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Many extrasolar planetary systems containing multiple super-Earths have beendiscovered. N-body simulations taking into account standard type-I planetarymigration suggest that protoplanets are captured into mean-motion resonantorbits near the inner disk edge at which the migration is halted. PreviousN-body simulations suggested that orbital stability of the resonant systemsdepends on number of the captured planets. In the unstable case, through closescattering and merging between planets, non-resonant multiple systems arefinally formed. In this paper, we investigate the critical number of theresonantly trapped planets beyond which orbital instability occurs after diskgas depletion. We find that when the total number of planets ($N$) is largerthan the critical number ($N_{\rm crit}$), crossing time that is a timescale ofinitiation of the orbital instability is similar to non-resonant cases, whilethe orbital instability never occurs within the orbital calculation time($10^8$ Kepler time) for $N\leq N_{\rm crit}$. Thus, the transition of crossingtime across the critical number is drastic. When all the planets are trapped in7:6 resonance of adjacent pairs, $N_{\rm crit} = 4$. We examine the dependenceof the critical number of 4:3, 6:5 and 8:7 resonance by changing the orbitalseparation in mutual Hill radii and planetary mass. The critical numberincreases with increasing the orbital separation in mutual Hill radii withfixed planetary mass and increases with increasing planetary mass with fixedthe orbital separation in mutual Hill radii. We also calculate the case of asystem which is not composed of the same resonance. The sharp transition of thestability can be responsible for the diversity of multiple super-Earths(non-resonant or resonant), that is being revealed by $Kepler$ mission.

The Orbital Stability of Planets Trapped in the First-Order Mean-Motion Resonances