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

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.

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

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

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

Detectability of Orbital Motion in Stellar Binary and Planetary Microlenses

A standard binary microlensing event lightcurve allows just two parameters of the lensing system to be measured: the mass ratio of the companion to its host, and the projected separation of the components in units of the Einstein radius. However, other exotic effects can provide more information about the lensing system. Orbital motion in the lens is one such effect, which if detected, can be used to constrain the physical properties of the lens. To determine the fraction of binary lens lightcurves affected by orbital motion (the detection efficiency) we simulate lightcurves of orbiting binary star and star-planet (planetary) lenses and simulate the continuous, high-cadence photometric monitoring that will be conducted by the next generation of microlensing surveys that are beginning to enter operation. The effect of orbital motion is measured by fitting simulated lightcurve data with standard static binary microlensing models; lightcurves that are poorly fit by these models are considered to be detections of orbital motion. We correct for systematic false positive detections by also fitting the lightcurves of static binary lenses. For a continuous monitoring survey without intensive follow-up of high magnification events, we find the orbital motion detection efficiency for planetary events with caustic crossings to be 0.061+-0.010, consistent with observational results, and 0.0130+-0.0055 for events without caustic crossings (smooth events). Similarly for stellar binaries, the orbital motion detection efficiency is 0.098+-0.011 for events with caustic crossings and is 0.048+-0.006 for smooth events. These result in combined (caustic crossing and smooth) orbital motion detection efficiencies of 0.029+-0.005 for planetary lenses and 0.070+-0.006 for stellar binary lenses. We also investigate how various microlensing parameters affect the orbital motion detectability. [Abridged]Comment: 21 pages, 22 figures, 5 table

Rapidly Rotating Lenses: Repeating features in the lightcurves of short period binary microlenses

Microlensing is most sensitive to binary lenses with relatively large orbital separations, and as such, typical binary microlensing events show little or no orbital motion during the event. However, despite the strength of binary microlensing features falling off rapidly as the lens separation decreases, we show that it is possible to detect repeating features in the lightcurve of binary microlenses that complete several orbits during the microlensing event. We investigate the lightcurve features of such Rapidly Rotating Lens (RRL) events. We derive analytical limits on the range of parameters where these effects are detectable, and confirm these numerically. Using a population synthesis Galactic model we estimate the RRL event rate for a ground-based and space-based microlensing survey to be 0.32fb and 7.8fb events per year respectively, assuming year-round monitoring and where fb is the binary fraction. We detail how RRL event parameters can be quickly estimated from their lightcurves, and suggest a method to model RRL events using timing measurements of lightcurve features. Modelling RRL lightcurves will yield the lens orbital period and possibly measurements of all orbital elements including the inclination and eccentricity. Measurement of the period from the lightcurve allows a mass-distance relation to be defined, which when combined with a measurement of microlens parallax or finite source effects, can yield a mass measurement to a two-fold degeneracy. With sub-percent accuracy photometry it is possible to detect planetary companions, but the likelihood of this is very small.Comment: 16 pages, 14 figures, accepted for publication in MNRAS. Equation 21 simplifie

Search for exoplanets in M31 with pixel-lensing and the PA-99-N2 event revisited

Several exoplanets have been detected towards the Galactic bulge with the microlensing technique. We show that exoplanets in M31 may also be detected with the pixel-lensing method, if telescopes making high cadence observations of an ongoing microlensing event are used. Using a Monte Carlo approach we find that the mean mass for detectable planetary systems is about $2 M_{\rm {J}}$. However, even small mass exoplanets ($M_{\rm P} < 20 M_{\oplus}$) can cause significant deviations, which are observable with large telescopes. We reanalysed the POINT-AGAPE microlensing event PA-99-N2. First, we test the robustness of the binary lens conclusion for this light curve. Second, we show that for such long duration and bright microlensing events, the efficiency for finding planetary-like deviations is strongly enhanced with respect to that evaluated for all planetary detectable events.Comment: 14 pages, 8 figures. Paper presented at the "II Italian-Pakistani Workshop on Relativistic Astrophysics, Pescara, July 8-10, 2009. To be published in a special issue of General Relativity and Gravitation (eds. F. De Paolis, G.F.R. Ellis, A. Qadir and R. Ruffini

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