Abstract
This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. (Solar Phys. 272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5 – 0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.
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References
Asgari-Targhi, M., van Ballegooijen, A.A.: 2012, Astrophys. J. 746, 81.
Aschwanden, M.J., De Pontieu, B., Schrijver, C.J., Title, A.: 2002, Solar Phys. 206, 99. ADS: 2002SoPh..206...99A , doi: 10.1023/A:1014916701283 .
Berger, M.A., Asgari-Targhi, M.: 2009, Astrophys. J. 705, 347.
Boozer, A.H.: 1986, J. Plasma Phys. 35, 133.
Close, R.M., Parnell, C.E., Mackay, D.H., Priest, E.R.: 2003, Solar Phys. 212, 251. ADS: 2003SoPh..212..251C , doi: 10.1023/A:1022961913168 .
Close, R.M., Parnell, C.E., Longcope, D.W., Priest, E.R.: 2004, Astrophys. J. Lett. 612, L81.
Cranmer, S.R., van Ballegooijen, A.A.: 2010, Astrophys. J. 720, 824.
De Moortel, I., Pascoe, D.J.: 2009, Astrophys. J. Lett. 699, L72.
de Wijn, A.G., Lites, B.W., Berger, T.E., Frank, Z.A., Tarbell, T.D., Ishikawa, R.: 2008, Astrophys. J. 684, 1469.
DeForest, C.E., Hagenaar, H.J., Lamb, D.A., Parnell, C.E., Welsch, B.T.: 2007, Astrophys. J. 666, 576.
Galsgaard, K., Nordlund, Å.: 1996, Astrophys. Lett. Commun. 34, 175.
Habbal, S.R., Grace, E.: 1991, Astrophys. J. 382, 667.
Habbal, S.R., Withbroe, G.L.: 1981, Solar Phys. 69, 77. ADS: 1981SoPh...69...77H , doi: 10.1007/BF00151257 .
Hagenaar, H.J., DeRosa, M.L., Schrijver, C.J.: 2008, Astrophys. J. 678, 541.
Harvey, K.L., Martin, S.F.: 1973, Solar Phys. 32, 389. ADS: 1973SoPh...32..389H , doi: 10.1007/BF00154951 .
Harvey-Angle, K.L.: 1993, Ph.D. thesis, Utrecht University.
Haynes, A.L., Parnell, C.E., Galsgaard, K., Priest, E.R.: 2007, Proc. Roy. Soc. London Ser. A, Math. Phys. Sci. 463, 1097.
Leighton, R.B., Noyes, R.W., Simon, G.W.: 1962, Astrophys. J. 135, 474.
Livingston, W.C., Harvey, J.: 1975, Bull. Am. Astron. Soc. 7, 346.
Longcope, D.W.: 1998, Astrophys. J. 507, 433.
Longcope, D.W., Parnell, C.E.: 2009, Solar Phys. 254, 51. ADS: 2009SoPh..254...51L , doi: 10.1007/s11207-008-9281-x .
Mackay, D.H., Green, L.M., van Ballegooijen, A.A.: 2011, Astrophys. J. 729, 97.
Mackay, D.H., van Ballegooijen, A.A.: 2006, Astrophys. J. 641, 577.
Mackay, D.H., van Ballegooijen, A.A.: 2009, Solar Phys. 260, 321. ADS: 2009SoPh..260..321M , doi: 10.1007/s11207-009-9468-9 .
Martin, S.F.: 1984, In: Keil, S.L. (ed.) Small Scale Dynamical Processes in Quiet Stellar Atmospheres, National Solar Observatory, Sunspot, 30.
Martin, S.F.: 1988, Solar Phys. 117, 243. ADS: 1988SoPh..117..243M , doi: 10.1007/BF00147246 .
Meyer, K.A., Mackay, D.H., van Ballegooijen, A.A.: 2012, Solar Phys. 278, 149 (Article II). ADS: 2012SoPh..278..149M , doi: 10.1007/s11207-012-0166-7 .
Meyer, K.A., Mackay, D.H., van Ballegooijen, A.A., Parnell, C.E.: 2011, Solar Phys. 272, 29 (Article I). ADS: 2011SoPh..272...29M , doi: 10.1007/s11207-011-9809-3 .
Nakariakov, V.M., Ofman, L.: 2001, Astron. Astrophys. 372, L53.
Parker, E.N.: 1988, Astrophys. J. 330, 474.
Parnell, C.E., De Moortel, I.: 2012, Phil. Trans. Roy. Soc. London A 370, 3217.
Parnell, C.E., Galsgaard, K.: 2004, Astron. Astrophys. 428, 595.
Priest, E.R., Heyvaerts, J.F., Title, A.M.: 2002, Astrophys. J. 576, 533.
Pontin, D.I., Wilmot-Smith, A.L., Hornig, G., Galsgaard, K.: 2011, Astron. Astrophys. 525, A57.
Rappazzo, A.F., Velli, M., Einaudi, G., Dahlburg, R.B.: 2008, Astrophys. J. 677, 1348.
Régnier, S., Parnell, C.E., Haynes, A.L.: 2008, Astron. Astrophys. 484, L47.
Rieutord, M., Rincon, F.: 2010, Living Rev. Solar Phys. 7(2). http://solarphysics.livingreviews.org/Articles/lrsp-2010-2/ .
Schrijver, C.J.: 2010, Astrophys. J. 710, 1480.
Schrijver, C.J., Hagenaar, H.J., Title, A.M.: 1997, Astrophys. J. 475, 328.
Schrijver, C.J., Title, A.M.: 2002, Astrophys. J. 207, 223.
Simon, G.W., Leighton, R.B.: 1964, Astrophys. J. 140, 1120.
Thornton, L.M., Parnell, C.E.: 2011, Solar Phys. 269, 13. ADS: 2011SoPh..269...13T , doi: 10.1007/s11207-010-9656-7 .
van Ballegooijen, A.A., Cranmer, S.R.: 2008, Astrophys. J. 682, 644.
van Ballegooijen, A.A., Asgari-Targhi, M., Cranmer, S.R., DeLuca, E.E.: 2011, Astrophys. J. 736, 3.
Van Doorsselaere, T., Nakariakov, V.M., Young, P.R., Verwichte, E.: 2008, Astron. Astrophys. 487, L17.
Verwichte, E., Nakariakov, V.M., Ofman, L., DeLuca, E.E.: 2004, Solar Phys. 223, 77. ADS: 2004SoPh..223...77V , doi: 10.1007/s11207-004-0807-6 .
Wang, T.J., Inees, D.E., Qiu, J.: 2007, Astrophys. J. 656, 598.
Wang, H., Zirin, H.: 1989, Solar Phys. 120, 1. ADS: 1989SoPh..120....1W , doi: 10.1007/BF00148532 .
Wang, H., Tang, F., Zirin, H., Wang, J.: 1996, Solar Phys. 165, 223. ADS: 1996SoPh..165..223W , doi: 10.1007/BF00149712 .
West, M.J., Zhukov, A.N., Dolla, L., Rodriguez, L.: 2011, Astrophys. J. 730, 122.
Wilmot-Smith, A.L., Hornig, G., Priest, E.R.: 2009, Geophys. Astrophys. Fluid Dyn. 103, 515.
Withbroe, G.L., Noyes, R.W.: 1977, Annu. Rev. Astron. Astrophys. 15, 363.
Yang, W.H., Sturrock, P.A., Antiochos, S.K.: 1986, Astrophys. J. 309, 383.
Yeates, A.R., Mackay, D.H., van Ballegooijen, A.A.: 2008, Solar Phys. 247, 103. ADS: 2008SoPh..247..103Y , doi: 10.1007/s11207-007-9097-0 .
Zhou, G.P., Wang, J.X., Jin, C.L.: 2010, Solar Phys. 267, 63. ADS: 2010SoPh..267...63Z , doi: 10.1007/s11207-010-9641-1 .
Zirin, H.: 1985, Aust. J. Phys. 38, 961.
Acknowledgements
KAM and DHM gratefully acknowledge the support of the Leverhulme Trust and the STFC. DHM would like to thank the Royal Society for their support through the Research Grant Scheme. DHM and CEP acknowledge support from the EU under FP7.
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magnet48b_free_ht.mpg (1.9 MB)
magnet48b_free_xz.mpg (882 kB)
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Appendix: Images from Movies
Appendix: Images from Movies
This appendix contains four figures, each with six images spaced one hour apart from t=144 hours to t=149 hours, taken from some of the x–y-plane movies included with this article.
Free magnetic-energy density integrated along the line-of-sight for the three-gauss overlying field simulation. The images are shown in the x–y-plane saturated at ± 1.9×1022 ergs. Contours of B z at z=0 Mm are over-plotted where red contours represent the positive magnetic field and green contours represent the negative field at levels of ± [7,13,27,53,106] gauss. The images are shown at (a) t=144 hours, (b) t=145 hours, (c) t=146 hours, (d) t=147 hours, (e) t=148 hours, and (f) t=149 hours. An animation of this figure is available in the online journal.
Normalised j 2 integrated in z, shown in the x–y-plane, for the three-gauss overlying field simulation. Darker regions correspond to higher values. Contours of B z at z=0 Mm are over-plotted where red contours represent the positive magnetic field and green contours represent the negative field at levels of ± [7,13,27,53,106] gauss. The images are shown at (a) t=144 hours, (b) t=145 hours, (c) t=146 hours, (d) t=147 hours, (e) t=148 hours, and (f) t=149 hours. An animation of this figure is available in the online journal.
Rate of energy dissipation [Q] integrated along the line-of-sight, for the three-gauss overlying field simulation. The images are shown in the x–y-plane saturated at 1.5×105 ergs cm−2 s−1. Darker regions correspond to higher values. Contours of B z at z=0 Mm are over-plotted, where red contours represent the positive magnetic field and green contours represent the negative field at levels of ± [7,13,27,53,106] gauss. The images are shown at (a) t=144 hours, (b) t=145 hours, (c) t=146 hours, (d) t=147 hours, (e) t=148 hours, and (f) t=149 hours. An animation of this figure is available in the online journal.
Rate of energy dissipation [Q] for the three-gauss overlying field simulation. The images are shown in the x–y-plane at z=3 Mm, saturated at 810 ergs cm−2 s−1. Darker regions correspond to higher values. They are shown at (a) t=144 hours, (b) t=145 hours, (c) t=146 hours, (d) t=147 hours, (e) t=148 hours, and (f) t=149 hours. An animation of this figure is available in the online journal.
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Meyer, K.A., Mackay, D.H., van Ballegooijen, A.A. et al. Solar Magnetic Carpet III: Coronal Modelling of Synthetic Magnetograms. Sol Phys 286, 357–384 (2013). https://doi.org/10.1007/s11207-013-0272-1
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DOI: https://doi.org/10.1007/s11207-013-0272-1