  Context: Transit surveys, both ground- and space- based, have already
accumulated a large number of light curves that span several years. Aims: The
search for transiting planets in these long time series is computationally
intensive. We wish to optimize the search for both detection and computational
efficiencies. Methods: We assume that the searched systems can be well
described by Keplerian orbits. We then propagate the effects of different
system parameters to the detection parameters. Results: We show that the
frequency information content of the light curve is primarily determined by the
duty cycle of the transit signal, and thus the optimal frequency sampling is
found to be cubic and not linear. Further optimization is achieved by
considering duty-cycle dependent binning of the phased light curve. By using
the (standard) BLS one is either rather insensitive to long-period planets, or
less sensitive to short-period planets and computationally slower by a
significant factor of ~330 (for a 3yr long dataset). We also show how the
physical system parameters, such as the host star's size and mass, directly
affect transit detection. This understanding can then be used to optimize the
search for every star individually. Conclusions: By considering Keplerian
dynamics explicitly rather than implicitly one can optimally search the BLS
parameter space. The presented Optimal BLS enhances the detectability of both
very short and very long period planets while allowing such searches to be done
with much reduced resources and time. The Matlab/Octave source code for Optimal
BLS is made available.
