The determination of time delays as an inverse problem - the case of the double quasar 0957+561

A common problem in astronomy is the determination of the time shift between two otherwise identical time series of measured flux from a variable source, in short the determination of a time delay. One example of where this problem occurs is in the determination of the Hubble constant from multiple images of gravitationally lensed variable quasars. It is shown here that this problem is very similar to the problem of reverberation mapping of active galactic nuclei (AGN), and therefore the determination of time delays can also be seen as a restricted inverse problem. In this paper a method is developed that solves this inverse problem and it is applied to the time series measured for the double quasar QSO 0957+561. The resulting time delay is 425 +/- 17 d. This leads to a best value for the Hubble constant of H-0 = 66 +/- 10km s(-1) Mpc(-1).