Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-eccentricity Degeneracy
Abstract
The tidal perturbation of embedded protoplanets on their natal disks has been widely attributed to be the cause of gap-ring structures in submillimeter images of protoplanetary disks around T Tauri stars. Numerical simulations of this process have been used to propose scaling of characteristic dust-gap width/gap-ring distance with respect to planet mass. Applying such scaling to analyze observed gap samples yields a continuous mass distribution for a rich population of hypothetical planets in the range of several Earth to Jupiter masses. In contrast, the conventional core-accretion scenario of planet formation predicts a bimodal mass function due to (1) the onset of runaway gas accretion above ~20 Earth masses and (2) suppression of accretion induced by gap opening. Here, we examine the dust disk response to the tidal perturbation of eccentric planets as a possible resolution of this paradox. Based on simulated gas and dust distributions, we show the gap-ring separation of Neptune-mass planets with small eccentricities might become comparable to that induced by Saturn-mass planets on circular orbits. Furthermore, this degeneracy may obliterate the discrepancy between the theoretical bimodal mass distribution and the observed continuous gap width distribution. Despite damping due to planet–disk interaction, modest eccentricity may be sustained eithermore »
- Authors:
-
[1];
[3];
[5]
- Princeton Univ., NJ (United States); Tsinghua Univ., Beijing (China)
- Tsinghua Univ., Beijing (China)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. de Toulouse (France)
- Tsinghua Univ., Beijing (China); Univ. of California, Santa Cruz, CA (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- National Aeronautics and Space Administration (NASA)
- OSTI Identifier:
- 1866962
- Report Number(s):
- LA-UR-21-28245
Journal ID: ISSN 0004-637X; TRN: US2306118
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- The Astrophysical Journal
- Additional Journal Information:
- Journal Volume: 922; Journal Issue: 2; Journal ID: ISSN 0004-637X
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; astronomy and astrophysics; protoplanetary/protostellar disks; planet-disk interactions
Citation Formats
Chen, Yi-Xian, Wang, Zhuoxiao, Li, Ya-Ping, Baruteau, Clément, and Lin, Douglas N. C. Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-eccentricity Degeneracy. United States: N. p., 2021.
Web. doi:10.3847/1538-4357/ac23d7.
Chen, Yi-Xian, Wang, Zhuoxiao, Li, Ya-Ping, Baruteau, Clément, & Lin, Douglas N. C. Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-eccentricity Degeneracy. United States. https://doi.org/10.3847/1538-4357/ac23d7
Chen, Yi-Xian, Wang, Zhuoxiao, Li, Ya-Ping, Baruteau, Clément, and Lin, Douglas N. C. Tue .
"Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-eccentricity Degeneracy". United States. https://doi.org/10.3847/1538-4357/ac23d7. https://www.osti.gov/servlets/purl/1866962.
@article{osti_1866962,
title = {Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-eccentricity Degeneracy},
author = {Chen, Yi-Xian and Wang, Zhuoxiao and Li, Ya-Ping and Baruteau, Clément and Lin, Douglas N. C.},
abstractNote = {The tidal perturbation of embedded protoplanets on their natal disks has been widely attributed to be the cause of gap-ring structures in submillimeter images of protoplanetary disks around T Tauri stars. Numerical simulations of this process have been used to propose scaling of characteristic dust-gap width/gap-ring distance with respect to planet mass. Applying such scaling to analyze observed gap samples yields a continuous mass distribution for a rich population of hypothetical planets in the range of several Earth to Jupiter masses. In contrast, the conventional core-accretion scenario of planet formation predicts a bimodal mass function due to (1) the onset of runaway gas accretion above ~20 Earth masses and (2) suppression of accretion induced by gap opening. Here, we examine the dust disk response to the tidal perturbation of eccentric planets as a possible resolution of this paradox. Based on simulated gas and dust distributions, we show the gap-ring separation of Neptune-mass planets with small eccentricities might become comparable to that induced by Saturn-mass planets on circular orbits. Furthermore, this degeneracy may obliterate the discrepancy between the theoretical bimodal mass distribution and the observed continuous gap width distribution. Despite damping due to planet–disk interaction, modest eccentricity may be sustained either in the outer regions of relatively thick disks or through resonant excitation among multiple super Earths. Moreover, the ring-like dust distribution induced by planets with small eccentricities is axisymmetric even in low viscosity environments, consistent with the paucity of vortices in Atacama Large Millimeter/submillimeter Array images.},
doi = {10.3847/1538-4357/ac23d7},
journal = {The Astrophysical Journal},
number = 2,
volume = 922,
place = {United States},
year = {Tue Nov 30 00:00:00 EST 2021},
month = {Tue Nov 30 00:00:00 EST 2021}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
The excitation of density waves at the Lindblad and corotation resonances by an external potential
journal, October 1979
- Goldreich, P.; Tremaine, S.
- The Astrophysical Journal, Vol. 233
Gap Formation in Protoplanetary Disks
journal, April 1996
- Takeuchi, Taku; Miyama, Shoken M.; Lin, D. N. C.
- The Astrophysical Journal, Vol. 460
Eccentricity Evolution for Planets in Gaseous Disks
journal, March 2003
- Goldreich, Peter; Sari, Re’em
- The Astrophysical Journal, Vol. 585, Issue 2
Is the ring inside or outside the planet?: the effect of planet migration on dust rings
journal, October 2018
- Meru, Farzana; Rosotti, Giovanni P.; Booth, Richard A.
- Monthly Notices of the Royal Astronomical Society, Vol. 482, Issue 3
Toward a Deterministic Model of Planetary Formation. I. A Desert in the Mass and Semimajor Axis Distributions of Extrasolar Planets
journal, March 2004
- Ida, S.; Lin, D. N. C.
- The Astrophysical Journal, Vol. 604, Issue 1
The Three-dimensional Flow Field around Planets on Eccentric Orbits
journal, July 2021
- Bailey, Avery; Stone, James M.; Fung, Jeffrey
- The Astrophysical Journal, Vol. 915, Issue 2
Bridging the Gap between Protoplanetary and Debris Disks: Separate Evolution of Millimeter and Micrometer-sized Dust
journal, November 2021
- Michel, Arnaud; van der Marel, Nienke; Matthews, Brenda C.
- The Astrophysical Journal, Vol. 921, Issue 1
Multiple Disk Gaps and Rings Generated by a Single Super-Earth. II. Spacings, Depths, and Number of Gaps, with Application to Real Systems
journal, October 2018
- Dong, Ruobing; Li, Shengtai; Chiang, Eugene
- The Astrophysical Journal, Vol. 866, Issue 2
Rossby Wave Instability of Keplerian Accretion Disks
journal, March 1999
- Lovelace, R. V. E.; Li, H.; Colgate, S. A.
- The Astrophysical Journal, Vol. 513, Issue 2
Post‐oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems
journal, September 2007
- Zhou, Ji‐Lin; Lin, Douglas N. C.; Sun, Yi‐Sui
- The Astrophysical Journal, Vol. 666, Issue 1
An Empirically Derived Formula for the Shape of Planet-induced Gaps in Protoplanetary Disks
journal, January 2020
- Duffell, Paul C.
- The Astrophysical Journal, Vol. 889, Issue 1
Transitional and Pre-Transitional Disks: gap Opening by Multiple Planets?
journal, February 2011
- Zhu, Zhaohuan; Nelson, Richard P.; Hartmann, Lee
- The Astrophysical Journal, Vol. 729, Issue 1
Type I Planetary Migration in a Self‐Gravitating Disk
journal, May 2008
- Baruteau, C.; Masset, F.
- The Astrophysical Journal, Vol. 678, Issue 1
Planet-induced Vortices with Dust Coagulation in Protoplanetary Disks
journal, March 2020
- Li, Ya-Ping; Li, Hui; Li, Shengtai
- The Astrophysical Journal, Vol. 892, Issue 2
Disk eccentricity and embedded planets
journal, January 2006
- Kley, W.; Dirksen, G.
- Astronomy & Astrophysics, Vol. 447, Issue 1
Dynamics and Origin of the 2 : 1 Orbital Resonances of the GJ 876 Planets
journal, March 2002
- Lee, Man Hoi; Peale, S. J.
- The Astrophysical Journal, Vol. 567, Issue 1
Revisiting migration in a disc cavity to explain the high eccentricities of warm Jupiters
journal, October 2020
- Debras, Florian; Baruteau, Clément; Donati, Jean-François
- Monthly Notices of the Royal Astronomical Society, Vol. 500, Issue 2
Dust flow in gas disks in the presence of embedded planets
journal, June 2006
- Paardekooper, S. -J.; Mellema, G.
- Astronomy & Astrophysics, Vol. 453, Issue 3
Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics
journal, August 2017
- Bai, Xue-Ning
- The Astrophysical Journal, Vol. 845, Issue 1
Pileups and Migration Rates for Planets in Low-mass Disks
journal, March 2020
- Dempsey, Adam M.; Lee, Wing-Kit; Lithwick, Yoram
- The Astrophysical Journal, Vol. 891, Issue 2
Protoplanetary Migration in Turbulent Isothermal Disks
journal, January 2010
- Baruteau, C.; Lin, D. N. C.
- The Astrophysical Journal, Vol. 709, Issue 2
Observational Signatures of Planets in Protoplanetary Disks. i. gaps Opened by Single and Multiple Young Planets in Disks
journal, August 2015
- Dong (董若冰), Ruobing; Zhu (朱照寰), Zhaohuan; Whitney (韦韦), Barbara
- The Astrophysical Journal, Vol. 809, Issue 1
A torque formula for non-isothermal Type I planetary migration - II. Effects of diffusion: Non-isothermal Type I planet migration - II
journal, September 2010
- Paardekooper, S. -J.; Baruteau, C.; Kley, W.
- Monthly Notices of the Royal Astronomical Society, Vol. 410, Issue 1
On the tidal interaction between protoplanets and the primordial solar nebula. II - Self-consistent nonlinear interaction
journal, August 1986
- Lin, D. N. C.; Papaloizou, J.
- The Astrophysical Journal, Vol. 307
On the tidal interaction between protoplanets and the primordial solar nebula. I - Linear calculation of the role of angular momentum exchange
journal, October 1984
- Papaloizou, J.; Lin, D. N. C.
- The Astrophysical Journal, Vol. 285
On the migration-induced resonances in a system of two planets with masses in the Earth mass range
journal, October 2005
- Papaloizou, J. C. B.; Szuszkiewicz, E.
- Monthly Notices of the Royal Astronomical Society, Vol. 363, Issue 1
Gas and dust hydrodynamical simulations of massive lopsided transition discs – II. Dust concentration
journal, April 2016
- Baruteau, Clément; Zhu, Zhaohuan
- Monthly Notices of the Royal Astronomical Society, Vol. 458, Issue 4
Rossby Wave Instability of Thin Accretion Disks. III. Nonlinear Simulations
journal, April 2001
- Li, H.; Colgate, S. A.; Wendroff, B.
- The Astrophysical Journal, Vol. 551, Issue 2
Retention of Long-period Gas Giant Planets: Type II Migration Revisited
journal, August 2020
- Chen, Yi-Xian; Zhang, Xiaojia; Li, Ya-Ping
- The Astrophysical Journal, Vol. 900, Issue 1
On the orbital evolution of low mass protoplanets in turbulent, magnetised disks
journal, November 2005
- Nelson, R. P.
- Astronomy & Astrophysics, Vol. 443, Issue 3
The Effect of Internal Dissipation and Surface Irradiation on the Structure of Disks and the Location of the Snow Line around Sun‐like Stars
journal, January 2007
- Garaud, P.; Lin, D. N. C.
- The Astrophysical Journal, Vol. 654, Issue 1
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants
journal, April 2018
- Bitsch, Bertram; Morbidelli, Alessandro; Johansen, Anders
- Astronomy & Astrophysics, Vol. 612
Mass Estimates of a Giant Planet in a Protoplanetary disk from the gap Structures
journal, June 2015
- Kanagawa, Kazuhiro D.; Muto, Takayuki; Tanaka, Hidekazu
- The Astrophysical Journal, Vol. 806, Issue 1
On the Corotation Torque in a Radiatively Inefficient Disk
journal, January 2008
- Baruteau, C.; Masset, F.
- The Astrophysical Journal, Vol. 672, Issue 2
Imaging diagnostics for transitional discs
journal, December 2013
- de Juan Ovelar, M.; Min, M.; Dominik, C.
- Astronomy & Astrophysics, Vol. 560
Layered Accretion in T Tauri Disks
journal, January 1996
- Gammie, Charles F.
- The Astrophysical Journal, Vol. 457
Compact Disks in a High-resolution ALMA Survey of Dust Structures in the Taurus Molecular Cloud
journal, August 2019
- Long, Feng; Herczeg, Gregory J.; Harsono, Daniel
- The Astrophysical Journal, Vol. 882, Issue 1
Characterization of exoplanets from their formation: I. Models of combined planet formation and evolution
journal, November 2012
- Mordasini, C.; Alibert, Y.; Klahr, H.
- Astronomy & Astrophysics, Vol. 547
On the Dust Signatures Induced by Eccentric Super-Earths in Protoplanetary Disks
journal, November 2019
- Li, Ya-Ping; Li, Hui; Li, Shengtai
- The Astrophysical Journal, Vol. 886, Issue 1
Planet gap opening across stellar masses
journal, February 2020
- Sinclair, Catriona A.; Rosotti, Giovanni P.; Juhasz, Attila
- Monthly Notices of the Royal Astronomical Society, Vol. 493, Issue 3
ALMA 870 μm continuum observations of HD 100546: Evidence of a giant planet on a wide orbit
journal, July 2021
- Fedele, D.; Toci, C.; Maud, L.
- Astronomy & Astrophysics, Vol. 651
A torque formula for non-isothermal type I planetary migration - I. Unsaturated horseshoe drag
journal, January 2010
- Paardekooper, S. -J.; Baruteau, C.; Crida, A.
- Monthly Notices of the Royal Astronomical Society, Vol. 401, Issue 3
The interaction of a giant planet with a disc with MHD turbulence — II. The interaction of the planet with the disc
journal, March 2003
- Nelson, Richard P.; Papaloizou, John C. B.
- Monthly Notices of the Royal Astronomical Society, Vol. 339, Issue 4
Wind-Driven Accretion in Protoplanetary Disks. i. Suppression of the Magnetorotational Instability and Launching of the Magnetocentrifugal wind
journal, May 2013
- Bai, Xue-Ning; Stone, James M.
- The Astrophysical Journal, Vol. 769, Issue 1
Rossby Wave Instability of Thin Accretion Disks. II. Detailed Linear Theory
journal, April 2000
- Li, H.; Finn, J. M.; Lovelace, R. V. E.
- The Astrophysical Journal, Vol. 533, Issue 2
The Dynamics of Planetary Rings
journal, September 1982
- Goldreich, Peter; Tremaine, Scott
- Annual Review of Astronomy and Astrophysics, Vol. 20, Issue 1
Migration and Growth of Protoplanetary Embryos. ii. Emergence of Proto-Gas-Giant Cores Versus Super Earth Progenitors
journal, December 2014
- Liu, Beibei; Zhang, Xiaojia; Lin, Douglas N. C.
- The Astrophysical Journal, Vol. 798, Issue 1
Formation of the Giant Planets by Concurrent Accretion of Solids and Gas
journal, November 1996
- Pollack, James B.; Hubickyj, Olenka; Bodenheimer, Peter
- Icarus, Vol. 124, Issue 1
The structure of protoplanetary discs around evolving young stars
journal, February 2015
- Bitsch, Bertram; Johansen, Anders; Lambrechts, Michiel
- Astronomy & Astrophysics, Vol. 575
Effects of Ringed Structures and Dust Size Growth on Millimeter Observations of Protoplanetary Disks
journal, June 2019
- Li, Ya-Ping; Li, Hui; Ricci, Luca
- The Astrophysical Journal, Vol. 878, Issue 1
Migration and Growth of Protoplanetary Embryos. iii. mass and Metallicity Dependence for fgkm Main-Sequence Stars
journal, June 2016
- Liu, Beibei; Zhang, Xiaojia; Lin, Douglas N. C.
- The Astrophysical Journal, Vol. 823, Issue 2
Toward a Deterministic Model of Planetary Formation. vii. Eccentricity Distribution of gas Giants
journal, September 2013
- Ida, S.; Lin, D. N. C.; Nagasawa, M.
- The Astrophysical Journal, Vol. 775, Issue 1
Eccentric Jupiters via Disk–Planet Interactions
journal, October 2015
- Duffell, Paul C.; Chiang, Eugene
- The Astrophysical Journal, Vol. 812, Issue 2
FARGO: A fast eulerian transport algorithm for differentially
rotating disks
journal, January 2000
- Masset, F.
- Astronomy and Astrophysics Supplement Series, Vol. 141, Issue 1
A Three-dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk Using DCO +
journal, July 2017
- Flaherty, Kevin M.; Hughes, A. Meredith; Rose, Sanaea C.
- The Astrophysical Journal, Vol. 843, Issue 2
Disk-Satellite Interaction via Density Waves and the Eccentricity Evolution of Bodies Embedded in Disks
journal, December 1993
- Artymowicz, Pawel
- The Astrophysical Journal, Vol. 419
Ring Morphology with Dust Coagulation in Protoplanetary Disks
journal, January 2020
- Laune, Jt; Li, Hui; Li, Shengtai
- The Astrophysical Journal, Vol. 889, Issue 1
The newborn planet population emerging from ring-like structures in discs
journal, March 2019
- Lodato, Giuseppe; Dipierro, Giovanni; Ragusa, Enrico
- Monthly Notices of the Royal Astronomical Society, Vol. 486, Issue 1
Disk-satellite interactions
journal, October 1980
- Goldreich, P.; Tremaine, S.
- The Astrophysical Journal, Vol. 241
The Importance of disk Structure in Stalling type i Migration
journal, July 2012
- Kretke, Katherine A.; Lin, D. N. C.
- The Astrophysical Journal, Vol. 755, Issue 1
Radial Migration of Gap-opening Planets in Protoplanetary Disks. II. The Case of a Planet Pair
journal, May 2020
- Kanagawa, Kazuhiro D.; Szuszkiewicz, Ewa
- The Astrophysical Journal, Vol. 894, Issue 1
Weak Turbulence in the hd 163296 Protoplanetary disk Revealed by alma co Observations
journal, November 2015
- Flaherty, Kevin M.; Hughes, A. Meredith; Rosenfeld, Katherine A.
- The Astrophysical Journal, Vol. 813, Issue 2
On the Diversity of Asymmetries in Gapped Protoplanetary Disks
journal, December 2020
- van der Marel, Nienke; Birnstiel, Til; Garufi, Antonio
- The Astronomical Journal, Vol. 161, Issue 1
A comparative study of disc-planet interaction
journal, August 2006
- De Val-Borro, M.; Edgar, R. G.; Artymowicz, P.
- Monthly Notices of the Royal Astronomical Society, Vol. 370, Issue 2
The diffusion of contaminant through an accretion disc
journal, November 1988
- Clarke, C. J.; Pringle, J. E.
- Monthly Notices of the Royal Astronomical Society, Vol. 235, Issue 2
The Disk Substructures at High Angular Resolution Project (DSHARP). I. Motivation, Sample, Calibration, and Overview
journal, December 2018
- Andrews, Sean M.; Huang, Jane; Pérez, Laura M.
- The Astrophysical Journal, Vol. 869, Issue 2
The Disk Substructures at High Angular Resolution Project (DSHARP). II. Characteristics of Annular Substructures
journal, December 2018
- Huang, Jane; Andrews, Sean M.; Dullemond, Cornelis P.
- The Astrophysical Journal, Vol. 869, Issue 2
ALMA observations require slower Core Accretion runaway growth
journal, June 2019
- Nayakshin, S.; Dipierro, G.; Szulágyi, J.
- Monthly Notices of the Royal Astronomical Society: Letters, Vol. 488, Issue 1
The minimum mass of detectable planets in protoplanetary discs and the derivation of planetary masses from high-resolution observations
journal, March 2016
- Rosotti, Giovanni P.; Juhasz, Attila; Booth, Richard A.
- Monthly Notices of the Royal Astronomical Society, Vol. 459, Issue 3
The Disk Substructures at High Angular Resolution Project (DSHARP). VII. The Planet–Disk Interactions Interpretation
journal, December 2018
- Zhang, Shangjia; Zhu, Zhaohuan; Huang, Jane
- The Astrophysical Journal, Vol. 869, Issue 2
On the evolution of eccentric and inclined protoplanets embedded in protoplanetary disks
journal, July 2007
- Cresswell, P.; Dirksen, G.; Kley, W.
- Astronomy & Astrophysics, Vol. 473, Issue 1
Millimetre spectral indices of transition disks and their relation to the cavity radius
journal, April 2014
- Pinilla, P.; Benisty, M.; Birnstiel, T.
- Astronomy & Astrophysics, Vol. 564
Potential Vorticity Evolution of a Protoplanetary Disk with an Embedded Protoplanet
journal, May 2005
- Li, Hui; Li, Shengtai; Koller, Josef
- The Astrophysical Journal, Vol. 624, Issue 2
The Evolution of Viscous Discs and the Origin of the Nebular Variables
journal, September 1974
- Lynden-Bell, D.; Pringle, J. E.
- Monthly Notices of the Royal Astronomical Society, Vol. 168, Issue 3
The minimum-mass extrasolar nebula: in situ formation of close-in super-Earths
journal, April 2013
- Chiang, Eugene; Laughlin, Gregory
- Monthly Notices of the Royal Astronomical Society, Vol. 431, Issue 4
Diffusive Migration of Low‐Mass Protoplanets in Turbulent Disks
journal, August 2006
- Johnson, Eric T.; Goodman, Jeremy; Menou, Kristen
- The Astrophysical Journal, Vol. 647, Issue 2
Which planets trigger longer lived vortices: low-mass or high-mass?
journal, April 2021
- Hammer, Michael; Lin, Min-Kai; Kratter, Kaitlin M.
- Monthly Notices of the Royal Astronomical Society, Vol. 504, Issue 3
Gaps and Rings in an ALMA Survey of Disks in the Taurus Star-forming Region
journal, December 2018
- Long, Feng; Pinilla, Paola; Herczeg, Gregory J.
- The Astrophysical Journal, Vol. 869, Issue 1
Measuring Turbulent Motion in Planet-forming Disks with ALMA: A Detection around DM Tau and Nondetections around MWC 480 and V4046 Sgr
journal, June 2020
- Flaherty, Kevin; Hughes, A. Meredith; Simon, Jacob B.
- The Astrophysical Journal, Vol. 895, Issue 2
Orbital eccentricity growth through disc-companion tidal interaction
journal, January 2001
- Papaloizou, J. C. B.; Nelson, R. P.; Masset, F.
- Astronomy & Astrophysics, Vol. 366, Issue 1
Effects of dust Feedback on Vortices in Protoplanetary Disks
journal, October 2014
- Fu, Wen; Li, Hui; Lubow, Stephen
- The Astrophysical Journal, Vol. 795, Issue 2
Accretion of Gas Giants Constrained by the Tidal Barrier
journal, January 2021
- Li, Ya-Ping; Chen, Yi-Xian; Lin, Douglas N. C.
- The Astrophysical Journal, Vol. 906, Issue 1
Shallow Cavities in Multiple-Planet Systems
journal, March 2015
- Duffell, Paul C.; Dong, Ruobing
- The Astrophysical Journal, Vol. 802, Issue 1
Orbital evolution of eccentric planets in radiative discs
journal, November 2010
- Bitsch, B.; Kley, W.
- Astronomy & Astrophysics, Vol. 523
Migration and Growth of Protoplanetary Embryos. i. Convergence of Embryos in Protoplanetary Disks
journal, November 2014
- Zhang, Xiaojia; Liu, Beibei; Lin, Douglas N. C.
- The Astrophysical Journal, Vol. 797, Issue 1
Multiple Disk Gaps and Rings Generated by a Single Super-Earth
journal, July 2017
- Dong, Ruobing; Li, Shengtai; Chiang, Eugene
- The Astrophysical Journal, Vol. 843, Issue 2
Modeling the resonant planetary system GJ 876
journal, June 2005
- Kley, W.; Lee, M. H.; Murray, N.
- Astronomy & Astrophysics, Vol. 437, Issue 2
On the Interaction between Protoplanets and Protostellar Disks
journal, September 2000
- Bryden, G.; Rożyczka, M.; Lin, D. N. C.
- The Astrophysical Journal, Vol. 540, Issue 2
Circumstellar Dust Distribution in Systems with Two Planets in Resonance
journal, January 2019
- Marzari, Francesco; D’Angelo, Gennaro; Picogna, Giovanni
- The Astronomical Journal, Vol. 157, Issue 2
Inferring giant planets from ALMA millimeter continuum and line observations in (transition) disks
journal, April 2018
- Facchini, S.; Pinilla, P.; van Dishoeck, E. F.
- Astronomy & Astrophysics, Vol. 612
Nonlinear spiral density waves - Viscous damping
journal, December 1985
- Shu, F. H.; Dones, L.; Lissauer, J. J.
- The Astrophysical Journal, Vol. 299