Combining time delays and image positions for quadruple lenses: a moment
  approach
  Time delays in gravitational lenses can be used to determine the Hubble
constant and the lens potential. In future surveys, many gravitational lenses
can be discovered, and their time delays and image positions can in principle
be measured. Using an elliptical power-law potential, we show that combinations
of image positions and time delays for quadruple lenses yield simple analytical
expressions that are connected with observable quantities. These relations can
be used to obtain the approximate axis ratio q, the Einstein radius and the
slope. We apply this method to RX J1131-1231, and show that our analytical
results match the full numerical determinations approximately. Our approach can
quickly determine rough values of lens parameters, which can then be used as
initial guesses for further refinement through numerical modelling and may be
useful for automated lens search in large surveys.
