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Smoothed Particle Hydrodynamics for astrophysical flows

The dynamics of protostellar discs

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Abstract

In this paper we describe the application of the Smoothed Particle Hydrodynamics (SPH) method to the dynamics of protostellar discs, and in particular to the problem of characterising gravitational instabilities in such discs. Initially, we briefly describe the basic features of SPH, a Lagrangian mesh-free method of solving the equations of fluid dynamics which is widely used in astrophysics. We highlight those features of SPH that should be particularly kept in mind when simulating accretion discs --these include both physical and artificial viscosity-- that directly affect the transport of angular momentum in the code. We then describe some recent advances in our understanding of the development and non-linear behaviour of gravitational instabilities in accretion discs, paying particular attention to the problem of numerical convergence within SPH simulations of self-gravitating discs.

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References

  1. L.B. Lucy, Astron. J. 82, 1013 (1977)

    Article  ADS  Google Scholar 

  2. R.A. Gingold, J.J. Monaghan, Mon. Not. R. Astron. Soc. 181, 375 (1977)

    ADS  MATH  Google Scholar 

  3. W. Benz, in The Numerical Modeling of Nonlinear Stellar Pulsations, edited by J. Buchler (Kluwer, Dordrecht, 1990)

  4. J.J. Monaghan, Annu. Rev. Astron. Astrophys. 30, 543 (1992)

    Article  ADS  Google Scholar 

  5. V. Springel, Mon. Not. R. Astron. Soc. 364, 1105 (2005)

    Article  ADS  Google Scholar 

  6. V. Springel, S.D.M. White, A. Jenkins, C.S. Frenk, N. Yoshida, L. Gao, J. Navarro, R. Thacker, D. Croton, J. Helly et al., Nature 435, 629 (2005)

    Article  ADS  Google Scholar 

  7. S. Borgani, G. Murante, V. Springel, A. Diaferio, K. Dolag, L. Moscardini, G. Tormen, L. Tornatore, P. Tozzi, Mon. Not. R. Astron. Soc. 348, 1078 (2004)

    Article  ADS  Google Scholar 

  8. S. Callegari, L. Mayer, S. Kazantzidis, M. Colpi, F. Governato, T. Quinn, J. Wadsley, Astrophys. J. Lett. 696, L89 (2009)

    Article  ADS  Google Scholar 

  9. S. Rosswog, Astrophys. J. 634, 1202 (2005)

    Article  ADS  Google Scholar 

  10. D.J. Price, S. Rosswog, Science 312, 719 (2006)

    Article  ADS  Google Scholar 

  11. S. Rosswog, E. Ramirez-Ruiz, W.R. Hix, Astrophys. J. 695, 404 (2009)

    Article  ADS  Google Scholar 

  12. E.M. Rossi, G. Lodato, P.J. Armitage, J.E. Pringle, A.R. King, Mon. Not. R. Astron. Soc. 401, 2021 (2010)

    Article  ADS  Google Scholar 

  13. C.R. Evans, C.S. Kochanek, Astrophys. J. 346, L13 (1989)

    Article  ADS  Google Scholar 

  14. G. Lodato, A.R. King, J.E. Pringle, Mon. Not. R. Astron. Soc. 392, 332 (2009)

    Article  ADS  Google Scholar 

  15. C.L. Dobbs, I.A. Bonnell, Mon. Not. R. Astron. Soc. 385, 1893 (2008)

    Article  ADS  Google Scholar 

  16. C.L. Dobbs, D.J. Price, Mon. Not. R. Astron. Soc. 383, 497 (2008)

    Article  ADS  Google Scholar 

  17. M.R. Bate, I.A. Bonnell, V. Bromm, Mon. Not. R. Astron. Soc. 339, 577 (2003)

    Article  ADS  Google Scholar 

  18. M.R. Bate, Mon. Not. R. Astron. Soc. 404, L79 (2010)

    Article  ADS  Google Scholar 

  19. G. Lodato, W.K.M. Rice, Mon. Not. R. Astron. Soc. 351, 630 (2004)

    Article  ADS  Google Scholar 

  20. G. Lodato, W.K.M. Rice, Mon. Not. R. Astron. Soc. 358, 1489 (2005)

    Article  ADS  Google Scholar 

  21. P. Cossins, G. Lodato, C.J. Clarke, Mon. Not. R. Astron. Soc. 393, 1157 (2009)

    Article  ADS  Google Scholar 

  22. L. Mayer, G. Lufkin, T. Quinn, J. Wadsley, Astrophys. J. 661, L77 (2007)

    Article  ADS  Google Scholar 

  23. J.J. Monaghan, Rep. Prog. Phys. 68, 1703 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  24. M.J. Berger, P. Colella, J. Comput. Phys. 82, 64 (1989)

    Article  ADS  MATH  Google Scholar 

  25. L. Hernquist, N. Katz, Astrophys. J. Suppl. 70, 419 (1989)

    Article  ADS  Google Scholar 

  26. M.R. Bate, I.A. Bonnell, N.M. Price, Mon. Not. R. Astron. Soc. 277, 362 (1995)

    ADS  Google Scholar 

  27. O. Flebbe, S. Muenzel, H. Herold, H. Riffert, H. Ruder, Astrophys. J. 431, 754 (1994)

    Article  ADS  Google Scholar 

  28. P. Espa\~n, Phys. Rev. E 67, 026705 (2003)

    Article  ADS  Google Scholar 

  29. D. Sijacki, V. Springel, Mon. Not. R. Astron. Soc. 371, 1025 (2006)

    Article  ADS  Google Scholar 

  30. S.C. Whitehouse, M.R. Bate, J.J. Monaghan, Mon. Not. R. Astron. Soc. 364, 1367 (2005)

    Article  ADS  Google Scholar 

  31. L. Tornatore, S. Borgani, F. Matteucci, S. Recchi, P. Tozzi, Mon. Not. R. Astron. Soc. 349, L19 (2004)

    Article  ADS  Google Scholar 

  32. W. Benz, F. Thielemann, J.G. Hills, Astrophys. J. 342, 986 (1989)

    Article  ADS  Google Scholar 

  33. D.J. Price, J.J. Monaghan, Mon. Not. R. Astron. Soc. 348, 123 (2004)

    Article  ADS  Google Scholar 

  34. D.J. Price, J.J. Monaghan, Mon. Not. R. Astron. Soc. 348, 139 (2004)

    Article  ADS  Google Scholar 

  35. D.J. Price, J.J. Monaghan, Mon. Not. R. Astron. Soc. 364, 384 (2005)

    ADS  Google Scholar 

  36. D.J. Price, Mon. Not. R. Astron. Soc. 401, 1475 (2010)

    Article  ADS  Google Scholar 

  37. S. Rosswog, J. Comput. Phys. 229, 8591 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. S. Rosswog, New Astron. Rev. 53, 78 (2009)

    Article  ADS  Google Scholar 

  39. J.J. Monaghan, D.J. Price, Mon. Not. R. Astron. Soc. 328, 381 (2001)

    Article  ADS  Google Scholar 

  40. D. Price, PhD Thesis, ArXiv Astrophysics e-prints 0507472 (2005)

  41. D.J. Price, ArXiv e-prints (2010) 1012.1885

  42. P.J. Cossins, arXiv:1007.1245 (2010)

  43. M.S. Fulbright, W. Benz, M.B. Davies, Astrophys. J. 440, 254 (1995)

    Article  ADS  Google Scholar 

  44. D.A. Fulk, D.W. Quinn, J. Comput. Phys. 126, 165 (1996)

    Article  ADS  MATH  Google Scholar 

  45. J.J. Monaghan, Comput. Phys. Rep. 3, 71 (1985) ISSN 0167-7977

    Article  ADS  Google Scholar 

  46. J.I. Read, T. Hayfield, O. Agertz, Mon. Not. R. Astron. Soc. 405, 1513 (2010)

    ADS  Google Scholar 

  47. J.J. Monaghan, J.C. Lattanzio, Astron. Astrophys. 149, 135 (1985)

    ADS  MATH  Google Scholar 

  48. L. Cullen, W. Dehnen, Mon. Not. R. Astron. Soc. 408, 669 (2010)

    Article  ADS  Google Scholar 

  49. C. Eckart, Phys. Fluids 3, 421 (1960)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. W. Dehnen, Mon. Not. R. Astron. Soc. 324, 273 (2001)

    Article  ADS  Google Scholar 

  51. D.J. Price, J.J. Monaghan, Mon. Not. R. Astron. Soc. 374, 1347 (2007)

    Article  ADS  Google Scholar 

  52. V. Springel, L. Hernquist, Mon. Not. R. Astron. Soc. 333, 649 (2002)

    Article  ADS  Google Scholar 

  53. V. Springel, N. Yoshida, S.D.M. White, New Astron. Rev. 6, 79 (2001)

    Article  Google Scholar 

  54. B.M. Johnson, C.F. Gammie, Astrophys. J. 597, 131 (2003)

    Article  ADS  Google Scholar 

  55. D. Forgan, K. Rice, D. Stamatellos, A. Whitworth, Mon. Not. R. Astron. Soc. 394, 882 (2009)

    Article  ADS  Google Scholar 

  56. M. Petkova, V. Springel, Mon. Not. R. Astron. Soc. 396, 1383 (2009)

    Article  ADS  Google Scholar 

  57. S. Nayakshin, S. Cha, A. Hobbs, Mon. Not. R. Astron. Soc. 397, 1314 (2009)

    Article  ADS  Google Scholar 

  58. J.J. Monaghan, J. Comput. Phys. 136, 298 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  59. D.S. Balsara, PhD Thesis, Illinois University, Urbana-Champaign (1991)

  60. J.P. Morris, J.J. Monaghan, J. Comput. Phys. 136, 41 (1997)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  61. N.I. Shakura, R.A. Sunyaev, Astron. Astrophys. 24, 337 (1973)

    ADS  Google Scholar 

  62. A.R. King, J.E. Pringle, M. Livio, Mon. Not. R. Astron. Soc. 376, 1740 (2007)

    Article  ADS  Google Scholar 

  63. L. Hartmann, N. Calvet, E. Gullbring, P. D’Alessio, Astrophys. J. 495, 385 (1998)

    Article  ADS  Google Scholar 

  64. G. Lodato, C.J. Clarke, Mon. Not. R. Astron. Soc. 353, 841 (2004)

    Article  ADS  Google Scholar 

  65. G. Lodato, D.J. Price, Mon. Not. R. Astron. Soc. 405, 1212 (2010)

    ADS  Google Scholar 

  66. P. Artymowicz, S.H. Lubow, Astrophys. J. 421, 651 (1994)

    Article  ADS  Google Scholar 

  67. J.R. Murray, Mon. Not. R. Astron. Soc. 279, 402 (1996)

    ADS  Google Scholar 

  68. D.J. Price, C. Federrath, Mon. Not. R. Astron. Soc. 406, 1659 (2010)

    ADS  Google Scholar 

  69. O. Agertz, B. Moore, J. Stadel, D. Potter, F. Miniati, J. Read, L. Mayer, A. Gawryszczak, A. Kravtsov, Å. Nordlund et al., Mon. Not. R. Astron. Soc. 380, 963 (2007)

    Article  ADS  MATH  Google Scholar 

  70. D.J. Price, J. Comput. Phys. 227, 10040 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  71. S. Inutsuka, J. Comput. Phys. 179, 238 (2002)

    Article  ADS  MATH  Google Scholar 

  72. S.H. Cha, A.P. Whitworth, Mon. Not. R. Astron. Soc. 340, 73 (2003)

    Article  ADS  Google Scholar 

  73. F. Shu, Astrophys. J. 214, 488 (1977)

    Article  ADS  Google Scholar 

  74. F. Shu, F.C. Adams, S. Lizano, Annu. Rev. Astron. Astrophys. 25, 23 (1987)

    Article  ADS  Google Scholar 

  75. C.F. McKee, E.C. Ostriker, Annu. Rev. Astron. Astrophys. 45, 565 (2007)

    Article  ADS  Google Scholar 

  76. S.A. Balbus, Annu. Rev. Astron. Astrophys. 41, 555 (2003)

    Article  ADS  Google Scholar 

  77. W.K.M. Rice, P.J. Armitage, M.R. Bate, I.A. Bonnell, Mon. Not. R. Astron. Soc. 339, 1025 (2003)

    Article  ADS  Google Scholar 

  78. W.K.M. Rice, G. Lodato, P.J. Armitage, Mon. Not. R. Astron. Soc. 364, L56 (2005)

    ADS  Google Scholar 

  79. P. Cossins, G. Lodato, C. Clarke, Mon. Not. R. Astron. Soc. 401, 2587 (2010)

    Article  ADS  Google Scholar 

  80. D. Stamatellos, D.A. Hubber, A.P. Whitworth, Mon. Not. R. Astron. Soc. 382, L30 (2007)

    Article  ADS  Google Scholar 

  81. D. Stamatellos, A.P. Whitworth, Astron. Astrophys. 480, 879 (2008)

    Article  ADS  Google Scholar 

  82. D. Stamatellos, A.P. Whitworth, Mon. Not. R. Astron. Soc. 392, 413 (2009)

    Article  ADS  Google Scholar 

  83. D. Stamatellos, A.P. Whitworth, Mon. Not. R. Astron. Soc. 400, 1563 (2009)

    Article  ADS  Google Scholar 

  84. S. Walch, A. Burkert, A. Whitworth, T. Naab, M. Gritschneder, Mon. Not. R. Astron. Soc. 400, 13 (2009)

    Article  ADS  Google Scholar 

  85. S. Walch, T. Naab, A. Whitworth, A. Burkert, M. Gritschneder, Mon. Not. R. Astron. Soc. 402, 2253 (2010)

    Article  ADS  Google Scholar 

  86. G. Bertin, Dynamics of Galaxies (Cambridge University Press, 2000)

  87. G. Bertin, Astrophys. J. 478, L71 (1997)

    Article  ADS  Google Scholar 

  88. G. Bertin, G. Lodato, Astron. Astrophys. 350, 694 (1999)

    ADS  Google Scholar 

  89. M. Krumholz, A. Burkert, Astrophys. J. 724, 895 (2010)

    Article  ADS  Google Scholar 

  90. A. Toomre, Astrophys. J. 139, 1217 (1964)

    Article  ADS  Google Scholar 

  91. W.K.M. Rice, G. Lodato, P.J. Armitage, Mon. Not. R. Astron. Soc. 364, L56 (2005)

    ADS  Google Scholar 

  92. W.K.M. Rice, P.J. Armitage, I.A. Bonnell, M.R. Bate, S.V. Jeffers, S.G. Vine, Mon. Not. R. Astron. Soc. 346, L36 (2003)

    Article  ADS  Google Scholar 

  93. C.F. Gammie, Astrophys. J. 553, 174 (2001)

    Article  ADS  Google Scholar 

  94. A.P. Boss, Science 276, 1836 (1997)

    Article  ADS  Google Scholar 

  95. A.P. Boss, Nature 393, 141 (1998)

    Article  ADS  Google Scholar 

  96. A.P. Boss, Astrophys. J. 536, L101 (2000)

    Article  ADS  Google Scholar 

  97. A.C. Boley, Astrophys. J. Lett. 695, L53 (2009) 0902.3999

    Article  ADS  Google Scholar 

  98. A.C. Boley, T. Hayfield, L. Mayer, R.H. Durisen, Icarus 207, 509 (2010)

    Article  ADS  Google Scholar 

  99. R. Rafikov, Astrophys. J. 621, 69 (2005)

    Article  ADS  Google Scholar 

  100. C.J. Clarke, Mon. Not. R. Astron. Soc. 396, 1066 (2009)

    Article  ADS  Google Scholar 

  101. E.I. Vorobyov, S. Basu, Astrophys. J. 714, L133 (2010)

    Article  ADS  Google Scholar 

  102. E.I. Vorobyov, S. Basu, Astrophys. J. 719, 1896 (2010)

    Article  ADS  Google Scholar 

  103. B. Paczynski, Acta Astron. 28, 91 (1978)

    ADS  Google Scholar 

  104. G. Lodato, Riv. Nuovo Cimento 30, 293 (2007)

    Google Scholar 

  105. B.K. Pickett, A.C. Mejía, R.H. Durisen, P.M. Cassen, D.K. Berry, R.P. Link, Astrophys. J. 590, 1060 (2003)

    Article  ADS  Google Scholar 

  106. A.C. Mejia, R.H. Durisen, M.K. Pickett, K. Cai, Astrophys. J. 619, 1098 (2005)

    Article  ADS  Google Scholar 

  107. A.C. Boley, A.C. Mejía, R.H. Durisen, K. Cai, M.K. Pickett, P. D’Alessio, Astrophys. J. 651, 517 (2006)

    Article  ADS  Google Scholar 

  108. J.E. Pringle, Annu. Rev. Astron. Astrophys. 19, 137 (1981)

    Article  ADS  Google Scholar 

  109. Z. Fan, Y.Q. Lou, Mon. Not. R. Astron. Soc. 307, 645 (1999)

    Article  ADS  Google Scholar 

  110. F. Meru, M.R. Bate, Mon. Not. R. Astron. Soc. 410, 559 (2011)

    Article  ADS  Google Scholar 

  111. F. Meru, M.R. Bate, Mon. Not. R. Astron. Soc. 411, L1 (2011)

    Article  ADS  Google Scholar 

  112. G. Lodato, C.C. Clarke, ArXiv e-prints (2011) 1101.2448

  113. A.P. Boss, Astrophys. J. 610, 456 (2004)

    Article  ADS  Google Scholar 

  114. A.P. Boss, Astrophys. J. 641, 1148 (2006)

    Article  ADS  Google Scholar 

  115. M.R. Bate, A. Burkert, Mon. Not. R. Astron. Soc. 288, 1060 (1997)

    ADS  Google Scholar 

  116. A.F. Nelson, Mon. Not. R. Astron. Soc. 373, 1039 (2006)

    Article  ADS  Google Scholar 

  117. C. Marois, B. Macintosh, T. Barman, B. Zuckerman, I. Song, J. Patience, D. Lafreni\`e, Science 322, 1348 (2008)

    Article  ADS  Google Scholar 

  118. A. Lagrange, D. Gratadour, G. Chauvin, T. Fusco, D. Ehrenreich, D. Mouillet, G. Rousset, D. Rouan, F. Allard, \’E, Astron. Astrophys. 493, L21 (2009)

    Article  ADS  Google Scholar 

  119. P. Kalas, J.R. Graham, E. Chiang, M.P. Fitzgerald, M. Clampin, E.S. Kite, K. Stapelfeldt, C. Marois, J. Krist, Science 322, 1345 (2008)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, Milano, Italy

    G. Lodato

  2. Department of Physics and Astronomy, University of Leicester, LE1 7RH, Leicester, UK

    P. J. Cossins

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  1. G. Lodato
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Lodato, G., Cossins, P.J. Smoothed Particle Hydrodynamics for astrophysical flows. Eur. Phys. J. Plus 126, 44 (2011). https://doi.org/10.1140/epjp/i2011-11044-6

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