6,552 research outputs found
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 . 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
. 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 . This combined approach reproduces very accurately
the different plasma correlation regimes encountered in this range of values of
. This paper extends to low 's an earlier Monte Carlo
simulation study devoted to strongly coupled systems for ({J.-M. Caillol}, {J. Chem. Phys.} \textbf{111}, 6538 (1999)). Analytical
fits of in the range are provided with a
precision that we claim to be not smaller than . HNC equation and
exact asymptotic expressions are shown to give reliable results for
only in narrow intervals, i.e. and 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
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