The distribution of microlensed light curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.Comment: 12 pages, including 9 figures. Submitted to M.N.R.A.S. Revised version includes a short section on the applicability of the metho

Exotic Statistics for Ordinary Particles in Quantum Gravity

Objects exhibiting statistics other than the familiar Bose and Fermi ones are natural in theories with topologically nontrivial objects including geons, strings, and black holes. It is argued here from several viewpoints that the statistics of ordinary particles with which we are already familiar are likely to be modified due to quantum gravity effects. In particular, such modifications are argued to be present in loop quantum gravity and in any theory which represents spacetime in a fundamentally piecewise-linear fashion. The appearance of unusual statistics may be a generic feature (such as the deformed position-momentum uncertainty relations and the appearance of a fundamental length scale) which are to be expected in any theory of quantum gravity, and which could be testable.Comment: Awarded an honourable mention in the 2008 Gravity Research Foundation Essay Competitio

An accurate equation of state for the one component plasma in the low coupling regime

An accurate equation of state of the one component plasma is obtained in the low coupling regime $0 \leq \Gamma \leq 1$. The accuracy results from a smooth combination of the well-known hypernetted chain integral equation, Monte Carlo simulations and asymptotic analytical expressions of the excess internal energy $u$. In particular, special attention has been brought to describe and take advantage of finite size effects on Monte Carlo results to get the thermodynamic limit of $u$. This combined approach reproduces very accurately the different plasma correlation regimes encountered in this range of values of $\Gamma$. This paper extends to low $\Gamma$'s an earlier Monte Carlo simulation study devoted to strongly coupled systems for $1 \leq \Gamma \leq 190$ ({J.-M. Caillol}, {J. Chem. Phys.} \textbf{111}, 6538 (1999)). Analytical fits of $u(\Gamma)$ in the range $0 \leq \Gamma \leq 1$ are provided with a precision that we claim to be not smaller than $p= 10^{-5}$. HNC equation and exact asymptotic expressions are shown to give reliable results for $u(\Gamma)$ only in narrow $\Gamma$ intervals, i.e. $0 \leq \Gamma \lesssim 0.5$ and $0 \leq \Gamma \lesssim 0.3$ respectively

A small source in Q2237+0305 ?

Microlensing in Q2237+0305 between 1985 and 1995 (eg. Irwin et al. 1989; Corrigan et al. 1991; Ostensen et al. 1996) has been interpreted in two different ways; as microlensing by stellar mass objects of a continuum source having dimensions significantly smaller than the microlens Einstein radius (ER) (eg. Wambsganss, Paczynski & Schneider 1990; Rauch & Blandford 1991), and as microlensing by very low mass objects of a source as large as 5 ER (Refsdal & Stabell 1993; Haugan 1996). In this paper we present evidence in favour of a small source. Limits on the source size (in units of ER) are obtained from the combination of limits on the number of microlens Einstein radii crossed by the source during the monitoring period with two separate light-curve features. Firstly, recently published monitoring data (Wozniak et al. 2000; OGLE web page) show large variations (~0.8-1.5 magnitudes) between image brightnesses over a period of 700 days or ~15% of the monitoring period. Secondly, the 1988 peak in the image A light-curve had a duration that is a small fraction (<0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large-rapid variation limits the source size to be <0.2 ER (95% confidence). The width of the light-curve peak provides a stronger constraint of <0.02 ER (99% confidence). The Einstein radius (projected into the source plane) of the average microlens mass (m) in Q2237+0305 is ER ~ 10^{17}\sqrt{m} cm. The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.Comment: 8 pages, 3 figures, accepted for publication in M.N.R.A.

The Influence of Central Black Holes on Gravitational Lenses

Recent observations indicate that many if not all galaxies host massive central black holes. In this paper we explore the influence of black holes on the lensing properties. We model the lens as an isothermal ellipsoid with a finite core radius plus a central black hole. We show that the presence of the black hole substantially changes the critical curves and caustics. If the black hole mass is above a critical value, then it will completely suppress the central images for all source positions. Realistic central black holes likely have masses below this critical value. Even in such sub-critical cases, the black hole can suppress the central image when the source is inside a zone of influence, which depends on the core radius and black hole mass. In the sub-critical cases, an additional image may be created by the black hole in some regions, which for some radio lenses may be detectable with high-resolution and large dynamic-range VLBI maps. The presence of central black holes should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.Comment: 7 pages, 3 figures; submitted to MNRA

Gravitational Microlensing Near Caustics I: Folds

We study the local behavior of gravitational lensing near fold catastrophes. Using a generic form for the lensing map near a fold, we determine the observable properties of the lensed images, focusing on the case when the individual images are unresolved, i.e., microlensing. Allowing for images not associated with the fold, we derive analytic expressions for the photometric and astrometric behavior near a generic fold caustic. We show how this form reduces to the more familiar linear caustic, which lenses a nearby source into two images which have equal magnification, opposite parity, and are equidistant from the critical curve. In this case, the simplicity and high degree of symmetry allows for the derivation of semi-analytic expressions for the photometric and astrometric deviations in the presence of finite sources with arbitrary surface brightness profiles. We use our results to derive some basic properties of astrometric microlensing near folds, in particular we predict for finite sources with uniform and limb darkening profiles, the detailed shape of the astrometric curve as the source crosses a fold. We find that the astrometric effects of limb darkening will be difficult to detect with the currently planned accuracy of the Space Interferometry Mission. We verify our results by numerically calculating the expected astrometric shift for the photometrically well-covered Galactic binary lensing event OGLE-1999-BUL-23, finding excellent agreement with our analytic expressions. Our results can be applied to any lensing system with fold caustics, including Galactic binary lenses and quasar microlensing.Comment: 37 pages, 7 figures. Revised version includes an expanded discussion of applications. Accepted to ApJ, to appear in the August 1, 2002 issue (v574