We develop a novel method of measuring the lensing distortion profiles of clusters with stacking the “ scaled ” amplitudes of background galaxy ellipticities as a function of the “ scaled ” centric radius according to the Navarro-Frenk-White ( NFW ) prediction of each cluster , based on the assumption that the different clusters in a sample follow the universal NFW profile .
First we demonstrate the feasibility of this method using both the analytical NFW model and simulated halos in a suite of high-resolution N -body simulations .
We then apply , as a proof of concept , this method to the Subaru weak lensing data and the XMM / Chandra X-ray observables for a sample of 50 massive clusters in the redshift range 0.15 \leq z \leq 0.3 , where their halo masses differ from each other by up to a factor of 10 .
To estimate the NFW parameters of each cluster , we use the halo mass proxy relation of X-ray observables , based on either the hydrostatic equilibrium or the gas mass , and then infer the halo concentration from the model scaling relation of halo concentration with halo mass .
We evaluate a performance of the NFW scaling analysis by measuring the scatters of 50 cluster lensing profiles relative to the NFW predictions over a range of radii , 0.14 \leq R / [ h ^ { -1 } { Mpc } ] \leq 2.8 .
We found a 4 – 6 \sigma level evidence of the universal NFW profile in 50 clusters , for both the X-ray halo mass proxy relations , although the gas mass appears to be a better proxy of the underlying true mass .
By comparing the measurements with the simulations of cluster lensing profiles taking into account the statistical errors of intrinsic galaxy shapes in the Subaru data , we argue that additional halo mass errors or intrinsic scatters of \sigma ( M _ { 500 c } ) / M _ { 500 c } \sim 0.2 – 0.3 could reconcile a difference between the measurements and the simulations .
This method allows us to some extent to preserve characteristics of individual clusters in the statistical weak lensing analysis , thereby yielding a new means of exploiting the underlying genuine form of the halo mass profile and the halo mass proxy relations via weak lensing information , under the assumption of the existence of the universal profile .