Hopfield Neural Network deconvolution for weak lensing measurement

Weak gravitational lensing has the potential to place tight constraints on the equation of the state of dark energy. However, this will only be possible if shear measurement methods can reach the required level of accuracy. We present a new method to measure the ellipticity of galaxies used in weak lensing surveys. The method makes use of direct deconvolution of the data by the total Point Spread Function (PSF). We adopt a linear algebra formalism that represents the PSF as a Toeplitz matrix. This allows us to solve the convolution equation by applying the Hopfield Neural Network iterative scheme. The ellipticity of galaxies in the deconvolved images are then measured using second order moments of the autocorrelation function of the images. To our knowledge, it is the first time full image deconvolution is used to measure weak lensing shear. We apply our method to the simulated weak lensing data proposed in the GREAT10 challenge and obtain a quality factor of Q=87. This result is obtained after applying image denoising to the data, prior to the deconvolution. The additive and multiplicative biases on the shear power spectrum are then +0.000009 and +0.0357, respectively.Comment: 10 pages, 11 figures and 2 tables, accepted for publication in A&

Weak-lensing shear measurement with machine learning: teaching artificial neural networks about feature noise

Cosmic shear is a primary cosmological probe for several present and upcoming surveys investigating dark matter and dark energy, such as Euclid or WFIRST. The probe requires an extremely accurate measurement of the shapes of millions of galaxies based on imaging data. Crucially, the shear measurement must address and compensate for a range of interwoven nuisance effects related to the instrument optics and detector, noise, unknown galaxy morphologies, colors, blending of sources, and selection effects. This paper explores the use of supervised machine learning (ML) as a tool to solve this inverse problem. We present a simple architecture that learns to regress shear point estimates and weights via shallow artificial neural networks. The networks are trained on simulations of the forward observing process, and take combinations of moments of the galaxy images as inputs. A challenging peculiarity of this ML application is the combination of the noisiness of the input features and the requirements on the accuracy of the inverse regression. To address this issue, the proposed training algorithm minimizes bias over multiple realizations of individual source galaxies, reducing the sensitivity to properties of the overall sample of source galaxies. Importantly, an observational selection function of these source galaxies can be straightforwardly taken into account via the weights. We first introduce key aspects of our approach using toy-model simulations, and then demonstrate its potential on images mimicking Euclid data. Finally, we analyze images from the GREAT3 challenge, obtaining competitively low shear biases despite the use of a simple training set. We conclude that the further development of ML approaches is of high interest to meet the stringent requirements on the shear measurement in current and future surveys. A demonstration implementation of our technique is publicly available.Comment: 31 pages, 26 figures, minor changes to match the version published in A&A, code available at https://astro.uni-bonn.de/~mtewes/ml-shear-meas

Strong gravitational lensing by AGNs as a probe of the quasar-host relations in the distant Universe

The tight correlations found between the mass of the supermassive black holes (SMBH) and their host galaxy luminosity, stellar mass, and velocity dispersion are often interpreted as a sign of their co-evolution. Studying these correlations across redshift provides a powerful insight into the evolutionary path followed by the quasar and its host galaxy. While the mass of the black hole is accessible from single-epoch spectra, measuring the mass of its host galaxy is challenging as the quasar largely overshines its host. Here, we present a novel technique to probe quasar-host relations beyond the local universe with strong gravitational lensing, hence overcoming the use of stellar population models or velocity dispersion measurements, both prone to degeneracies. We study in detail one of the three known cases of strong lensing by a quasar to accurately measure the mass of its host and to infer a total lensing mass of $\log_{10}(M_{\rm Tot, h}/M_{\odot}) = 10.27^{+0.06}_{-0.07}~$ within the Einstein radius of 1.2 kpc. The lensing measurement is more precise than any other alternative techniques and compatible with the local $M_{BH}$-$M_{\star, h}$ scaling relation. The sample of such quasar-galaxy or quasar-quasar lensing systems should reach a few hundreds with Euclid and Rubin-LSST, thus enabling the application of such a method with statistically significant sample sizes.Comment: Author's pre-review version, published in Nature Astronomy, 13 pages, 5 figure

Further Evidence that Quasar X-Ray Emitting Regions Are Compact: X-Ray and Optical Microlensing in the Lensed Quasar Q J0158-4325

We present four new seasons of optical monitoring data and six epochs of X-ray photometry for the doubly-imaged lensed quasar Q J0158-4325. The high-amplitude, short-period microlensing variability for which this system is known has historically precluded a time delay measurement by conventional methods. We attempt to circumvent this limitation by application of a Monte Carlo microlensing analysis technique, but we are only able to prove that the delay must have the expected sign (image A leads image B). Despite our failure to robustly measure the time delay, we successfully model the microlensing at optical and X-ray wavelengths to find a half light radius for soft X-ray emission log(r_{1/2,X,soft}/cm) = 14.3^{+0.4}_{-0.5}, an upper limit on the half-light radius for hard X-ray emission log(r_{1/2,X,hard}/cm) <= 14.6 and a refined estimate of the inclination-corrected scale radius of the optical R-band (rest frame 3100 Angstrom) continuum emission region of log(r_s/cm) = 15.6+-0.3.Comment: 9 pages, 6 figures, submitted to Ap

GREAT3 results I: systematic errors in shear estimation and the impact of real galaxy morphology

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S\'{e}rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity.Comment: 32 pages + 15 pages of technical appendices; 28 figures; submitted to MNRAS; latest version has minor updates in presentation of 4 figures, no changes in content or conclusion

GREAT3 results - I. Systematic errors in shear estimation and the impact of real galaxy morphology

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by ∼1percent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the Sérsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticit

Measuring the size of the broad line region in quasars with Microlensing-aided reverberation mapping

Owing to the advent of large area photometric surveys, the possibility to use broad band photometric data, instead of spectra, to measure the size of the broad line region of active galactic nuclei, has raised a large interest. We will describe a new method using time-delay lensed quasars where one (or several) images are affected by microlensing due to stars in the lensing galaxy. Because microlensing decreases (or increases) the flux of the continuum compared to the broad line region, it changes the contrast between these two emission components. We show that this effect can be used to effectively disentangle the intrinsic variability of those two regions, offering the opportunity to perform reverberation mapping based on single band photometric data. Based on simulated light curves, we show that measurement of the size of the broad line region can be achieved using this method, provided one spectrum has been obtained independently during the monitoring. This method is complementary to photometric reverberation mapping and could also be extended to multi-band data

COSMOGRAIL: Measuring Time Delays of Gravitationally Lensed Quasars to Constrain Cosmology

COSMOGRAIL is a long-term programme for the photometric monitoring of gravitationally lensed quasars. It makes use of several medium-size telescopes to derive long and well-sampled light curves of lensed quasars, in order to measure the time delays between the quasar images. These delays directly relate to the Hubble constant H0, without any need for secondary distance calibrations. COSMOGRAIL was initiated in 2004, and has now secured almost a decade of data, resulting in cosmological constraints that are very complementary to other cosmological probes