Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Planet heating prevents inward migration of planetary cores

Abstract

Planetary systems are born in the disks of gas, dust and rocky fragments that surround newly formed stars. Solid content assembles into ever-larger rocky fragments that eventually become planetary embryos. These then continue their growth by accreting leftover material in the disk. Concurrently, tidal effects in the disk cause a radial drift in the embryo orbits, a process known as migration1,2,3,4. Fast inward migration is predicted by theory for embryos smaller than three to five Earth masses5,6,7. With only inward migration, these embryos can only rarely become giant planets located at Earth's distance from the Sun and beyond8,9, in contrast with observations10. Here we report that asymmetries in the temperature rise associated with accreting infalling material11,12 produce a force (which gives rise to an effect that we call ‘heating torque’) that counteracts inward migration. This provides a channel for the formation of giant planets8 and also explains the strong planet–metallicity correlation found between the incidence of giant planets and the heavy-element abundance of the host stars13,14.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Comparison of the torques in the cases with and without heating.
Figure 2: Heating torque for different growth timescales.
Figure 3: Density in the vicinity of an irradiating embryo.

Similar content being viewed by others

References

  1. Goldreich, P. & Tremaine, S. Disk-satellite interactions. Astrophys. J. 241, 425–441 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  2. Ward, W. R. Protoplanet migration by nebula tides. Icarus 126, 261–281 (1997).

    Article  ADS  CAS  Google Scholar 

  3. Kley, W. & Nelson, R. P. Planet-disk interaction and orbital evolution. Annu. Rev. Astron. Astrophys. 50, 211–249 (2012).

    Article  ADS  Google Scholar 

  4. Baruteau, C. et al. Planet-disc interactions and early evolution of planetary systems. Preprint at http://arxiv.org/abs/1312.4293 (2013).

  5. Paardekooper, S.-J., Baruteau, C. & Kley, W. A torque formula for nonisothermal type I planetary migration—II. Effects of diffusion. Mon. Not. R. Astron. Soc. 410, 293–303 (2011).

    Article  ADS  Google Scholar 

  6. Masset, F. S. & Casoli, J. Saturated torque formula for planetary migration in viscous disks with thermal diffusion: recipe for protoplanet population synthesis. Astrophys. J. 723, 1393–1417 (2010).

    Article  ADS  Google Scholar 

  7. Tanaka, H., Takeuchi, T. & Ward, W. R. Three-dimensional interaction between a planet and an isothermal gaseous disk. I. Corotation and Lindblad torques and planet migration. Astrophys. J. 565, 1257–1274 (2002).

    Article  ADS  Google Scholar 

  8. Levison, H. F., Thommes, E. & Duncan, M. J. Modeling the formation of giant planet cores. I. Evaluating key processes. Astron. J. 139, 1297–1314 (2010).

    Article  ADS  Google Scholar 

  9. Cossou, C., Raymond, S. N., Hersant, F. & Pierens, A. Hot super-Earths and giant planet cores from different migration histories. Astron. Astrophys. 569, A56 (2014).

    Article  ADS  Google Scholar 

  10. Howard, A. W. Observed properties of extrasolar planets. Science 340, 572–576 (2013).

    Article  ADS  CAS  Google Scholar 

  11. Pollack, J. B. et al. Formation of the giant planets by concurrent accretion of solids and gas. Icarus 124, 62–85 (1996).

    Article  ADS  Google Scholar 

  12. Mordasini, C., Mollière, P., Dittkrist, K.-M., Jin, S. & Alibert, Y. Global models of planet formation and evolution. Preprint at http://arxiv.org/abs/1406.5604 (2014).

  13. Fischer, D. A. & Valenti, J. The planet-metallicity correlation. Astrophys. J. 622, 1102–1117 (2005).

    Article  ADS  CAS  Google Scholar 

  14. Wang, J. & Fischer, D. A. Revealing a universal planet-metallicity correlation for planets of different solar-type stars. Astron. J. 149, 14 (2015).

    Article  ADS  Google Scholar 

  15. Bitsch, B., Crida, A., Morbidelli, A., Kley, W. & Dobbs-Dixon, I. Stellar irradiated discs and implications on migration of embedded planets. I. Equilibrium discs. Astron. Astrophys. 549, A124 (2013).

    Article  ADS  Google Scholar 

  16. Jenkins, J. S. et al. in European Physical Journal Web of Conferences Vol. 47, 5001 (2013); http://dx.doi.org/10.1051/epjconf/20134705001.

  17. Hansen, B. M. S. & Murray, N. Testing in situ assembly with the Kepler Planet Candidate Sample. Astrophys. J. 775, 53 (2013).

    Article  ADS  Google Scholar 

  18. Chiang, E. & Laughlin, G. The minimum-mass extrasolar nebula: in situ formation of close-in super-Earths. Mon. Not. R. Astron. Soc. 431, 3444–3455 (2013).

    Article  ADS  Google Scholar 

  19. Walsh, K. J., Morbidelli, A., Raymond, S. N., O'Brien, D. P. & Mandell, A. M. A low mass for Mars from Jupiter's early gas-driven migration. Nature 475, 206–209 (2011).

    Article  ADS  CAS  Google Scholar 

  20. Ramsey, J. P. & Dullemond, C. P. Radiation hydrodynamics including irradiation and adaptive mesh refinement with AZEuS. I. Methods. Preprint at http://arxiv.org/abs/1409.3011 (2014).

  21. Hayashi, C., Nakazawa, K. & Nakagawa, Y. in Protostars and Planets II (eds Black, D. C. & Matthews, M. S.) 1100–1153, 1985.

  22. Stone, J. M. & Norman, M. L. ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. I—The hydrodynamic algorithms and tests. Astrophys. J. Suppl. Ser. 80, 753–790 (1992).

    Article  ADS  Google Scholar 

  23. Masset F. FARGO: A fast eulerian transport algorithm for differentially rotating disks. Astron. Astrophys. Suppl. 141, 165–173 (2000).

    Article  ADS  Google Scholar 

  24. Szulágyi, J., Morbidelli, A., Crida, A. & Masset, F. Accretion of Jupiter-mass planets in the limit of vanishing viscosity. Astrophys. J. 782, 65 (2014).

    Article  ADS  Google Scholar 

  25. Commerçon, B., Debout, V. & Teyssier, R. A fast, robust, and simple implicit method for adaptive time-stepping on adaptive mesh-refinement grids. Astron. Astrophys. 563, A11 (2014).

    Article  ADS  Google Scholar 

  26. Crida, A., Baruteau, C., Kley, W. & Masset, F. The dynamical role of the circumplanetary disc in planetary migration. Astron. Astrophys. 502, 679–693 (2009).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank A. Morbidelli for a critical reading of a first version of this manuscript. P.B.-Ll. thanks CONICET for financial support. This research was supported by UNAM grants PAPIIT IA101113 and IN105313 and by CONACyT grants 178377 and 129343. J.Sz. acknowledges support from the Capital Fund Management's J. P. Aguilar Grant. We also thank U. Amaya Olvera, R. García Carreón and J. Verleyen for their assistance in setting up the GPU cluster on which the calculations presented here have been run.

Author information

Authors and Affiliations

Authors

Contributions

P.B.-Ll. performed the numerical simulations and their subsequent reduction. F.M. designed the project and wrote the Methods. G.K. wrote the main paper. J.Sz. provided assistance with the radiative transfer module. All authors contributed to the discussion presented in this manuscript.

Corresponding author

Correspondence to Frédéric Masset.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Exploration of the parameter space.

Heating torque ΓH normalized to the absolute value of the torque of the non-accreting case |ΓNH|, as a function of embryo mass Mp, opacity κ and mass doubling time τ. Whenever one parameter is varying, others have the value of the fiducial run. Mass-doubling times are given in units of years and show that a positive torque results for τ 60,000 years. The right axis shows the total torque Γ = ΓH + ΓNH, also normalized to |ΓNH|. The horizontal dashed line corresponds to no migration. Source data for this figure are available online.

Source data

PowerPoint slides

Source data

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Benítez-Llambay, P., Masset, F., Koenigsberger, G. et al. Planet heating prevents inward migration of planetary cores. Nature 520, 63–65 (2015). https://doi.org/10.1038/nature14277

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature14277

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing