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

Extended Source Diffraction Effects Near Gravitational Lens Fold Caustics

Calculations are presented detailing the gravitational lens diffraction due to the steep brightness gradient of the limb of a stellar source. The lensing case studied is the fold caustic crossing. The limb diffraction signal greatly exceeds that due to the disk as a whole and should be detectable for white dwarf sources in our Galaxy and it's satellites with existing telescopes. Detection of this diffraction signal would provide an additional mathematical constraint, reducing the degeneracy among models of the lensing geometry. The diffraction pattern provides pico-arcsecond resolution of the limb profile.Comment: 19 pages including 17 figures, Accepted for publication in ApJ, Minor conceptual change from previous versio

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

Computer techniques for sensor validation during EBR-II natural circulation

"November, 1984.""Includes MIT technical contributions from D.D. Lanning, J.E. Meyer, A.L. Schor, R.J. Witt and R.D. Wittmeier.""U.S. Dept. of Energy Breeder Technology Program, Division of Educational Programs, Argonne National Laboratory."Includes bibliographical references (leaf 17)Final project report; November, 198

ALS Resistant Smooth Pigweed in Western Kentucky

Pigweeds The pigweed, or Amaranthus, family contains some of the most commonly occurring weeds of midwest agriculture. Species from this family that occur in Kentucky include smooth pigweed (Amaranthus hybridus, most common), tumble pigweed, prostrate pigweed, spiny amaranth,Palmer amaranth,common waterhemp, and tall waterhemp. Research has shown that some pigweed species respond differently to various herbicides, therefore, proper identification is necessary to achieve acceptable control. Pigweed identification in early stages of seedling growth can be difficult because the distinguishing physical characteristics do not appear until plants are mature or have produced seed. Also, some pigweed species may cross-pollinate to produce hybrid plants that exhibit characteristics of both parents

Double precision trajectory program /DPTRAJ 2.2C/

Four part program computes trajectory of space probe moving in solar system and subject to variety of forces

Convenient Versus Unique Effective Action Formalism in 2D Dilaton-Maxwell Quantum Gravity

The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effective action are calculated in three different covariant gauges: (i) De Witt, (ii) $\Omega$-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of the $S$-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renormalizable dilaton and Maxwell potentials are found which coincide in the cases of convenient and unique effective actions. A detailed comparison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective action in two-dimensional dilaton-Yang-Mills gravity is calculated.Comment: 25 pages, LaTeX file, HUPD-93-0

Microlensing of gamma ray bursts by stars and MACHOs

The microlensing interpretation of the optical afterglow of GRB 000301C seems naively surprising, since a simple estimate of the stellar microlensing rate gives less than one in four hundred for a flat Omega_Lambda=0.7 cosmology, whereas one event was seen in about thirty afterglows. Considering baryonic MACHOs making up half of the baryons in the universe, the microlensing probability per burst can be roughly 5% for a GRB at redshift z=2. We explore two effects that may enhance the probability of observing microlensed gamma-ray burst afterglows: binary lenses and double magnification bias. We find that the consideration of binary lenses can increase the rate only at the ~15% level. On the other hand, because gamma-ray bursts for which afterglow observations exist are typically selected based on fluxes at widely separated wavebands which are not necessarily well correlated (e.g. localization in X-ray, afterglow in optical/infrared), magnification bias can operate at an enhanced level compared to the usual single-bias case. We find that existing estimates of the slope of the luminosity function of gamma-ray bursts, while as yet quite uncertain, point to enhancement factors of more than three above the simple estimates of the microlensing rate. We find that the probability to observe at least one microlensing event in the sample of 27 measured afterglows can be 3-4% for stellar lenses, or as much as 25 Omega_lens for baryonic MACHOs. We note that the probability to observe at least one event over the available sample of afterglows is significant only if a large fraction of the baryons in the universe are condensed in stellar-mass objects. (ABRIDGED)Comment: 22 pages, 4 figures, 2 table

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.