Infrared Photometry and Dust Absorption in Highly Inclined Spiral Galaxies

We present JHK surface photometry of 15 highly inclined, late-type (Sab-Sc) spirals and investigate the quantitative effects of dust extinction. Using the (J - H, H - K) two-color diagram, we compare the color changes along the minor axis of each galaxy to the predictions from different models of radiative transfer. Models in which scattering effects are significant and those with more than a small fraction of the light sources located near the edge of the dust distribution do not produce enough extinction to explain the observed color gradients across disk absorption features. The optical depth in dust near the plane as deduced from the color excess depends sensitively on the adopted dust geometry, ranging from tau = 4 to 15 in the visual band. This suggests that a realistic model of the dust distribution is required, even for infrared photometry, to correct for dust extinction in the bulges of nearly edge-on systems.Comment: Accepted for publication in the March 1996 AJ. LaTex source which generates 27 pages of text and tables (no figures). Complete (text + figs) compressed Postscript preprint is also available at ftp://bessel.mps.ohio-state.edu/pub/terndrup/inclined.ps.Z (854 Mbyte

Gravitational lensing by point masses on regular grid points

It is shown that gravitational lensing by point masses arranged in an infinitely extended regular lattice can be studied analytically using the Weierstrass functions. In particular, we draw the critical curves and the caustic networks for the lenses arranged in regular-polygonal -- square, equilateral triangle, regular hexagon -- grids. From this, the mean number of positive parity images as a function of the average optical depth is derived and compared to the case of the infinitely extended field of randomly distributed lenses. We find that the high degree of the symmetry in the lattice arrangement leads to a significant bias towards canceling of the shear caused by the neighboring lenses on a given lens position and lensing behaviour that is qualitatively distinct from the random star field. We also discuss some possible connections to more realistic lensing scenarios.Comment: to appear in Monthly Notices of RAS, including 17 figs, 1 appendix. High-res figs and F95 code used available upon reques

The Chang-Refsdal Lens Revisited

This paper provides a complete theoretical treatment of the point-mass lens perturbed by constant external shear, often called the Chang-Refsdal lens. We show that simple invariants exist for the products of the (complex) positions of the four images, as well as moment sums of their signed magnifications. The image topographies and equations of the caustics and critical curves are also studied. We derive the fully analytic expressions for precaustics, which are the loci of non-critical points that map to the caustics under the lens mapping. They constitute boundaries of the region in the image domain that maps onto the interior of the caustics. The areas under the critical curves, caustics and precaustics are all evaluated, which enables us to calculate the mean magnification of the source within the caustics. Additionally, the exact analytic expression for the magnification distribution for the source in the triangular caustics is derived, as well as a useful approximate expression. Finally, we find that the Chang-Refsdal lens with the convergence greater than unity can exhibit third-order critical behaviour, if the reduced shear is exactly equal to \sqrt{3}/2, and that the number of images for N-point masses with non-zero constant shear cannot be greater than 5N-1.Comment: to appear in MNRAS (including 6 figures, 3 appendices; v2 - minor update with corrected typos etc.

On Multiple Einstein Rings

A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-plane lensing. Surprisingly, we show that it is possible for a single source to produce more than one Einstein ring. If two point masses (or two isothermal spheres) in different planes are aligned with observer and source on the optical axis, we show that there are up to three Einstein rings. We also discuss the image morphologies for these two models if axisymmetry is broken, and give the first instances of magnification invariants in the case of two lens planes.Comment: MNRAS, in press (extra figure included

Microlensing Characterization of Wide-Separation Planets

With their excellent photometric precision and dramatic increase in monitoring frequency, future microlensing survey experiments are expected to be sensitive to very short time-scale, isolated events caused by free-floating and wide-separation planets with mass as low as a few lunar masses. We estimate the probability of measuring the Einstein radius \theta_E for bound and free-floating planets. We carry out detailed simulations of the planetary events expected in next-generation surveys and estimate the resulting uncertainty in \theta_E for these events. We show that, for main-sequence sources and Jupiter-mass planets, the caustic structure of wide-separation planets with projected separations of < 20 AU substantially increases the probability of measuring the dimensionless source size and thus determining \theta_E compared to the case of unbound planets. In this limit where the source is much smaller than the caustic, the effective cross-section to measure \theta_E to 10% is ~25% larger than the full width of the caustic. Measurement of the lens parallax is possible for low-mass planetary events by combined observations from the ground and a satellite located in an L2 orbit; this would complete the mass measurements for such wide-separation planets. Finally, short-duration events caused by bound planets can be routinely distinguished from those caused by free-floating planets for planet-star separations < 20 AU from either the deviations due to the planetary caustic or (more often) the low-amplitude bump from the magnification due to the parent star.Comment: 10 pages including 7 figures. ApJ, in pres

Gravitational lens under perturbations: Symmetry of perturbing potentials with invariant caustics

When the gravitational lensing potential can be approximated by that of circularly symmetric system affected by weak perturbations, it is found that the shape of the resulting (tangential) caustics is entirely specified by the local azimuthal behaviour of the affecting perturbations. This provides a common mathematical groundwork for understanding problems such as the close-wide (d 1/d) separation degeneracy of binary lens microlensing lightcurves and the shear-ellipticity degeneracy of quadruple image lens modelling.Comment: to appear in MNRAS, including 4 figures, typo corrected, essentially identical to the version to be publishe

A Simple Model for Lensing by Black Holes in Galactic Nuclei

The lensing properties of the Plummer model with a central point mass and external shear are derived, including the image multiplicities, critical curves and caustics. This provides a simple model for a flattened galaxy with a central supermassive black hole. For the Plummer model with black hole, the maximum number of images is 4, provided the black hole mass is less than an upper bound which is calculated analytically. This introduces a method to constrain black hole masses by counting images, thus applicable at cosmological distance. With shear, the maximum number of images is 6 and we illustrate the occurrence of an astroid caustic and two metamorphoses.Comment: 7 pages, 4 figures, MNRAS, in press, small changes mad

The Importance of Binary Gravitational Microlensing Events Through High-Magnification Channel

We estimate the detection efficiency of binary gravitational lensing events through the channel of high-magnification events. From this estimation, we find that binaries in the separations ranges of 0.1 < s < 10, 0.2 < s < 5, and 0.3 < s < 3 can be detected with ~ 100% efficiency for events with magnifications higher than A=100, 50, and 10, respectively, where s represents the projected separation between the lens components normalized by the Einstein radius. We also find that the range of high efficiency covers nearly the whole mass-ratio range of stellar companions. Due to the high efficiency in wide ranges of parameter space, we point out that majority of binary-lens events will be detected through the high-magnification channel in lensing surveys that focus on high-magnification events for efficient detections of microlensing planets. In addition to the high efficiency, the simplicity of the efficiency estimation makes the sample of these binaries useful in the statistical studies of the distributions of binary companions as functions of mass ratio and separation. We also discuss other importance of these events.Comment: 5 pages, 1 figure, 1 tabl

Strong Lensing by Binary Galaxies Modelled as Isothermal Spheres

We study the problem of gravitational lensing by binary galaxies, idealized as two isothermal spheres. In a wide binary, each galaxy possesses individual tangential, nearly astroidal, caustics and roundish radial caustics. As the separation of the binary is made smaller, the caustics undergo a sequence of metamorphoses. The first metamorphosis occurs when the tangential caustics merge to form a single six-cusped caustic, lying interior to the radial caustics. At still smaller separations, the six-cusped caustic undergoes the second metamorphosis and splits into a four-cusped caustic and two three-cusped caustics, which shrink to zero size (an elliptic umbilic catastrophe) before they enlarge again and move away from the origin perpendicular to the binary axis. Finally, a third metamorphosis occurs as the three-cusp caustics join the radial caustics, leaving an inner distorted astroid caustic enclosed by two outer caustics. The maximum number of images possible is 7. Classifying the multiple imaging according to critical isochrones, there are only 8 possibilities: 2 three-image cases, 3 five-image cases, and 3 seven-image cases. When the isothermal spheres are singular, the core images vanish into the central singularity. The number of images may then be 1, 2, 3, 4 or 5, depending on the source location, and the separation and masses of the pair of lensing galaxies. The locations of metamorphoses, and the onset of threefold and fivefold multiple imaging, can be worked out analytically in this case.Comment: MNRAS, in pres