Astrophysics and Space Science

, Volume 317, Issue 1–2, pp 3–8 | Cite as

The formation of fragments at corotation in isothermal protoplanetary disks

  • Richard H. Durisen
  • Thomas W. Hartquist
  • Megan K. Pickett
Original Article

Abstract

Numerical hydrodynamics simulations have established that disks which are evolved under the condition of local isothermality will fragment into small dense clumps due to gravitational instabilities when the Toomre stability parameter Q is sufficiently low. Because fragmentation through disk instability has been suggested as a gas giant planet formation mechanism, it is important to understand the physics underlying this process as thoroughly as possible. In this paper, we offer analytic arguments for why, at low Q, fragments are most likely to form first at the corotation radii of growing spiral modes, and we support these arguments with results from 3D hydrodynamics simulations.

Keywords

Accretion, accretion disks Hydrodynamics Instabilities Planetary systems: formation Planetary systems: protoplanetary disks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Binney, J., Tremaine, S.A.: Galactic Dynamics. Princeton University Press, Princeton (1987) MATHGoogle Scholar
  2. Boley, A.C., Durisen, R.H.: Hydraulic/shock jumps in protoplanetary disks. Astrophys. J. 641, 534–546 (2006) CrossRefADSGoogle Scholar
  3. Boley, A.C., Mejía, A.C., Durisen, R.H., Cai, K., Pickett, M.K.: The thermal regulation of gravitational instabilities in protoplanetary disks. III. Simulations with radiative cooling and realistic opacities. Astrophys. J. 651, 517–534 (2006) CrossRefADSGoogle Scholar
  4. Boley, A.C., Durisen, R.H., Nordlund, A., Lord, J.: 3D radiative hydrodynamics for disk stability simulations: A proposed testing standard and new results. Astrophys. J. 665, 1254–1267 (2007) CrossRefADSGoogle Scholar
  5. Boss, A.P.: Giant planet formation by gravitational instability. Science 267, 1836–1839 (1997) CrossRefADSGoogle Scholar
  6. Boss, A.P.: Evolution of the Solar Nebula. IV. Giant gaseous protoplanet formation. Astrophys. J. 503, 923–937 (1998) CrossRefADSGoogle Scholar
  7. Boss, A.P.: Possible rapid gas giant planet formation in the Solar Nebula. Astrophys. J. Lett. 536, L101–L104 (2000) CrossRefADSGoogle Scholar
  8. Boss, A.P.: Gas giant protoplanet formation: Disk instability models with thermodynamics and radiative transfer. Astrophys. J. 563, 367–373 (2001) CrossRefADSGoogle Scholar
  9. Boss, A.P.: Evolution of the Solar Nebula. V. Disk instabilities with varied thermodynamics. Astrophys. J. 576, 462–472 (2002) CrossRefADSGoogle Scholar
  10. Boss, A.P.: Gas giant protoplanet formation: Disk instability models with detailed thermodynamics and varied artificial viscosity. Lun. Planet. Inst. 34, 1075–1076 (2003) ADSGoogle Scholar
  11. Boss, A.P.: Convective cooling of protoplanetary disks and rapid giant planet formation. Astrophys. J. 610, 456–463 (2004) CrossRefADSGoogle Scholar
  12. Boss, A.P.: Evolution of the Solar Nebula. VII. Formation and survival of protoplanets formed by disk instability. Astrophys. J. 629, 535–548 (2005) CrossRefADSGoogle Scholar
  13. Boss, A.P.: Testing disk instability models for giant planet formation. Astrophys. J. Lett. 661, L73–L76 (2007) CrossRefADSGoogle Scholar
  14. Cai, K., Durisen, R.H., Michael, S., Boley, A.C., Mejía, A.C., Pickett, M.K., D’Alessio, P.: The effects of metallicity and grain size on gravitational instabilities in protoplanetary disks. Astrophys. J. Lett. 636, L149–L152 (2006) CrossRefADSGoogle Scholar
  15. Durisen, R.H., Boss, A.P., Mayer, L., Nelson, A.F., Quinn, T., Rice, W.K.M.: Gravitational instabilities in gaseous protoplanetary disks and implications for giant planet formation. In: Reipurth, B., Jewitt, D. (eds.) Protostars and Planets V, pp. 607–622. Lunar & Planetary Institute Press, Houston (2007) Google Scholar
  16. Durisen, R.H., Mejía, A.C., Pickett, B.K.: Gravitational instabilities in protostellar and protoplanetary disks. Rec. Dev. Astrophys. 1, 173–201 (2003) Google Scholar
  17. Gammie, C.F.: Nonlinear outcome of gravitational instability in cooling, gaseous disks. Astrophys. J. 553, 174–183 (2001) CrossRefADSGoogle Scholar
  18. Johnson, B.M., Gammie, C.F.: Nonlinear outcome of gravitational instability in disks with realistic cooling. Astrophys. J. 597, 131–141 (2003) CrossRefADSGoogle Scholar
  19. Mayer, L., Lufkin, G., Quinn, T., Wadsley, J.: Fragmentation of gravitationally unstable gaseous protoplanetary disks with radiative transfer. Astrophys. J. Lett. 661, L77–L80 (2007) CrossRefADSGoogle Scholar
  20. Mayer, L., Quinn, T., Wadsley, J., Stadel, J.: Formation of giant planets by fragmentation of protoplanetary disks. Science 298, 1756–1759 (2002) CrossRefADSGoogle Scholar
  21. Mayer, L., Quinn, T., Wadsley, J., Stadel, J.: The evolution of gravitationally unstable protoplanetary disks: Fragmentation and possible giant planet formation. Astrophys. J. 609, 1045–1064 (2004) CrossRefADSGoogle Scholar
  22. Mejía, A.C., Durisen, R.H., Pickett, M.K., Cai, K.: The thermal regulation of gravitational instabilities in protoplanetary disks. II. Extended simulations with varied cooling rates. Astrophys. J. 619, 1098–1113 (2005) CrossRefADSGoogle Scholar
  23. Nelson, A.F.: Numerical requirements for simulations of self gravitating and non-self-gravitating disks. Mon. Not. R. Astron. Soc. 373, 1039–1073 (2006) CrossRefADSGoogle Scholar
  24. Nelson, A.F., Benz, W., Adams, F.C., Arnett, D.: Dynamics of circumstellar disks. Astrophys. J. 502, 342–371 (1998) CrossRefADSGoogle Scholar
  25. Nelson, A.F., Benz, W., Ruzmaikina, T.V.: Dynamics of circumstellar disks. II. Heating and cooling. Astrophys. J. 529, 357–390 (2000) CrossRefADSGoogle Scholar
  26. Pickett, M.K., Durisen, R.H.: Numerical viscosity and the survival of gas giant planets in disk simulations. Astrophys. J. Lett. 654, L155–L158 (2007) CrossRefADSGoogle Scholar
  27. Pickett, M.K., Durisen, R.H., Maas, R.: The dependence of fragmentation and modes of fragmentation on Toomre Q in isothermal disk simulations. Astrophys. Space Sci. (2008, in preparation) Google Scholar
  28. Pickett, B.K., Cassen, P., Durisen, R.H., Link, R.: The effects of thermal energetics on three-dimensional hydrodynamic instabilities in massive protostellar disks. Astrophys. J. 504, 468–491 (1998) CrossRefADSGoogle Scholar
  29. Pickett, B.K., Cassen, P., Durisen, R.H., Link, R.: The effects of thermal energetics on three-dimensional hydrodynamic instabilities in massive protostellar disks. II. High-resolution and adiabatic evolutions. Astrophys. J. 529, 1034–1053 (2000) CrossRefADSGoogle Scholar
  30. Pickett, B.K., Mejía, A.C., Durisen, R.H., Cassen, P., Berry, D.K., Link, R.P.: The thermal regulation of gravitational instabilities in protoplanetary disks. Astrophys. J. 590, 1060–1080 (2003) CrossRefADSGoogle Scholar
  31. Rafikov, R.R.: Can gas giants form by direct gravitational instability? Astrophys. J. Lett. 621, L69–L72 (2005) CrossRefADSGoogle Scholar
  32. Rafikov, R.R.: Convective cooling and fragmentation of gravitationally unstable disks. Astrophys. J. 662, 642–650 (2006) CrossRefADSGoogle Scholar
  33. Rice, W.K.M., Armitage, P.J., Bate, M.R., Bonnel, I.A.: The effect of cooling on the global stability of self-gravitating protoplanetary discs. Mon. Not. R. Astron. Soc. 339, 1025–1030 (2003) CrossRefADSGoogle Scholar
  34. Rice, W.K.M., Lodato, G., Armitage, P.J.: Investigating fragmentation conditions in self-gravitating accretion disks. Mon. Not. R. Astron. Soc. 364, L56–L60 (2005) ADSGoogle Scholar
  35. Toomre, A.: On the gravitational stability of a disk of stars. Astrophys. J. 139, 1217–1238 (1964) CrossRefADSGoogle Scholar
  36. Truelove, J.K., Klein, R.I., McKee, C.F., Holliman, J.H. II, Howell, L.H., Greenough, J.A.: The Jeans condition: A new constraint on spatial resolution in simulations of isothermal self-gravitational hydrodynamics. Astrophys. J. Lett. 89, L179–L183 (1997) CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Richard H. Durisen
    • 1
  • Thomas W. Hartquist
    • 2
  • Megan K. Pickett
    • 3
  1. 1.Astronomy DepartmentIndiana UniversityBloomingtonUSA
  2. 2.School of Physics and AstronomyUniversity of LeedsLeedsUK
  3. 3.Department of PhysicsLawrence UniversityAppletonUSA

Personalised recommendations