have pedagogical value and deepen our understanding of the mechanism of gravitational lensing.
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