Jes Ford, Hendrik Hildebrandt, Ludovic Van Waerbeke, Alexie Leauthaud, Peter Capak, Alexis Finoguenov, Masayuki Tanaka, Matthew R. George, Jason Rhodes
We report on the detection of gravitational lensing magnification by a population of galaxy groups, at a significance level of 4.9 sigma. Using X-ray selected groups in the COSMOS 1.64 deg^2 field, and high-redshift Lyman break galaxies as sources, we measure a lensing-induced angular cross-correlation between the samples. After satisfying consistency checks that demonstrate we have indeed detected a magnification signal, and are not suffering from contamination by physical overlap of samples, we proceed to implement an optimally weighted cross-correlation function to further boost the signal to noise of the measurement. Interpreting this optimally weighted measurement allows us to study properties of the lensing groups. We model the full distribution of group masses using a composite-halo approach, considering both the singular isothermal sphere and Navarro-Frenk-White profiles, and find our best fit values to be consistent with those recovered using the weak-lensing shear technique. We argue that future weak-lensing studies will need to incorporate magnification along with shear, both to reduce residual systematics and to make full use of all available source information, in an effort to maximize scientific yield of the observations.
We propose a new approach for measuring the mass profile and shape of groups and clusters of galaxies, which uses lensing magnification of distant background galaxies. The main advantage of lensing magnification is that, unlike lensing shear, it relies on accurate photometric redshifts only and not galaxy shapes, thus enabling the study of the dark matter distribution with unresolved source galaxies. We present a feasibility study, using a real population of z > 2.5 Lyman Break Galaxies as source galaxies, and where, similar to galaxy-galaxy lensing, foreground lenses are stacked in order to i…
Weak lensing is commonly measured using shear through galaxy ellipticities, or using the effect of magnification bias on galaxy number densities. Here, we report on the first detection of weak lensing magnification with a new, independent technique using the distribution of galaxy sizes and magnitudes. These data come for free in galaxy surveys designed for measuring shear. We present the magnification estimator and apply it to an X-ray selected sample of galaxy groups in the COSMOS HST survey. The measurement of the projected surface density Σ(r) is consistent with the shear measurements with…
Many distant objects can only be detected, or become more scientifically valuable, if they have been highly magnified by strong gravitational lensing. We use EAGLE and BAHAMAS, two recent cosmological hydrodynamical simulations, to predict the probability distribution for both the lens mass and lens redshift when point sources are highly magnified by gravitational lensing. For sources at a redshift of two, we find the distribution of lens redshifts to be broad, peaking at z=0.6. The contribution of different lens masses is also fairly broad, with most high-magnification lensing due to lenses w…
We present an analytical model which reproduces measured galaxy number counts from surveys in the wavelength range of 500 micron to 2 mm. The model involves a single high-redshift galaxy population with a Schechter luminosity function which has been gravitationally lensed by galaxy clusters in the mass range 10^13 to 10^15 Msun. This simple model reproduces both the low flux and the high flux end of the number counts reported by the BLAST, SCUBA, AzTEC and the SPT surveys. In particular, our model accounts for the most luminous galaxies detected by SPT as the result of high magnifications by g…
The magnification of galaxies in modern galaxy surveys induces additional correlations in the cosmic shear, galaxy-galaxy lensing and clustering observables used in modern lensing "3x2pt" analyses, due to sample selection. In this paper, we emulate the magnification contribution to all three observables utilising the SLICS simulations suite, and test the sensitivity of the cosmological model, galaxy bias and redshift distribution calibration to un-modelled magnification in a Stage-IV-like survey using Monte-Carlo sampling. We find that magnification cannot be ignored in any single or combined …
Cosmic magnification has been detected through cross correlation between foreground and background populations (galaxies or quasars). It has been shown that weighing each background object by its $α-1$ can significantly improve the cosmic magnification measurement \citep{Menard02,Scranton05}. Here, $α$ is the logarithmic slope of the luminosity function of background populations. However, we find that this weighting function is optimal only for sparse background populations in which intrinsic clustering is negligible with respect to shot noise. We derive the optimal weighting function for gene…
Magnification changes the observed number counts of galaxies on the sky. This biases the observed tangential shear profiles around galaxies, the so-called galaxy-galaxy lensing (GGL) signal, and the related excess mass profile. Correspondingly, inference of physical quantities, such as the mean mass profile of halos around galaxies, are affected by magnification effects. We use simulated shear and galaxy data of the Millennium Simulation to quantify the effect on shear and mass estimates from magnified lens and source number counts. The former are due to the large-scale matter distribution in …
Using about 450,000 galaxies in the Deep Lens Survey, we present a detection of the gravitational magnification of z > 4 Lyman Break Galaxies by massive foreground galaxies with 0.4 < z < 1.0, grouped by redshift. The magnification signal is detected at S/N greater than 20, and rigorous checks confirm that it is not contaminated by any galaxy sample overlap in redshift. The inferred galaxy mass profiles are consistent with earlier lensing analyses at lower redshift. We then explore the tomographic lens magnification signal by splitting our foreground galaxy sample into 7 redshift bins. Combini…
Measurements of galaxy clustering in upcoming surveys such as those planned for the Euclid and Roman satellites, and the SKA Observatory, will be sensitive to distortions from lensing magnification and Doppler effects, beyond the standard redshift-space distortions. The amplitude of these contributions depends sensitively on magnification bias and evolution bias in the galaxy number density. Magnification bias quantifies the change in the observed number of galaxies gained or lost by lensing magnification, while evolution bias quantifies the physical change in the galaxy number density relativ…
Aims. The main goal of this paper is to derive observational constraints on the halo mass fuction (HMF) by performing a tomographic analysis of the magnification bias signal on a sample of background submillimeter galaxies. The results can then be compared with those from a non-tomographic study. Methods. We measure the cross-correlation function between a sample of foreground GAMA galaxies with spectroscopic redshifts in the range $0.1 < z < 0.8$ (and divided up into four bins) and a sample of background submillimeter galaxies from H-ATLAS with photometric redshifts in the range $1.2 < z < 4.…
In this paper we investigate magnetic fields generated in the early Universe. These fields are important candidates at explaining the origin of astrophysical magnetism observed in galaxies and galaxy clusters, whose genesis is still by and large unclear. Compared to the standard inflationary power spectrum, intermediate to small scales would experience further substantial matter clustering, were a cosmological magnetic field present prior to recombination. As a consequence, the bias and redshift distribution of galaxies would also be modified. Hitherto, primordial magnetic fields (PMFs) have b…
Weak lensing, Big Magnification: Recovering hidden lensing information from galaxy positions
Institute of Space Sciences (ICE, CSIC)（空间科学研究所）；Universitat Autònoma de Barcelona (UAB)（巴塞罗那自治大学）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所）；The Barcelona Institute of Science and Technology（巴塞罗那科学技术研究院）
In this paper, we motivate the use of galaxy clustering measurements using photometric redshift information, including a contribution from flux magnification, as a probe of cosmology. We present cosmological forecasts when clustering data alone is used, and when clustering is combined with a cosmic shear analysis. We consider two types of clustering analysis: firstly, clustering with only redshift auto-correlations in tomographic redshift bins; secondly, using all available redshift bin correlations. Finally, we consider how inferred cosmological parameters may be biased using each analysis wh…
Recent works have shown that weak lensing magnification must be included in upcoming large-scale structure analyses, such as for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), to avoid biasing the cosmological results. In this work we investigate whether including magnification has a positive impact on the precision of the cosmological constraints, as well as being necessary to avoid bias. We forecast this using an LSST mock catalog and a halo model to calculate the galaxy power spectra. We find that including magnification has little effect on the precision of the cosmo…
Aims. The main purpose of this work is to provide a method to derive tabulated observational constraints on the halo mass function (HMF) by studying the magnification bias effect on high-redshift submillimeter galaxies. Under the assumption of universality, we parametrize the HMF according to two traditional models, namely the Sheth and Tormen (ST) and Tinker fits and assess their performance in explaining the measured data within the Λ cold dark matter (ΛCDM) model. We also study the potential influence of the halo occupation distribution (HOD) parameters in this analysis and discuss two impo…
We present a statistical weak-lensing magnification analysis on an optically selected sample of 3029 \texttt{CAMIRA} galaxy clusters with richness $N>15$ at redshift $0.2\leq z <1.1$ in the Subaru Hyper Suprime-Cam (HSC) survey. We use two distinct populations of color-selected, flux-limited background galaxies, namely the low-$z$ and high-$z$ samples at mean redshifts of $\approx1.1$ and $\approx1.4$, respectively, from which to measure the weak-lensing magnification signal by accounting for cluster contamination as well as masking effects. Our magnification bias measurements are found to be …
Gravitational lensing magnification modifies the observed spatial distribution of galaxies and can severely bias cosmological probes of large-scale structure if not accurately modelled. Standard approaches to modelling this magnification bias may not be applicable in practice as many galaxy samples have complex, often implicit, selection functions. We propose and test a procedure to quantify the magnification bias induced in clustering and galaxy-galaxy lensing (GGL) signals in galaxy samples subject to a selection function beyond a simple flux limit. The method employs realistic mock data to …
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…
We assess the effect of magnification bias on the $E_G$ statistic for probing gravity. $E_G$, a statistic constructed from power spectrum estimates of both weak lensing and redshift space distortions (RSD), directly tests general relativity (GR) while in principle being independent of clustering bias. This property has motivated its recent use in multiple tests of GR. Recent work has suggested that the magnification bias of galaxies due to foreground matter perturbations breaks the bias-independence of the $E_G$ statistic. The magnitude of this effect is very sensitive to the clustering and ma…
Measuring and calibrating relations between cluster observables is critical for resource-limited studies. The mass-richness relation of clusters offers an observationally inexpensive way of estimating masses. Its calibration is essential for cluster and cosmological studies, especially for high-redshift clusters. Weak gravitational lensing magnification is a promising and complementary method to shear studies, that can be applied at higher redshifts. We employed the weak lensing magnification method to calibrate the mass-richness relation up to a redshift of 1.4. We used the Spitzer Adaptation…
Evolution of structure growth during dark energy domination: Insights from the cross-correlation of DESI galaxies with CMB lensing and galaxy magnification
Magnification bias is a gravitational lensing effect that is normally overlooked because it is considered sub-optimal in comparison with the lensing shear. Thanks to the demonstrated optimal characteristics of the sub-millimetre galaxies (SMGs) for lensing analysis, in this work we were able to measure the magnification bias produced by a sample of QSOs acting as lenses, $0.2<z<1.0$, on the SMGs observed by Herschel at $1.2<z<4.0$. Two different methodologies were successfully applied: the traditional cross-correlation function approach and the Davis-Peebles estimator through stacking techniqu…
We present a detection of the enhancement in the number densities of background galaxies induced from lensing magnification and use it to test the Sunyaev-Zel'dovich effect (SZE) inferred masses in a sample of 19 galaxy clusters with median redshift $z\simeq0.42$ selected from the South Pole Telescope SPT-SZ survey. Two background galaxy populations are selected for this study through their photometric colours; they have median redshifts ${z}_{\mathrm{median}}\simeq0.9$ (low-$z$ background) and ${z}_{\mathrm{median}}\simeq1.8$ (high-$z$ background). Stacking these populations, we detect the ma…
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…
Using data from the Pantheon SN Ia compilation and the Sloan Digital Sky Survey (SDSS), we propose an estimator for weak lensing convergence incorporating positional and photometric data of foreground galaxies. The correlation between this and the Hubble diagram residuals of the supernovae has $3.6σ$ significance, and is consistent with weak lensing magnification due to dark matter halos centered on galaxies. We additionally constrain the properties of the galactic haloes, such as the mass-to-light ratio $Γ$ and radial profile of the halo matter density $ρ(r)$. We derive a new relationship for…
We present a Bayesian framework to account for the magnification bias from both strong and weak gravitational lensing in estimates of high-redshift galaxy luminosity functions. We illustrate our method by estimating the $z\sim8$ UV luminosity function using a sample of 97 Y-band dropouts (Lyman break galaxies) found in the Brightest of Reionizing Galaxies (BoRG) survey and from the literature. We find the luminosity function is well described by a Schechter function with characteristic magnitude of $M^\star = -19.85^{+0.30}_{-0.35}$, faint-end slope of $α= -1.72^{+0.30}_{-0.29}$, and number de…
We consider the effect of lensing magnification on high redshift sources in the case that magnification varies on the sky, as expected in wide fields of view or within observed galaxy clusters. We give expressions for number counts, flux and flux variance as integrals over the probability distribution of the magnification. We obtain these through a simple mapping between averages over the observed sky and over the magnification probability distribution in the source plane. Our results clarify conflicting expressions in the literature and can be used to calculate a variety of magnification effe…
Prospects for measuring the Doppler magnification dipole with LSST and DESI
Jodrell Bank Centre for Astrophysics, University of Manchester（曼彻斯特大学乔德雷尔银行天体物理学中心）；Department of Physics and Astronomy, University of Western Cape（西开普大学物理与天文系）；Institute for Astronomy, University of Edinburgh, Royal Observatory（爱丁堡大学天文研究所皇家天文台）；School of Physical and Chemical Sciences, Queen Mary University of London（伦敦大学玛丽女王学院物理与化学科学学院）
The magnification effect of gravitational lensing is a powerful probe of the distribution of matter in the universe, yet it is frequently overlooked due to the fact that its signal to noise is smaller than that of lensing shear. Because its systematic errors are quite different from those of shear, magnification is nevertheless an important approach with which to study the distribution of large scale structure. We present lensing mass profiles of spectroscopic luminous red galaxies (LRGs) and galaxy clusters determined through measurements of the weak lensing magnification of photometric LRGs …
We study lensing magnification of source galaxies by intervening galaxy groups and clusters using a halo model. Halos are modeled with truncated NFW profiles with ellipticity added to their lensing potential and propagated to observable lensing statistics. We present the formalism to calculate observable effects due to a distribution of halos of different masses at different redshifts along the l ine of sight. We calculate the effects of magnification on the number counts of high-redshift galaxies. Using BLAST survey data for submillimeter galaxies (SMGs), we find that magnification affects th…
We describe a new method for measuring galaxy magnification due to weak gravitational lensing. Our method makes use of a tight scaling relation between galaxy properties that are modified by gravitational lensing, such as apparent size, and other properties that are not, such as surface brightness. In particular, we use a version of the well-known fundamental plane relation for early type galaxies. This modified "photometric fundamental plane" replaces velocity dispersions with photometric galaxy properties, thus obviating the need for spectroscopic data. We present the first detection of magn…
Following on our purpose of developing a unified pipeline for large-scale structure data analysis with angular (i.e. harmonic-space) power spectra, we now include the weak lensing effect of magnification bias on galaxy clustering in a publicly available, modular parameter estimation code. We thus forecast constraints on the parameters of the concordance cosmological model, dark energy, and modified gravity theories from galaxy clustering tomographic angular power spectra. We find that a correct modelling of magnification is crucial in order not to bias the estimation of cosmological parameters…
We propose a novel method to detect cosmic magnification signals by cross-correlating foreground convergence fields constructed from galaxy shear measurements with background galaxy positional distributions, namely shear-number density correlation. We apply it to the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) survey data. With 27 non-independent data points and their full covariance, $χ_0^2\approx 34.1$ and $χ_T^2\approx 24.0$ with respect to the null and the cosmological model with the parameters from HSC shear correlation analyses in Hamana et al. 2020 (arXiv:1906.06041), respectiv…
Accurate measurement of galaxy cluster masses is an essential component not only in studies of cluster physics, but also for probes of cosmology. However, different mass measurement techniques frequently yield discrepant results. The SDSS MaxBCG catalog's mass-richness relation has previously been constrained using weak lensing shear, Sunyaev-Zeldovich (SZ), and X-ray measurements. The mass normalization of the clusters as measured by weak lensing shear is >~25% higher than that measured using SZ and X-ray methods, a difference much larger than the stated measurement errors in the analyses. We…
Similar to the magnification of the galaxies' fluxes by gravitational lensing, the extinction of the fluxes by comic dust, whose existence is recently detected by Menard et al (2009), also modify the distribution of a flux-selected galaxy sample. We study the anisotropic distortion by dust extinction to the 3D galaxy correlation function, including magnification bias and redshift distortion at the same time. We find the extinction distortion is most significant along the line of sight and at large separations, similar to that by magnification bias. The correction from dust extinction is negati…
We study the impact of lensing magnification on the observed three-dimensional galaxy clustering in redshift space. We used the RayGal suite of N-body simulations, from which we extracted samples of dark matter particles and haloes in the redshift regime of interest for future large redshift surveys. Several magnitude-limited samples were built that reproduce various levels of magnification bias ranging from s = 0 to s = 1.2, where s is the logarithmic slope of the cumulative magnitude number counts, in three redshift intervals within 1 < z < 1.95. We studied the two-point correlation function…
Gravitational lensing magnification is measured with a significance of 9.7 sigma on a large sample of galaxy clusters in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). This survey covers ~154 deg^2 and contains over 18,000 cluster candidates at redshifts 0.2 <= z <= 0.9, detected using the 3D-Matched Filter cluster-finder of Milkeraitis et al. (2010). We fit composite-NFW models to the ensemble, accounting for cluster miscentering, source-lens redshift overlap, as well as nearby structure (the 2-halo term), and recover mass estimates of the cluster dark matter halos in range of …
Measuring weak lensing cosmic magnification signal is very challenging due to the overwhelming intrinsic clustering in the observed galaxy distribution. In this paper, we modify the Internal Linear Combination (ILC) method to reconstruct the lensing signal with an extra constraint to suppress the intrinsic clustering. To quantify the performance, we construct a realistic galaxy catalogue for the LSST-like photometric survey, covering $20\,000\ °^2$ with mean source redshift at $z_s\sim 1$. We find that the reconstruction performance depends on the width of the photo-z bin we choose. Due to the…
We present a comprehensive analysis of strong-lensing, weak-lensing shear and magnification data for a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters selected from the CLASH survey. Our analysis combines constraints from 16-band HST observations and wide-field multi-color imaging taken primarily with Subaru/Suprime-Cam. We reconstruct surface mass density profiles of individual clusters from a joint analysis of the full lensing constraints, and determine masses and concentrations for all clusters. We find internal consistency of the ensemble mass calibration to be $\le 5\%…
Weak lensing surveys exploit measurements of galaxy ellipticities. These measurements are subject to errors which degrade the cosmological information that can be extracted from the surveys. Here we propose a way of using the galaxy data themselves to calibrate the measurement errors. In particular, the cosmic shear field, which causes the galaxies to appear elliptical, also changes their sizes and fluxes. Information about the sizes and fluxes of the galaxies can be added to the shape information to obtain more robust information about the cosmic shear field. The net result will be tighter co…
We investigate the importance of lensing magnification for estimates of galaxy clustering and its cross-correlation with shear for the photometric sample of Euclid. Using updated specifications, we study the impact of lensing magnification on the constraints and the shift in the estimation of the best fitting cosmological parameters that we expect if this effect is neglected. We follow the prescriptions of the official Euclid Fisher matrix forecast for the photometric galaxy clustering analysis and the combination of photometric clustering and cosmic shear. The slope of the luminosity function…
We present forecast results for constraining the primordial non-Gaussianity from photometric surveys through a large-scale enhancement of the galaxy clustering amplitude. In photometric surveys, the distribution of observed galaxies at high redshifts suffers from the gravitational-lensing magnification, which systematically alters the number density for magnitude-limited galaxy samples. We estimate size of the systematic bias in the best-fit cosmological parameters caused by the magnification effect, particularly focusing on the primordial non-Gaussianity. For upcoming deep and/or wide photome…
SN HFF14Tom is a Type Ia Supernova (SN) discovered at z = 1.3457 +- 0.0001 behind the galaxy cluster Abell 2744 (z = 0.308). In a cosmology-independent analysis, we find that HFF14Tom is 0.77 +- 0.15 magnitudes brighter than unlensed Type Ia SNe at similar redshift, implying a lensing magnification of mu_obs = 2.03 +- 0.29. This observed magnification provides a rare opportunity for a direct empirical test of galaxy cluster lens models. Here we test 17 lens models, 13 of which were generated before the SN magnification was known, qualifying as pure "blind tests". The models are collectively fa…
In this paper, I investigated the Doppler magnification effect in the flux-limited galaxy number counts with finite redshift bin width. In contradiction with our intuition, the number counts correction formula for different redshift bin are different. For the redshift window as delta function and constant function, the correction formulas have been derived analytically in this paper. These two windows correspond to two extreme cases(i.e. extremely narrow bin and extremely broad bin). An simulation have been implemented to test these formulas. The simulation results indicate the perturbation ch…
In gravitational lensing, the magnification effect changes the luminosity and size of a background galaxy. If the image sizes are not small compared to the scale over which the magnification and shear vary, higher-order distortions occur which are termed differential magnification. We give an approximation of the magnification gradient for several halo models. Assuming a symmetric distribution of source brightness, estimates for the differential magnification are obtained and then tested with simulations. One of the main uncertainties of our estimators comes from the finite resolution of the i…
We study the effects on the number counts of sub-millimetre galaxies due to gravitational lensing. We explore the effects on the magnification cross section due to halo density profiles, ellipticity and cosmological parameter (the power-spectrum normalisation $σ_8$). We show that the ellipticity does not strongly affect the magnification cross section in gravitational lensing while the halo radial profiles do. Since the baryonic cooling effect is stronger in galaxies than clusters, galactic haloes are more concentrated. In light of this, a new scenario of two halo population model is explored …
Spatial correlations of the observed sizes and luminosities of galaxies can be used to estimate the magnification that arises through weak gravitational lensing. However, the intrinsic prop- erties of galaxies can be similarly correlated through local physical effects, and these present a possible contamination to the weak lensing estimation. In an earlier paper (Ciarlariello et al. 2015) we modelled the intrinsic size correlations using the halo model, assuming the galaxy sizes reflect the mass in the associated halo. Here we extend this work to consider galaxy magnitudes and show that these …
Warm Dark Matter (WDM) models offer an attractive alternative to the current Cold Dark Matter (CDM) cosmological model. We present a novel method to differentiate between WDM and CDM cosmologies, namely using weak lensing; this provides a unique probe as it is sensitive to all the "matter in the beam", not just dark matter haloes and the galaxies that reside in them, but also the diffuse material between haloes. We compare the weak lensing maps of CDM clusters to those in a WDM model corresponding to a thermally produced $0.5$~keV dark matter particle. Our analysis clearly shows that the weak …
