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.
Similar content being viewed by others
References
Binney, J., Tremaine, S.A.: Galactic Dynamics. Princeton University Press, Princeton (1987)
Boley, A.C., Durisen, R.H.: Hydraulic/shock jumps in protoplanetary disks. Astrophys. J. 641, 534–546 (2006)
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)
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)
Boss, A.P.: Giant planet formation by gravitational instability. Science 267, 1836–1839 (1997)
Boss, A.P.: Evolution of the Solar Nebula. IV. Giant gaseous protoplanet formation. Astrophys. J. 503, 923–937 (1998)
Boss, A.P.: Possible rapid gas giant planet formation in the Solar Nebula. Astrophys. J. Lett. 536, L101–L104 (2000)
Boss, A.P.: Gas giant protoplanet formation: Disk instability models with thermodynamics and radiative transfer. Astrophys. J. 563, 367–373 (2001)
Boss, A.P.: Evolution of the Solar Nebula. V. Disk instabilities with varied thermodynamics. Astrophys. J. 576, 462–472 (2002)
Boss, A.P.: Gas giant protoplanet formation: Disk instability models with detailed thermodynamics and varied artificial viscosity. Lun. Planet. Inst. 34, 1075–1076 (2003)
Boss, A.P.: Convective cooling of protoplanetary disks and rapid giant planet formation. Astrophys. J. 610, 456–463 (2004)
Boss, A.P.: Evolution of the Solar Nebula. VII. Formation and survival of protoplanets formed by disk instability. Astrophys. J. 629, 535–548 (2005)
Boss, A.P.: Testing disk instability models for giant planet formation. Astrophys. J. Lett. 661, L73–L76 (2007)
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)
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)
Durisen, R.H., Mejía, A.C., Pickett, B.K.: Gravitational instabilities in protostellar and protoplanetary disks. Rec. Dev. Astrophys. 1, 173–201 (2003)
Gammie, C.F.: Nonlinear outcome of gravitational instability in cooling, gaseous disks. Astrophys. J. 553, 174–183 (2001)
Johnson, B.M., Gammie, C.F.: Nonlinear outcome of gravitational instability in disks with realistic cooling. Astrophys. J. 597, 131–141 (2003)
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)
Mayer, L., Quinn, T., Wadsley, J., Stadel, J.: Formation of giant planets by fragmentation of protoplanetary disks. Science 298, 1756–1759 (2002)
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)
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)
Nelson, A.F.: Numerical requirements for simulations of self gravitating and non-self-gravitating disks. Mon. Not. R. Astron. Soc. 373, 1039–1073 (2006)
Nelson, A.F., Benz, W., Adams, F.C., Arnett, D.: Dynamics of circumstellar disks. Astrophys. J. 502, 342–371 (1998)
Nelson, A.F., Benz, W., Ruzmaikina, T.V.: Dynamics of circumstellar disks. II. Heating and cooling. Astrophys. J. 529, 357–390 (2000)
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)
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)
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)
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)
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)
Rafikov, R.R.: Can gas giants form by direct gravitational instability? Astrophys. J. Lett. 621, L69–L72 (2005)
Rafikov, R.R.: Convective cooling and fragmentation of gravitationally unstable disks. Astrophys. J. 662, 642–650 (2006)
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)
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)
Toomre, A.: On the gravitational stability of a disk of stars. Astrophys. J. 139, 1217–1238 (1964)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Durisen, R.H., Hartquist, T.W. & Pickett, M.K. The formation of fragments at corotation in isothermal protoplanetary disks. Astrophys Space Sci 317, 3–8 (2008). https://doi.org/10.1007/s10509-008-9863-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-008-9863-y