Weak Lensing Reconstruction Research Articles

A method of weak lensing reconstruction through cosmic magnification with multiband photometry information

ABSTRACT Weak gravitational lensing induces flux-dependent fluctuations in the observed galaxy number density distribution. This cosmic magnification (magnification bias) effect in principle enables lensing reconstruction alternative to cosmic shear and cosmic microwave background lensing. However, the intrinsic galaxy clustering, which otherwise overwhelms the signal, has hindered its application. Through a scaling relation found by principal component analysis of the galaxy clustering in multiband photometry space, we design a minimum variance linear estimator to suppress the intrinsic galaxy clustering and to reconstruct the lensing convergence map. In combination of the CosmoDC2 galaxy mock and the CosmicGrowth simulation, we test this proposal for an LSST (Large Synoptic Survey Telescope)-like galaxy survey with ugrizY photometry bands. (1) The scaling relation holds excellently at multipole ℓ < 103, and remains reasonably well to ℓ ∼ 3000. (2) The linear estimator efficiently suppresses the galaxy intrinsic clustering, by a factor of ∼102. (3) For galaxies in the photo-z range 0.8 < zκ < 1.2, the reconstructed convergence map is cosmic variance limited per ℓ mode at ℓ < 102, and shot noise limited at $\ell \gtrsim 200$. (4) Its cross-correlation with cosmic shear of galaxies can achieve $\mathrm{ S/N}\gtrsim 200$. When the source redshift of cosmic shear galaxies zγ < zκ, the systematic error is negligible at all investigated scales (ℓ < 3000). When zγ ≥ zκ, the systematic error caused by the residual intrinsic galaxy clustering becomes non-negligible. We discuss possible mitigation of the residual intrinsic galaxy clustering required for accurate measurement at ℓ > 103. This work further demonstrates the potential of lensing measurement through cosmic magnification to enhance the weak lensing cosmology.

A combined X-ray, optical, and radio view of the merging galaxy cluster MACS J0417.5–1154

We present a comprehensive multi-wavelength analysis of the merging galaxy cluster MACS~J0417.5-1154 at a redshift of $z=0.44$, using available images red obtained with \chandra\ in X-ray, {\it Subaru}, {\it Hubble Space Telescope} (HST) in optical, {\it Giant Metrewave Radio Telescope} (GMRT) in radio and {\it Bolocam} at 2.1~mm wavelength. This is an example of a complex merging galaxy cluster also hosting a steep-spectrum Mpc scale radio halo. The mass distribution obtained by weak lensing reconstruction shows that MACS~J0417.5-1154 belongs to the dissociative class of mergers, where one of its substructures has had its gas content detached after the pericentric passage. We find the main cluster mass $M_{200}~=~11.5^{+3.0}_{-3.5} \times 10^{14}\ M_\odot$ and the smaller second (sub)cluster mass to be $M_{200}~=~1.96^{+1.60}_{-0.95} \times 10^{14}\ M_\odot$, leading to a large total mass of $M_{200}~=~13.8^{+2.6}_{-2.8} \times 10^{14}\ M_\odot$. The overall structure, surface brightness profile, temperature and metal abundance of the intra-cluster medium (ICM) all point towards the presence of a cold front and merger induced gas-sloshing motion near the core. We detect a surface brightness edge to the south$-$east direction at a projected distance of $\sim$45 arcsec ($\sim$255\,kpc) from the centre of this cluster. The X-ray spectral analysis across the inner and outer edge allows us to confirm the detected edge as a cold front. The GMRT 235\,MHz observation shows a comet$-$like extended sychrotron radio halo emission trailing behind the cold front. The peak of the Sunyaev-Zel'dovich decrement is found displaced from the centre of X-ray emission, which is interpreted as consequence of the merger dynamics.

THE GRISM LENS-AMPLIFIED SURVEY FROM SPACE (GLASS). IV. MASS RECONSTRUCTION OF THE LENSING CLUSTER ABELL 2744 FROM FRONTIER FIELD IMAGING AND GLASS SPECTROSCOPY

We present a strong and weak lensing reconstruction of the massive cluster Abell 2744, the first cluster for which deep Hubble Frontier Field (HFF) images and spectroscopy from the Grism Lens-Amplified Survey from Space (GLASS) are available. By performing a targeted search for emission lines in multiply imaged sources using the GLASS spectra, we obtain 5 high-confidence spectroscopic redshifts and 2 tentative ones. We confirm 1 strongly lensed system by detecting the same emission lines in all 3 multiple images. We also search for additional line emitters blindly and use the full GLASS spectroscopic catalog to test reliability of photometric redshifts for faint line emitters. We see a reasonable agreement between our photometric and spectroscopic redshift measurements, when including nebular emission in photometric redshift estimations. We introduce a stringent procedure to identify only secure multiple image sets based on colors, morphology, and spectroscopy. By combining 7 multiple image systems with secure spectroscopic redshifts (at 5 distinct redshift planes) with 18 multiple image systems with secure photometric redshifts, we reconstruct the gravitational potential of the cluster pixellated on an adaptive grid, using a total of 72 images. The resulting mass map is compared with a stellar mass map obtained from the deep Spitzer Frontier Fields data to study the relative distribution of stars and dark matter in the cluster. We find that the stellar to total mass ratio varies substantially across the cluster field, suggesting that stars do not trace exactly the total mass in this interacting system. The maps of convergence, shear, and magnification are made available in the standard HFF format.

Weak lensing reconstructions in 2D and 3D: implications for cluster studies

We compare the efficiency with which 2D and 3D weak lensing mass mapping techniques are able to detect clusters of galaxies using two state-of-the-art mass reconstruction techniques: MRLens in 2D and GLIMPSE in 3D. We simulate otherwise-empty cluster fields for 96 different virial mass-redshift combinations spanning the ranges $3\times10^{13}h^{-1}M_\odot \le M_{vir}\le 10^{15}h^{-1}M_\odot$ and $0.05 \le z_{\rm cl} \le 0.75$, and for each generate 1000 realisations of noisy shear data in 2D and 3D. For each field, we then compute the cluster (false) detection rate as the mean number of cluster (false) detections per reconstruction over the sample of 1000 reconstructions. We show that both MRLens and GLIMPSE are effective tools for the detection of clusters from weak lensing measurements, and provide comparable quality reconstructions at low redshift. At high redshift, GLIMPSE reconstructions offer increased sensitivity in the detection of clusters, yielding cluster detection rates up to a factor of $\sim 10\times$ that seen in 2D reconstructions using MRLens. We conclude that 3D mass mapping techniques are more efficient for the detection of clusters of galaxies in weak lensing surveys than 2D methods, particularly since 3D reconstructions yield unbiased estimators of both the mass and redshift of the detected clusters directly.

Weak lensing reconstruction through cosmic magnification – II. Improved power spectrum determination and map-making

The existence of galaxy intrinsic clustering severely hampers the weak lensing reconstruction from cosmic magnification. In paper I \citep{Yang2011}, we proposed a minimal variance estimator to overcome this problem. By utilizing the different dependences of cosmic magnification and galaxy intrinsic clustering on galaxy flux, we demonstrated that the otherwise overwhelming galaxy intrinsic clustering can be significantly suppressed such that lensing maps can be reconstructed with promising accuracy. This procedure relies heavily on the accuracy of determining the galaxy bias from the same data. Paper I adopts an iterative approach, which degrades toward high redshift. The current paper presents an alternative method, improving over paper I. We prove that the measured galaxy clustering between flux bins allows for simultaneous determination of the lensing power spectrum and the flux dependence of galaxy bias, at this redshift bin. Comparing to paper I, the new approach is not only more straightforward, but also more robust. It identifies an ambiguity in determining the galaxy bias and further discovers a mathematically robust way to suppress this ambiguity to non-negligible level ($\sim 0.1%$). The accurately determined galaxy bias can then be applied to the minimal variance estimator proposed in paper I to improve the lensing map-making. The gain at high redshift is significant. These maps can be used to measure other statistics, such as cluster finding and peak statistics. Furthermore, by including galaxy clustering measurement between different redshift bins, we can also determine the lensing cross power spectrum between these bins, up to a small and correctable multiplicative factor.

GLIMPSE: accurate 3D weak lensing reconstructions using sparsity

We present GLIMPSE - Gravitational Lensing Inversion and MaPping with Sparse Estimators - a new algorithm to generate density reconstructions in three dimensions from photometric weak lensing measurements. This is an extension of earlier work in one dimension aimed at applying compressive sensing theory to the inversion of gravitational lensing measurements to recover 3D density maps. Using the assumption that the density can be represented sparsely in our chosen basis - 2D transverse wavelets and 1D line of sight dirac functions - we show that clusters of galaxies can be identified and accurately localised and characterised using this method. Throughout, we use simulated data consistent with the quality currently attainable in large surveys. We present a thorough statistical analysis of the errors and biases in both the redshifts of detected structures and their amplitudes. The GLIMPSE method is able to produce reconstructions at significantly higher resolution than the input data; in this paper we show reconstructions with 6x finer redshift resolution than the shear data. Considering cluster simulations with 0.05 <= z <= 0.75 and 3e13/h Msun <= Mvir <= 1e15/h Msun, we show that the redshift extent of detected peaks is typically 1-2 pixels, or Dz <~ 0.07, and that we are able to recover an unbiased estimator of the redshift of a detected cluster by considering many realisations of the noise. We also recover an accurate estimator of the mass, that is largely unbiased when the redshift is known, and whose bias is constrained to <~ 5% in the majority of our simulations when the estimated redshift is taken to be the true redshift. This shows a substantial improvement over earlier 3D inversion methods, which showed redshift smearing with a typical standard deviation of 0.2-0.3, a significant damping of the amplitude of the peaks detected, and a bias in the detected redshift.

Probing the neutrino mass hierarchy with cosmic microwave background weak lensing

We forecast constraints on cosmological parameters with primary cosmic microwave background (CMB) anisotropy information and weak lensing reconstruction with a future post-Planck CMB experiment, the Cosmic Origins Explorer (COrE), using oscillation data on the neutrino mass splittings as prior information. Our Markov chain Monte Carlo (MCMC) simulations in flat models with a non-evolving equation of state of dark energy w give typical 68 per cent upper bounds on the total neutrino mass of 0.136 and 0.098 eV for the inverted and normal hierarchies, respectively, assuming the total summed mass is close to the minimum allowed by the oscillation data for the respective hierarchies (0.10 and 0.06 eV). Including geometric information from future baryon acoustic oscillation measurements with the complete Baryon Oscillation Spectroscopic Survey, Type Ia supernovae distance moduli from Wide-Field Infrared Survey Telescope (WFIRST) and a realistic prior on the Hubble constant, these upper limits shrink to 0.118 and 0.080 eV for the inverted and normal hierarchies, respectively. Addition of these distance priors also yields per cent-level constraints on w. We find tension between our MCMC results and the results of a Fisher matrix analysis, most likely due to a strong geometric degeneracy between the total neutrino mass, the Hubble constant and w in the unlensed CMB power spectra. If the minimal-mass, normal hierarchy were realized in nature, the inverted hierarchy should be disfavoured by the full data combination at typically greater than the 2σ level. For the minimal-mass inverted hierarchy, we compute the Bayes factor between the two hierarchies for various combinations of our forecast data sets, and find that the future cosmological probes considered here should be able to provide ‘strong’ evidence (odds ratio 12:1) for the inverted hierarchy. Finally, we consider potential biases of the other cosmological parameters from assuming the wrong hierarchy and find that all biases on the parameters are below their 1σ marginalized errors.

Weak lensing reconstruction through cosmic magnification - I. A minimal variance map reconstruction

We present a concept study on weak lensing map reconstruction through the cosmic magnification effect in galaxy number density distribution. We propose a minimal variance linear estimator to minimize both the dominant systematical and statistical errors in the map reconstruction. It utilizes the distinctively different flux dependences to separate the cosmic magnification signal from the overwhelming galaxy intrinsic clustering noise. It also minimizes the shot noise error by an optimal weighting scheme on the galaxy number density in each flux bin. Our method is in principle applicable to all galaxy surveys with reasonable redshift information. We demonstrate its applicability against the planned Square Kilometer Array survey, under simplified conditions. Weak lensing maps reconstructed through our method are complementary to that from cosmic shear and CMB and 21cm lensing. They are useful for cross checking over systematical errors in weak lensing reconstruction and for improving cosmological constraints.

Gravitational lensing of the cosmic microwave background by non-linear structures

Weak gravitational lensing changes the angular power spectra of the cosmic microwave background (CMB) temperature and polarization in a characteristic way containing valuable information for cosmological parameter estimation and weak lensing reconstructions. So far, analytical expressions for the lensed CMB power spectra assume the probability density function (PDF) of the lensing excursion angle to be Gaussian. However, coherent light deflection by nonlinear structures at low redshifts causes deviations from a pure Gaussian PDF. Working in the flat-sky limit we develop a method for computing the lensed CMB power spectra which takes these non-Gaussian features into account. Our method does not assume any specific PDF but uses instead an expansion of the characteristic function of the lensing excursion angle into its moments. Measuring these in the CMB lensing deflection field obtained from the Millennium Simulation we show that the change in the lensed power spectra is only at the 0.1% - 0.4% level on very small scales (below 4 arcmin) and demonstrate that the assumption of a Gaussian lensing excursion angle PDF is well applicable.

Reducing distance errors for standard candles and standard sirens with weak-lensing shear and flexion maps

Gravitational lensing induces significant errors in the measured distances to high-redshift standard candles and standard sirens such as type-Ia supernovae, gamma-ray bursts, and merging supermassive black hole binaries. There will therefore be a significant benefit from correcting for the lensing error by using independent and accurate estimates of the lensing magnification. We investigate how accurately the magnification can be inferred from convergence maps reconstructed from galaxy shear and flexion data. We employ ray-tracing through the Millennium Simulation to simulate lensing observations in large fields, and perform a weak-lensing reconstruction on these fields. We identify optimal ways to filter the reconstructed convergence maps and to convert them to magnification maps. We find that a shear survey with 100 galaxies/arcmin^2 can help to reduce the lensing-induced distance errors for standard candles/sirens at redshifts z=1.5 (z=5) on average by 20% (10%), whereas a futuristic survey with shear and flexion estimates from 500 galaxies/arcmin^2 yields much larger reductions of 50% (35%). For redshifts z>=3, a further improvement by 5% can be achieved, if the individual redshifts of the galaxies are used in the reconstruction. Moreover, the reconstruction allows one to identify regions for which the convergence is low, and in which an error reduction by up to 75% can be achieved.

DARK MATTER STRUCTURES IN THE DEEP LENS SURVEY

We present a regularized maximum likelihood weak lensing reconstruction of the Deep Lens Survey F2 field (4 deg^2). High signal-to-noise ratio peaks in our lensing significance map appear to be associated with possible projected filamentary structures. The largest apparent structure extends for over a degree in the field and has contributions from known optical clusters at three redshifts (z ~ 0.3, 0.43, 0.5). Noise in weak lensing reconstructions is known to potentially cause positives; we use Monte Carlo techniques to estimate the contamination in our sample, and find that 10-25% of the peaks are expected to be false detections. For significant lensing peaks we estimate the total signal-to-noise ratio of detection using a method that accounts for pixel-to-pixel correlations in our reconstruction. We also report the detection of a candidate relative underdensity in the F2 field with a total signal-to-noise ratio of ~ 5.5.

Precision of diffuse 21-cm lensing

We study the limits of accuracy for weak lensing maps of dark matter using diffuse 21-cm radiation from the pre-reionization epoch using simulations. We improve on previous ‘optimal’ quadratic lensing estimators by using shear and convergence instead of deflection angles. This is a generalization of the deflection estimator, and is more optimal for non-Gaussian sources. The cross-power spectrum of shear and convergence is an unbiased estimator of lensing power spectrum which does not require knowledge of the source four-point function. We find that non-Gaussianity provides a limit to the accuracy of weak lensing reconstruction, even if instrumental noise is reduced to zero. The best reconstruction result is equivalent to Gaussian sources with effective independent cell of side length 2.0 h−1Mpc. Using a source full map from z= 10 to 20, this limiting sensitivity allows mapping of dark matter at a signal-to-noise ratio greater than 1 out to l≲ 6000, which is better than any other proposed technique for large-area weak lensing mapping.

Strong and weak lensing united

We have shown that the cluster-mass reconstruction method which combines strong and weak gravitational lensing data, developed in the first paper in the series, successfully reconstructs the mass distribution of a simulated cluster. In this paper we apply the method to the ground-based high-quality multi-colour data of RX J1347.5-1145 , the most X-ray luminous cluster to date. A new analysis of the cluster core on very deep, multi-colour data analysis of VLT/FORS data reveals many more arc candidates than previously known for this cluster. The combined strong and weak lensing reconstruction confirms that the cluster is indeed very massive. If the redshift and identification of the multiple-image system as well as the redshift estimates of the source galaxies used for weak lensing are correct, we determine the enclosed cluster mass in a cylinder to M(<360 h -1 kpc)= (1.2± 0.3) x 1015 M⊙. In addition the reconstructed mass distribution follows the distribution found with independent methods (X-ray measurements, SZ). With higher resolution (e.g. HST imaging data) more reliable multiple imaging information can be obtained and the reconstruction can be improved to accuracies greater than what is currently possible with weak and strong lensing techniques.

X-ray and weak lensing measurements of the mass profile of MS1008.1–1224: Chandra and VLT data

We analyse the Chandra dataset of the galaxy cluster MS1008.1-1224 to recover an estimate of the gravitating mass as function of the radius and compare these results with the weak lensing reconstruction of the mass distribution obtained from deep FORS1-VLT multicolor imaging. Even though the X-ray morphology is disturbed with a significant excess in the northern direction suggesting that the cluster is not in a relaxed state, we are able to match the two mass profiles both in absolute value and in shape within 1 sigma uncertainty and up to 1100 h50^-1 kpc. The recovered X-ray mass estimate does not change by using either the azimuthally averaged gas density and temperature profiles or the results obtained in the northern sector alone where the signal-to-noise ratio is higher.

Weak lensing of the CMB: extraction of lensing information from the trispectrum

We discuss the four-point correlation function, or the trispectrum in Fourier space, of CMB temperature and polarization anisotropies due to the weak gravitational lensing effect by intervening large scale structure. We discuss the squared temperature power spectrum as a probe of this trispectrum and, more importantly, as an observational approach to extracting the power spectrum of the deflection angle associated with the weak gravitational lensing effect on the CMB. We extend previous discussions on the trispectrum and associated weak lensing reconstruction from CMB data by calculating non-Gaussian noise contributions, beyond the previously discussed dominant Gaussian noise. Non-Gaussian noise contributions are generated by lensing itself and by the correlation between the lensing effect and other foreground secondary anisotropies in the CMB such as the Sunyaev–Zel’dovich (SZ) effect. When the SZ effect is removed from temperature maps using its spectral dependence, we find these additional non-Gaussian noise contributions to be an order of magnitude lower than the dominant Gaussian noise. If the noise-bias due to the dominant Gaussian part of the temperature squared power spectrum is removed, then these additional non-Gaussian contributions provide the limiting noise level for the lensing reconstruction. The temperature squared power spectrum allows a high signal-to-noise extraction of the lensing deflections and a confusion-free separation of the curl (or B-mode) polarization due to inflationary gravitational waves from that due to lensed gradient (or E-mode) polarization. The small angular scale temperature and polarization anisotropy measurements provide a novel approach to weak lensing studies, complementing the approach based on galaxy ellipticities.

Weak Gravitational Lensing by the Nearby Cluster Abell 3667.

We present two weak lensing reconstructions of the nearby (zcl=0.055) merging cluster Abell 3667, based on observations taken approximately 1 yr apart under different seeing conditions. This is the lowest redshift cluster with a weak lensing mass reconstruction to date. The reproducibility of features in the two mass maps demonstrates that weak lensing studies of low-redshift clusters are feasible. These data constitute the first results from an X-ray luminosity-selected weak lensing survey of 19 low-redshift (z<0.1) southern clusters.