arXiv subjects

Masato Shirasaki

Publications and source records attributed to Masato Shirasaki.

At least 91 records · Page 5Linked to original sources

arXiv2017

Probing the shape and internal structure of dark matter halos with the halo-shear-shear three-point correlation function

Weak lensing three-point statistics are powerful probes of the structure of dark matter halos. We propose to use the correlation of the positions of galaxies with the shapes of background galaxy pairs, known as the halo-shear-shear correlation (HSSC), to measure the mean halo ellipticity and the abundance of subhalos in a statistical manner. We run high-resolution cosmological $N$-body simulations and use the outputs to measure the HSSC for galaxy halos and cluster halos. Non-spherical halos cause a characteristic azimuthal variation of the HSSC, and massive subhalos in the outer region near the virial radius contribute to $\sim10\%$ of the HSSC amplitude. Using the HSSC and its covariance estimated from our $N$-body simulations, we make forecast for constraining the internal structure of dark matter halos with future galaxy surveys. With 1000 galaxy groups with mass greater than $10^{13.5}\, h^{-1}M_{\odot}$, the average halo ellipticity can be measured with an accuracy of ten percent. A spherical, smooth mass distribution can be ruled out at a $\sim5σ$ significance level. The existence of subhalos whose masses are in 1-10 percent of the main halo mass can be detected with $\sim10^4$ galaxies/clusters. We conclude that the HSSC provides valuable information on the structure of dark halos and hence on the nature of dark matter.

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arXiv2017

Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments

We present 108 full-sky gravitational lensing simulation data sets generated by performing multiple-lens plane ray-tracing through high-resolution cosmological $N$-body simulations. The data sets include full-sky convergence and shear maps from redshifts $z=0.05$ to $5.3$ at intervals of $150 \, h^{-1}{\rm Mpc}$ comoving radial distance (corresponding to a redshift interval of $Δz \simeq 0.05$ at the nearby universe), enabling the construction of a mock shear catalog for an arbitrary source distribution up to $z=5.3$. The dark matter halos are identified from the same $N$-body simulations with enough mass resolution to resolve the host halos of the Sloan Digital Sky Survey (SDSS) CMASS and Luminous Red Galaxies (LRGs). Angular positions and redshifts of the halos are provided by a ray-tracing calculation, enabling the creation of a mock halo catalog to be used for galaxy-galaxy and cluster-galaxy lensing. The simulation also yields maps of gravitational lensing deflections for a source redshift at the last scattering surface, and we provide 108 realizations of lensed cosmic microwave background (CMB) maps in which the post-Born corrections caused by multiple light scattering are included. We present basic statistics of the simulation data, including the angular power spectra of cosmic shear, CMB temperature and polarization anisotropies, galaxy-galaxy lensing signals for halos, and their covariances. The angular power spectra of the cosmic shear and CMB anisotropies agree with theoretical predictions within $5\%$ up to $\ell = 3000$ (or at an angular scale $θ> 0.5$ arcsin). The simulation data sets are generated primarily for the ongoing Subaru Hyper Suprime-Cam survey but are freely available for download at http://cosmo.phys.hirosaki-u.ac.jp/takahasi/allsky_raytracing.

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arXiv2017

Galaxy-galaxy weak gravitational lensing in $f(R)$ gravity

We present an analysis of galaxy-galaxy weak gravitational lensing (GGL) in chameleon $f(R)$ gravity - a leading candidate of non-standard gravity models. For the analysis we have created mock galaxy catalogues based on dark matter haloes from two sets of numerical simulations, using a halo occupation distribution (HOD) prescription which allows a redshift dependence of galaxy number density. To make a fairer comparison between the $f(R)$ and $Λ$CDM models, their HOD parameters are tuned so that the galaxy two-point correlation functions in real space (and therefore the projected two-point correlation functions) match. While the $f(R)$ model predicts an enhancement of the convergence power spectrum by up to $\sim30\%$ compared to the standard $Λ$CDM model with the same parameters, the maximum enhancement of GGL is only half as large and less than 5\% on separations above $\sim1$-$2h^{-1}$Mpc, because the latter is a cross correlation of shear (or matter, which is more strongly affected by modified gravity) and galaxy (which is weakly affected given the good match between galaxy auto correlations in the two models) fields. We also study the possibility of reconstructing the matter power spectrum by combination of GGL and galaxy clustering in $f(R)$ gravity. We find that the galaxy-matter cross correlation coefficient remains at unity down to $\sim2$-$3h^{-1}$Mpc at relevant redshifts even in $f(R)$ gravity, indicating joint analysis of GGL and galaxy clustering can be a powerful probe of matter density fluctuations in chameleon gravity. The scale dependence of the model differences in their predictions of GGL can potentially allow to break the degeneracy between $f(R)$ gravity and other cosmological parameters such as $Ω_m$ and $σ_8$.

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arXiv2017

Robust covariance estimation of galaxy-galaxy weak lensing: validation and limitation of jackknife covariance

We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations and their inherent halo catalogs. Using the mock catalog to study the error covariance matrix of galaxy-galaxy weak lensing, we compare the full covariance with the "jackknife" (JK) covariance, the method often used in the literature that estimates the covariance from the resamples of the data itself. We show that there exists the variation of JK covariance over realizations of mock lensing measurements, while the average JK covariance over mocks can give a reasonably accurate estimation of the true covariance up to separations comparable with the size of JK subregion. The scatter in JK covariances is found to be $\sim10\%$ after we subtract the lensing measurement around random points. However, the JK method tends to underestimate the covariance at the larger separations, more increasingly for a survey with a higher number density of source galaxies. We apply our method to the the Sloan Digital Sky Survey (SDSS) data, and show that the 48 mock SDSS catalogs nicely reproduce the signals and the JK covariance measured from the real data. We then argue that the use of the accurate covariance, compared to the JK covariance, allows us to use the lensing signals at large scales beyond a size of the JK subregion, which contains cleaner cosmological information in the linear regime.

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arXiv2017

Large-scale clustering as a probe of the origin and the host environment of fast radio bursts

We propose to use degree-scale angular clustering of fast radio bursts (FRBs) to identify their origin and the host galaxy population. We study the information content in autocorrelation of the angular positions and dispersion measures (DM) and in cross-correlation with galaxies. We show that the cross-correlation with Sloan Digital Sky Survey (SDSS) galaxies will place stringent constraints on the mean physical quantities associated with FRBs. If $\sim$10,000 FRBs are detected with $\lesssim \rm deg$ resolution in the SDSS field, the clustering analysis with the intrinsic DM scatter of $100\, {\rm pc}/{\rm cm}^3$ can constrain the global abundance of free electrons at $z\lt1$ and the large-scale bias of FRB host galaxies (the statistical relation between the distribution of host galaxies and cosmic matter density field) with fractional errors (with a $68\%$ confidence level) of $\sim10\%$ and $\sim20\%$, respectively. The mean near-source dispersion measure and the delay time distribution of FRB rates relative to the global star forming rate can be also determined by combining the clustering and the probability distribution function of DM. Our approach will be complementary to high-resolution ($\ll {\rm deg}$) event localization using e.g., VLA and VLBI for identifying the origin of FRBs and the source environment. We strongly encourage future observational programs such as CHIME, UTMOST, and HIRAX to survey FRBs in the SDSS field.

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arXiv2017

The imprint of $f(R)$ gravity on weak gravitational lensing II : Information content in cosmic shear statistics

We investigate the information content of various cosmic shear statistics on the theory of gravity. Focusing on the Hu-Sawicki-type $f(R)$ model, we perform a set of ray-tracing simulations and measure the convergence bispectrum, peak counts and Minkowski functionals. We first show that while the convergence power spectrum does have sensitivity to the current value of extra scalar degree of freedom $|f_{\rm R0}|$, it is largely compensated by a change in the present density amplitude parameter $σ_{8}$ and the matter density parameter $Ω_{\rm m0}$. With accurate covariance matrices obtained from 1000 lensing simulations, we then examine the constraining power of the three additional statistics. We find that these probes are indeed helpful to break the parameter degeneracy, which can not be resolved from the power spectrum alone. We show that especially the peak counts and Minkowski functionals have the potential to rigorously (marginally) detect the signature of modified gravity with the parameter $|f_{\rm R0}|$ as small as $10^{-5}$ ($10^{-6}$) if we can properly model them on small ($\sim 1\, \mathrm{arcmin}$) scale in a future survey with a sky coverage of 1,500 squared degrees. We also show that the signal level is similar among the additional three statistics and all of them provide complementary information to the power spectrum. These findings indicate the importance of combining multiple probes beyond the standard power spectrum analysis to detect possible modifications to General Relativity.

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arXiv2016

Statistical connection of peak counts to power spectrum and moments in weak lensing field

The number density of local maxima of weak lensing field, referred to as weak-lensing peak counts, can be used as a cosmological probe. However, its relevant cosmological information is still unclear. We study the relationship between the peak counts and other statistics in weak lensing field by using 1000 ray-tracing simulations. We construct a local transformation of lensing field $\cal K$ to a new Gaussian field $y$, named local-Gaussianized transformation. We calibrate the transformation with numerical simulations so that the one-point distribution and the power spectrum of $\cal K$ can be reproduced from a single Gaussian field $y$ and monotonic relation between $y$ and $\cal K$. Therefore, the correct information of two-point clustering and any order of moments in weak lensing field should be preserved under local-Gaussianized transformation. We then examine if local-Gaussianized transformation can predict weak-lensing peak counts in simulations. The local-Gaussianized transformation is insufficient to explain weak-lensing peak counts in the absence of shape noise. The prediction by local-Gaussianized transformation underestimates the simulated peak counts with a level of $\sim20-30\%$ over a wide range of peak heights. Local-Gaussianized transformation can predict the weak-lensing peak counts with a $\sim10\%$ accuracy in the presence of shape noise. Our analyses suggest that the cosmological information beyond power spectrum and its moments would be necessary to predict the weak-lensing peak counts with a percent-level accuracy, which is an expected statistical uncertainty in upcoming wide-field galaxy surveys.

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arXiv2016

Cosmological constraints on dark matter annihilation and decay: Cross-correlation analysis of the extragalactic $γ$-ray background and cosmic shear

We derive constraints on dark matter (DM) annihilation cross section and decay lifetime from cross-correlation analyses of the data from Fermi-LAT and weak lensing surveys that cover a wide area of $\sim660$ squared degrees in total. We improve upon our previous analyses by using an updated extragalactic $γ$-ray background data reprocessed with the Fermi Pass 8 pipeline, and by using well-calibrated shape measurements of about twelve million galaxies in the Canada-France-Hawaii Lensing Survey (CFHTLenS) and Red-Cluster-Sequence Lensing Survey (RCSLenS). We generate a large set of full-sky mock catalogs from cosmological $N$-body simulations and use them to estimate statistical errors accurately. The measured cross correlation is consistent with null detection, which is then used to place strong cosmological constraints on annihilating and decaying DM. For leptophilic DM, the constraints are improved by a factor of $\sim100$ in the mass range of O(1) TeV when including contributions from secondary $γ$ rays due to the inverse-Compton upscattering of background photons. Annihilation cross-sections of $\langle σv \rangle \sim 10^{-23}\, {\rm cm}^3/{\rm s}$ are excluded for TeV-scale DM depending on channel. Lifetimes of $\sim 10^{25}$ sec are also excluded for the decaying TeV-scale DM. Finally, we apply this analysis to wino DM and exclude the wino mass around 200 GeV. These constraints will be further tightened, and all the interesting wino DM parameter region can be tested, by using data from future wide-field cosmology surveys.

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arXiv2016

Covariance in the Thermal SZ-Weak Lensing Mass Scaling Relation of Galaxy Clusters

The thermal Sunyaev-Zel'dovich (tSZ) effect signal is widely recognized as a robust mass proxy of galaxy clusters with small intrinsic scatter. However, recent observational calibration of the tSZ scaling relation using weak lensing (WL) mass exhibits considerably larger scatter than the intrinsic scatter predicted from numerical simulations. This raises a question as to whether we can realize the full statistical power of ongoing and upcoming tSZ-WL observations of galaxy clusters. In this work, we investigate the origin of observed scatter in the tSZ-WL scaling relation, using mock maps of galaxy clusters extracted from cosmological hydrodynamic simulations. We show that the inferred intrinsic scatter from mock tSZ-WL analyses is considerably larger than the intrinsic scatter measured in simulations, and comparable to the scatter in the observed tSZ-WL relation. We show that this enhanced scatter originates from the combination of the projection of correlated structures along the line of sight and the uncertainty in the cluster radius associated with WL mass estimates, causing the amplitude of the scatter to depend on the covariance between tSZ and WL signals. We present a statistical model to recover the unbiased cluster scaling relation and cosmological parameter by taking into account the covariance in the tSZ-WL mass relation from multi-wavelength cluster surveys.

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arXiv2016

Cosmological Constraint on the Light Gravitino Mass from CMB Lensing and Cosmic Shear

Light gravitinos of mass $\lesssim \mathcal{O} (10)$ eV are of particular interest in cosmology, offering various baryogenesis scenarios without suffering from the cosmological gravitino problem. The gravitino may contribute considerably to the total matter content of the Universe and affect structure formation from early to present epochs. After the gravitinos decouple from other particles in the early Universe, they free-stream and consequently suppress density fluctuations of (sub-)galactic length scales. Observations of structure at the relevant length-scales can be used to infer or constrain the mass and the abundance of light gravitinos. We derive constraints on the light gravitino mass using the data of cosmic microwave background (CMB) lensing from Planck and of cosmic shear from the Canada France Hawaii Lensing Survey, combined with analyses of the primary CMB anisotropies and the signature of baryon acoustic oscillations in galaxy distributions. The obtained constraint on the gravitino mass is $m_{3/2} < 4.7$ eV (95% C.L.), which is substantially tighter than the previous constraint from clustering analysis of Ly-$α$ forests.

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arXiv2016

The imprint of $f(R)$ gravity on weak gravitational lensing I: Connection between observables and large scale structure

We study the effect of $f(R)$ gravity on the statistical properties of various large-scale structures which can be probed in weak gravitational lensing measurements. A set of ray-tracing simulations of gravitational lensing in $f(R)$ gravity enables us to explore cosmological information on (i) stacking analyses of weak lensing observables and (ii) peak statistics in reconstructed lensing mass maps. For the $f(R)$ model proposed by Hu \& Sawicki, the measured lensing signals of dark matter haloes in the stacking analysis would show a $\simlt10\%$ difference between the standard $Λ$CDM and the $f(R)$ model when the additional degree of freedom in $f(R)$ model would be $|f_{\rm R0}|\sim10^{-5}$. Among various large-scale structures to be studied in stacking analysis, troughs, i.e, underdensity regions in projected plane of foreground massive haloes, could be promising to constrain the model with $|f_{\rm R0}|\sim10^{-5}$, while stacking analysis around voids is found to be difficult to improve the constraint of $|f_{\rm R0}|$ even in future lensing surveys with a sky coverage of $\sim1000$ square degrees. On the peak statistics, we confirm the correspondence between local maxima and dark matter haloes along the line of sight, regardless of the modification of gravity in our simulation. Thus, the number count of high significance local maxima would be useful to probe the mass function of dark matter haloes even in the $f(R)$ model with $|f_{\rm R0}|\simlt10^{-5}$. We also find that including local minima in lensing mass maps would be helpful to improve the constant on $f(R)$ gravity down to $|f_{\rm R0}|=10^{-5}$ in ongoing weak lensing surveys.

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arXiv2015

Cross-Correlation of the Extragalactic Gamma-ray Background with Luminous Red Galaxies

Measurements of the cross-correlation between the extragalactic gamma-ray background (EGB) and large-scale structure provide a novel probe of dark matter on extragalactic scales. We focus on luminous red galaxies (LRGs) as optimal targets to search for the signal of dark matter annihilation. We measure the cross-correlation function of the EGB taken from the Fermi Large Area Telescope with the LRGs from the Sloan Digital Sky Survey. Statistical errors are calculated using a large set of realistic mock LRG catalogs. The amplitude of the measured cross-correlation is consistent with null detection. Based on an accurate theoretical model of the distribution of dark matter associated with LRGs, we exclude dark matter annihilation cross-sections over $\langle σv\rangle =3\times10^{-25}-10^{-26}\, {\rm cm}^3 \,{\rm s}^{-1}$ for a 10 GeV dark matter. We further investigate systematic effects due to uncertainties in the Galactic gamma-ray foreground emission, which we find to be an order of magnitude smaller than the current statistical uncertainty. We also estimate the contamination from astrophysical sources in the LRGs by using known scaling relations between gamma-ray luminosity and star-formation rate, finding them to be negligibly small. Based on these results, we suggest that LRGs remain ideal targets for probing dark matter annihilation with future EGB measurement and galaxy surveys. Increasing the number of LRGs in upcoming galaxy surveys such as LSST would lead to big improvements of factors of several in sensitivity.

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arXiv2015

Probing cosmology with weak lensing selected clusters II: Dark energy and f(R) gravity models

Ongoing and future wide-field galaxy surveys can be used to locate a number of clusters of galaxies with cosmic shear measurement alone. We study constraints on cosmological models using statistics of weak lensing selected galaxy clusters. We extend our previous theoretical framework to model the statistical properties of clusters in variants of cosmological models as well as in the standard $Λ$CDM model. Weak lensing selection of clusters does not rely on the conventional assumption such as the relation between luminosity and mass and/or hydrostatic equilibrium, but a number of observational effects compromise robust identification. We use a large set of realistic mock weak-lensing catalogs as well as analytic models to perform a Fisher analysis and make forecast for constraining two competing cosmological models, $w$CDM model and $f(R)$ model proposed by Hu & Sawicki, with our lensing statistics. We show that weak lensing selected clusters are excellent probe of cosmology when combined with cosmic shear power spectrum even in presence of galaxy shape noise and masked regions. With the information of weak lensing selected clusters, the precision of cosmological parameter estimate can be improved by a factor of $\sim1.6$ and $\sim8$ for $w$CDM model and $f(R)$ model, respectively. Hyper Suprime-Cam survey with sky coverage of $1250$ squared degrees can constrain the equation of state of dark energy $w_{0}$ with a level of $Δw_0 \sim0.1$. It can also constrain the additional scalar degree of freedom in $f(R)$ model with a level of $|f_{R0}| \sim5\times10^{-6}$, when constraints from cosmic microwave background measurements are incorporated. Future weak lensing surveys with sky coverage of $20,000$ squared degrees will place tighter constraints on $w_{0}$ and $|f_{R0}|$ even without cosmic microwave background measurements.

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arXiv2015

Probing cosmology with weak lensing selected clusters I: Halo approach and all-sky simulations

We explore a variety of statistics of clusters selected with cosmic shear measurement by utilizing both analytic models and large numerical simulations. We first develop a halo model to predict the abundance and the clustering of weak lensing selected clusters. Observational effects such as galaxy shape noise are included in our model. We then generate realistic mock weak lensing catalogs to test the accuracy of our analytic model. To this end, we perform full-sky ray-tracing simulations that allow us to have multiple realizations of a large continuous area. We model the masked regions on the sky using the actual positions of bright stars, and generate 200 mock weak lensing catalogs with sky coverage of ~1000 squared degrees. We show that our theoretical model agrees well with the ensemble average of statistics and their covariances calculated directly from the mock catalogues. With a typical selection threshold, ignoring shape noise correction causes overestimation of the clustering of weak lensing selected clusters with a level of about 10%, and shape noise correction boosts the cluster abundance by a factor of a few. We calculate the cross-covariances using the halo model with accounting for the effective reduction of the survey area due to masks. The covariance of the cosmic shear auto power spectrum is affected by the mode-coupling effect that originates from sky masking. Our model and the results can be readily used for cosmological analysis with ongoing and future weak lensing surveys.

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arXiv2015

Impact of Baryonic Processes on Weak Lensing Cosmology: Power Spectrum, Non-Local Statistics, and Parameter Bias

We study the impact of baryonic physics on cosmological parameter estimation with weak lensing surveys. We run a set of cosmological hydrodynamics simulations with different galaxy formation models. We then perform ray-tracing simulations through the total matter density field to generate 100 independent convergence maps of 25 ${\rm deg}^2$ field-of-view, and use them to examine the ability of the following three lensing statistics as cosmological probes; power spectrum, peak counts, and Minkowski functionals. For the upcoming wide-field observations such as Subaru Hyper Suprime-Cam (HSC) survey with a sky coverage of 1400 ${\rm deg}^2$, these three statistics provide tight constraints on the matter density, density fluctuation amplitude, and dark energy equation of state, but parameter bias is induced by the baryonic processes such as gas cooling and stellar feedback. The bias can be significant when the statistical errors become small in future observations with a much larger survey area. We find the bias is induced in different directions in the parameter space depending on the statistics employed. While the two-point statistic, i.e. power spectrum, yields robust results against baryonic effects, the overall constraining power is weak compared with peak counts and Minkowski functionals. On the other hand, using one of peak counts or Minkowski functionals, or combined analysis with multiple statistics, results in biased parameter estimate. The bias can be as large as $1σ$ for HSC survey, and will be more significant for upcoming wider area surveys. We suggest to use an optimized combination so that the baryonic effects on parameter estimation are mitigated. Such `calibrated' combination can place stringent and robust constraints on cosmological parameters.

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arXiv2014

Weak gravitational lensing as a probe of physical properties of substructures in dark matter halos

We propose a novel method to select satellite galaxies in outer regions of galaxy groups or clusters using weak gravitational lensing. The method is based on the theoretical expectation that the tangential shear pattern around satellite galaxies would appear with negative values at an offset distance from the center of the main halo. We can thus locate the satellite galaxies statistically with an offset distance of several lensing smoothing scales by using the standard reconstruction of surface mass density maps from weak lensing observation. We test the idea using high-resolution cosmological simulations. We show that subhalos separated from the center of the host halo are successfully located even without assuming the position of the center. For a number of such subhalos, the characteristic mass and offset length can be also estimated on a statistical basis. We perform a Fisher analysis to show how well upcoming weak lensing surveys can constrain the mass density profile of satellite galaxies. In the case of the Large Synoptic Survey Telescope with a sky coverage of 20,000 square degrees, the mass of the member galaxies in the outer region of galaxy clusters can be constrained with an accuracy of ~0.1 dex for galaxy clusters with mass 10^14 Msun/h at z=0.15. Finally we explore the detectability of tidal stripping features for subhalos having a wide range of masses of 10^11-10^13 Msun/h.

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arXiv2014

Cross-Correlation of Cosmic Shear and Extragalactic Gamma-ray Background: Constraints on the Dark Matter Annihilation Cross-Section

We present the first measurement of the cross-correlation of weak gravitational lensing and the extragalactic gamma-ray background emission using data from the Canada-France-Hawaii Lensing Survey and the Fermi Large Area Telescope. The cross-correlation is a powerful probe of signatures of dark matter annihilation, because both cosmic shear and gamma-ray emission originate directly from the same DM distribution in the universe, and it can be used to derive constraints on dark matter annihilation cross-section. We show that the measured lensing-gamma correlation is consistent with a null signal. Comparing the result to theoretical predictions, we exclude dark matter annihilation cross sections of =10^{-24}-10^{-25} cm^3 s^-1 for a 100 GeV dark matter. If dark matter halos exist down to the mass scale of 10^-6 M_sun, we are able to place constraints on the thermal cross sections ~ 3 x 10^{-26} cm^3 s^-1 for a 10 GeV dark matter annihilation into tau^{+} tau^{-}. Future gravitational lensing surveys will increase sensitivity to probe annihilation cross sections of ~ 5 x 10^{-26} cm^3 s^-1 even for a 100 GeV dark matter. Detailed modeling of the contributions from astrophysical sources to the cross correlation signal could further improve the constraints by ~ 40-70 %.

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arXiv2014

Statistical and Systematic Errors in Measurement of Weak-Lensing Minkowski Functionals: Application to Canada-France-Hawaii Lensing Survey

The measurement of cosmic shear using weak gravitational lensing is a challenging task that involves a number of complicated procedures. We study in detail the systematic errors in the measurement of weak lensing Minkowski Functionals (MFs). Specifically, we focus on systematics associated with galaxy shape measurements, photometric redshift errors, and shear calibration correction. We first generate mock weak-lensing catalogs that directly incorporate the actual observational characteristics of the Canada-France-Hawaii Lensing Survey (CFHTLenS). We then perform a Fisher analysis using the large set of mock catalogs for various cosmological models. We find that the statistical error associated with the observational effects degrades the cosmological parameter constraints by a factor of a few. The Subaru Hyper Suprime-Cam (HSC) survey with a sky coverage of ~1400 deg2 will constrain the dark energy equation of the state parameter with an error of Delta w_0 ~ 0.25 by the lensing MFs alone, but biases induced by the systematics can be comparable to the 1-sigma error. We conclude that the lensing MFs are powerful statistics beyond the two-point statistics, only if well-calibrated measurement of both the redshifts and the shapes of source galaxies is performed. Finally, we analyze the CFHTLenS data to explore the ability of the MFs to break degeneracies between a few cosmological parameters. Using a combined analysis of the MFs and the shear correlation function, we derive the matter density Omega_m0= 0.256+0.054-0.046.

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