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On the Modeling of a Compressible MHD Turbulence of an Accretion Protoplanetary Disk

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Abstract

In the framework of the basic problem of cosmogony, which is associated with the reconstruction of the protoplanetary solar disk at the very early stages of its existence, a closed system of MHD equations on the mean flow scale is formulated. This system is intended for numerical solution of problems on interconsistent simulation of the structure and evolution of the accretion protoplanetary disk and its corona. The model of a thin (but optically thick) disk is considered, in which turbulence dissipation due to kinematic and magnetic viscosity, opaqueness of the medium, accretion from the surrounding space, and the action of turbulent αω dynamo on the generation of magnetic field, as well as the magnetic force and energy interaction between the disk and its corona are taken into account.

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REFERENCES

  1. Kolesnichenko, A.V., Modeling of the turbulent transport coefficients in a gas–dust accretion disk, Sol. Syst. Res., 2000, vol. 34, no. 6, pp. 469–480.

    Article  ADS  Google Scholar 

  2. Kolesnichenko, A.V., Hydrodynamic aspects of modeling of the mass transfer and coagulation processes in turbulent accretion disks, Sol. Syst. Res., 2001, vol. 35, no. 2, pp. 125–140.

    Article  ADS  Google Scholar 

  3. Kolesnichenko, A.V., Synergetic approach to describing stationary nonequilibrium turbulence of astrophysical systems in Sovremennye problemy mekhaniki i fiziki kosmosa (Modern Problems of Mechanics and Physics of Space), Moscow: Fizmatlit, 2003, pp. 123–162.

    Google Scholar 

  4. Kolesnichenko, A.V., Thermodynamic modeling of developed structural turbulence taking into account fluctuations of energy dissipation, Sol. Syst. Res., 2004, vol. 38, pp. 124–146.

    Article  ADS  Google Scholar 

  5. Kolesnichenko, A.V., On the possibility of synergetic birth of mesoscale coherent structures in the macroscopic theory of developed turbulence, Mat. Model., 2005, vol. 17, no. 10, pp. 47–79.

    MathSciNet  Google Scholar 

  6. Kolesnichenko, A.V. and Marov, M.Ya., Fundamentals of the mechanics of heterogeneous media in the circumsolar protoplanetary cloud: The effects of solid particles on disk turbulence, Sol. Syst. Res., 2006, vol. 40, pp. 1–56.

    Article  ADS  Google Scholar 

  7. Kolesnichenko, A.V. and Marov, M.Ya., The effect of spirality on the evolution of turbulence in the solar protoplanetary cloud, Sol. Syst. Res., 2007, vol. 41, no. 1, pp. 1–18.

    Article  ADS  Google Scholar 

  8. Kolesnichenko, A.V., Kontinual’nye modeli prirodnykh i kosmicheskikh sred: Problemy termodinamicheskogo modelirovaniya (Continuum Models of Natural and Cosmic Media: Problems of Thermodynamic Modeling), Moscow: LENAND, 2017.

  9. Marov, M.Ya. and Kolesnichenko, A.V., Mechanics of Turbulence of Multicomponent Gases, Dordrecht: Kluwer Academic Publishers, 2002.

    Google Scholar 

  10. Marov M.Ya. and Kolesnichenko A.V. Chaotic and ordered structures in the developed turbulence, in Astrophysical Disks: Collective and Stochastic Phenomena, Fridman, A.M. and Marov, M.Ya., Dordrecht: Springer, 2006, pp. 23–54.

  11. Sano, T. and Miyama, S.M., Magnetorotational instability in protoplanetary disks. I. On the global stability of weakly ionized disks with ohmic dissipation, Astrophys. J., 1999, vol. 515, pp. 776–786.

    Article  ADS  Google Scholar 

  12. Sano, T., Miyama, S.M., Umebayashi, T., and Nakano, T., Magnetorotational instability in protoplanetary disks. II. Ionization state and unstable regions, Astrophys. J., 2000, vol. 543, pp. 486–501.

    Article  ADS  Google Scholar 

  13. Velikhov, E.P., Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic fluid, Sov. Phys. JETP, 1959, vol. 9, pp. 995–998.

    ADS  MathSciNet  Google Scholar 

  14. Hawley, J.F. and Balbus, S.A., A powerful local shear instability in weakly magnetized disks. II. Nonlinear evolution, Astrophys. J., 1991, vol. 376, pp. 223–233.

    Article  ADS  Google Scholar 

  15. Eardley, D.M. and Lightman, A.P., Magnetic viscosity in relativistic accretion disks, Astrophys. J., 1975, vol. 200, pp. 187–203.

    Article  ADS  Google Scholar 

  16. Alfven, H. and Arrhenius, G., Evolution of the Solar System, Washington, DC: NASA, 1976.

    Google Scholar 

  17. Galeev, A.A., Rosner, R., and Viana, G.S., Structured coronae of accretion disks, Astrophys. J., 1979, vol. 229, pp. 318–326.

    Article  ADS  Google Scholar 

  18. Coroniti, F.V., On the magnetic viscosity in Keplerian accretion disks, Astrophys. J., 1981, vol. 244, pp. 587–599.

    Article  ADS  Google Scholar 

  19. Tout, C. and Pringle, J.E., Accretion disk viscosity—a simple model for a magnetic dynamo, Mon. Not. R. Astron. Soc., 1992, vol. 259, pp. 604–612.

    Article  ADS  Google Scholar 

  20. Brandenburg, A., Nordlund, A., Stein, R.F., and Torkelsson, U., The disk accretion rate for dynamo-generated turbulence, Astrophys. J., 1996, vol. 458, pp. 145–148.

    Article  Google Scholar 

  21. Lesch, H., Magnetic reconnection in accretion disc coronae, in Solar and Asrophysical Magnetohydrodynamic Flows, Tsinganos, K.C., Ed., Dordrecht: Kluwer, 1996, pp. 673–682.

    Google Scholar 

  22. Bisnovaty-Kogan, G.S. and Lovelace, R.V.E., Advective accretion disks and related problems including magnetic fields, New Astron. Rev., 2001, vol. 45, pp. 663–742.

    Article  ADS  Google Scholar 

  23. Armitage, P.J., Livio, M., and Pringle, J.E., Episodic accretion in magnetically layered protoplanetary disks, Mon. Not. R. Astron. Soc., 2001, vol. 324, pp. 705–711.

    Article  ADS  Google Scholar 

  24. Kadomtsev, B.B., Magnetic field line reconnection, Rep. Prog. Phys., 1987, vol. 50, p. 115.

    Article  ADS  Google Scholar 

  25. Zel’dovich, Ya.B., Ruzmaikin, A.A., and Sokolov, D.D., Magnitnye polya v astrofizike (Magnetic Fields in Astrophysics), Moskva–Izhevsk: NITs Regulyarnaya i khaoticheskaya dinamika, 2006.

  26. Moffat, H.K., Magnetic Field Generation in Electrically Conducting Fluids, Cambridge: Cambridge Univ. Press, 1978.

    Google Scholar 

  27. Vainshtein, S.I., Zel’dovich, Ya.B., and Ruzmaikin, A.A., Turbulentnoe dinamo v astrofizike (Turbulent Dynamo in Astropysics), Moscow: Nauka, 1980.

  28. Parker, E.N., Hydromagnetic dynamo model, Astrophys. J., 1955, vol. 122, pp. 293–314.

    Article  ADS  MathSciNet  Google Scholar 

  29. Heyvaerts, J. and Priest, E.R., A self-consistent turbulent model for solar coronal heating, Astrophys. J., 1992, vol. 390, pp. 297–308.

    Article  ADS  Google Scholar 

  30. Inverauity, G.W., Priest, E.R., and Heyvaerts, J., Turbulent coronal heating. I. Sheared arcade, Astron. Astrophys., 1995, vol. 293, pp. 913–926.

    ADS  Google Scholar 

  31. Pudritz, R.E. and Norman, C.A., Bipolar hydromagnetic winds from disks around protostellar objects, Astrophys. J., 1986, vol. 301, pp. 571–586.

    Article  ADS  Google Scholar 

  32. Campbell, C.G., Disc–wind field matching in accretion discs with magnetically influenced wind, Mon. Not. R. Astron. Soc., 2005, vol. 361, pp. 396–404.

    Article  ADS  Google Scholar 

  33. Konigl, A. and Pudritz, R.E., Disk winds and the accretion–outflow connection, in Protostars and Planets IV, Mannings, V. Boss, A.P., Russell, S.S., Eds., Tucson: Univ. Arizona Press, 2000, pp. 759–788.

    Google Scholar 

  34. Wang, J.C.L., Sulkanen, M.E., and Lovelace, R.V.E., Self-collimated electro-magnetic jets from magnetized accretion disks: the even-symmetry case, Astrophys. J., 1990, vol. 355, pp. 38–43.

    Article  ADS  Google Scholar 

  35. Favre, A., Statistical equations of turbulent gases, in Problems of Hydrodynamics and Continuum Mechanics, Philadelphia: SIAM, 1969, pp. 231–267.

    Google Scholar 

  36. Kolesnichenko, A.V. and Marov, M.Ya., Turbulentnost’ i samoorganizatsiya. Problemy modelirovaniya kosmicheskikh i prirodnykh sred (Turbulence and Self-Organization. Problems of Modeling Space and Natural Environments), Moscow: BINOM. Laboratoriya znanii, 2009.

  37. Lazarian, A. and Vishniac, E.T., Reconnection in a weakly stochastic field, Astrophys. J., 1999, vol. 517, pp. 700–718.

    Article  ADS  Google Scholar 

  38. Pudritz, R.E., Dynamo action in turbulent accretion discs around black holes—I. The fluctuations, Mon. Not. R. Astron. Soc., 1981a, vol. 195, pp. 881–896.

    Article  ADS  Google Scholar 

  39. Blackadar, A.K., Extension of the laws of thermodynamics to turbulent system, J. Meteorol., 1955, vol. 12.

  40. Jou, D., Casas-Vázquez, J., and Lebon, G., Extended Irreversible Thermodynamics, Berlin: Springer, 2001.

    Book  Google Scholar 

  41. Ievlev, V.M., Turbulentnoe dvizhenie vysokotemperaturnykh sploshnykh sred (Turbulent Movement of High-Temperature Continuous Media), Moscow: Nauka, 1975.

  42. Fridman, A.M. and Bisikalo, D.V., The nature of accretion disks of close binary stars: overreflection instability and developed turbulence, Phys. Usp., 2008, vol. 51, no. 6, pp. 551–576.

    Article  ADS  Google Scholar 

  43. Frank-Kamenetskii, D.A., Fizicheskie protsessy vnutri zvezd (Physical Processes inside Stars), Moscow: Fizmatlit, 1959.

  44. Krause, F. and Rädler, K.-H., Mean-Field Magnetodynamics and Dynamo Theory, Berlin: Akademie-Verlag 1980.

    Google Scholar 

  45. Steenbeck, M., Krause, F., and Rädler, K.-H., Berechnung der mittleren Lorentz-Feldstärke \(\overline {{\text{V} \times B}} \) für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinfluβter Bewegung, Z. Naturforsch, 1966, vol. 21a, pp. 369–376.

    Article  ADS  Google Scholar 

  46. Shakura, N.I. and Sunyaev, R.A., Black holes in binary systems. Observational appearance, Astron. Astrophys., 1973, vol. 24, pp. 337–355.

    ADS  Google Scholar 

  47. Pringle, J.E. and King, A.R., Astrophysical Flow, Cambridge: Cambridge Univ. Press, 2007.

    Book  Google Scholar 

  48. Tassoul, J.-L., Theory of Rotating Stars, Princeton, NJ: Princeton Univ. Press, 1978.

    Google Scholar 

  49. Shakura, N.I., Disk model of gas accretion on a relativistic star in a close binary system, Sov. Astron., 1973, vol. 16, p. 756.

    ADS  Google Scholar 

  50. Lynden-Bell, D. and Pringle, J.E., The evolution of viscous discs and the origin of the nebular variables, Mon. Not. R. Astron. Soc., 1974, vol. 168, p. 603.

    Article  ADS  Google Scholar 

  51. Bath, G.T. and Pringle, J.E., The evolution of viscous discs. I. Mass transfer variations, Mon. Not. R. Astron. Soc., 1981, vol. 194, p. 967.

    Article  ADS  Google Scholar 

  52. Eardley, D.M., Lightman, A.P., Payne, D.G., and Shapiro, S.L., Accretion discs around massive black holes; persistent emission spectra, Astrophys. J., 1978, vol. 234, p. 53.

    Article  ADS  Google Scholar 

  53. Heyvaerts, J., Priest, E.R., and Bardou, A., Magnetic field diffusion in self-consistently turbulent accretion disks, Astrophys. J., 1996, vol. 473, pp. 403–421.

    Article  ADS  Google Scholar 

  54. Priest, E. and Forbes, T., Magnetic Reconnection: MHD Theory and Applications, Cambridge: Cambridge Univ. Press, 2000.

    Book  Google Scholar 

  55. Shapiro, S. and Teukolsky, S., Black Holes, White Dwarfs, and Neutron Stars, New York: Wiley, 1983.

    Book  Google Scholar 

  56. Pudritz, R.E., Dynamo action in turbulent accretion discs around black holes—II. The mean magnetic field, Mon. Not. R. Astron. Soc., 1981b, vol. 195, pp. 897–914.

    Article  ADS  Google Scholar 

  57. Lovelace, R.V.E., Wang, J.C.L., and Sulkanen, M.E., Self-collimated electro-magnetic jets from magnetized accretion disks, Astron. J., 1987, vol. 515, pp. 504–535.

    Article  Google Scholar 

  58. Pudritz, R.E. and Fahlman, G.G., The structure and variability of dynamo driven accretion discs, Mon. Not. R. Astron. Soc., 1982, vol. 198, pp. 689–706.

    Article  ADS  Google Scholar 

  59. Campbell, C.G. and Caunt, S.E., An analytic model for magneto-viscous accretion discs, Mon. Not. R. Astron. Soc., 1999, vol. 306, pp. 122–136.

    Article  ADS  Google Scholar 

  60. Marov, M.Ya., Kolesnichenko, A.V., Makalkin, A.B., Dorofeeva, V.A., Ziglina, I.N., and Chernov, A.V., From a protosolar cloud to a planetary system: A model for the evolution of a gas–dust disk, in Problemy zarozhdeniya i evolyutsii biosfery (Problems of the Origin and Evolution of the Biosphere), Galimov, E.M., Ed., Moscow: Knizhnyi dom LIBROKOM, 2008.

  61. Casse, F. and Ferreira, J., Magnetized accretion-ejection structures. IV. Magnetically-driven jets from resistive, viscous, Keplerian discs, Astron. Astrophys., 2000, vol. 353, pp. 1115–1128.

    ADS  Google Scholar 

  62. Kolesnichenko, A.V., Thermodynamic Construction of the MHD Model of Turbulence of Electroconductive Fluid Medium, Sol. Syst. Res., 2023, vol. 57, no. 7, pp. 56–76.

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  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    A. V. Kolesnichenko

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Translated by N. Wadhwa

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Kolesnichenko, A.V. On the Modeling of a Compressible MHD Turbulence of an Accretion Protoplanetary Disk. Sol Syst Res 57, 727–747 (2023). https://doi.org/10.1134/S0038094623070067

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  • DOI: https://doi.org/10.1134/S0038094623070067

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