Radio Weak Lensing Shear Measurement in the Visibility Domain - I.
  Methodology
  The high sensitivity of the new generation of radio telescopes such as the
Square Kilometre Array (SKA) will allow cosmological weak lensing measurements
at radio wavelengths that are competitive with optical surveys. We present an
adaptation to radio data of lensfit, a method for galaxy shape measurement
originally developed and used for optical weak lensing surveys. This likelihood
method uses an analytical galaxy model and makes a Bayesian marginalisation of
the likelihood over uninteresting parameters. It has the feature of working
directly in the visibility domain, which is the natural approach to adopt with
radio interferometer data, avoiding systematics introduced by the imaging
process. As a proof of concept, we provide results for visibility simulations
of individual galaxies with flux density S >= 10 muJy at the phase centre of
the proposed SKA1-MID baseline configuration, adopting 12 frequency channels in
the band 950 - 1190 MHz. Weak lensing shear measurements from a population of
galaxies with realistic flux and scalelength distributions are obtained after
natural gridding of the raw visibilities. Shear measurements are expected to be
affected by "noise bias": we estimate the bias in the method as a function of
signal-to-noise ratio (SNR). We obtain additive and multiplicative bias values
that are comparable to SKA1 requirements for SNR > 18 and SNR > 30,
respectively. The multiplicative bias for SNR > 10 is comparable to that found
in ground-based optical surveys such as CFHTLenS, and we anticipate that
similar shear measurement calibration strategies to those used for optical
surveys may be used to good effect in the analysis of SKA radio interferometer
data.
