J/A+A/664/A138 Planet/star systems torque density distributions (Schib+, 2022)
Calibrated gas accretion and orbital migration of protoplanets in 1D
disc models.
Schib O., Mordasini C., Helled R.
<Astron. Astrophys. 664, A138 (2022)>
=2022A&A...664A.138S 2022A&A...664A.138S (SIMBAD/NED BibCode)
ADC_Keywords: Models ; Accretion ; Planets
Keywords: protoplanetary disks - accretion, accretion disks -
planets and satellites: formation
Abstract:
Orbital migration and gas accretion are two interdependent key
processes that govern the evolution of planets in protoplanetary
discs. The final planetary properties such as masses and orbital
periods strongly depend on the treatment of those two processes.
We aim to develop a simple prescription for migration and accretion in
1D disc models, calibrated with results of 3D hydrodynamic
simulations. Our focus lies on non-self-gravitating discs, but we also
discuss to what degree our prescription could be applied when the
discs are self-gravitating.
We study migration using torque densities. Our model for the torque
density is based on existing fitting formulas, which we subsequently
modify to prevent premature gap-opening. At higher planetary masses,
we also apply torque densities from hydrodynamic simulations directly
to our 1D model. These torque densities allow modelling the orbital
evolution of an initially low-mass planet that undergoes
runaway-accretion to become a massive planet. The two-way exchange of
angular momentum between disc and planet is included. This leads to a
self-consistent treatment of gap formation that only relies on
directly accessible disc parameters. We present a formula for Bondi-
and Hill- gas accretion in the disc-limited regime. This formula is
self-consistent in the sense that mass is removed from the disc in the
location from where it is accreted. The prescription is appropriate
when the planet is smaller than, comparable to, or larger than the
disc scale height.
We find that the resulting evolution in mass and semi-major axis in
the 1D framework is in good agreement with those from 3D
hydrodynamical simulations for a range of parameters.
Our prescription is valuable for simultaneously modelling migration
and accretion in 1D-models, which allows to follow a planet's
evolution over the entire lifetime of a disc. It is applicable also in
situations where the surface density is significantly disturbed by
multiple gap-opening planets or processes like infall. We conclude
that it is appropriate and beneficial to apply torque densities from
hydrodynamic simulations in 1D models, at least in the parameter space
we study here. More work is needed to in order to determine whether
our approach is also applicable in an even wider parameter space and
in situations with more complex disc thermodynamics, or when the disc
is self-gravitating.
Description:
Digitised data, torque density distributions in a locally isothermal
disk for various values of the planet-to-star mass ratio Mp/Ms, from
Figure 15 in D'Angelo & Lubow (2010ApJ...724..730D 2010ApJ...724..730D).
File Summary:
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FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
upp_1e-4.dat 46 97 Torque density distributions in a locally
isothermal disk for various values of the
planet-to-star mass ratio Mp/Ms=10-4
upp_2e-4.dat 46 57 Torque density distributions in a locally
isothermal disk for various values of the
planet-to-star mass ratio Mp/Ms=2*10-4
upp_3e-4.dat 46 51 Torque density distributions in a locally
isothermal disk for various values of the
planet-to-star mass ratio Mp/Ms=3*10-4
upp_6e-5.dat 46 82 Torque density distributions in a locally
isothermal disk for various values of the
planet-to-star mass ratio Mp/Ms=6*10-5
low_1e-3.dat 47 91 Torque density distributions in a locally
isothermal disk for various values of the
planet-to-star mass ratio Mp/Ms=10-3
low_2e-3.dat 47 101 Torque density distributions in a locally
isothermal disk for various values of the
planet-to-star mass ratio Mp/Ms=2*10-3
low_3e-4.dat 46 62 Torque density distributions in a locally
isothermal disk for various values of the
planet-to-star mass ratio Mp/Ms=3*10-4
low_7e-4.dat 47 76 Torque density distributions in a locally
isothermal disk for various values of the
planet-to-star mass ratio Mp/Ms=7*10-4
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Byte-by-byte Description of file: upp*.dat
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Bytes Format Units Label Explanations
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1- 21 F21.18 --- (r-a)/H Normalized radius, (r-a)/H (1)
24- 47 E24.21 --- dJ/dM Magnitude of the torque densities, scaled
by Ω2*a2(Mp/Ms)2(a/H)4
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Note (1): where a is the planet orbital radius and H the pressure scale height.
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Byte-by-byte Description of file: low_*.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
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1- 20 F20.17 --- (r-a)/RH Normalized radius, (r-a)/RH (1)
24- 47 F24.21 --- dJ/dM Magnitude of the torque densities, scaled
by Ω2*a2(Mp/Ms)2(a/H)4
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Note (1): where a is the planet orbital radius and RH the Hill radius of the
planet.
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Acknowledgements:
Oliver Schib, oliver.schib(at)unibe.ch
References:
D'angelo & Lubow, 2010ApJ...724..730D 2010ApJ...724..730D,
Three-dimensional disk-planet torques in a locally isothermal disk
(End) Patricia Vannier [CDS] 11-Aug-2022