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In strong gravitational lensing, the multiple images we see correspond to light rays that leave the source in slightly different directions. If the source emission is anisotropic, the images may differ from conventional lensing predictions (which assume isotropy). To identify scales on which source anisotropy may be important, we study the angle δ between the light rays emerging from the source, for different lensing configurations. If the lens has a power-law profile , the angle δ initially increases with lens redshift and then either diverges (for a steep profile ), remains constant (for an isothermal profile ), or vanishes (for a shallow profile ) as . The scaling with lens mass is roughly . The results for an Navarro–Frenk–White (NFW) profile are qualitatively similar to those for a shallow power law, with δ peaking at about half the redshift of the source (not half the distance). In practice, beaming could modify the statistics of beamed sources lensed by massive clusters: for an opening angle , there is a probability as high as that one of the lensed images may be missed (for ). Differential absorption within active galactic nuclei (AGNs) could modify the flux ratios of AGNs lensed by clusters; a sample of AGNs lensed by clusters could provide further constraints on the sizes of absorbing regions. Source anisotropy is not likely to be a significant effect in galaxy-scale strong lensing. [ABSTRACT FROM AUTHOR]

Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton, Gaudi & Petters, this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies. [ABSTRACT FROM AUTHOR]

We study microlensing of the faint images that form close to the centres of strong gravitational lens galaxies. These central images, which have finally begun to yield to observations, naturally appear in dense stellar fields and may be particularly sensitive to fine granularity in the mass distribution. The microlensing magnification maps for overfocused (i.e. demagnified) images differ strikingly from those for magnified images. In particular, the familiar ‘fold’ and ‘cusp’ features of maps for magnified images are only present for certain values of the fraction f of the surface mass density contained in stars. For central images, the dispersion in microlensing magnifications is generally larger than for normal (minimum and saddle) images, especially when the source is comparable to or larger than the stellar Einstein radius. The dispersion depends in a complicated way on f; this behaviour may hold the key to using microlensing as a probe of the relative densities of stars and dark matter in the cores of distant galaxies. Quantitatively, we predict that the central image C in PMN J1632−0033 has a magnification dispersion of 0.6 mag for , or 0.3 mag for . For comparison, the dispersions are 0.5–0.6 mag for image B and 0.05–0.1 mag for image A, if ; and just 0.1 mag for B and 0.008 mag for A if . (The dispersions can be extrapolated to larger sources sizes as .) Thus, central images are more susceptible than other lensed images to microlensing and hence good probes for measuring source sizes. [ABSTRACT FROM AUTHOR]

Microlensing promises to be a powerful tool for studying distant galaxies and quasars. As the data and models improve, there are systematic effects that need to be explored. Quasar continuum and broad-line regions may respond differently to microlensing due to their different sizes; to understand this effect, we study microlensing of finite sources by a mass function of stars. We find that microlensing is insensitive to the slope of the mass function but does depend on the mass range. For negative-parity images, diluting the stellar population with dark matter increases the magnification dispersion for small sources and decreases it for large sources. This implies that the quasar continuum and broad-line regions may experience very different microlensing in negative-parity lensed images. We confirm earlier conclusions that the surface brightness profile and geometry of the source have little effect on microlensing. Finally, we consider non-circular sources. We show that elliptical sources that are aligned with the direction of shear have larger magnification dispersions than sources with perpendicular alignment, an effect that becomes more prominent as the ellipticity increases. Elongated sources can lead to more rapid variability than circular sources, which raises the prospect of using microlensing to probe source shape. [ABSTRACT FROM AUTHOR]

Flux ratio ‘anomalies’ in quadruply imaged gravitational lenses can be explained with galactic substructure of the sort predicted by ΛCDM, but the strength and uniqueness of that hypothesis need to be further assessed. A good way to do that is to use the physical scale associated with the size of the source quasar, and its dependence on wavelength. We develop a toy model to study finite source effects in substructure lensing. Treating substructure as a singular isothermal sphere allows us to compute the images of a finite source analytically, and then to explore how the image configurations and magnifications depend on source position and size. Although simplified, our model yields instructive general principles: image positions and magnifications are basically independent of source size until the source is large enough to intersect a substructure caustic; even sources that are much larger than the substructure Einstein radius can be perturbed at a detectable level; and, most importantly, there is a tremendous amount to be learned from comparing image positions and magnifications at wavelengths that correspond to different source sizes. In a separate analysis, we carefully study four observed radio lenses to determine which of the images are anomalous. In B0712+472, the evidence for a radio flux ratio anomaly is marginal, but if the anomaly is real then image C is probably the culprit. In B1422+231, the anomaly is in image A. Interestingly, B2045+265 and B1555+375 both appear to have two anomalous images. Coincidentally, in each system one of the anomalies is in image C, and the other is in either image A or image B (both possibilities lead to acceptable models). It remains to be seen whether ΛCDM predicts enough substructure to explain multiple anomalies in multiple lenses. When we finally join our modelling results and substructure theory, we obtain lower bounds on the masses of the substructures responsible for the observed anomalies. The mass bounds are broadly consistent with expectations for ΛCDM. Perhaps more importantly, we outline various systematic effects in the mass bounds; poor knowledge of whether the substructure lies within the main lens galaxy or elsewhere along the line of sight appears to be the dominant systematic. [ABSTRACT FROM AUTHOR]

We study the impact of lens galaxy environments on the image separation distribution of lensed quasars. We account for both environmental convergence and shear, using a joint distribution derived from galaxy formation models calibrated by galaxy–galaxy lensing data and number counts of massive elliptical galaxies. We find that the external field enhances lensing probabilities, particularly, at large image separations; the increase is ∼30 per cent at and ∼200 per cent at , when we adopt a power-law source luminosity function . The enhancement is mainly driven by convergence, which boosts both the image separation and magnification bias (for a fixed lens galaxy mass). These effects have been neglected in previous studies of lens statistics. Turning the problem around, we derive the posterior convergence and shear distributions and point out that they are strong functions of image separation; lens systems with larger image separations are more likely to lie in dense environments. [ABSTRACT FROM AUTHOR]

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 (and including shear) yields a model that is physical but implausible. Going to higher order 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 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+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. [ABSTRACT FROM AUTHOR]

Studies of strong gravitational lensing in current and upcoming wide and deep photometric surveys, and of stellar kinematics from (integral-field) spectroscopy at increasing redshifts, promise to provide valuable constraints on galaxy density profiles and shapes. However, both methods are affected by various selection and modelling biases, which we aim to investigate in a consistent way. In this first paper in a series, we develop a flexible but efficient pipeline to simulate lensing by realistic galaxy models. These galaxy models have separate stellar and dark matter components, each with a range of density profiles and shapes representative of early-type, central galaxies without significant contributions from other nearby galaxies. We use Fourier methods to calculate the lensing properties of galaxies with arbitrary surface density distributions, and Monte Carlo methods to compute lensing statistics such as point-source lensing cross-sections. Incorporating a variety of magnification bias modes lets us examine different survey limitations in image resolution and flux. We rigorously test the numerical methods for systematic errors and sensitivity to basic assumptions. We also determine the minimum number of viewing angles that must be sampled in order to recover accurate orientation-averaged lensing quantities. We find that for a range of non-isothermal stellar and dark matter density profiles typical of elliptical galaxies, the combined density profile and corresponding lensing properties are surprisingly close to isothermal around the Einstein radius. The converse implication is that constraints from strong lensing and/or stellar kinematics, which are indeed consistent with isothermal models near the Einstein radius, cannot trivially be extrapolated to smaller and larger radii. [ABSTRACT FROM AUTHOR]

Many current and future astronomical surveys will rely on samples of strong gravitational lens systems to draw conclusions about galaxy mass distributions. We use a new strong lensing pipeline (presented in Paper I of this series) to explore selection biases that may cause the population of strong lensing systems to differ from the general galaxy population. Our focus is on point-source lensing by early-type galaxies with two mass components (stellar and dark matter) that have a variety of density profiles and shapes motivated by observational and theoretical studies of galaxy properties. We seek not only to quantify but also to understand the physics behind selection biases related to: galaxy mass, orientation and shape; dark matter profile parameters such as inner slope and concentration; and adiabatic contraction. We study how all of these properties affect the lensing Einstein radius, total cross-section, quad/double ratio and image separation distribution, with a flexible treatment of magnification bias to mimic different survey strategies. We present our results for two families of density profiles: cusped and deprojected Sérsic models. While we use fixed lens and source redshifts for most of the analysis, we show that the results are applicable to other redshift combinations, and we also explore the physics of how our results change for very different redshifts. We find significant (factors of several) selection biases with mass; orientation, for a given galaxy shape at fixed mass; cusped dark matter profile inner slope and concentration; concentration of the stellar and dark matter deprojected Sérsic models. Interestingly, the intrinsic shape of a galaxy does not strongly influence its lensing cross-section when we average over viewing angles. Our results are an important first step towards understanding how strong lens systems relate to the general galaxy population. [ABSTRACT FROM AUTHOR]

Abstract: Gravitational lensing assists in the detection of quasar hosts by amplifying and distorting the host light away from the unresolved quasar core images. We present the results of HST observations of 30 quasar hosts at redshifts 1< z <4.5. The hosts are small in size (r e ≲6kpc), and span a range of morphologies consistent with early-types (though smaller in mass) to disky/late-type. The ratio of the black hole mass (, from the virial technique) to the bulge mass (, from the stellar luminosity) at 1≲ z ≲1.7 is broadly consistent with the local value; while at z ≳1.7 is a factor of 3–6 higher than the local value. But, depending on the stellar content the ratio may decline at z ≳4 (if E/S0-like), flatten off to 6–10 times the local value (if Sbc-like), or continue to rise (if Im-like). We infer that galaxy bulge masses must have grown by a factor of 3–6 over the redshift range 3≳ z ≳1, and then changed little since z ∼1. This suggests that the peak epoch of galaxy formation for massive galaxies is above z ∼1. We also estimate the duty cycle of luminous AGNs at z ≳1 to be ∼1%, or 107 yr, with sizable scatter. [Copyright &y& Elsevier]