The DOI matches its Crossref record; 44 of the 44 references it cites were found in a registry or an index.
A torque formula for non-isothermal type I planetary migration - I. Unsaturated horseshoe drag
Open accessAbstract
We study the torque on low-mass planets embedded in protoplanetary discs in the two-dimensional approximation, incorporating non-isothermal effects. We couple linear estimates of the Lindblad (or wave) torque to a simple, but non-linear, model of adiabatic corotation torques (or horseshoe drag), resulting in a simple formula that governs type I migration in non-isothermal discs. This formula should apply in optically thick regions of the disc, where viscous and thermal diffusion act to keep the horseshoe drag unsaturated. We check this formula against numerical hydrodynamical simulations, using three independent numerical methods, and find good agreement.
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Cites
Formation of the Giant Planets by Concurrent Accretion of Solids and Gas
Pollack, J. B., Hubickyj, O., Bodenheimer, P., Lissauer, J. J., Podolak, M., & Greenzweig, Y. (1996) · Icarus · doi:10.1006/icar.1996.0190 · Cited by 3,127
Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
Van Leer, B. (1977) · Journal of Computational Physics · doi:10.1016/0021-9991(77)90095-x · Cited by 2,433
Aerodynamics of solid bodies in the solar nebula
Weidenschilling, S. J. (1977) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/180.2.57 · Cited by 1,984
Giant Planet Formation by Gravitational Instability
Boss, A. P. (1997) · Science · doi:10.1126/science.276.5320.1836 · Cited by 1,124 · cited 1×
“An alternative scenario involves direct fragmentation of the disc (Boss 1997), which is probably only possible in the outermost regions of the disc (Boley 2009).”
BackgroundTanaka, H., Takeuchi, T., & Ward, W. R. (2002) · The Astrophysical Journal · doi:10.1086/324713 · Cited by 1,076
Protoplanet Migration by Nebula Tides
Ward, W. R. (1997) · Icarus · doi:10.1006/icar.1996.5647 · Cited by 1,071
Lin, D. N. C., & Papaloizou, J. (1986) · The Astrophysical Journal · doi:10.1086/164653 · Cited by 1,054
The excitation of density waves at the Lindblad and corotation resonances by an external potential
Goldreich, P., & Tremaine, S. (1979) · The Astrophysical Journal · doi:10.1086/157448 · Cited by 892
Models of giant planet formation with migration and disc evolution
Alibert, Y., Mordasini, C., Benz, W., & Winisdoerffer, C. (2005) · Astronomy & Astrophysics · doi:10.1051/0004-6361:20042032 · Cited by 685
Rossby Wave Instability of Keplerian Accretion Disks
Lovelace, R. V. E., Li, H., Colgate, S. A., & Nelson, A. F. (1999) · The Astrophysical Journal · doi:10.1086/306900 · Cited by 621
Cited by
PLANET OCCURRENCE WITHIN 0.25 AU OF SOLAR-TYPE STARS FROM KEPLER
Howard, A. W., Marcy, G. W., Bryson, S. T., Jenkins, J. M., Rowe, J. F., Batalha, N. M., Borucki, W. J., Koch, D. G., Dunham, E. W., Gautier, T. N., et al. (2012) · The Astrophysical Journal Supplement Series · doi:10.1088/0067-0049/201/2/15 · Cited by 1,151
Planet-Disk Interaction and Orbital Evolution
Kley, W., & Nelson, R. P. (2012) · Annual Review of Astronomy and Astrophysics · doi:10.1146/annurev-astro-081811-125523 · Cited by 722
Self-citationThe structure of protoplanetary discs around evolving young stars
Bitsch, B., Johansen, A., Lambrechts, M., & Morbidelli, A. (2015) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201424964 · Cited by 300
GAS GIANT PLANETS AS DYNAMICAL BARRIERS TO INWARD-MIGRATING SUPER-EARTHS
Izidoro, A., Raymond, S. N., Morbidelli, A., Hersant, F., & Pierens, A. (2015) · The Astrophysical Journal · doi:10.1088/2041-8205/800/2/l22 · Cited by 114
Giant planet formation in radially structured protoplanetary discs
Coleman, G. A. L., & Nelson, R. P. (2016) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stw1177 · Cited by 79
Metadata
- Authors
- Paardekooper, S.-J., Baruteau, C., Crida, A., & Kley, W.
- Venue
- Monthly Notices of the Royal Astronomical Society
- Publisher
- Oxford University Press (OUP)
- Published
- 2010-01-21
- Volume
- 401
- Issue
- 3
- Pages
- 1950-1964
- ISSN
- 0035-8711 (ISSN-L)
- 1365-2966
- OpenAlex
- W2149048791
- Cited by
- 448
- References
- 44
- FWCI
- 13.71
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Paardekooper, S.-J., Baruteau, C., Crida, A., & Kley, W. (2010). A torque formula for non-isothermal type I planetary migration - I. Unsaturated horseshoe drag. Monthly Notices of the Royal Astronomical Society. https://doi.org/10.1111/j.1365-2966.2009.15782.x
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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