On corotation torques , horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration

نویسندگان

  • S. - J. Paardekooper
  • J. C. B. Papaloizou
چکیده

We study the torque on low mass protoplanets on fixed circular orbits, embedded in a protoplanetary disc in the isothermal limit. We consider a wide range of surface density distributions including cases where the surface density increases smoothly outwards. We perform both linear disc response calculations and non linear numerical simulations. We consider a large range of viscosities, including the inviscid limit, as well as a range of protoplanet mass ratios, with special emphasis on the coorbital region and the corotation torque acting between disc and protoplanet. For low mass protoplanets and large viscosity the corotation torque behaves as expected from linear theory. However, when the viscosity becomes small enough to enable horseshoe turns to occur, the linear corotation torque exists only temporarily after insertion of a planet into the disc, being replaced by the horseshoe drag first discussed by Ward. This happens after a time that is equal to the horseshoe libra-tion period reduced by a factor amounting to about twice the disc aspect ratio. This torque scales with the radial gradient of specific vorticity, as does the linear torque, but we find it to be many times larger. If the viscosity is large enough for viscous diffusion across the coorbital region to occur within a libration period, we find that the horseshoe drag may be sustained. If not, the corotation torque saturates leaving only the linear Lindblad torques. As the magnitude of the non linear coorbital torque (horseshoe drag) is always found to be larger than the linear torque, we find that the sign of the total torque may change even for for mildly positive surface density gradients. In combination with a kinematic viscosity large enough to keep the torque from saturating, strong sustained deviations from linear theory and outward or stalled migration may occur in such cases.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the horseshoe drag of a low-mass planet. II Migration in adiabatic disks

We evaluate the horseshoe drag exerted on a low-mass planet embedded in a gaseous disk, assuming the disk’s flow in the coorbital region to be adiabatic. We restrict this analysis to the case of a planet on a circular orbit, and we assume a steady flow in the corotating frame. We also assume that the corotational flow upstream of the U-turns is unperturbed, so that we discard saturation effects...

متن کامل

On disc protoplanet interactions in a non-barotropic disc with thermal diffusion

Aims. We study the disc planet interactions of low-mass protoplanets embedded in a circumstellar disc. We extend the standard theory of planet migration from the usual locally isothermal assumption to include non-barotropic effects, focusing on the validity of linear theory. Methods. We compared solutions of the linear equations with results from non-linear hydrodynamic simulations, where in bo...

متن کامل

00 9 On the horseshoe drag of a low - mass planet . I - Migration in isothermal disks

We investigate the unsaturated horseshoe drag exerted on a low-mass planet by an isothermal gaseous disk. In the globally isothermal case, we use a formalism, based on the use of a Bernoulli invariant, that takes into account pressure effects, and that extends the torque estimate to a region wider than the horseshoe region. We find a result that is strictly identical to the standard horseshoe d...

متن کامل

On the coorbital corotation torque in a viscous disk and its impact on planetary migration

We evaluate the coorbital corotation torque on a planet on a fixed circular orbit embedded in a viscous protoplanetary disk, for the case of a steady flow in the planet frame. This torque can be evaluated just from the flow properties at the separatrix between the librating (horseshoe) and circulating streamlines. A stationary solution is searched for the flow in the librating region. When used...

متن کامل

On the width and shape of the corotation region for low-mass planets

We study the coorbital flow for embedded, low mass planets. We provide a simple semi-analytic model for the corotation region, which is subsequently compared to high resolution numerical simulations. The model is used to derive an expression for the half-width of the horseshoe region, xs, which in the limit of zero softening is given by xs/rp = 1.68(q/h) , where q is the planet to central star ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009