10,654 research outputs found
Parameter degeneracies and (un)predictability of gravitational microlensing events
(abridged) Some difficulties in determining the physical properties that lead
to observed anomalies in microlensing light curves, such as the mass and
separation of extra-solar planets orbiting the lens star, or the relative
source-lens parallax, are already anchored in factors that limit the amount of
information available from ordinary events and in the adopted parametrization.
Moreover, a real-time detection of deviations from an ordinary light curve
while these are still in progress can only be done against a known model of the
latter, and such is also required for properly prioritizing ongoing events for
monitoring in order to maximize scientific returns. Despite the fact that
ordinary microlensing light curves are described by an analytic function that
only involves a handful of parameters, modelling these is far less trivial than
one might be tempted to think. A well-known degeneracy for small impacts, and
another one for the initial rise of an event, makes an interprediction of
different phases impossible, while determining a complete set of model
parameters requires the assessment of the fundamental characteristics of all
these phases. While the wing of the light curve provides valuable information
about the time-scale that absorbs the physical properties, the peak flux of the
event can be meaningfully predicted only after about a third of the total
magnification has been reached. Parametrizations based on observable features
not only ease modelling by bringing the covariance matrix close to diagonal
form, but also allow good predictions of the measured flux without the need to
determine all parameters accurately. Campaigns intending to infer planet
populations from observed microlensing events need to invest some time into
acquiring data that allows to properly determine the magnification function.Comment: 6 pages with 4 EPS figures embedded; MNRAS accepte
The binary gravitational lens and its extreme cases
The transition of the binary gravitational lens from the equal mass case to
small (planetary) mass ratios q is studied. It is shown how the limit of a
(pure shear) Chang-Refsdal lens is approached, under what conditions the
Chang-Refsdal approximation is valid, and how the 3 different topologies of the
critical curves and caustics for a binary lens are mapped onto the 2 different
topologies for a Chang-Refsdal lens with pure shear. It is shown that for wide
binaries, the lensing in the vicinity of both lens objects can be described by
a Taylor-expansion of the deflection term due to the other object, where the
Chang-Refsdal approximation corresponds to a truncation of this series. For
close binaries, only the vicinity of the secondary, less massive, object can be
described in this way. However, for image distances much larger than the
separation of the lens objects, any binary lens can be approximated by means of
multipole expansion, where the first non-trivial term is the quadrupole term.
It is shown that an ambiguity exists between wide and close binary lenses,
where the shear at one of the objects due to the other object for the wide
binary is equal to the absolute value of the eigenvalues of the quadrupole
moment for the close binary. This analysis provides the basis for a
classification of binary lens microlensing events, especially of planetary
events, and an understanding of present ambiguities.Comment: 20 pages in LaTeX2e format with 9 embedded PostScript figures;
figures modified and embedded; accepted for publication in A&
Stochastical distributions of lens and source properties for observed galactic microlensing events
A comprehensive new approach is presented for deriving probability densities
of physical properties characterizing lens or source that constitute an
observed galactic microlensing event. While previously encountered problems are
overcome, constraints from event anomalies and model parameter uncertainties
can be incorporated into the estimate. Probability densities for given events
need to be carefully distinguished from the statistical distribution of the
same parameters among the underlying population from which the actual lenses
and sources are drawn. Using given model distributions of the mass spectrum,
the mass density, and the velocity distribution of Galactic disk and bulge
constituents, probability densities of lens mass, distance, and the effective
lens-source velocities are derived, where the effect on the distribution that
arises from additional observations of annual parallax or finite-source
effects, or the absence of significant effects, is shown. The presented
formalism can also be used to calculate probabilities for the lens to belong to
one or another population and to estimate parameters that characterize
anomalies. Finally, it is shown how detection efficiency maps for binary-lens
companions in the physical parameters companion mass and orbital semi-major
axis arise from values determined for the mass ratio and dimensionless
projected separation parameter, including the deprojection of the orbital
motion for elliptical orbits. Compared to the naive estimate based on 'typical
values', the detection efficiency for low-mass companions is increased by
mixing in higher detection efficiencies for smaller mass ratios (i.e. smaller
masses of the primary).Comment: 25 pages with 22 embedded EPS-figures, uses mn2e.cls. Adopted mass
function revised and one example event replaced, content rearranged, some
minor changes. Submitted to MNRA
Astrometric Resolution of Severely Degenerate Binary Microlensing Events
We investigate whether the "close/wide" class of degeneracies in
caustic-crossing binary microlensing events can be broken astrometrically.
Dominik showed that these degeneracies are particularly severe because they
arise from a degeneracy in the lens equation itself rather than a mere
"accidental" mimicking of one light curve by another. A massive observing
campaign of five microlensing collaborations was unable to break this
degeneracy photometrically in the case of the binary lensing event MACHO
98-SMC-1. We show that this degeneracy indeed causes the image centroids of the
wide and close solutions to follow an extremely similar pattern of motion
during the time when the source is in or near the caustic. Nevertheless, the
two image centroids are displaced from one another and this displacement is
detectable by observing the event at late times. Photometric degeneracies
therefore can be resolved astrometrically, even for these most severe cases.Comment: 11 pages, including 4 figures. Submitted to Ap
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