Weak lensing by large-scale structure with the first radio survey

We present the first measurement of weak lensing by large-scale structure on scales of 1degrees-4degrees based on radio observations. We utilize the FIRST radio survey, a quarter-sky, 20 cm survey produced with the NRAO Very Large Array (VLA). The large angular scales afforded by the FIRST survey provide a measurement in the linear regime of the matter power spectrum, thus avoiding the necessity of applying uncertain nonlinear corrections. Moreover, since the VLA interferometer has a well-known and deterministic beam, our measurement does not suffer from the irreproducible effects of atmospheric seeing that limit ground-based optical surveys. We use the shapelet method described in an earlier paper to estimate the shear from the shape of radio sources derived directly from the interferometric measurements in the Fourier (u; v)-plane. With realistic simulations we verify that the method yields unbiased shear estimators. We study and quantify the systematic effects that can produce spurious shears, analytically and with simulations, and carefully correct for them. We measure the shear correlation functions on angular scales of 0.degrees5 - 40degrees and compute the corresponding aperture mass statistics. On 1degrees - 4degrees 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 nearby 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 on these scales to constrain the mass power spectrum normalization sigma(8) and the median redshift z(m) of the unidentified radio sources. We find sigma(8)(z(m)/2)(0.6) similar or equal to 1.0 +/- 0.2, where the 1 sigma error bars include statistical errors, cosmic variance, and systematics. This is consistent with earlier determinations of sigma(8) from cosmic shear, the cosmic microwave background, and cluster abundance, and with our current knowledge of the redshift distribution of radio sources. Taking the prior sigma(8) = 0.9 +/- 0.1 (68% CL) from the WMAP experiment, this corresponds to z(m) = 2.2 +/- 0.9 (68% CL) for radio sources without optical counterparts, consistent with existing models for the radio source luminosity function. Our results offer promising prospects for precision measurements of cosmic shear with future radio interferometers such as LOFAR and the SKA.