Formation of giant planets by fragmentation of protoplanetary disks

Science

Volumn 298, Issue 5599, 2002, Pages 1756-1759

  Mayer, Lucio ^a,d   Quinn, Thomas ^a   Wadsley, James ^b   Stadel, Joachim ^c,d  

^a UNIVERSITY OF WASHINGTON   (United States)

^b MCMASTER UNIVERSITY   (Canada)

^c UNIVERSITY OF VICTORIA   (Canada)

^d UNIVERSITY OF ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

GASES; HYDRODYNAMICS;

PROTOPLANETARY DISKS;

PLANETS;

FORMATION MECHANISM; FRAGMENTATION; PLANETARY EVOLUTION;

ARTICLE; ASTRONOMY; COOLING; EVOLUTION; GAS ANALYSIS; GRAVITY; HEATING; HYDRODYNAMICS; PARTICLE RADIATION; PRIORITY JOURNAL; TEMPERATURE MEASUREMENT; THREE DIMENSIONAL IMAGING;

COMPUTER SIMULATION; EVOLUTION, PLANETARY; GASES; GRAVITATION; HYDROGEN; JUPITER; PLANETS;

EID: 0037195639     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.1077635     Document Type: Article

References (35)

1. G. W. Marcy, R. P. Butler, Publ. Astron. Soc. Pac. 112, 137 (2000).
2. _, Annu. Rev. Astron. Astrophys. 36, 57 (1998).
3. J. B. Pollack et al., Icarus 124, 62 (1996).
4. J. Lissauer, Nature 409, 23 (2001).
5. J. Bally, L. Testi, A. Sargent, J. Carlstrom, Astron. J. 116, 854 (1998).
6. C. Briceno et al., Science 291, 93 (2001).
7. K. E. Haisch Jr., E. A. Lada, C. J. Lada, Astrophys. J. 553, L153 (2001).
8. H. B. Throop, J. Bally, J. L. W. Esposito, M. J. McCaughrean, Science 292, 1686 (2001).
9. D. N. C. Lin, J. C. B. Papaloizou, Astrophys. J. 309, 846 (1986).
10. G. Bryden, X. Chen, D. N. C. Lin, R. P. Nelson, J. C. B. Papaloizou, Astrophys. J. 514, 344 (1999).
11. R. P. Nelson, J. C. B. Papaloizou, F. Masset, W. Kley, Mon. Not. R. Astron. Soc. 318, 18 (2000).
12. H. Tanaka, T. Takeuchi, W. Ward, Astrophys. J. 565, 1257 (2002).
13. A. P. Boss, Astrophys. J. 503, 923 (1998),
14. S. J. Weidenschilling, Astrophys. Space. Sci. 51, 153, (1977).
15. A. P. Boss, Science 276, 1836 (1997).
16. _, Astrophys. J. 563, 367 (2001).
17. _, Annu. Rev. Astron. Astrophys. 26, 53 (1998).
18. P. D'Alessio, N. Calvet, L. Hartmann, Astrophys. J. 553, 321 (2001).
19. T. Guillot, Science 286, 72 (1999).
20. A. P. Boss, G. W. Wetherill, N. Haghighipour, Icarus 156, 291 (2002).
21. R. A. Gingold, J. J. Monaghan, Mon. Not. R. Astron. Soc. 181, 357 (1977).
22. G. Laughlin, P. Bodenheimer, Astrophys. J. 436, 335 (1994).
23. A. F. Nelson, W. Benz, F. C. Adams, D. Arnett, Astrophys. J. 502, 342 (1998).
24. A. F. Nelson, W. Benz, T. V. Ruzmaikina, Astrophys. J. 529, 457 (2000).
25. B. K. Pickett, P. Cassen, R. H. Durisen, R. Link, Astrophys. J. 529, 1034 (2000).
26. B. K. Pickett, R. H. Durisen, P. Cassen, C. Mejia, Astrophys. J. 540, L95 (2000).
27. Artificial viscosity is used in both the momentum and the energy equation, but its contribution is minimized when the local flow is purely shearing by means of a correction term originally introduced by D. S. Balsara [Comput. Phys. 121, 357 (1995)]; the latter term is necessary to prevent SPH from generating a large artificial viscosity in a purely shearing flow. In addition, when the disk evolves following a locally isothermal equation of state, any entropy generated by the viscosity term is assumed to be instantly radiated away.
28. The Jeans mass is always resolved by more than several thousand particles at the locations of the clumps; this resolution is more than an order of magnitude higher than required to avoid artificial fragmentation based on the criteria developed by M. Bate and A. Burkert [Mon. Not. R. Astron. Soc. 288, 1060 (1997)] for 3D SPH simulations.
29. In this regime, reversible heating arising from compressions is not radiated away, and the artificial viscosity creates irreversible heating in regions where shock waves occur.
30. C. Terquem, J. C. B. Papaloizou, Mon. Not. R. Astron. Soc. 332, L39 (2002).
31. For this test, we increased the temperature of the more massive disk model (resolved by 200,000 partic[es) by a factor of two, reaching 100 K in the outer region; 350 years after the start of the simulations, the disk was still fairly axisymmetric and we started cooling it at the constant rate of about 0.2 K/year. The disk underwent increasingly strong spiral instabilities as it was cooled down, which produced an inward flux of mass and outward flux of angular momentum, but, overall, the outer surface density barely changed. Therefore, reaching a temperature only slightly smaller than that used in the standard initial conditions (42 K as opposed to 50 K) was enough to compensate for the decrease of surface density and give rise to clump formation after about 650 years. (Cooling was stopped when fragmentation was approached.)
32. K. L. Luhman, R. Jayawardhana, Astrophys. J. 566, 1132 (2002).
33. E. W. Thommes, M. J. Duncan, H. F. Levison, Astron. J, 123, 2862 (2002).
34. J. Stadel, J. Wadsley, D. Richardson, in High Performance Computing Systems and Applications, M. J. Dimoupulos, K. F. Lie, Eds. (Kluwer Academic, Boston, 2002), p. 501.
35. The authors thank G. Laughlin, D. Hollenbach, and A. Boss for useful and stimulating discussions. Simulations were carried outat the Pittsburgh Supercomputing Center and at Consorzio Interuniversitario per il Calcolo Automatico dell'Italia Nord Orientale. This research was supported by a grant from the NSF and by the NASA Astrobiology Institute.