The dynamical origin of the multi-planetary system HD 45364

Abstract

The recently discovered planetary system HD 45364, which consists of a Jupiter and Saturn-mass planet, is very likely in a 3:2 mean motion resonance. The standard scenario for forming planetary commensurabilities is convergent migration of two planets embedded in a protoplanetary disc. When the planets are initially separated by a period ratio larger than two, convergent migration will most likely lead to a very stable 2:1 resonance. Rapid type III migration of the outer planet crossing the 2:1 resonance is one possible way around this problem. In this paper, we investigate this idea in detail. We present an estimate of the required convergent migration rate and confirm this with N-body and hydrodynamical simulations. If the dynamical history of the planetary system had a phase of rapid inward migration that forms a resonant configuration, we predict that the orbital parameters of the two planets will always be very similar and thus should show evidence of that. We use the orbital parameters from our simulation to calculate a radial velocity curve and compare it to observations. Our model provides a fit that is as good as the previously reported one. The eccentricities of both planets are considerably smaller and the libration pattern is different. Within a few years, it will be possible to observe the planet-planet interaction directly and thus distinguish between these different dynamical states.

On the orbital evolution of a pair of giant planets in mean motion resonance

“…Thus observing a system in 5:3 resonance is unlikely. We remark that although the planet mass ratios differed and the transition was from a 2:1 resonance to a 3:2 resonance, qualitatively similar behaviour to that described above, up until the instability at late stages, was found in simulations of Rein et al (2010) (see their Fig. 6).…”

“…Although 3:2 resonances may be produced in other situations (eg. Rein et al 2010 and see the end of Section 4.3 above) characteristic evolution times are again short.…”

A new scenario for the origin of the 3/2 resonant system HD 45364

“…Although we also suggest resonance-trapping following planetary migration from disk-planet interactions, there are some important differences: (i) we assume a slower migration rate than predicted by either type I or type II migration modes; (ii) we adopt different disk parameters, especially a lower surface density; (iii) we introduce mass growth during both the migration and the resonance-trapping processes; and (iv) we assume that the migration process begins when the planets are in the embryonic Article published by EDP Sciences A65, page 1 of 10 stage (∼0.1 M ⊕ ) and thus much smaller than the present-day Saturn-size planets. We show that depending on just one parameter, our scenario is able to reproduce the averaged magnitudes of the orbital elements and the resonant behavior of the best fits of Correia et al (2009), also for the solution given in Rein et al (2010). In addition, we study the phase space of the 3/2 MMR using a semi-analytical model originally developed by Michtchenko et al (2008a).…”

“…However, one fact, already noted by Rein et al (2010), attracted our attention: the discrepancy in the dynamical behavior of the simulated solution and that obtained from the best fit of Correia et al (2009). The difference lies mainly in the magnitudes of the planet eccentricities (it was explained by the authors as caused by possible errors in the radial velocity data).…”

“…The difference lies mainly in the magnitudes of the planet eccentricities (it was explained by the authors as caused by possible errors in the radial velocity data). Moreover, other discrepancies appear when the dynamics of the Rein et al (2010) solution is analyzed in detail. An N-body simulation shows that the proposed solution does not lie within the libration zone of the 3/2 MMR, but exhibits a quasi-resonant behavior.…”