Interpolating point spread function anisotropy

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). We also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics $\sigma_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones

Evaluating the effect of stellar multiplicity on the PSF of space-based weak lensing surveys

The next generation of space-based telescopes used for weak lensing surveys will require exquisite point spread function (PSF) determination. Previously negligible effects may become important in the reconstruction of the PSF, in part because of the improved spatial resolution. In this paper, we show that unresolved multiple star systems can affect the ellipticity and size of the PSF and that this effect is not cancelled even when using many stars in the reconstruction process. We estimate the error in the reconstruction of the PSF due to the binaries in the star sample both analytically and with image simulations for different PSFs and stellar populations. The simulations support our analytical finding that the error on the size of the PSF is a function of the multiple stars distribution and of the intrinsic value of the size of the PSF, i.e. if all stars were single. Similarly, the modification of each of the complex ellipticity components (e1,e2) depends on the distribution of multiple stars and on the intrinsic complex ellipticity. Using image simulations, we also show that the predicted error in the PSF shape is a theoretical limit that can be reached only if large number of stars (up to thousands) are used together to build the PSF at any desired spatial position. For a lower number of stars, the PSF reconstruction is worse. Finally, we compute the effect of binarity for different stellar magnitudes and show that bright stars alter the PSF size and ellipticity more than faint stars. This may affect the design of PSF calibration strategies and the choice of the related calibration fields.Comment: 10 pages, 6 figures, accepted in A&

Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds

We establish results on holomorphic extension of CR-mappings of class $C^\infty$ between a real-analytic CR-submanifold of \C^N and a real-algebraic CR-submanifold of \C^{N'}

Palomar 13: a velocity dispersion inflated by binaries ?

Recently, combining radial velocities from Keck/HIRES echelle spectra with published proper motion membership probabilities, Cote et al (2002) observed a sample of 21 stars, probable members of Palomar 13, a globular cluster in the Galactic halo. Their projected velocity dispersion sigma_p = 2.2 +/-0.4 km/s gives a mass-to-light ratio M/L_V = 40 +24/-17, about one order of magnitude larger than the usual estimate for globular clusters. We present here radial velocities measured from three different CCD frames of commissioning observations obtained with the new ESO/VLT instrument FLAMES (Fibre Large Array Multi Element Spectrograph). From these data, now publicly available, we measure the homogeneous radial velocities of eight probable members of this globular cluster. A new projected velocity dispersion sigma_p = 0.6-0.9 +/-0.3 km/s implies Palomar 13 mass-to-light ratio M/L_V = 3-7, similar to the usual value for globular clusters. We discuss briefly the two most obvious reasons for the previous unusual mass-to-light ratio finding: binaries, now clearly detected, and more homogeneous data from the multi-fibre FLAMES spectrograph.Comment: 9 pages, 2 Postscript figure

Microlensing of the broad line region in 17 lensed quasars

When an image of a strongly lensed quasar is microlensed, the different components of its spectrum are expected to be differentially magnified owing to the different sizes of the corresponding emitting region. Chromatic changes are expected to be observed in the continuum while the emission lines should be deformed as a function of the size, geometry and kinematics of the regions from which they originate. Microlensing of the emission lines has been reported only in a handful of systems so far. In this paper we search for microlensing deformations of the optical spectra of pairs of images in 17 lensed quasars. This sample is composed of 13 pairs of previously unpublished spectra and four pairs of spectra from literature. Our analysis is based on a spectral decomposition technique which allows us to isolate the microlensed fraction of the flux independently of a detailed modeling of the quasar emission lines. Using this technique, we detect microlensing of the continuum in 85% of the systems. Among them, 80% show microlensing of the broad emission lines. Focusing on the most common lines in our spectra (CIII] and MgII) we detect microlensing of either the blue or the red wing, or of both wings with the same amplitude. This observation implies that the broad line region is not in general spherically symmetric. In addition, the frequent detection of microlensing of the blue and red wings independently but not simultaneously with a different amplitude, does not support existing microlensing simulations of a biconical outflow. Our analysis also provides the intrinsic flux ratio between the lensed images and the magnitude of the microlensing affecting the continuum. These two quantities are particularly relevant for the determination of the fraction of matter in clumpy form in galaxies and for the detection of dark matter substructures via the identification of flux ratio anomalies.Comment: Accepted for publication in Astronomy and Astrophysics. Main data set available via the German virtual observatory http://dc.g-vo.org/mlqso/q/web/form and soon via CDS. Additional material available on reques

COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses X. Modeling based on high-precision astrometry of a sample of 25 lensed quasars: consequences for ellipticity, shear, and astrometric anomalies

(abridged) Gravitationally lensed quasars can be used as powerful cosmological and astrophysical probes. We can (i) infer the Hubble constant based on the time-delay technique, (ii) unveil substructures along the l.o.s. toward distant galaxies, and (iii) compare the shape and the slope of baryons and dark matter distributions in galaxies. To reach these goals, we need high-accuracy astrometry and morphology measurements of the lens. In this work, we first present new astrometry for 11 lenses with measured time delays. Using MCS deconvolution on NIC2 HST images, we reached an astrometric accuracy of about 1-2.5 mas and an accurate shape measurement of the lens galaxy. Second, we combined these measurements with those of 14 other systems to present new mass models of these lenses. This led to the following results: 1) In 4 double-image quasars, we show that the influence of the lens environment on the time delay can easily be quantified and modeled, hence putting these lenses with high priority for time-delay determination. 2) For quadruple-image quasars, the difficulty often encountered in reproducing the image positions to milli-arcsec accuracy (astrometric anomaly) is overcome by explicitly including the nearest visible galaxy in the model. However, one anomalous system (J1131-1231) does not show any luminous perturber in its vicinity, and three others (WFI2026-4536, WFI2033-4723, and B2045+265) have problematic modeling. These 4 systems are the best candidates for a pertubation by a dark matter substructure. 3) We find a significant correlation between the PA of the light and of the mass distributions in lensing galaxies. In contrast with other studies, we find that the ellipticity of the light and of the mass also correlate well, suggesting that the overall spatial distribution of matter is not very different from the baryon distribution in the inner \sim 5 kpc of lensing galaxies.Comment: Accepted for publication in Astronomy and Astrophysics abridged abstrac

Firedec: a two-channel finite-resolution image deconvolution algorithm

We present a two-channel deconvolution method that decomposes images into a parametric point-source channel and a pixelized extended-source channel. Based on the central idea of the deconvolution algorithm proposed by Magain, Courbin & Sohy (1998), the method aims at improving the resolution of the data rather than at completely removing the point spread function (PSF). Improvements over the original method include a better regularization of the pixel channel of the image, based on wavelet filtering and multiscale analysis, and a better controlled separation of the point source vs. the extended source. In addition, the method is able to simultaneously deconvolve many individual frames of the same object taken with different instruments under different PSF conditions. For this purpose, we introduce a general geometric transformation between individual images. This transformation allows the combination of the images without having to interpolate them. We illustrate the capability of our algorithm using real and simulated images with complex diffraction-limited PSF.Comment: Accepted in A&A. An application of the technique to real data is available in Cantale et al. http://arxiv.org/abs/1601.05192v

Probing the inner structure of distant AGNs with gravitational lensing

Microlensing is a powerful technique which can be used to study the continuum and the broad line emitting regions in distant AGNs. After a brief description of the methods and required data, we present recent applications of this technique. We show that microlensing allows one to measure the temperature profile of the accretion disc, estimate the size and study the geometry of the region emitting the broad emission lines.Comment: 6 pages, Proceedings of the Seyfert 2012 conferenc

Exploring the gravitationally lensed system HE 1104-1805: Near-IR Spectroscopy

(Abridged) A new technique for the spatial deconvolution of spectra is applied to near-IR (0.95 - 2.50 micron) NTT/SOFI spectra of the lensed, radio-quiet quasar HE 1104-1805. The continuum of the lensing galaxy is revealed between 1.5 and 2.5 micron. It is used in combination with previous optical and IR photometry to infer a plausible redshift in the range 0.8 < z < 1.2. Modeling of the system shows that the lens is probably composed of the red galaxy seen between the quasar images and a more extended component associated with a galaxy cluster with fairly low velocity dispersion (~ 575 km/s). The spectra of the two lensed images of the source show no trace of reddening at the redshift of the lens nor at the redshift of the source. Additionally, the difference between the spectrum of the brightest component a nd that of a scaled version of the faintest component is a featureless continuum. Broad and narrow emission lines, including the FeII features, are perfectly subtracted. The very good quality of our spectrum makes it possible to fit precisely the optical Fe II feature, taking into account the underlying continuum over a wide wavelength range. HE 1104-1805 can be classified as a weak Fe II emitter. Finally, the slope of the continuum in the brightest image is steeper than the continuum in the faintest image and supports the finding by Wisotzki et al. (1993) that the brightest image is microlensed. This is particularly interesting in view of the new source reconstruction methods from multiwavelength photometric monitoring.Comment: to be published in A&A, 8 pages, 9 postscript figure