Skip to main content
SpringerLink
Log in

Nonlinear Numerical Simulations of Magneto-Acoustic Wave Propagation in Small-Scale Flux Tubes

  • HELIOSEISMOLOGY, ASTEROSEISMOLOGY, AND MHD CONNECTIONS
  • Published:
Solar Physics Aims and scope Submit manuscript

Abstract

We present results of nonlinear, two-dimensional, numerical simulations of magneto-acoustic wave propagation in the photosphere and chromosphere of small-scale flux tubes with internal structure. Waves with realistic periods of three to five minutes are studied, after horizontal and vertical oscillatory perturbations are applied to the equilibrium model. Spurious reflections of shock waves from the upper boundary are minimized by a special boundary condition. This has allowed us to increase the duration of the simulations and to make it long enough to perform a statistical analysis of oscillations. The simulations show that deep horizontal motions of the flux tube generate a slow (magnetic) mode and a surface mode. These modes are efficiently transformed into a slow (acoustic) mode in the v A<c S atmosphere. The slow (acoustic) mode propagates vertically along the field lines, forms shocks, and remains always within the flux tube. It might effectively deposit the energy of the driver into the chromosphere. When the driver oscillates with a high frequency, above the cutoff, nonlinear wave propagation occurs with the same dominant driver period at all heights. At low frequencies, below the cutoff, the dominant period of oscillations changes with height from that of the driver in the photosphere to its first harmonic (half period) in the chromosphere. Depending on the period and on the type of the driver, different shock patterns are observed.

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

  • Bellot Rubio, L.R., Collados, M., Ruiz Cobo, B., Rodríguez Hidalgo, I.: 2000, Oscillations in the photosphere of a sunspot umbra from the inversion of infrared stokes profiles. Astrophys. J. 534, 989 – 996.

    Article  ADS  Google Scholar 

  • Berenger, J.P.: 1994, A perfectly mached layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185 – 200.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Berger, T.E., Rouppe van der Voort, L., Löfdahl, M.: 2007, Contrast analysis of solar faculae and magnetic bright points. Astrophys. J. 661, 1272 – 1288.

    Article  ADS  Google Scholar 

  • Bloomfield, D.S., Lagg, A., Solanki, S.K.: 2007, Observations of running waves in a sunspot chromosphere. In: Heinzel, P., Dorotovic, I., Rutten, R.J. (eds.) The Physics of Chromospheric Plasmas, ASP Conf. Ser. 368, ASP, San Francisco, 239.

    Google Scholar 

  • Bloomfield, D.S., McAteer, R.T.J., Mathioudakis, M., Keenan, F.P.: 2006, The influence of magnetic field on oscillations in the solar chromosphere. Astrophys. J. 652, 812 – 819.

    Article  ADS  Google Scholar 

  • Bogdan, T.J., Judge, P.G.: 2006, Observational aspects of sunspot oscillations. Phil. Trans. Roy. Soc. 364(1839), 313 – 331.

    Article  ADS  Google Scholar 

  • Bogdan, T.J., Carlsson, M., Hansteen, V., McMurry, A., Rosenthal, C.S., Johnson, M., Petty-Powell, S., Zita, E.J., Stein, R.F., McIntosh, S.W., Nordlund, A.: 2003, Waves in the magnetized solar atmosphere. ii. waves from localized sources in magnetic flux concentrations. Astrophys. J. 599, 626 – 660.

    Article  ADS  Google Scholar 

  • Braun, D.C., Lindsey, C.: 1999, Helioseismic images of an active region complex. Astrophys. J. 513, L79 – L82.

    Article  ADS  Google Scholar 

  • Brynildsen, N., Maltby, P., Leifsen, T., Kjeldseth-Moe, O., Wilhelm, K.: 2000, Observations of sunspot transition region oscillations. Solar Phys. 191, 129 – 159.

    Article  ADS  Google Scholar 

  • Brynildsen, N., Maltby, P., Fredvik, T., Kjeldseth-Moe, O.: 2002, Oscillations above sunspots. Solar Phys. 207, 259 – 290.

    Article  ADS  Google Scholar 

  • Cally, P.: 2006, Dispersion relations, rays and ray splitting in magnetohelioseismology. Roy. Soc. Lond. Trans. Ser. A 364, 333 – 349.

    Article  ADS  Google Scholar 

  • Cally, P.: 2007, What to look for in the seismology of solar active regions. Astron. Nachr. 328, 286.

    Article  ADS  Google Scholar 

  • Carlsson, M., Stein, R.F.: 1997, Formation of Solar Calcium H and K Bright Grains. Astrophys. J. 481, 500.

    Article  ADS  Google Scholar 

  • Centeno, R., Collados, M., Trujillo Bueno, J.: 2006a, Spectropolarimetric investigation of the propagation of magnetoacoustic waves and shock formation in sunspot atmospheres. Astrophys. J. 640, 1153 – 1162.

    Article  ADS  Google Scholar 

  • Centeno, R., Collados, M., Trujillo Bueno, J.: 2006b, Oscillations and wave propagation in different solar magnetic features. In: Casini, R., Lites, B.W. (eds.) Solar Polarization 4, ASP Conf. Ser. 358, ASP, San Francisco, 465 – 470.

    Google Scholar 

  • Christopoulou, E.B., Georgakilas, A.A., Koutchmy, S.: 2000, Oscillations and running waves observed in sunspots. Astron. Astrophys. 354, 305 – 314.

    ADS  Google Scholar 

  • Christopoulou, E.B., Georgakilas, A.A., Koutchmy, S.: 2001, Oscillations and running waves observed in sunspots. iii. multilayer study. Astron. Astrophys. 375, 617 – 628.

    Article  ADS  Google Scholar 

  • Collados, M., Trujillo Bueno, J., Bellot Rubio, L.R., Socas-Navarro, H.: 2001, In: Ballester, J.L., Roberts, B. (eds.) INTAS Workshop on MHD Waves in Astrophysical Plasmas, Universitat de les Illes Balears, 151 – 154.

  • De Moortel, I., Ireland, J., Hood, A.W., Walsh, R.W.: 2002, The detection of 3 & 5 min period oscillations in coronal loops. Astron. Astrophys. 387, L13 – L16.

    Article  ADS  Google Scholar 

  • De Pontieu, B., Erdelyi, R., de Wijn, A.G.: 2003, Intensity oscillations in the upper transition region above active region plage. Astrophys. J. 595, L63 – L66.

    Article  ADS  Google Scholar 

  • De Pontieu, B., Erdelyi, R.J., Stewart, P.: 2004, Solar chromospheric spicules from the leakage of photospheric oscillations and flows. Nature 430, 536 – 539.

    Article  ADS  Google Scholar 

  • Fleck, B., Schmitz, F.: 1991, The 3-min oscillations of the solar chromosphere – a basc physical effect? Astron. Astrophys. 250, 235 – 244.

    ADS  Google Scholar 

  • Fleck, B., Schmitz, F.: 1993, On the interactions of hydrodynamic shock waves in stellar atmospheres. Astron. Astrophys. 273, 671.

    ADS  Google Scholar 

  • Gurman, J.B., Leibacher, J.W.: 1984, Linear models of acoustic waves in sunspot umbrae. Astrophys. J. 283, 859 – 869.

    Article  ADS  Google Scholar 

  • Hasan, S.S., Ulmschneider, P.: 2004, Dynamisc and heating of the magnetic network on the sun. efficiency of mode transformation. Astron. Astrophys. 422, 1085 – 1091.

    Article  ADS  Google Scholar 

  • Hasan, S.S., Kalkofen, W., van Ballegooijen, A.A., Ulmschneider, P.: 2003, Kink and longitudinal oscillations in the magnetic network of the sun: Nonlinear effects and mode transformation. Astrophys. J. 585, 1138 – 1146.

    Article  ADS  Google Scholar 

  • Hasan, S.S., van Ballegooijen, A.A., Kalkofen, W., Steiner, O.: 2005, Dynamics of solar magnetic network: two-dimensional mhd simulations. Astrophys. J. 631, 1270 – 1280.

    Article  ADS  Google Scholar 

  • Judge, P.G., Tarbell, T.D., Wilhelm, K.: 2001, A study of chromospheric oscillations using the soho and trace spacecraft. Astrophys. J. 554, 424 – 444.

    Article  ADS  Google Scholar 

  • Kalkofen, W., Rossi, P., Bodo, G., Massaglia, S.: 1994, Propagation of acoustic waves in a stratified atmosphere. Astron. Astrophys. 284, 976 – 984.

    ADS  Google Scholar 

  • Khomenko, E., Collados, M.: 2006, Numerical modeling of magnetohydrodynamic wave propagation and refraction in sunspots. Astrophys. J. 653, 739 – 755.

    Article  ADS  Google Scholar 

  • Khomenko, E.V., Collados, M., Bellot Rubio, L.R.: 2003, Magnetoacoustic waves in sunspots. Astrophys. J. 588, 606 – 619.

    Article  ADS  Google Scholar 

  • Korn, G.A., Korn, T.M.: 2000, Mathematical Handbook for Scientists and Engineers, Dover, New York.

    Google Scholar 

  • Krijger, J.M., Rutten, R.J., Lites, B.W., Straus, T., Shine, R.A., Tarbell, T.D.: 2001, Dynamics of the solar chromosphere. III. Ultraviolet brightness oscillations from trace. Astron. Astrophys. 379, 1052 – 1082.

    Article  ADS  Google Scholar 

  • Lites, B.W.: 1984, Photoelectric observations of chromospheric sunspot oscillations. II. Propagation characteristics. Astrophys. J. 277, 874 – 888.

    Article  ADS  Google Scholar 

  • Lites, B.W.: 1986, Photoelectric observations of chromospheric umbral oscillations. IV. The Ca ii h line and He i 1830. Astrophys. J. 301, 1005 – 1017.

    Article  ADS  Google Scholar 

  • Lites, B.W.: 1988, Photoelectric observations of chromospheric umbral oscillations. V. Penumbral oscillations. Astrophys. J. 334, 1054 – 1065.

    Article  ADS  Google Scholar 

  • Lites, B.W., Rutten, R.J., Kalkofen, W.: 1993, Dynamics of the solar chromosphere. I. Long-period network oscillations. Astrophys. J. 414, 345 – 356.

    Article  ADS  Google Scholar 

  • Lites, B.W., Thomas, J.H., Bogdan, T.J., Cally, P.S.: 1998, Velocity and magnetic field fluctuations in the photosphere of a sunspot. Astrophys. J. 497, 464 – 482.

    Article  ADS  Google Scholar 

  • Maltby, P., Brynildsen, N., Fredvik, T., Kjeldseth-Moe, O., Wilhelm, K.: 1999, On the sunspot transition region. Solar Phys. 190, 437 – 458.

    Article  ADS  Google Scholar 

  • Maltby, P., Brynildsen, N., Kjeldseth-Moe, O., Wilhelm, K.: 2001, Plumes and oscillations in the sunspot transition region. Astron. Astrophys. 373, L1 – L4.

    Article  ADS  Google Scholar 

  • Marsh, M.S., Walsh, R.W.: 2005, Observed wave propagtion along the sunspot magnetic field through the chromosphere, transition region and corona. In: Chromospheric and Coronal Magnetic fields 596, ESA SP, Noordwijk, 75.1.

    Google Scholar 

  • Marsh, M.S., Walsh, R.W.: 2006, p-mode propagation through the transition region into the solar corona. I. Observations. Astrophys. J. 643, 540 – 548.

    Article  ADS  Google Scholar 

  • Pneuman, G.W., Solanki, S.K., Stenflo, J.O.: 1986, Structure and merging of solar magnetic fluxtubes. Astron. Astrophys. 154, 231 – 242.

    MATH  ADS  Google Scholar 

  • Roberts, B.: 1981, Wave propagation in a magnetically structured atmosphere. I. Surface waves at a magnetic interface. Solar Phys. 69, 27 – 38.

    Article  ADS  Google Scholar 

  • Roberts, B.: 1983, Wave propagation in intense flux tubes. Solar Phys. 87, 77 – 93.

    Article  ADS  Google Scholar 

  • Rosenthal, C.S., Bogdan, T.J., Carlsson, M., Dorch, S.B.F., Hansteen, V., McIntosh, S.W., McMurry, A., Nordlund, A., Stein, R.F.: 2002, Waves in the magnetized solar atmosphere. I. Basic processes and internetwork oscillations. Astrophys. J. 564, 508 – 524.

    Article  ADS  Google Scholar 

  • Rüedi, I., Solanki, S.K., Stenflo, J., Tarbell, T., Scherrer, P.H.: 1998, Oscillations of sunspot magnetic fields. Astron. Astrophys. 335, L97 – L100.

    ADS  Google Scholar 

  • Socas-Navarro, H., Trujillo Bueno, J., Ruiz Cobo, B.: 2000, Anomalous circular polarization profiles in sunspot chromospheres. Astrophys. J. 544, 1141 – 1154.

    Article  ADS  Google Scholar 

  • Thomas, J.H., Stanchfield, D.C.H.: 2000, Fine-scale magnetic effects on p-modes and higher frequency acoustic waves in a solar active region. Astrophys. J. 537, 1086 – 1093.

    Article  ADS  Google Scholar 

  • Tziotziou, K., Tsiropoula, G., Mein, N., Mein, P.: 2006, Observational characteristics and association of umbral oscillations and running penumbral waves. Astron. Astrophys. 456, 689 – 695.

    Article  ADS  Google Scholar 

  • Tziotziou, K., Tsiropoula, G., Mein, N., Mein, P.: 2007, Dual-line spectral and phase analysis of sunspot oscillations. Astron. Astrophys. 463, 1153 – 1163.

    Article  ADS  Google Scholar 

  • Rouppe van der Voort, L.H.M.R., Rutten, R.J., Sütterlin, P., Sloover, P.J., Krijger, J.M.: 2003, La Palma observations of umbral flashes. Astron. Astrophys. 403, 277 – 285.

    Article  ADS  Google Scholar 

  • Vecchio, A., Cauzzi, G., Reardon, K.P., Janssen, K., Rimmele, T.: 2007, Solar atmospheric oscillations and the chromospheric magnetic topology. Astron. Astrophys. 461, L1 – L4.

    Article  ADS  Google Scholar 

  • Vernazza, J.E., Avrett, E.H., Loeser, R.: 1981, Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet sun. Astrophys. J. 45, 635 – 725.

    Article  ADS  Google Scholar 

  • Zhugzhda, Y.D.: 2007, Astron. Lett. 44(9), 622 – 643.

    Article  ADS  Google Scholar 

  • Zhugzhda, Y.D., Locans, V.: 1981, Resonance oscillations in sunspots. Sov. Astron. Lett. 7, 25 – 27.

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Astrofísica de Canarias, C/ Vía Láctea, s/n, 38205, Tenerife, Spain

    E. Khomenko, M. Collados & T. Felipe

  2. Main Astronomical Observatory, NAS, Zabolotnogo str. 27, 03680, Kyiv, Ukraine

    E. Khomenko

Authors
  1. E. Khomenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Collados
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Felipe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Khomenko.

Additional information

Helioseismology, Asteroseismology, and MHD Connection Guest Editors: Laurent Gizon and Paul Cally.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khomenko, E., Collados, M. & Felipe, T. Nonlinear Numerical Simulations of Magneto-Acoustic Wave Propagation in Small-Scale Flux Tubes. Sol Phys 251, 589–611 (2008). https://doi.org/10.1007/s11207-008-9133-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11207-008-9133-8

Keywords

Search

Navigation