Skip to main content
SpringerLink
Log in

Magnetic fields in protoplanetary disks

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary disks. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface. Magnetically-driven mixing has implications for disk chemistry and evolution of the grain population, and the effective viscous response of the disk determines whether planets migrate inwards or outwards. However, the weak ionisation of protoplanetary disks means that magnetic fields may not be able to effectively couple to the matter. I examine the magnetic diffusivity in a minimum solar nebula model and present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas, except at the disk surfaces where the low density of neutrals permits the ions to remain attached to the field lines. For a standard population of 0.1 μm grains the active surface layers have a combined column Σactive≈2 g cm−2 at 1 AU; by the time grains have aggregated to 3 μm, Σactive≈80 g cm−2. Ionisation in the active layers is dominated by stellar X-rays. In the absence of grains, X-rays maintain magnetic coupling to 10% of the disk material at 1 AU (i.e. Σactive≈150 g cm−2). At 5 AU the Σactive≈Σtotal once grains have aggregated to 1 μm in size.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Andrews, S.M., Williams, J.P.: Circumstellar dust disks in Taurus-Auriga: the submillimeter perspective. Astrophys. J. 631, 1134–1160 (2005)

    Article  ADS  Google Scholar 

  • Balbus, S.A.: Enhanced angular momentum transport in accretion disks. Annu. Rev. Astron. Astrophys. 41, 555–597 (2003)

    Article  ADS  Google Scholar 

  • Balbus, S.A., Hawley, J.F.: A powerful local shear instability in weakly magnetized disks: I. Linear analysis. Astrophys. J. 376, 214–233 (1991)

    Article  ADS  Google Scholar 

  • Balbus, S.A., Terquem, C.: Linear analysis of the Hall effect in protostellar disks. Astrophys. J. 552, 235–247 (2001)

    Article  ADS  Google Scholar 

  • Blandford, R.D., Payne, D.G.: Hydromagnetic flows from accretion disks and the production of radio jets. Mon. Not. Roy. Astron. Soc. 199, 883–903 (1982)

    MATH  ADS  Google Scholar 

  • Calvet, N., Hartmann, L., Strom, S.E.: Evolution of disk accretion. In: Mannings, V., Boss, A.P., Russell, S.S. (eds.) Protostars and Planets IV, pp. 377–400. University of Arizona Press, Tucson (2000)

    Google Scholar 

  • Chambers, J.E.: Planet formation with migration. Astrophys. J. 652, L133–L136 (2006)

    Article  ADS  Google Scholar 

  • Chapman, J.F., Wardle, M.: Dust grain dynamics in C-type shock waves in molecular clouds. Mon. Not. Roy. Astron. Soc. 371, 513–529 (2006)

    Article  ADS  Google Scholar 

  • Ciesla, F.J.: Dust coagulation and settling in layered protoplanetary disks. Astrophys. J. 654, L159–L162 (2007)

    Article  ADS  Google Scholar 

  • Cowling, T.G.: Magnetohydrodynamics. Hilger, London (1976)

    MATH  Google Scholar 

  • Draine, B.T., Sutin, B.: Collisional charging of interstellar grains. Astrophys. J. 320, 803–817 (1987)

    Article  ADS  Google Scholar 

  • Dullemond, C.P., Hollenbach, D., Kamp, I., D’Alessio, P.: Models of the structure and evolution of protoplanetary disks. In: Reipurth, B., Jewitt, D., Keil, K. (eds.) Protostars and Planets V, pp. 555–572. University of Arizona Press, Tucson (2007)

    Google Scholar 

  • 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., Keil, K. (eds.) Protostars and Planets V, pp. 607–622. University of Arizona Press, Tucson (2007)

    Google Scholar 

  • Fendt, C.: Magnetically driven outflows from Jovian circum-planetary accretion disks. Astron. Astrophys. 411, 623–635 (2003)

    Article  ADS  Google Scholar 

  • Fleming, T., Stone, J.M.: Local magnetohydrodynamical models of layered accretion disks. Astrophys. J. 585, 908–920 (2003)

    Article  ADS  Google Scholar 

  • Fromang, S., Papaloizou, J.: Dust settling in local simulations of turbulent protoplanetary disks. Astron. Astrophys. 452, 751–762 (2006)

    Article  ADS  Google Scholar 

  • Gammie, C.F.: Layered accretion in T Tauri disks. Astrophys. J. 457, 355–362 (1996)

    Article  ADS  Google Scholar 

  • Glassgold, A.E., Najita, J., Igea, J.: X-ray ionization of protoplanetary disks. Astrophys. J. 480, 344–350 (1997)

    Article  ADS  Google Scholar 

  • Hawley, J.F., Gammie, C.F., Balbus, S.A.: Local three-dimensional magnetohydrodynamic simulations of accretion disks. Astrophys. J. (1994)

  • Hayashi, C.: Structure of the solar nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the nebula. Prog. Theor. Phys. Suppl. 70, 35–52 (1981)

    Article  ADS  Google Scholar 

  • Igea, J., Glassgold, A.E.: X-ray ionization of the disks of young stellar objects. Astrophys. J. 518, 848–858 (1999)

    Article  ADS  Google Scholar 

  • Ilgner, M., Nelson, R.P.: On the ionisation fraction in protoplanetary disks. I. Comparing different reaction networks. Astron. Astrophys. 445, 205–222 (2006)

    Article  ADS  Google Scholar 

  • Johansen, A., Klahr, H.: Dust diffusion in protoplanetary disks by magnetorotational turbulence. Astrophys. J. 634, 1353–1371 (2005)

    Article  ADS  Google Scholar 

  • Johnson, E.T., Goodman, J., Menou, K.: Diffusive migration of low-mass protoplanets in turbulent disks. Astrophys. J. 647, 1413–1425 (2006)

    Article  ADS  Google Scholar 

  • Kitamura, Y., Momose, M., Yokogawa, S., Kawabe, R., Tamura, M., Ida, S.: Investigation of the physical properties of protoplanetary disks around T Tauri stars by a 1 arcsecond imaging survey: evolution and diversity of the disks in their accretion stage. Astrophys. J. 581, 357–380 (2002)

    Article  ADS  Google Scholar 

  • Levy, E.H., Sonett, C.P.: Meteorite magnetism and early solar system magnetic fields. In: Gehrels, T. (ed.) Protostars and Planets: Studies of Star Formation and of the Origin of the Solar System, pp. 516–532. University of Arizona Press, Tucson (1978)

    Google Scholar 

  • Matsumura, S., Pudritz, R.E.: The origin of Jovian planets in protostellar disks: the role of dead zones. Astrophys. J. 598, 645–656 (2003)

    Article  ADS  Google Scholar 

  • Nishi, R., Nakano, T., Umebayashi, T.: Magnetic flux loss from interstellar clouds with various grain-size distributions. Astrophys. J. 368, 181–194 (1991)

    Article  ADS  Google Scholar 

  • Nomura, H., Nakagawa, Y.: Dust size growth and settling in a protoplanetary disk. Astrophys. J. 640, 1099–1109 (2006)

    Article  ADS  Google Scholar 

  • Quillen, A.C., Trilling, D.E.: Do proto-Jovian planets drive outflows? Astrophys. J. 508, 707–713 (1998)

    Article  ADS  Google Scholar 

  • Sano, T., Stone, J.M.: The effect of the Hall term on the nonlinear evolution of the magnetorotational instability. I. Local axisymmetric simulations. Astrophys. J. 570, 314–328 (2002)

    Article  ADS  Google Scholar 

  • Sano, T., Miyama, S.M., Umebayashi, T., Nakano, T.: Magnetorotational instability in protoplanetary disks. II. Ionization state and unstable regions. Astrophys. J. 543, 486–501 (2000)

    Article  ADS  Google Scholar 

  • Sano, T., Inutsuka, S.-I., Turner, N.J., Stone, J.M.: Angular momentum transport by magnetohydrodynamic turbulence in accretion disks: gas pressure dependence of the saturation level of the magnetorotational instability. Astrophys. J. 605, 321–339 (2004)

    Article  ADS  Google Scholar 

  • Semenov, D., Wiebe, D., Henning, T.: Reduction of chemical networks. II. Analysis of the fractional ionisation in protoplanetary discs. Astron. Astrophys. 417, 93–106 (2004)

    Article  ADS  Google Scholar 

  • Semenov, D., Wiebe, D., Henning, T.: Gas-phase co in protoplanetary disks: a challenge for turbulent mixing. Astrophys. J. 647, L57–L60 (2006)

    Article  ADS  Google Scholar 

  • Spitzer, L., Jr.: The dynamics of the interstellar medium. I. Local equilibrium. Astrophys. J. 93, 369 (1941)

    Article  ADS  Google Scholar 

  • Toomre, A.: On the gravitational stability of a disk of stars. Astrophys. J. 139, 1217–1238 (1964)

    Article  ADS  Google Scholar 

  • Turner, N.J., Willacy, K., Bryden, G., Yorke, H.W.: Turbulent mixing in the outer solar nebula. Astrophys. J. 639, 1218–1226 (2006)

    Article  ADS  Google Scholar 

  • Umebayashi, T., Nakano, T.: Fluxes of energetic particles and the ionization rate in very dense interstellar clouds. Publ. Astron. Soc. Jpn. 33, 617 (1981)

    ADS  Google Scholar 

  • Umebayashi, T., Nakano, T.: Magnetic flux loss from interstellar clouds. Mon. Not. Roy. Astron. Soc. 243, 103–113 (1990)

    ADS  Google Scholar 

  • Wardle, M.: Magnetically-driven winds from protostellar disks. In: Wickramasinghe, D., Ferrario, L., Bicknell, G. (eds.) Accretion Phenomena and Related Outflows. Proc. IAU Colloq, vol. 163, pp. 561–565. Astronomical Society of the Pacific, San Francisco (1997)

    Google Scholar 

  • Wardle, M.: The Balbus–Hawley instability in weakly ionised discs. Mon. Not. Roy. Astron. Soc. 307, 849–856 (1999)

    Article  ADS  Google Scholar 

  • Wardle, M., Königl, A.: The structure of protostellar accretion disks and the origin of bipolar flows. Astrophys. J. 410, 218–238 (1993)

    Article  ADS  Google Scholar 

  • Wardle, M., Ng, C.: The conductivity of dense molecular gas. Mon. Not. Roy. Astron. Soc. 303, 239–246 (1999)

    Article  ADS  Google Scholar 

  • Weidenschilling, S.J.: The distribution of mass in the planetary system and solar nebula. Astrophys. Space Sci. 51, 153–158 (1977)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Macquarie University, Sydney, NSW, 2109, Australia

    Mark Wardle

Authors
  1. Mark Wardle
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark Wardle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wardle, M. Magnetic fields in protoplanetary disks. Astrophys Space Sci 311, 35–45 (2007). https://doi.org/10.1007/s10509-007-9575-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10509-007-9575-8

Keywords

Search

Navigation