No abstract

To maximize the number of planet detections, current microlensing follow-up observations are focusing on high-magnification events which have a higher chance of being perturbed by central caustics. In this paper, we investigate the properties of central caustics and the perturbations induced by them. We derive analytic expressions of the location, size, and shape of the central caustic as a function of the star-planet separation, $s$, and the planet/star mass ratio, $q$, under the planetary perturbative approximation and compare the results with those based on numerical computations. While it has been known that the size of the planetary caustic is \propto \sqrt{q}, we find from this work that the dependence of the size of the central caustic on $q$ is linear, i.e., \propto q, implying that the central caustic shrinks much more rapidly with the decrease of $q$ compared to the planetary caustic. The central-caustic size depends also on the star-planet separation. If the size of the caustic is defined as the separation between the two cusps on the star-planet axis (horizontal width), we find that the dependence of the central-caustic size on the separation is \propto (s+1/s). While the size of the central caustic depends both on $s$ and q, its shape defined as the vertical/horizontal width ratio, R_c, is solely dependent on the planetary separation and we derive an analytic relation between R_c and s. Due to the smaller size of the central caustic combined with much more rapid decrease of its size with the decrease of q, the effect of finite source size on the perturbation induced by the central caustic is much more severe than the effect on the perturbation induced by the planetary caustic. Abridged.Comment: 5 pages, 4 figures, ApJ accepte

In this paper, we show that the pattern of microlensing light curve anomalies induced by multiple planets is well described by the superposition of those of the single-planet systems where the individual planet -primary binary pairs act as independent lens systems. As the outer deviation regions around the planetary caustics of the individual planets occur in general at different locations, we find that the pattern of anomalies in these regions is barely affected by the existence of other planet(s). This implies that even if an event is caused by a multiple planetary system, a simple single-planet lensing model is good enough for the description of most anomalies caused by the passage of the source through the outer deviation regions. Detection of the anomalies resulting from the source trajectory passing both the outer deviation regions caused by more than two planets will provide a new channel for detecting multiple planets.

We present a study of the largest available sample of near-infrared selected (i.e., stellar mass selected) dynamically close pairs of galaxies at low redshifts (z < 0.3). We combine this sample with new estimates of the major-merger pair fraction for stellar mass selected galaxies at z < 0.8, from the Red Sequence Cluster Survey (RCS1). We construct our low-redshift K−band selected sample using photometry from the UKIRT Infrared Deep Sky Survey (UKIDSS) and the Two Micron All Sky Survey (2MASS) in the K−band (∼ 2.2 µm). Combined with all available spectroscopy, our K−band selected sample contains ∼ 250, 000 galaxies and is > 90% spectroscopically complete. The depth and large volume of this sample allow us to investigate the low-redshift pair fraction and merger rate of galaxies over a wide range in K−band luminosity. We find the major-merger pair fraction to be flat at ∼ 2% as a function of K−band luminosity for galaxies in the range 10 8 − 10 12 L ⊙ , in contrast to recent results from studies in the local group that find a substantially higher low-mass pair fraction. This low-redshift major-merger pair fraction is ∼ 40 − 50% higher than previous estimates drawn from K−band samples, which were based on 2MASS photometry alone. Combining with the RCS1 sample we find a much flatter evolution (m = 0.7 ± 0.1), in the relation f pair ∝ (1 + z) m , than indicated in many previous studies. These results indicate that a typical L ∼ L * galaxy has undergone ∼ 0.2 − 0.8 major mergers since z = 1 (depending on the assumptions of merger timescale and percentage of pairs that actually merge).

In this paper, we study the astrometric properties of gravitational microlensing events caused by binary lenses. By investigating the centroid shifts for various types of binary-lens events, we find that the deviations of the centroid shift trajectories from the elliptical ones of single-lens events are characterized by distortions, twistings, and big jumps. We study the conditions of binary-lens system configurations and source star trajectories for individual types of deviations. We find dramatic differences in the astrometric centroid shifts for binary-lens microlensing events that would be degenerate had their parameters been determined photometrically. Therefore, when additional astrometric observations of a binary-lens event are available, one can resolve the ambiguity of the binary-lens fit, and uniquely determine the binary-lens parameters.