We present a Subaru weak lensing measurement of ACT-CL J0022.2 - 0036 , one of the most luminous , high-redshift ( z = 0.81 ) Sunyaev-Zel ’ dovich ( SZ ) clusters discovered in the 268 deg ^ { 2 } equatorial region survey of the Atacama Cosmology Telescope that overlaps with SDSS Stripe 82 field .
Ours is the first weak lensing study with Subaru at such high redshifts .
For the weak lensing analysis using i ^ { \prime } -band images , we use a model-fitting ( Gauss-Laguerre shapelet ) method to measure shapes of galaxy images , where we fit galaxy images in different exposures simultaneously to obtain best-fit ellipticities taking into account the different PSFs in each exposure .
We also take into account the astrometric distortion effect on galaxy images by performing the model fitting in the world coordinate system .
To select background galaxies behind the cluster at z = 0.81 , we use photometric redshift ( photo- z ) estimates for every galaxy derived from the co-added images of multi-passband Br ^ { \prime } i ^ { \prime } z ^ { \prime } Y , with PSF matching/homogenization .
After a photo- z cut for background galaxy selection , we detect the tangential weak lensing distortion signal with a total signal-to-noise ratio of about 3.7 .
By fitting a Navarro-Frenk-White model to the measured shear profile , we find the cluster mass to be M _ { 200 \bar { \rho } _ { m } } = \left [ 7.5 ^ { +3.2 } _ { -2.8 } ( { stat . } ) ^ { +1.3 } _ { -0.6 } ( { sys% . } ) \right ] \times 10 ^ { 14 } M _ { \odot } / h .
The weak lensing-derived mass is consistent with previous mass estimates based on the SZ observation , with assumptions of hydrostatic equilibrium and virial theorem , as well as with scaling relations between SZ signal and mass derived from weak lensing , X-ray , and velocity dispersion , within the measurement errors .
We also show that the existence of ACT-CL J0022.2 - 0036 at z = 0.81 is consistent with the cluster abundance prediction of the \Lambda -dominated cold dark matter structure formation model .
We thus demonstrate the capability of Subaru-type ground-based images for studying weak lensing of high-redshift clusters .