ABSTRACT The number of gravitational arcs systems detected is increasing quickly and should even increase at a faster rate in the near future. This wealth of new gravitational arcs requires the ...development of a purely automated method to reconstruct the lens and source. A general reconstruction method based on the singular perturbative approach is proposed in this paper. This method generates a lens and source reconstruction directly from the gravitational arc image. The method is fully automated and works in two steps. The first step is to generate a guess solution based on the circular solution in the singular perturbative approach. The second step is to break the sign degeneracy and to refine the solution by using a general source model. The refinement of the solution is conducted step-by-step to avoid the source-lens degeneracy issue. One important asset of this automated method is that the lens solution is written in universal terms which allows the computation of statistics. Considering the large number of lenses which should be available in the near future this ability to compute unbiased statistics is an important asset.
ABSTRACT
This paper analyses the properties of minimal solutions for the reconstruction of the lens potential in the singular perturbative approach. These minimal solutions corresponds to an ...expansion with a minimal degree in Fourier expansion of the perturbative fields. Using these minimal solutions prevent spurious physically meaningless terms in the reconstruction of the fields. In effect, a perturbative analysis indicates that a small change in the source model will corresponds to the higher order terms in the expansion of the fields. The results of the perturbative analysis are valid not only for slightly non-circular sources but also for more distorted sources to order two. It is, thus, of crucial importance to minimize the number of terms used in the modelling of the lens. Another important asset of the minimal solutions is that they offer a de-coupling between the source and lens model, and thus help to break the source lens degeneracy issue. The possible drawback of minimal solutions is to underestimate the higher order terms in the solution. However, this bias has its merit since the detection of higher order terms using this method will ensure that these terms are real. This type of analysis using minimal solutions will be of particular interest when considering the statistical analysis of a large number of lenses, especially in light of the incoming satellite surveys.
Abstract
The extension of the singular perturbative approach to the second order is presented in this paper. The general expansion to the second order is derived. The second-order expansion is ...considered as a small correction to the first-order expansion. Using this approach, it is demonstrated that in practice the second-order expansion is reducible to a first order expansion via a re-definition of the first-order pertubative fields. Even if in usual applications the second-order correction is small the reducibility of the second-order expansion to the first-order expansion indicates a potential degeneracy issue. In general, this degeneracy is hard to break. A useful and simple second-order approximation is the thin source approximation, which offers a direct estimation of the correction. The practical application of the corrections derived in this paper is illustrated by using an elliptical NFW lens model. The second-order pertubative expansion provides a noticeable improvement, even for the simplest case of thin source approximation. To conclude, it is clear that for accurate modelization of gravitational lenses using the perturbative method the second-order perturbative expansion should be considered. In particular,
an evaluation of the degeneracy due to the second-order term should be performed, for which the thin source approximation is particularly useful.
Abstract
The reconstruction of the cosmic horseshoe gravitational lens using the perturbative method reveals the presence of significant third-order terms. The presence of these higher order terms is ...apparent in the numerical expansion of the perturbative fields in Fourier series. The expansion of the fields at order 2 produces a higher value of the chi-square. Expanding at order 3 provides a very significant improvement, while order 4 does not bring a significant improvement over order 3. The presence of the order 3 terms is not a consequence of limiting the perturbative expansion to the first order. The amplitude and signs of the third-order terms are recovered by including the contribution of the other group members. This analysis demonstrates that the fine details of the potential of the lens could be recovered independently of any initial assumptions by using the perturbative approach.
This paper explores the self-similar solutions of the Vlasov-Poisson system and their relation to the gravitational collapse of dynamically cold systems. Analytic solutions are derived for power-law ...potentials in one dimension, and extensions of these solutions in three dimensions are proposed. Next, the self-similarity of the collapse of cold dynamical systems is investigated numerically. The fold system in phase space is consistent with analytic self-similar solutions, which present all the proper self-similar scaling. An additional point is the appearance of an
law at the centre of the system for initial conditions with power-law index larger than
(the Binney conjecture). It is found that the first appearance of the
law corresponds to the formation of a singularity very close to the centre. Finally, the general properties of self-similar multidimensional solutions near equilibrium are investigated. Smooth and continuous self-similar solutions have power-law behaviour at equilibrium. However, cold initial conditions result in discontinuous phase-space solutions, and the smoothed phase-space density loses its auto-similar properties. This problem is easily solved by observing that the probability distribution of the phase-space density P is identical except for scaling parameters to the probability distribution of the smoothed phase-space density P
S. As a consequence, P
S inherits the self-similar properties of P. This particular property is at the origin of the universal power law observed in numerical simulation for
. The self-similar properties of P
S imply that other quantities should also have a universal power-law behaviour with predictable exponents. This hypothesis is tested using a numerical model of the phase-space density of cold dark matter haloes, and excellent agreement is obtained.
The cosmological simulations indicates that dark matter halos have specific self-similar properties. However, the halo similarity is affected by the baryonic feedback. By using momentum-driven winds ...as a model to represent the baryon feedback, an equilibrium condition is derived which directly implies the emergence of a new type of similarity. The new self-similar solution has constant acceleration at a reference radius for both dark matter and baryons. This model receives strong support from the observations of galaxies. The new self-similar properties imply that the total acceleration at larger distances is scale-free, the transition between the dark matter and baryons dominated regime occurs at a constant acceleration, and the maximum amplitude of the velocity curve at larger distances is proportional to M super(1/4). These results demonstrate that this self-similar model is consistent with the basics of modified Newtonian dynamics (MOND) phenomenology. In agreement with the observations, the coincidence between the self-similar model and MOND breaks at the scale of clusters of galaxies. Some numerical experiments show that the behavior of the density near the origin is closely approximated by a Einasto profile.
Studies have shown that the remnants of destroyed planets and debris-disk planetesimals can survive the volatile evolution of their host stars into white dwarfs, but few intact planetary bodies ...around white dwarfs have been detected. Simulations predict that planets in Jupiter-like orbits around stars of ≲8 Mꙩ (solar mass) avoid being destroyed by the strong tidal forces of their stellar host, but as yet, there has been no observational confirmation of such a survivor. Here we report the non-detection of a main-sequence lens star in the microlensing event MOA-2010-BLG-477Lb using near-infrared observations from the Keck Observatory. We determine that this system contains a 0.53 ± 0.11 Mꙩ white-dwarf host orbited by a 1.4 ± 0.3 Jupiter-mass planet with a separation on the plane of the sky of 2.8 ± 0.5 astronomical units, which implies a semi-major axis larger than this. This system is evidence that planets around white dwarfs can survive the giant and asymptotic giant phases of their host’s evolution, and supports the prediction that more than half of white dwarfs have Jovian planetary companions. Located at approximately 2.0 kiloparsecs towards the center of our Galaxy, it is likely to represent an analogue to the end stages of the Sun and Jupiter in our own Solar System.
Image subtraction is a method by which one image is matched against another by using a convolution kernel, so that they can be differenced to detect and measure variable objects. It has been ...demonstrated that constant optimal-kernel solutions can be derived over small sub-areas of dense stellar fields. Here we generalize the theory to the case of space-varying kernels. In particular, it is shown that the CPU cost required for this new extension of the method is almost the same as for fitting a constant kernel solution. It is also shown that constant flux scaling between the images (constant kernel integral) can be imposed in a simple way. The method is demonstrated with a series of Monte-Carlo images. Differential PSF variations and differential rotation between the images are simulated. It is shown that the new method is able to achieve optimal results even in these difficult cases, thereby automatically correcting for these common instrumental problems. It is also demonstrated that the method does not suffer due to problems associated with under-sampling of the images. Finally, the method is applied to images taken by the OGLE II collaboration. It is proved that, in comparison to the constant-kernel method, much larger sub-areas of the images can be used for the fit, while still maintaining the same accuracy in the subtracted image. This result is especially important in case of variables located in low density fields, like the Huchra lens. Many other useful applications of the method are possible for major astrophysical problems; Supernova searches and Cepheids surveys in other galaxies, to mention but two. Many other applications will certainly show-up, since variability searches are a major issue in astronomy.
Aims. The structure and potential of a complex gravitational lens is reconstructed using the perturbative method presented in Alard (2007, MNRAS, 382, L58; 2008, MNRAS, 388, 375). This lens is ...composed of 6 galaxies belonging to a small group. Methods. The lens inversion is reduced to the problem of reconstructing non-degenerate quantities: the 2 fields of the perturbative theory of strong gravitational lenses. Since in the perturbative theory the circular source solution is analytical, the general properties of the perturbative solution can be inferred directly from the data. As a consequence, the reconstruction of the perturbative fields is not affected by degeneracy, and finding the best solution is only a matter of numerical refinement. Results. The local shape of the potential and density of the lens are inferred from the perturbative solution, revealing the existence of an independent dark component that does not follow light. Conclusions. The most likely explanation is that the particular shape of the dark halo is due to the merging of cold dark matter halos. This is a new result illustrating the structure of dark halos on the scale of galaxies.
We present the Strong Lensing Legacy Survey-ARCS (SARCS) sample compiled from the final T0006 data release of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) covering a total ...non-overlapping area of 159 deg super(2). We adopt a semi-automatic method to find gravitational arcs in the survey that makes use of an arc-finding algorithm. The candidate list is pruned by visual inspection and ranking to form the final SARCS sample. This list also includes some serendipitously discovered lens candidates which the automated algorithm did not detect. The SARCS sample consists of 127 lens candidates which span arc radii ~2"-18" within the unmasked area of ~150 deg super(2). Within the sample, 54 systems are promising lenses among which, we find 12 giant arcs (length-to-width ratio > or =, slanted8). We also find two radial arc candidates in SL2SJ141447+544704. From our sample, we detect a systematic alignment of the giant arcs with the major axis of the baryonic component of the putative lens in concordance with previous studies. This alignment is also observed for all arcs in the sample and does not vary significantly with increasing arc radius. The mean values of the photometric redshift distributions of lenses corresponding to the giant arcs and all arcs sample are at z ~ 0.6. Owing to the large area and depth of the CFHTLS, we find the largest sample of lenses probing mass scales that are intermediate to cluster and galaxy lenses for the first time. We compare the observed image separation distribution (ISD) of our arcs with theoretical models. A two-component density profile for the lenses which accounts for both the central galaxy and the dark matter component is required by the data to explain the observed ISD. Unfortunately, current levels of uncertainties and degeneracies accommodate models both with and without adiabatic contraction. We also show the effects of changing parameters of the model that predict the ISD and that a larger lens sample might constrain relations such as the concentration-mass relation, mass-luminosity relation, and the faint-end slope of the luminosity function.
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