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We study the stability of mean-motion resonances (MMR) between two planetsduring their migration in a protoplanetary disk. We use an analytical model ofresonances, and describe the effect of the disk by a migration timescale(T_{m,i}) and an eccentricity damping timescale (T_{e,i}) for each planet(i=1,2 respectively for the inner and outer planet). We show that the resonantconfiguration is stable if T_{e,1}/T_{e,2} > (e_1/e_2)^2. This general resultcan be used to put constraints on specific models of disk-planet interactions.For instance, using classical prescriptions for type I migration, we show thatwhen the angular momentum deficit (AMD) of the inner orbit is larger than theouter's orbit AMD, resonant systems must have a locally inverted disk densityprofile to stay locked in resonance during the migration. This inversion isvery untypical of type I migration and our criterion can thus provide anevidence against classical type I migration. That is indeed the case for theJupiter-mass resonant systems HD 60532b, c (3:1 MMR), GJ 876b, c (2:1 MMR), andHD 45364b, c (3:2 MMR). This result may be an evidence for type II migration(gap opening planets), which is compatible with the large masses of theseplanets.

Stability of resonant configurations during the migration of planets and constraints on disk-planet interactions