Skip to main content
SpringerLink
Log in

Effects of Radiative Diffusion on Thin Flux Tubes in Turbulent Solar-like Convection

  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

We study the combined effects of convection and radiative diffusion on the evolution of thin magnetic flux tubes in the solar interior. Radiative diffusion is the primary supplier of heat to convective motions in the lower convection zone, and it results in a heat input per unit volume of magnetic flux tubes that has been ignored by many previous thin flux tube studies. We use a thin flux tube model subject to convection taken from a rotating spherical shell of turbulent, solar-like convection as described by Weber, Fan, and Miesch (Astrophys. J. 741, 11, 2011; Solar Phys. 287, 239, 2013), now taking into account the influence of radiative heating on 1022 Mx flux tubes, corresponding to flux tubes of large active regions. Our simulations show that flux tubes of ≤ 60 kG that are subject to solar-like convective flows do not anchor in the overshoot region, but rather drift upward because of the increased buoyancy of the flux tube earlier in its evolution, which results from including radiative diffusion. Flux tubes of magnetic field strengths ranging from 15 kG to 100 kG have rise times of ≤ 0.2 years and exhibit a Joy’s Law tilt-angle trend. Our results suggest that radiative heating is an effective mechanism by which flux tubes can escape from the stably stratified overshoot region. Moreover, flux tubes do not necessarily need to be anchored in the overshoot region to produce emergence properties similar to those of active regions on the Sun.

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

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10

Similar content being viewed by others

References

  • Achterberg, A.: 1996, Variational principle for slender flux tubes. I. General equations and added mass effects. Astron. Astrophys. 313, 1008. ADS .

    ADS  Google Scholar 

  • Basu, S.: 1997, Seismology of the base of the solar convection zone. Mon. Not. Roy. Astron. Soc. 288, 572. ADS .

    Article  ADS  Google Scholar 

  • Basu, S., Antia, H.M.: 2003, Changes in solar dynamics from 1995 to 2002. Astrophys. J. 585, 553. DOI . ADS .

    Article  ADS  Google Scholar 

  • Basu, S., Antia, H.M., Narasimha, D.: 1994, Helioseismic measurement of the extent of overshoot below the solar convection zone. Mon. Not. Roy. Astron. Soc. 267, 209. ADS .

    Article  ADS  Google Scholar 

  • Browning, M.K., Miesch, M.S., Brun, A.S., Toomre, J.: 2006, Dynamo action in the solar convection zone and tachocline: pumping and organization of toroidal fields. Astrophys. J. Lett. 648, L157. DOI . ADS .

    Article  ADS  Google Scholar 

  • Brummell, N.H., Clune, T.L., Toomre, J.: 2002, Penetration and overshooting in turbulent compressible convection. Astrophys. J. 570, 825. DOI . ADS .

    Article  ADS  Google Scholar 

  • Caligari, P., Moreno-Insertis, F., Schüssler, M.: 1995, Emerging flux tubes in the solar convection zone. 1: Asymmetry, tilt, and emergence latitude. Astrophys. J. 441, 886. DOI . ADS .

    Article  ADS  Google Scholar 

  • Caligari, P., Schüssler, M., Moreno-Insertis, F.: 1998, Emerging flux tubes in the solar convection zone. II. The influence of initial conditions. Astrophys. J. 502, 481. DOI . ADS .

    Article  ADS  Google Scholar 

  • Charbonneau, P.: 2010, Dynamo models of the solar cycle. Living Rev. Solar Phys. 7, 3. DOI . ADS .

    Article  ADS  Google Scholar 

  • Charbonneau, P., Christensen-Dalsgaard, J., Henning, R., Larsen, R.M., Schou, J., Thompson, M.J., Tomczyk, S.: 1999, Helioseismic constraints on the structure of the solar tachocline. Astrophys. J. 527, 445. DOI . ADS .

    Article  ADS  Google Scholar 

  • Cheng, J.: 1992, Equations for the motion of an isolated thin magnetic flux tube. Astron. Astrophys. 264, 243. ADS .

    ADS  Google Scholar 

  • Choudhuri, A.R., Gilman, P.A.: 1987, The influence of the Coriolis force on flux tubes rising through the solar convection zone. Astrophys. J. 316, 788. DOI . ADS .

    Article  ADS  Google Scholar 

  • Christensen-Dalsgaard, J., Gough, D.O., Thompson, M.J.: 1991, The depth of the solar convection zone. Astrophys. J. 378, 413. DOI . ADS .

    Article  ADS  Google Scholar 

  • Christensen-Dalsgaard, J., Dappen, W., Ajukov, S.V., Anderson, E.R., Antia, H.M., Basu, S., Baturin, V.A., Berthomieu, G., Chaboyer, B., Chitre, S.M., Cox, A.N., Demarque, P., Donatowicz, J., Dziembowski, W.A., Gabriel, M., Gough, D.O., Guenther, D.B., Guzik, J.A., Harvey, J.W., Hill, F., Houdek, G., Iglesias, C.A., Kosovichev, A.G., Leibacher, J.W., Morel, P., Proffitt, C.R., Provost, J., Reiter, J., Rhodes, E.J. Jr., Rogers, F.J., Roxburgh, I.W., Thompson, M.J., Ulrich, R.K.: 1996, The current state of solar modeling. Science 272, 1286. DOI . ADS .

    Article  ADS  Google Scholar 

  • Christensen-Dalsgaard, J., Monteiro, M.J.P.F.G., Rempel, M., Thompson, M.J.: 2011, A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology. Mon. Not. Roy. Astron. Soc. 414, 1158. DOI . ADS .

    Article  ADS  Google Scholar 

  • Dasi-Espuig, M., Solanki, S.K., Krivova, N.A., Cameron, R., Peñuela, T.: 2010, Sunspot group tilt angles and the strength of the solar cycle. Astron. Astrophys. 518, A7. DOI . ADS .

    Article  ADS  Google Scholar 

  • Defouw, R.J.: 1976, Wave propagation along a magnetic tube. Astrophys. J. 209, 266. DOI . ADS .

    Article  ADS  Google Scholar 

  • D’Silva, S., Choudhuri, A.R.: 1993, A theoretical model for tilts of bipolar magnetic regions. Astron. Astrophys. 272, 621. ADS .

    ADS  Google Scholar 

  • Fan, Y.: 2009, Magnetic fields in the solar convection zone. Living Rev. Solar Phys. 6, 4. DOI . ADS .

    Article  ADS  Google Scholar 

  • Fan, Y., Fisher, G.H.: 1996, Radiative heating and the buoyant rise of magnetic flux tubes in the solar interior. Solar Phys. 166, 17. DOI . ADS .

    Article  ADS  Google Scholar 

  • Fan, Y., Fisher, G.H., Deluca, E.E.: 1993, The origin of morphological asymmetries in bipolar active regions. Astrophys. J. 405, 390. DOI . ADS .

    Article  ADS  Google Scholar 

  • Fan, Y., Fisher, G.H., McClymont, A.N.: 1994, Dynamics of emerging active region flux loops. Astrophys. J. 436, 907. DOI . ADS .

    Article  ADS  Google Scholar 

  • Ferriz-Mas, A., Schuessler, M., Anton, V.: 1989, Dynamics of magnetic flux concentrations – the second-order thin flux tube approximation. Astron. Astrophys. 210, 425. ADS .

    ADS  MATH  Google Scholar 

  • Ferriz-Mas, A., Schüssler, M.: 1993, Instabilities of magnetic flux tubes in a stellar convection zone I. Equatorial flux rings in differentially rotating stars. Geophys. Astrophys. Fluid Dyn. 72, 209. DOI . ADS .

    Article  ADS  Google Scholar 

  • Fisher, G.H., Fan, Y., Howard, R.F.: 1995, Comparisons between theory and observation of active region tilts. Astrophys. J. 438, 463. DOI . ADS .

    Article  ADS  Google Scholar 

  • Galloway, D.J., Weiss, N.O.: 1981, Convection and magnetic fields in stars. Astrophys. J. 243, 945. DOI . ADS .

    Article  ADS  Google Scholar 

  • Gilman, P.A.: 2000, Fluid dynamics and MHD of the solar convection zone and tachocline: current understanding and unsolved problems – (Invited review). Solar Phys. 192, 27. ADS .

    Article  ADS  Google Scholar 

  • Hale, G.E., Ellerman, F., Nicholson, S.B., Joy, A.H.: 1919, The magnetic polarity of sun-spots. Astrophys. J. 49, 153. DOI . ADS .

    Article  ADS  Google Scholar 

  • Howard, R.F.: 1996, Axial tilt angles of active regions. Solar Phys. 169, 293. DOI . ADS .

    ADS  Google Scholar 

  • Li, J., Ulrich, R.K.: 2012, Long-term measurements of sunspot magnetic tilt angles. Astrophys. J. 758, 115. DOI . ADS .

    Article  ADS  Google Scholar 

  • McClintock, B.H., Norton, A.A.: 2013, Recovering Joy’s law as a function of solar cycle, hemisphere, and longitude. Solar Phys. 287, 215. DOI . ADS .

    Article  ADS  Google Scholar 

  • Miesch, M.S.: 2005, Large-scale dynamics of the convection zone and tachocline. Living Rev. Solar Phys. 2, 1. DOI . ADS .

    Article  ADS  Google Scholar 

  • Miesch, M.S., Brun, A.S., Toomre, J.: 2006, Solar differential rotation influenced by latitudinal entropy variations in the tachocline. Astrophys. J. 641, 618. DOI . ADS .

    Article  ADS  Google Scholar 

  • Miesch, M.S., Toomre, J.: 2009, Turbulence, magnetism, and shear in stellar interiors. Annu. Rev. Fluid Mech. 41, 317. DOI . ADS .

    Article  ADS  Google Scholar 

  • Monteiro, M.J.P.F.G., Christensen-Dalsgaard, J., Thompson, M.J.: 1994, Seismic study of overshoot at the base of the solar convective envelope. Astron. Astrophys. 283, 247. ADS .

    ADS  Google Scholar 

  • Moreno-Insertis, F.: 1986, Nonlinear time-evolution of kink-unstable magnetic flux tubes in the convective zone of the Sun. Astron. Astrophys. 166, 291. ADS .

    ADS  MATH  Google Scholar 

  • Moreno-Insertis, F., Emonet, T.: 1996, The rise of twisted magnetic tubes in a stratified medium. Astrophys. J. Lett. 472, L53. DOI . ADS .

    Article  ADS  Google Scholar 

  • Moreno-Insertis, F., Schüssler, M., Ferriz-Mas, A.: 1992, Storage of magnetic flux tubes in a convective overshoot region. Astron. Astrophys. 264, 686. ADS .

    ADS  Google Scholar 

  • Moreno-Insertis, F., Schüssler, M., Glampedakis, K.: 2002, Thermal properties of magnetic flux tubes. I. Solution of the diffusion problem. Astron. Astrophys. 388, 1022. DOI . ADS .

    Article  ADS  Google Scholar 

  • Parker, E.N.: 1979, Cosmical Magnetic Fields: Their Origin and Their Activity, Clarendon, Oxford. ADS .

    Google Scholar 

  • Pidatella, R.M., Stix, M.: 1986, Convective overshoot at the base of the Sun’s convection zone. Astron. Astrophys. 157, 338. ADS .

    ADS  Google Scholar 

  • Rempel, M.: 2003, Thermal properties of magnetic flux tubes. II. Storage of flux in the solar overshoot region. Astron. Astrophys. 397, 1097. DOI . ADS .

    Article  ADS  Google Scholar 

  • Rempel, M.: 2004, Overshoot at the base of the solar convection zone: a semianalytical approach. Astrophys. J. 607, 1046. DOI . ADS .

    Article  ADS  Google Scholar 

  • Roberts, B., Webb, A.R.: 1978, Vertical motions in an intense magnetic flux tube. Solar Phys. 56, 5. DOI . ADS .

    Article  ADS  Google Scholar 

  • Schmitt, J.H.M.M., Rosner, R., Bohn, H.U.: 1984, The overshoot region at the bottom of the solar convection zone. Astrophys. J. 282, 316. DOI . ADS .

    Article  ADS  Google Scholar 

  • Skaley, D., Stix, M.: 1991, The overshoot layer at the base of the solar convection zone. Astron. Astrophys. 241, 227. ADS .

    ADS  Google Scholar 

  • Spiegel, E.A., Weiss, N.O.: 1980, Magnetic activity and variations in solar luminosity. Nature 287, 616. DOI . ADS .

    Article  ADS  Google Scholar 

  • Spruit, H.C.: 1981a, Equations for thin flux tubes in ideal MHD. Astron. Astrophys. 102, 129. ADS .

    ADS  MATH  Google Scholar 

  • Spruit, H.C.: 1981b, Motion of magnetic flux tubes in the solar convection zone and chromosphere. Astron. Astrophys. 98, 155. ADS .

    ADS  MATH  Google Scholar 

  • Stenflo, J.O., Kosovichev, A.G.: 2012, Bipolar magnetic regions on the Sun: global analysis of the SOHO/MDI data set. Astrophys. J. 745, 129. DOI . ADS .

    Article  ADS  Google Scholar 

  • Thompson, M.J., Christensen-Dalsgaard, J., Miesch, M.S., Toomre, J.: 2003, The internal rotation of the Sun. Annu. Rev. Astron. Astrophys. 41, 599. DOI . ADS .

    Article  ADS  Google Scholar 

  • Tobias, S.M., Brummell, N.H., Clune, T.L., Toomre, J.: 2001, Transport and storage of magnetic field by overshooting turbulent compressible convection. Astrophys. J. 549, 1183. DOI . ADS .

    Article  ADS  Google Scholar 

  • van Ballegooijen, A.A.: 1982, The overshoot layer at the base of the solar convective zone and the problem of magnetic flux storage. Astron. Astrophys. 113, 99. ADS .

    ADS  MATH  MathSciNet  Google Scholar 

  • van Ballegooijen, A.A., Choudhuri, A.R.: 1988, The possible role of meridional flows in suppressing magnetic buoyancy. Astrophys. J. 333, 965. DOI . ADS .

    Article  ADS  Google Scholar 

  • Wang, Y.-M., Sheeley, N.R. Jr.: 1989, Average properties of bipolar magnetic regions during sunspot cycle 21. Solar Phys. 124, 81. DOI . ADS .

    Article  ADS  Google Scholar 

  • Wang, H., Zirin, H.: 1989, Study of supergranules. Solar Phys. 120, 1. DOI . ADS .

    Article  ADS  Google Scholar 

  • Weber, M.A., Fan, Y., Miesch, M.S.: 2011, The rise of active region flux tubes in the turbulent solar convective envelope. Astrophys. J. 741, 11. DOI . ADS .

    Article  ADS  Google Scholar 

  • Weber, M.A., Fan, Y., Miesch, M.S.: 2013, Comparing simulations of rising flux tubes through the solar convection zone with observations of solar active regions: constraining the dynamo field strength. Solar Phys. 287, 239. DOI . ADS .

    Article  ADS  Google Scholar 

  • Zahn, J.-P.: 1991, Convective penetration in stellar interiors. Astron. Astrophys. 252, 179. ADS .

    ADS  Google Scholar 

Download references

Acknowledgements

The majority of this work was conducted while M.A. Weber was a Graduate Research Fellow at High Altitude Observatory (HAO), a division of the National Center for Atmospheric Research (NCAR). NCAR is sponsored by the National Science Foundation. This research was sponsored in part by NASA SHP grant NNX10AB81G to NCAR. M.A. Weber is now supported by the European Research Council under grant agreement 337705 (the CHASM project). We would like to thank Mark Miesch (HAO/NCAR) for providing the ASH convective flows used in this article. The authors are also grateful to Mausumi Dikpati (HAO/NCAR) and the anonymous referee for reading our manuscript and providing helpful comments.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK

    M. A. Weber

  2. High Altitude Observatory, National Center for Atmospheric Research, 3080 Center Green Drive, Boulder, CO, 80301, USA

    Y. Fan

Authors
  1. M. A. Weber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Weber.

Ethics declarations

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Weber, M.A., Fan, Y. Effects of Radiative Diffusion on Thin Flux Tubes in Turbulent Solar-like Convection. Sol Phys 290, 1295–1321 (2015). https://doi.org/10.1007/s11207-015-0674-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11207-015-0674-3

Keywords

Search

Navigation