On fitting planetary systems in counter-revolving configurations

In Gayon & Bois (2008) and Gayon etal (2009), (i) we studied the theoretical feasibility and efficiency of retrograde mean motion resonances (i.e. two planets are both in orbital resonance and in counter-revolving configuration), (ii) we showed that retrograde resonances can generate interesting mechanisms of stability, and (iii) we obtained a dynamical fit involving a counter-revolving configuration that is consistent with the observations of the HD73526 planetary system. In the present paper, we present and analyze data reductions assuming counter-revolving configurations for eight compact multi-planetary systems detected through the radial velocity method. In each case, we select the best fit leading to a dynamically stable solution. The resulting data reductions obtained in rms and chi values for counter-revolving configurations are of the same order, and sometimes slightly better, than for prograde configurations. In the end, these fits tend to show that, over the eight studied multi-planetary systems, six of them could be regulated by a mechanism involving a counter-revolving configuration.