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Propagation of Interplanetary Coronal Mass Ejections: The Drag-Based Model

  • OBSERVATIONS AND MODELLING OF THE INNER HELIOSPHERE
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Abstract

We present the “Drag-Based Model” (DBM) of heliospheric propagation of interplanetary coronal mass ejections (ICMEs). The DBM is based on the hypothesis that the driving Lorentz force, which launches a CME, ceases in the upper corona and that beyond a certain distance the dynamics becomes governed solely by the interaction of the ICME and the ambient solar wind. In particular, we consider the option where the drag acceleration has a quadratic dependence on the ICME relative speed, which is expected in a collisionless environment, where the drag is caused primarily by emission of magnetohydrodynamic (MHD) waves. In this paper we present the simplest version of DBM, where the equation of motion can be solved analytically, providing explicit solutions for the Sun–Earth ICME transit time and impact speed. This offers easy handling and straightforward application to real-time space-weather forecasting. Beside presenting the model itself, we perform an analysis of DBM performances, applying a statistical and case-study approach, which provides insight into the advantages and drawbacks of DBM. Finally, we present a public, DBM-based, online forecast tool.

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Acknowledgements

We are grateful to the anonymous referee for constructive comments and suggestions, which improved the manuscript considerably. The presented work has received funding from the European Commission’s Seventh Framework Programs (FP7/2007-2013) under the grant agreements No. 218816 (SOTERIA project, www.soteria-space.eu ) and No. 263252 (COMESEP project, www.comesep.eu ). M.T. acknowledges the Austrian Science Fund (FWF): FWF V195-N16. C.M. acknowledges the support by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme. Y.-J.M. has been supported by the WCU Program (No. R31-10016) and research grants (KRF-2008-314-C00158, 20090071744 and 20100014501) though the National Research Foundation of the Republic of Korea funded by the Ministry of Education, Science and Technology.

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Authors and Affiliations

  1. Hvar Observatory, Faculty of Geodesy, University of Zagreb, Kačićeva 26, 10000, Zagreb, Croatia

    B. Vršnak, T. Žic, D. Vrbanec, J. Čalogović & M. Dumbović

  2. IGAM, Institute of Physics, University of Graz, Universitätsplatz 5, 8010, Graz, Austria

    M. Temmer, T. Rollett, C. Möstl & A. Veronig

  3. Space Science Laboratory, University of California, Berkeley, CA, 94720, USA

    C. Möstl

  4. Karlovac University of Applied Sciences, Trg J.J.Strossmayera 9, 47000, Karlovac, Croatia

    S. Lulić

  5. School of Space Research, Kyung Hee University, Yongin, 446-701, Republic of Korea

    Y.-J. Moon

  6. Department of Physics, Arul Anandar College, Karumathur, 625 514, Madurai, India

    A. Shanmugaraju

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  1. B. Vršnak
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  2. T. Žic
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Correspondence to B. Vršnak.

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Observations and Modelling of the Inner Heliosphere

Guest Editors: Mario M. Bisi, Richard A. Harrison, and Noé Lugaz

Appendix

Appendix

Hereinafter, we present an open-access online forecast tool for predicting the ICME arrival at 1 AU, which is based on the previously described formulation of the DBM. This forecast tool was developed in the frame of the European Commission FP7 Project SOTERIA (SOlar-TERrestrial Investigations and Archives; www.soteria-space.eu ) and advanced within FP7 Project COMESEP (COronal Mass Ejections and Solar Energetic Particles; www.comesep.eu ). The tool is available at http://oh.geof.unizg.hr/CADBM/cadbm.php .

The input page of the DBM forecast web-site is presented in Figure 6. In the first two input boxes the user has to specify the date and time (UT) when the CME was located at a given distance R 0 (third input box). Preferably, R 0 should be around, or beyond, the radial distance of R∼20. Finally, the CME speed at R 0, v 0≡v(R 0), is required (fourth input box). The default values are set to R=20 and v 0=1000 km s−1.

Figure 6
figure 6

Input page of the Drag-Based Model forecast web-site, available at: http://oh.geof.unizg.hr/CADBM/cadbm.php .

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To complete the set of input parameters, the drag parameter γ (expressed in 10−7 km−1) and the solar-wind speed w (expressed in km s−1) have to be specified, too. In Sections 2 and 3 it was shown that γ and w most often attain values in the range 2×10−8−2×10−7 km−1 and 300 – 600 km s−1, respectively. In the case of massive ICMEs (generally meaning bright CMEs in the coronagraphic images) γ should have a small value, whereas in the case of low-density ICME (dim in coronagraphic images) it should be closer to the upper limit. In the slow-wind environment, w should be chosen between 300 and 400 km s−1. If there is an equatorial coronal hole in the vicinity of the ICME source region, one should apply a higher value, say, 500 – 600 km s−1. In such a case, a high value of solar-wind speed should be combined with a low value of γ, since the fast solar wind is characterized by a low density. Following the results presented in Section 3, the default values are set to γ=1×10−7 km−1 and w=500 km s−1. For inexperienced users we would recommend that beside the default values of w and γ to use also the mentioned limiting combinations to estimate a time-window within which the ICME arrival is expected.

After clicking the “Calculate” button, the output page appears (Figure 7). The model output provides an estimate of the arrival date and time of the ICME at 1 AU, as well as the travel time from R=R 0 to R=214 (=1 AU) and the impact speed v 1 at 1 AU. Beside the outcome of the calculation, the output page summarizes the input parameters used, as well as the a new input set, to provide a new calculation (see bottom part of Figure 7).

Figure 7
figure 7

Output page of the DBM forecast web-site.

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Again, we emphasize that the output values correspond to the front boundary of the ejecta, i.e., the ICME-associated shock should arrive several hours earlier. Furthermore, the present form of DBM does not take into account the direction of the ICME motion, i.e., in the case of flank-encounter the arrival time at the Earth might be delayed by several hours, in extreme cases up to one day. It is foreseen that in future a more advanced form of DBM will be developed, which will take these two effects into account.

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Vršnak, B., Žic, T., Vrbanec, D. et al. Propagation of Interplanetary Coronal Mass Ejections: The Drag-Based Model. Sol Phys 285, 295–315 (2013). https://doi.org/10.1007/s11207-012-0035-4

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