In addition, we also perform two new simulations changing the type I migration recipes from those of Tanaka et al. (2002) to those of Paardekooper et al. (2011) and Jiménez & Masset (2017). With this, we want to analyze whether or not the planet migration trap could be a robust result even using more sophisticated type I migration recipes, which were derived for nonisothermal disks. We remark that despite our simplifications in the computation of the thermodynamics of the disk, we compute the time evolution of the radial profiles of all the quantities needed to calculate the migration recipes mentioned above, that is, we compute the time evolution of the radial profiles of the density, pressure, opacity, and so on while the temperature radial profile remains fixed in time. Explicitly, the simplification lies in the fact that the evolution of the temperature is not linked self-consistently with the evolution of the gas surface density. We can see in Fig. 8 that the density and pressure maximum also acts as a planet migration trap using the type I migration recipes from Jiménez & Masset (2017). However, using the type I migration prescriptions from Paardekooper et al. (2011), the migration trap is broken close to the mass needed for the planet to open a gap in the disk. This happens because now the normalized torque is not only a function of the local gradient of the gas surface density (as in the isothermal case) but also of the local gradient of the temperature, the viscosity, and the mass of the planet (these last two dependencies through the corotation torque). Thus, the combination of such quantities breaks the migration trap at some moment. Guilera et al. (2019) showed that the main differences between the migration recipes from Jiménez & Masset (2017) and Paardekooper et al. (2011) lie in the computation on the corotation torque. Thus, in this case, when the planet reaches a mass of a several tens of Earth masses, the migration trap is broken. At this moment, the planet quickly migrates inwards (due to the fact that it has a mass of ~ 80 M⊕) until it opens a gap at ~1.15 au. We note that the time evolution of the mass of the core and the mass of the envelope for the simulations using the type I migration recipes from Paardekooper et al. (2011) and Jiménez & Masset (2017) are very similar to those of the fiducial simulation. In Fig. 9, we emphasize this by plotting the planet formation tracks as a function of time. Simulations also stopped when the planets opened a gap in the disk. This happens when the total mass of the planet is about 110 M⊕ for the case where we used the migration recipes from Paardekooper et al. (2011) and about 95 M⊕ for the case where we adopt the migration recipes from Jiménez & Masset (2017). The differences in the total mass at which the planet opens the gap are due to the fact that this mass depends on the viscosity of the disk. Inside the ice line, the viscosity is larger (because of the larger α-parameter), and therefore the total mass of the planet has to be higher to open a gap. For the second case, the planet opens the gap in the α transition region between 10−5 (outside the ice line) and 10−3 (inside the ice line). We note that if the thermodynamics of the disk are computed self-consistently, the migration trap can break at a different planet mass depending mainly on the viscosity and thermal diffusivity of the disk (see Morbidelli 2020).
Citation: Guilera et al. (2019)
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