Determination of the Hubble Constant from Quadruply Imaged Gravitational Lens Systems

Abstract.

Determining H ₀ from the time delays in quadruply imaged leng systems needs the knowledge of the deflecting potential $\psi (r,\theta)$. We present two different methods to solve this problem. On the one hand, we assume that the potential belongs to a broad class of non-elliptical models and we write down a system of equations which can be numerically solved to get all the parameters of the model using only the image positions and some physical constraints. On the other hand, we show how it is possible to estimate H ₀ from the time delays without completely reconstructing the potential, provided that $\psi (r,\theta) = r^{\alpha} F(\theta)$, whatever the shape function $F(\theta)$ is. After some tests on simulated cases, we apply both methods to the real quadruple lenges PG1115+080 and B1422+231 finally obtaining H ₀ = 58⁺¹⁷ _-15 km s^-1 Mpc^-1.