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Register a new userSemi-linear gravitational lens inversion
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We describe a new method for analyzing gravitational lens images, for the case where the source light distribution is pixelized. The method is suitable for high resolution, high S/N data of a multiply-imaged extended source. For a given mass distribution, we show that the step of inverting the image to obtain the deconvolved pixelized source light distribution, and the uncertainties, is a linear one. This means that the only parameters of the non-linear problem are those required to model the mass distribution. This greatly simplifies the search for a min.-chi^2 fit to the data and speeds up the inversion. The method is extended in a straightforward way to include linear regularization. We apply the method to simulated Einstein ring images and demonstrate the effectiveness of the inversion for both the unregularized and regularized cases.
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Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate how sparse optimisation can address the problem. As a first step towards a full free-form lens modelling technique, we consider linear inversion of the lensed source under sparse regularisation and joint deblending from the lens light profile. The method is based on morphological component analysis, assuming a known mass model. We show with numerical experiments that representing the lens and source light using an undecimated wavelet basis allows us to reconstruct the source and to separate it from the foreground lens at the same time. Both the source and lens light have a non-analytic form, allowing for the flexibility needed in the inversion to represent arbitrarily small and complex luminous structures in the lens and source. in addition, sparse regularisation avoids over-fitting the data and does not require the use of any adaptive mesh or pixel grid. As a consequence, our reconstructed sources can be represented on a grid of very small pixels. Sparse regularisation in the wavelet domain also allows for automated computation of the regularisation parameter, thus minimising the impact of arbitrary choice of initial parameters. Our inversion technique for a fixed mass distribution can be incorporated in future lens modelling technique iterating over the lens mass parameters. The python package corresponding to the algorithms described in this article can be downloaded via the github platform at https://github.com/herjy/SLIT.
Consider an infinite system [partial_tu_t(x)=(mathscr{L}u_t)(x)+ sigmabigl(u_t(x)bigr)partial_tB_t(x)] of interacting It^{o} diffusions, started at a nonnegative deterministic bounded initial profile. We study local and global features of the solution under standard regularity assumptions on the nonlinearity $sigma$. We will show that, locally in time, the solution behaves as a collection of independent diffusions. We prove also that the $k$th moment Lyapunov exponent is frequently of sharp order $k^2$, in contrast to the continuous-space stochastic heat equation whose $k$th moment Lyapunov exponent can be of sharp order $k^3$. When the underlying walk is transient and the noise level is sufficiently low, we prove also that the solution is a.s. uniformly dissipative provided that the initial profile is in $ell^1(mathbf {Z}^d)$.
Deep surveys planned as a Key Science Project of LOFAR provide completely new opportunities for gravitational lens searches. For the first time do large-scale surveys reach the resolution required for a direct selection of lens candidates using morphological criteria. We briefly describe the strategies that we will use to exploit this potential. The long baselines of an international E-LOFAR are essential for this project.
In this article we study the well-known strong lensing system SDSS J1004+4112. Not only does it host a large-separation lensed quasar with measured time-delay information, but several other lensed galaxies have been identified as well. A previously developed strong lens inversion procedure that is designed to handle a wide variety of constraints, is applied to this lensing system and compared to results reported in other works. Without the inclusion of a tentative central image of one of the galaxies as a constraint, we find that the model recovered by the other constraints indeed predicts an image at that location. An inversion which includes the central image provides tighter constraints on the shape of the central part of the mass map. The resulting model also predicts a central image of a second galaxy where indeed an object is visible in the available ACS images. We find masses of 2.5x10^13 M_O and 6.1x10^13 M_O within a radius of 60 kpc and 110 kpc respectively, confirming the results from other authors. The resulting mass map is compatible with an elliptical generalization of a projected NFW profile, with r_s = 58_{-13}^{+21} arcsec and c_vir = 3.91 +/- 0.74. The orientation of the elliptical NFW profile follows closely the orientation of the central cluster galaxy and the overall distribution of cluster members.
Strong gravitational lensing is a powerful technique for probing galaxy mass distributions and for measuring cosmological parameters. We present a pixelated approach to modeling simultaneously the lens potential and source intensity of strong gravitational lens systems with extended source-intensity distributions. For systems with sources of sufficient extent such that the separate lensed images are connected by intensity measurements, the accuracy in the reconstructed potential is solely limited by the quality of the data. We apply this potential reconstruction technique to deep HST observations of B1608+656, a four-image gravitational lens system formed by a pair of interacting lens galaxies. We present a comprehensive Bayesian analysis of the system that takes into account the extended source-intensity distribution, dust extinction, and the interacting lens galaxies. Our approach allows us to compare various models of the components of the lens system, which include the point-spread function (PSF), dust, lens galaxy light, source-intensity distribution, and lens potential. Using optimal combinations of the PSF, dust, and lens galaxy light models, we successfully reconstruct both the lens potential and the extended source-intensity distribution of B1608+656. The resulting reconstruction can be used as the basis of a measurement of the Hubble constant. We use our reconstruction of the gravitational potential to study the relative distribution of mass and light in the lensing galaxies. We find that the mass-to-light ratio for the primary lens galaxy is (2.0+/-0.2)h M_{sun} L_{B,sun}^{-1} within the Einstein radius 3.9 h^{-1} kpc, in agreement with what is found for noninteracting lens galaxies at the same scales. (Abridged)
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