Type I migration in radiatively efficient discs

Abstract

We study Type I migration of a planet in a radiatively efficient disc using global twodimensional hydrodynamic simulations. The large positive corotation torque is exerted on a planet by an adiabatic disc at early times when the disc has the steep negative entropy gradient. The gas on the horseshoe orbit of the planet is compressed adiabatically during the change of the orbit from the slow orbit to the fast orbit, increasing its density and exerting the positive torque on the planet. The planet would migrate outward in the adiabatic disc before saturation sets in. We further study the effect of energy dissipation by radiation on Type I migration of the planet. The corotation torque decreases when the energy dissipates effectively because the density of the gas on the horseshoe orbit does not increase by the compression compared with the gas of the adiabatic disc. The total torque is mainly determined by the negative Lindblad torque and becomes negative. The planet migrates inwards towards the central star in the radiatively efficient disc. The migration velocity is dependent on the radiative efficiency and is greatly reduced if the radiative cooling works inefficiently.

Outward migration of a super-Earth in a disc with outward propagating density waves excited by a giant planet

“…The latter depends on the disc surface density and temperature profiles and thermodynamics. When they are important, non‐linear effects play a role (Paardekooper et al 2011; Yamada & Inaba 2011). According to recent studies, a single low‐mass planet can migrate with a whole range of speeds, both inwards and outwards, depending on the assumed physical and structural properties of the disc in which it is embedded.…”

“…A number of potential mechanisms have been found by focusing on a single low‐mass planet embedded in a protoplanetary disc. These mechanisms involve, among others, entry into a magnetospheric cavity close to the star (Lin, Bodenheimer & Richardson 1996), effects arising from the orbital eccentricity of a protoplanet (Papaloizou & Larwood 2000), effects due to the possible eccentricity of the protoplanetary disc (Papaloizou 2002), magnetic fields (Terquem 2003), magnetohydrodynamic turbulence (Laughlin, Steinacker & Adams 2004; Nelson & Papaloizou 2004; Johnson, Goodman & Menou 2006; Adams & Bloch 2009), sudden jumps in disc state variables (Menou & Goodman 2004; Matsumura, Pudritz & Thommes 2007), corotation torques (Masset et al 2006; Paardekooper & Papaloizou 2009a,b), disc thermodynamics (Paardekooper & Mellema 2006; Baruteau & Masset 2008; Kley & Crida 2008; Paardekooper & Papaloizou 2008; Kley, Bitsch & Klahr 2009; Hasegawa & Pudritz 2010; Paardekooper et al 2010; Paardekooper, Baruteau & Kley 2011; Yamada & Inaba 2011) and instabilities of partial gap edges in low viscosity discs (Li et al 2009; Yu et al 2010).…”

Type I migration in optically thick accretion discs

“…Paardekooper & Mellema () showed that the corotation torque becomes positive in a disc with high opacity, reducing the migration velocity of a planet. This process was recognized and intensively studied by many researchers (Baruteau & Masset ; Paardekooper & Mellema ; Paardekooper & Papaloizou ; Masset & Casoli ; Ayliffe & Bate , ; Paardekooper et al , ; Yamada & Inaba ). The positive corotation torque cancels the negative Lindblad torque when the entropy distribution has a steep negative slope.…”

Migration of protoplanets with surfaces through discs with steep temperature gradients

“…This was further described by Baruteau & Masset (2008), who make clear that the radiation diffusion time‐scale must be greater than the period of a single horseshoe orbit to avoid returning to an isothermal like migration, and that outward migration can be related to the disc’s radial entropy gradient. Many numerical models have since also found evidence of outward migration in the Type I regime (Paardekooper & Mellema 2008; Paardekooper & Papaloizou 2008; Kley & Crida 2008; Kley, Bitsch & Klahr 2009; Ayliffe & Bate 2010; Yamada & Inaba 2011). Periods of outward migration can help to increase the overall migration time‐scale of a forming planet embedded in a disc, as is required by synthesis models to explain the population of exoplanets that has been observed (Ida & Lin 2008; Mordasini, Alibert & Benz 2009).…”