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ISSN  2096-3955

CN  10-1502/P

Citation: Qu, B. H., Lu, J. Y., Wang, M., Yuan, H. Z., Zhou, Y. and Zhang, H. X. (2021). Formation of the bow shock indentation: MHD simulation results. Earth Planet. Phys., 5(3), 259–269.

2021, 5(3): 259-269. doi: 10.26464/epp2021033

Formation of the bow shock indentation: MHD simulation results


Institute of Space Weather, School of Math & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, China


Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China

Corresponding author: JianYong Lu,

Received Date: 2020-11-20
Web Publishing Date: 2021-05-10

Simulation results from a global magnetohydrodynamic (MHD) model are used to examine whether the bow shock has an indentation and characterize its formation conditions, as well as its physical mechanism. The bow shock is identified by an increase in plasma density of the solar wind, and the indentation of the bow shock is determined by the shock flaring angle. It is shown that when the interplanetary magnetic field (IMF) is southward and the Alfvén Mach number (Mα) of solar wind is high (> 5), the bow shock indentation can be clearly determined. The reason is that the outflow region of magnetic reconnection (MR) that occurs in the low latitude area under southward IMF blocks the original flow in the magnetosheath around the magnetopause, forming a high-speed zone and a low-speed zone that are upstream and downstream of each other. This structure hinders the surrounding flow in the magnetosheath, and the bow shock behind the structure widens and forms an indentation. When Mα is low, the magnetosheath is thicker and the disturbing effect of the MR outflow region is less obvious. Under northward IMF, MR occurs at high latitudes, and the outflow region formed by reconnection does not block the flow inside the magnetosheath, thus the indentation is harder to form. The study of the conditions and formation process of the bow shock indentation will help to improve the accuracy of bow shock models.

Key words: indentation of bow shock, global MHD simulation, interplanetary magnetic field Bz, Alfvén Mach number

Cairns, I. H., and Lyon, J. G. (1995). MHD simulations of Earth's bow shock at low Mach numbers: Standoff distances. J. Geophys. Res., 100(A9), 17173–17180.

Chao, J. K., Wu, D. J., Lin, C. H., Yang, Y. H., Yang, X. Y., Kessel, M., Chen, S. H., and Lepping, R. P. (2002). Models for the size and shape of the Earth's magnetopause and bow shock. COSPAR Colloq. Ser., 12, 127–135.

Chapman, J. F., and Cairns, I. H. (2003). Three-dimensional modeling of earth's bow shock: shock shape as a function of Alfvén Mach number. J. Geophys. Res., 108(A5), SSH 1-1–SSH 1-10.

Cowley, S. W. H. (1981). Asymmetry effects associated with the x-component of the IMF in a magnetically open magnetosphere. Planet. Space Sci., 29(8), 809–818.

Dmitriev, A. V., Chao, J. K., and Wu, D. J. (2003). Comparative study of bow shock models using wind and geotail observations. J. Geophys. Res., 108(A12), SMP 24-1–SMP 24-19.

Fairfield, D. H. (1971). Average and unusual locations of the Earth's magnetopause and bow shock. J. Geophys. Res., 76(28), 6700–6716.

Farris, M. H., and Russell, C. T. (1994). Determining the standoff distance of the bow shock: Mach number dependence and use of models. J. Geophys. Res., 99(A9), 17681–17689.

Formisano, V. (1979). Orientation and shape of the Earth's bow shock in three dimensions. Planet. Space Sci., 27(9), 1151–1161.

Gombosi, T. I., Dezeeuw, D. L., Groth, C. P. T., and Powell, K. G. (2000). Magnetospheric configuration for parker-spiral IMF conditions: results of a 3d amr mhd simulation. Adv. Space Res., 26(1), 139–149.

Gonzalez, W. D., Joselyn, J. A., Kamide, Y., Kroehl, H. W., Rostoker, G., Tsurutani, B. T., and Vasyliunas, V. M. (1994). What is a geomagnetic storm?. J. Geophys. Res., 99(A4), 5771–5792.

Hu, H. P., Lu, J. Y., Zhou, Q., Wang, M., Yang, Y. F., Liu, Z. Q., and Pei, S. X. (2015). Simulation of three-dimensional Earth’s bow shock. Chin. J. Space Sci. (in Chinese) , 35(1), 1–8.

Jelínek, K., Němeček, Z., Šafránková., J., and Merka, J. (2008). Influence of the tilt angle on the bow shock shape and location. J. Geophys. Res., 113(A5), A05220.

Jelínek, K., Němeček, Z., and Šafránková, J. (2012). A new approach to magnetopause and bow shock modeling based on automated region identification. J. Geophys. Res., 117, A05208.

Jing, H., Lu, J. Y., Kabin, K., Zhao, J. S., Liu, Z. Q., Yang, Y. F., Zhao, M. X., and Wang, M. (2014). MHD simulation of energy transfer across magnetopause during sudden changes of the IMF orientation. Planet. Space Sci., 97, 50–59.

Kabin, K., Rankin, R., Rostoker, G., Marchand, R., Rae, I J., Ridley, A. J., Gombosi, T. I., Clauer, C. R., and Dezeeuw, D. L. (2004). Open-closed field line boundary position: a parametric study using an MHD model. J. Geophys. Res., 109(A5), A05222.

Liu, Z. Q., Lu, J. Y., Kabin, K., Yang, Y. F., Zhao, M. X., and Cao, X. (2012). Dipole tilt control of the magnetopause for southward IMF from global magnetohydrodynamic simulations. J. Geophys. Res., 117(A7), A07207.

Liu, Z. Q., Lu, J. Y., Wang, C., Kabin, K., Zhao, J. S., Wang, M., Han, J. P., Wang, J. Y., and Zhao, M. X. (2015). A three-dimensional high Mach number asymmetric magnetopause model from global MHD simulation. J. Geophys. Res., 120(7), 5645–5666.

Lu, J. Y., Liu, Z. Q., Kabin, K., Zhao, M. X., Liu, D. D., Zhou, Q., and Xiao, Y. (2011). Three dimensional shape of the magnetopause: Global MHD results. J. Geophys. Res., 116(A9), A09237.

Lu, J. Y., Liu, Z. Q., Kabin, K., Jing, H., Zhao, M. X., and Wang, Y. (2013). The IMF dependence of the magnetopause from global MHD simulations. J. Geophys. Res., 118(6), 3113–3125.

Lu, J. Y., Yuan, H. Z., Wang, M., and Yang, Y. F. (2017). Dipole tilt controls bow shock location and flaring angle. Sci. China Earth Sci., 60(1), 198–206.

Lu, J. Y., Zhou, Y., Ma, X., Wang, M., Kabin, K., and Yuan, H. Z. (2019a). Earth's bow shock: A new three-dimensional asymmetric model with dipole tilt effects. J. Geophys. Res., 124(7), 5396–5407.

Lu, J. Y., Zhang, H. X., Wang, M., Gu, C. L., and Guan, H. Y. (2019b). Magnetosphere response to the IMF turning from north to south. Earth Planet. Phys., 3(1), 8–16.

Merka, J., and Szabo, A. (2004). Bow shock's geometry at the magnetospheric flanks. J. Geophys. Res., 109(A12), A12224.

Merka, J., Szabo, A., Slavin, J. A., and Peredo, M. (2005). Three-dimensional position and shape of the bow shock and their variation with upstream Mach numbers and interplanetary magnetic field orientation. J. Geophys. Res., 110(A04), A04202.

Němeček, Z., and Šafránková, J. (1991). The Earth's bow shock and magnetopause position as a result of the solar wind-magnetosphere interaction. J. Atmos. Terr. Phys., 53(11-12), 1049–1054.

Peredo, M., Slavin, J. A., Mazur, E., and Curtis, S. A. (1995). Three-dimensional position and shape of the bow shock and their variation with Alfvénic, sonic and magnetosonic Mach numbers and interplanetary magnetic field orientation. J. Geophys. Res., 100(A5), 7907–7916.

Rae, I. J., Kabin, K., Lu, J. Y., Rankin, R., Milan, S. E., Fenrich, F. R., Watt, C. E. J., Zhang, J. C., Ridley, A. J., … DeZeeuw, D. L. (2010). Comparison of the open-closed separatrix in a global magnetospheric simulation with observations: the role of the ring current. J. Geophys. Res., 115(A8), A08216.

Shi, Q. Q., Zong, Q.-G., Zhang, H., Pu, Z. Y., Fu, S. Y., Xie, L., Wang, Y. F., Chen, Y., Li, L., …Lucek, E. (2009). Cluster observations of the entry layer equatorward of the cusp under northward interplanetary magnetic field. J. Geophys. Res., 114(A12), A12219.

Shi, Q. Q., Zong, Q. G., Fu, S. Y., Dunlop, M. W., Pu, Z. Y., Parks, G. K., Wei, Y., Li, W. H., Zhang , H., … Lucek, E. (2013). Solar wind entry into the high-latitude terrestrial magnetosphere during geomagnetically quiet times. Nat. Commun., 4(1), 1466.

Shi, Q. Q., Hartinger, M. D., Angelopoulos, V., Tian, A. M., Fu, S. Y., Zong, Q. G., Weygand, J. M., Raeder, J., Pu, Z. Y., … Shen, X. C. (2014). Solar wind pressure pulse‐driven magnetospheric vortices and their global consequences. J. Geophys. Res., 119(6), 4274–4280.

Shue, J. H., Chao, J. K., Fu, H. C., Russell, C. T., Song, P., Khurana, K. K., and Singer, H. J. (1997). A new functional form to study the solar wind control of the magnetopause size and shape. J. Geophys. Res., 102(A5), 9497–9511.

Song, P., DeZeeuw, D. L., Gombosi, T. I., Groth, C. P. T., and Powell, K. G. (1999). A numerical study of solar wind-magnetosphere interaction for northward interplanetary magnetic field. J. Geophys. Res., 104(A12), 28361–28378.

Song, P., DeZeeuw, D.L., Gombosi, T.I., Kozyra, J.U., Powell, K.G. (2001). Global MHD simulations for southward IMF: a pair of wings in the flanks. Adv. Space Res., 28(12), 1763–1771.

Spreiter, J. R., Summers, A. L., and Alksne, A. Y. (1966). Hydromagnetic flow around the magnetosphere. Planet. Space Sci., 14, 223–253.

Tóth, G., Sokolov, I. V., Gombosi, T. I., Chesney, D. R., Clauer, C. R., De Zeeuw, D. L., Hansen, K. C., Kane, K. J., Manchester, W. B., … Kóta, J. (2005). Space weather modeling framework: a new tool for the space science community. J. Geophys. Res., 110(A12), A12226.

Tóth, G., Zeeuw, D. L. D., Gombosi, T. I., Manchester, W. B., Ridley, A. J., Sokolov, I. V., and Roussev, I. (2007). Sun-to-thermosphere simulation of the 28-30 october 2003 storm with the space weather modeling framework. Space Weather, 5(6), S06003.

Verigin, M. I., Kotova, G. A., Slavin, J., Szabo, A., Kessel, M., Safrankova, J., Němeček, Z., Gombosi, T. I., Kabin, K., … Kalinchenko, A. (2001a). Analysis of the 3-d shape of the terrestrial bow shock by interball/magion 4 observations. Adv. Space Res., 28(6), 857–862.

Verigin, M., Kotova, G., Szabo, A., Slavin, J., Gombosi, T., Kabin, K., Shugaev, F., and Kalinchenko, A. (2001b). Wind observations of the terrestrial bow shock: 3-D shape and motion. Earth Planets Space., 53(10), 1001–1009.

Wang, J., Guo, Z. F., Ge, Y. S., Du, A. M., Huang, C., and Qin, P. F. (2018). The responses of the earth’s magnetopause and bow shock to the IMF Bz and the solar wind dynamic pressure: a parametric study using the AMR-CESE-MHD model. J. Space Weather Space Clim., 8(A41).

Wang, J., Huang, C., Ge, Y. S., Du, A., and Feng, X. (2020). Influence of the IMF Bx on the geometry of the bow shock and magnetopause. Planet. Space Sci., 182, 104844.

Wang, M., Lu, J. Y., Yuan, H. Z., Kabin, K., Liu, Z. Q., Zhao, M. X., and Li, G. (2015). The dipole tilt angle dependence of the bow shock for southward IMF: MHD results. Planet. Space Sci., 106, 99–107.

Wang, M., Lu, J. Y., Kabin, K., Yuan, H. Z., Ma, X., Liu, Z. Q., Yamh, Y. F., Zhao, J. S., Li, G. (2016). The influence of IMF clock angle on the cross section of the tail bow shock. J. Geophys. Res., 121(11), 11077–11085.

Wang, M., Lu, J. Y., Kabin, K., Yuan, H. Z., Liu, Z. Q., Zhao, J. S., and Li, G. (2018). The influence of IMF B-y on the bow shock: observation result. J. Geophys. Res., 123, 1915–1926.

Xiong, M., Peng, Z., Hu, Y. Q., and Zheng, H. N. (2009). Response of the Earth’s magnetosphere and ionosphere to solar wind driver and ionosphere load: results of global MHD simulations. Chin. Phys. Lett., 26(1), 015202.

Zong, Q. G., Fritz, T. A., Zhang, H., Korth, A., Daly, P. W., Dunlop, M. W., Glassmeier, K. H., Reme, H., and Balogh, A. (2004). Triple cusps observed by cluster—temporal or spatial effect?. Geophys. Res. Lett., 31(9), L09810.

Zong, Q. G., and Zhang, H. (2018). In situ detection of the electron diffusion region of collisionless magnetic reconnection at the high-latitude magnetopause. Earth Planet. Phys., 2(3), 231–237.


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Formation of the bow shock indentation: MHD simulation results

BaoHang Qu, JianYong Lu, Ming Wang, HuanZhi Yuan, Yue Zhou, HanXiao Zhang