The quest for companions to post-common envelope binaries IV. The 2:1 mean-motion resonance of the planets orbiting NN Serpentis

We present 69 new mid-eclipse times of the young post-common envelope binary (PCEB) NN Ser, which was previously suggested to possess two circumbinary planets. We have interpreted the observed eclipse-time variations in terms of the light-travel time effect caused by two planets, exhaustively covering the multi-dimensional parameter space by fits in the two binary and ten orbital parameters. We supplemented the fits by stability calculations for all models with an acceptable chi(2). An island of secularly stable 2:1 resonant solutions exists, which coincides with the global chi(2) minimum. Our best-fit stable solution yields current orbital periods P-o = 15.47 yr and P-i = 7.65 yr and eccentricities e(o) = 0.14 and e(i) = 0.22 for the outer and inner planets, respectively. The companions qualify as giant planets, with masses of 7.0 M-Jup and 1.7 M-Jup for the case of orbits coplanar with that of the binary. The two-planet model that starts from the present system parameters has a lifetime greater than 10(8) yr, which significantly exceeds the age of NN Ser of 10(6) yr as a PCEB. The resonance is characterized by libration of the resonant variable Theta(1) and circulation of omega(i)-omega(o), the difference between the arguments of periapse of the two planets. No stable nonresonant solutions were found, and the possibility of a 5:2 resonance suggested previously by us is now excluded at the 99.3% confidence level.