COSMOGRAIL: The COSmological MOnitoring of GRAvItational Lenses I. How to sample the light curves of gravitationally lensed quasars to measure accurate time delays

We use numerical simulations to test a broad range of plausible observational strategies designed to measure the time delay between the images of gravitationally lensed quasars. Artificial quasar light curves are created along with Monte-Carlo simulations in order to determine the best temporal sampling to adopt when monitoring the photometric variations of systems with time delays between 5 and 120 days, i.e., always shorter than the visibility window across the year. Few and realistic assumptions are necessary on the quasar photometric variations (peak-to-peak amplitude and time-scale of the variations) and on the accuracy of the individual photometric points. The output of the simulations is the ( statistical) relative error made on the time delay measurement, as a function of 1- the object visibility over the year; 2- the temporal sampling of the light curves; and 3- the time delay. Also investigated is the effect of long term microlensing variations which must be below the 5% level ( either intrinsically or by subtraction) if the goal is to measure time delays with an accuracy of 1-2%. However, while microlensing increases the random error on the time delay, it does not significantly increase the systematic error, which is always a factor 5 to 10 smaller than the random error. Finally, it is shown that, when the time delay is comparable to the visibility window of the object, a logarithmic sampling can significantly improve the time delay determination. All results are presented in the form of compact plots to be used to optimize the observational strategy of future monitoring programs.