604 research outputs found
Generalised model-independent characterisation of strong gravitational lenses IV: formalism-intrinsic degeneracies
Based on the standard gravitational lensing formalism with its effective,
projected lensing potential in a given background cosmology, we investigate
under which transformations of the source position and of the deflection angle
the observable properties of the multiple images, i.e. the time delay
differences, the relative image positions, relative shapes, and magnification
ratios, remain invariant. As these observables only constrain local lens
properties, we derive general, local invariance transformations in the areas
covered by the multiple images. We show that the known global invariance
transformations, e.g. the mass sheet transformation or the source position
transformation, are contained in our invariance transformations, when they are
restricted to the areas covered by the multiple images and when
lens-model-based degeneracies are ignored, like the freedom to add or subtract
masses in unconstrained regions without multiple images. Hence, we have
identified the general class of invariance transformations that can occur, in
particular in our model-independent local characterisation of strong
gravitational lenses.Comment: 10 pages, 4 figures, in press in A&A, comments very welcome (update
to accepted and improved version
Generalised model-independent characterisation of strong gravitational lenses III: perturbed axisymmetric lenses
In galaxy-galaxy strong gravitational lensing, Einstein rings are generated
when the lensing galaxy has an axisymmetric lensing potential and the source
galaxy is aligned with its symmetry centre along the line of sight. Using a
Taylor expansion around the Einstein radius and eliminating the unknown source,
I derive a set of analytic equations that determine differences of the
deflection angle of the perturber weighted by the convergence of the
axisymmetric lens and ratios of the convergences at the positions of the arcs
from the measurable thickness of the arcs. In the same manner, asymmetries in
the brightness distributions along an arc determine differences in the
deflection angle of the perturber if the source has a symmetric brightness
profile and is oriented parallel to or orthogonal to the caustic. These
equations are the only model-independent information retrievable from
observations to leading order in the Taylor expansion. General constraints on
the derivatives of the perturbing lens are derived such that the perturbation
does not change the number of critical curves. To infer physical properties
such as the mass of the perturber or its position, models need to be inserted.
The same conclusions about the scale of detectable masses and model-dependent
degeneracies as in other approaches are then found and supported by analysing
B1938 as an example. Yet, the model-independent equations show that there is a
fundamental degeneracy between the main lens and the perturber that can only be
broken if their relative position is known. This explains the degeneracies
between lens models already found in simulations from a more general viewpoint.
Depending on the properties of the pertuber, this degeneracy can be broken by
characterising the surrounding of the lens or by measuring the time delay
between quasar images embedded in the perturbed Einstein ring of the host
galaxy.Comment: 10 pages, 3 figures, 1 table, accepted for publication in Astronomy &
Astrophysics, comments welcom
Generalised model-independent characterisation of strong gravitational lenses II: Transformation matrix between multiple images
(shortened) We determine the transformation matrix T that maps multiple
images with resolved features onto one another and that is based on a
Taylor-expanded lensing potential close to a point on the critical curve within
our model-independent lens characterisation approach. From T, the same
information about the critical curve at fold and cusp points is derived as
determined by the quadrupole moment of the individual images as observables. In
addition, we read off the relative parities between the images, so that the
parity of all images is determined, when one is known. We compare all
retrievable ratios of potential derivatives to the actual ones and to those
obtained by using the quadrupole moment as observable for two and three image
configurations generated by a galaxy-cluster scale singular isothermal ellipse.
We conclude that using the quadrupole moments as observables, the properties of
the critical curve at the cusp points are retrieved to higher accuracy, at the
fold points to lower accuracy, and the ratios of second order potential
derivatives to comparable accuracy. We show that the approach using ratios of
convergences and reduced shear is equivalent to ours close to the critical
curve but yields more accurate results and is more robust because it does not
require a special coordinate system like the approach using potential
derivatives. T is determined by mapping manually assigned reference points in
the images onto each other. If the assignment of reference points is subject to
measurement uncertainties under noise, we find that the confidence intervals of
the lens parameters can be as large as the values, when the uncertainties are
larger than one pixel. Observed multiple images with resolved features are more
extended than unresolved ones, so that higher order moments should be taken
into account to improve the reconstruction.Comment: 13 pages, 12 figures, submitted to Astronomy & Astrophysics, comments
welcom
Model-independent characterisation of strong gravitational lenses
We develop a new approach to extracting model-independent information from
observations of strong gravitational lenses. The approach is based on the
generic properties of images near the fold and cusp catastrophes in caustics
and critical curves. Observables used are the relative image positions, the
magnification ratios and ellipticities of extended images, and time delays
between images with temporally varying intensity. We show how these observables
constrain derivatives and ratios of derivatives of the lensing potential near a
critical curve. Based on these measured properties of the lensing potential,
classes of parametric lens models can then easily be restricted to such
parameter values compatible with the measurements, thus allowing fast scans of
large varieties of models. Applying our approach to a representative galaxy
(JVAS B1422+231) and a galaxy-cluster lens (MACS J1149.5+2223), we show which
model-independent information can be extracted in those cases and demonstrate
that the parameters obtained by our approach for known parametric lens models
agree well with those found by detailed model fitting.Comment: 8 pages, 3 figures, submitted for publication to Astronomy &
Astrophysic
Model-independent and model-based local lensing properties of CL0024+1654 from multiply-imaged galaxies
We investigate to which precision local magnification ratios, ,
ratios of convergences, , and reduced shears, , can be
determined model-independently for the five resolved multiple images of the
source at in CL0024. We also determine if a comparison to
the respective results obtained by the parametric modelling program Lenstool
and by the non-parametric modelling program Grale can detect biases in the lens
models. For these model-based approaches we additionally analyse the influence
of the number and location of the constraints from multiple images on the local
lens properties determined at the positions of the five multiple images of the
source at . All approaches show high agreement on the local
values of , , and . We find that Lenstool obtains the
tightest confidence bounds even for convergences around one using constraints
from six multiple image systems, while the best Grale model is generated only
using constraints from all multiple images with resolved brightness features
and adding limited small-scale mass corrections. Yet, confidence bounds as
large as the values themselves can occur for convergences close to one in all
approaches. Our results are in agreement with previous findings, supporting the
light-traces-mass assumption and the merger hypothesis for CL0024. Comparing
the three different approaches allows to detect modelling biases. Given that
the lens properties remain approximately constant over the extension of the
image areas covered by the resolvable brightness features, the
model-independent approach determines the local lens properties to a comparable
precision but within less than a second. (shortened)Comment: 22 pages, published in A&A 612 A17, comments welcom
The first partnership experience and personality development. A propensity score matching study in young adulthood
Personality development in young adulthood has been associated with the experience of a number of new social roles. However, the causal interpretation of these findings is complicated by the fact that it is not possible to randomize young adults by their life experiences. To address this problem in the context of the first partnership experience, we applied propensity score matching to a sample of initially inexperienced singles and followed them across 4 years. Using matched samples, results indicated that the first partnership experience relatively robust increased life satisfaction. The first partnership experience between the ages of 23 and 25 (but not in other ages) was also related to higher self-esteem, extraversion, and conscientiousness and to lower neuroticism. The discussion highlights the effect of the first partnership on the development of a mature personality and the potential for propensity score matching to make useful contributions to social and personality research. (DIPF/Orig.
A model-independent characterisation of strong gravitational lensing by observables
When light from a distant source object, like a galaxy or a supernova,
travels towards us, it is deflected by massive objects that lie on its path.
When the mass density of the deflecting object exceeds a certain threshold,
multiple, highly distorted images of the source are observed. This strong
gravitational lensing effect has so far been treated as a model-fitting
problem. Using the observed multiple images as constraints yields a
self-consistent model of the deflecting mass density and the source object. As
several models meet the constraints equally well, we develop a lens
characterisation that separates data-based information from model assumptions.
The observed multiple images allow us to determine local properties of the
deflecting mass distribution on any mass scale from one simple set of
equations. Their solution is unique and free of model-dependent degeneracies.
The reconstruction of source objects can be performed completely
model-independently, enabling us to study galaxy evolution without a lens-model
bias. Our approach reduces the lens and source description to its data-based
evidence that all models agree upon, simplifies an automated treatment of large
datasets, and allows for an extrapolation to a global description resembling
model-based descriptions.Comment: Invited review-paper submitted to "Observing Gravitational Lenses:
Present and Future" in Universe, comments very welcom
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