Weak Lensing by Large‐Scale Structure with the FIRST Radio Survey

We present the first measurement of weak lensing by large-scale structure on 1-4 degree scales based on the FIRST Radio Survey, a quarter-sky, 20-cm survey produced with the NRAO Very Large Array (VLA). The large angular scales provide an unique measurement in the linear regime of the matter power spectrum. We use the shapelet method to estimate the shear of radio sources derived directly from the Fourier (uv) plane. With realistic simulations we verify that the method yields unbiased shear estimators. We quantify and correct for the systematic effects which can produce spurious shears, analytically and with simulations. We measure the shear correlation functions on angular scales of 0. 5-40 degrees, and compute the corresponding aperture mass statistics. On 1-4 degrees scales, we find that the B-modes are consistent with zero, and detect a lensing E-mode signal significant at the 3. 0 sigma level. After removing radio sources with an optical counterpart, the E-mode signal increases by 10-20%, as expected for a lensing signal derived from more distant sources. We use the E-mode measurement to constrain the mass power spectrum normalization sigma₈ and the median redshift zₘ of the unidentified radio sources. We find sigma₈* (zₘ/2) ^ (0. 6) ~ 1. 0 +/- 0. 2, where the 1 sigma error bars include statistical errors, cosmic variance, and systematics. This is consistent with earlier determinations of sigma₈, and with our current knowledge of the redshift distribution of radio sources. Taking the prior sigma₈ = 0. 9 +/- 0. 1 (68%CL) from the WMAP experiment, this corresponds to zₘ = 2. 2 +/- 0. 9 (68%CL) for radio sources without optical counterparts. Our results offer promising prospects for precision measurements of cosmic shear with future radio interferometers such as LOFAR and the SKA.