Gravitational lensing of anisotropic sources

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   M ∝ R ^γ  , the angle δ initially increases with lens redshift and then either diverges (for a steep profile  γ < 1  ), remains constant (for an isothermal profile  γ= 1  ), or vanishes (for a shallow profile  γ > 1  ) as   z _l→ z _s  . The scaling with lens mass is roughly  δ∝ M ^1/(2−γ)  . 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  θ_jet  , there is a probability as high as   P ∼ 0.02–0.07(θ_jet/0.5°)⁻¹  that one of the lensed images may be missed (for  2 ≲ z _s≲ 6  ). 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.     

Bathymetry of the Reykjanes Ridge

We present a series of 1:200,000 scale maps of the bathymetry of the Reykjanes Ridge. The data are divided into four maps, extending 630 km along the ridge axis and between 30 and 100 km off-axis. This compilation of bathymetry data is extremely detailed, gridded at approximately 100 m resolution, and with almost no gaps. The Reykjanes Ridge is one of the best examples of a hotspot-dominated ridge, whose characteristics are influenced by its proximity to the Iceland plume. Many fundamental questions may be addressed at the Reykjanes Ridge, which is why the BRIDGE programme identified it as one of its four regional projects. These maps represent a BRIDGE contribution to the general scientific community.     

The Reykjanes Ridge: structure and tectonics of a hot-spot-influenced, slow-spreading ridge, from multibeam bathymetry, gravity and magnetic investigations

We report a comprehensive morphological, gravity and magnetic survey of the oblique- and slow-spreading Reykjanes Ridge near the Iceland mantle plume. The survey extends from 57.9°N to 62.1°N and from the spreading axis to between 30 km (3 Ma) and 100 km (10 Ma) off-axis; it includes 100 km of one arm of a diachronous ‘V-shaped' or ‘chevron' ridge. Observed isochrons are extremely linear and 28° oblique to the spreading normal with no significant offsets. Along-axis there are ubiquitous, en-echelon axial volcanic ridges (AVRs), sub-normal to the spreading direction, with average spacing of 14 km and overlap of about one third of their lengths. Relict AVRs occur off-axis, but are most obvious where there has been least axial faulting, suggesting that elsewhere they are rapidly eroded tectonically. AVRs maintain similar plan views but have reduced heights nearer Iceland. They are flanked by normal faults sub-parallel to the ridge axis, the innermost of which occur slightly closer to the axis towards Iceland, suggesting a gradual reduction of the effective lithospheric thickness there. Generally, the amplitude of faulting decreases towards Iceland. We interpret this pattern of AVRs and faults as the response of the lithosphere to oblique spreading, as suggested by theory and physical modelling. An axial, 10–15 km wide zone of high acoustic backscatter marks the most recent volcanic activity. The zone's width is independent of the presence of a median valley, so axial volcanism is not primarily delimited by median valley walls, but is probably controlled by the lateral distance that the oblique AVRs can propagate into off-axis lithosphere. The mantle Bouguer anomaly (MBA) exhibits little mid- to short-wavelength variation above a few milliGals, and along-axis variations are small compared with other parts of the Mid-Atlantic Ridge. Nevertheless, there are small axial deeps and MBA highs spaced some 130 km along-axis that may represent subdued third-order segment boundaries. They lack coherent off-axis traces and cannot be linked to Oligocene fracture zones on the ridge flanks. The surveyed chevron ridge is morphologically discontinuous, comprising several parallel bands of closely spaced, elevated blocks. These reflect the surrounding tectonic fabric but have higher fault scarps. There is no evidence for off-axis volcanism or greater abundance of seamounts on the chevron. Free-air gravity over it is greater than expected from the observed bathymetry, suggesting compensation via regional rather than pointwise isostasy. Most of the observed variation along the ridge can be ascribed to varying distance from the mantle plume, reflecting changes in mantle temperature and consequently in crustal thickness and lithospheric strength. However, a second-order variation is superimposed. In particular, between 59°30′N and 61°30′N there is a minimum of large-scale faulting and crustal magnetisation, maximum density of seamounts, and maximum axial free-air gravity high. To the north the scale of faulting increases slightly, seamounts are less common, and there is a relative axial free-air low. We interpret the 59°30′N to 61°30′N region as where the latest chevron ridge intersects the Reykjanes Ridge axis, and suggest that the morphological changes that culminate there reflect a local temperature high associated with a transient pulse of high plume output at its apex.     

Microlensing of an extended source by a power-law mass distribution

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.     

Galaxy density profiles and shapes – II. Selection biases in strong lensing surveys

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.     

Galaxy density profiles and shapes – I. Simulation pipeline for lensing by realistic galaxy models

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.     

Analytic relations for magnifications and time delays in gravitational lenses with fold and cusp configurations

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.