Comprehensive Characterization of the Dynamics of Two Coronal Mass Ejections in the Outer Corona

Abstract

Coronal mass ejections (CMEs) play a key role in determining space-weather conditions. Therefore, it is important to understand their evolution throughout the heliosphere. In this work, we carefully analyze the evolution of two kinematically different CMEs that erupted on 16 June 2010 and 14 June 2011, in a range of heliospheric distances of approximately 4 – 18 solar radii. From nearly simultaneous coronagraph images from the Solar-Terrestrial Relations Observatory and Solar and Heliospheric Observatory, we estimate the three-dimensional speed and acceleration–time profiles. We use these profiles to calculate the dynamic and thermodynamic parameters of the CMEs, such as the contribution of the forces and the polytropic index by means of the Flux Rope Internal State (FRIS) model, which assumes a self-similar evolution. We further test the validity of this assumption by comparing with observed quantities near the Sun and at 1 AU. We find that the kinematic properties of the two events differ in their evolution, which has an impact on the relative importance of the internal forces and on the thermodynamic quantities. In addition, our analysis reveals that the assumption of self-similar evolution is valid for the behavior in the middle corona for both events. At larger distances, however, this only holds for the 16 June 2010 event, which is significantly slower than the other.

Appendices

Appendix A: CME Mass

Since the MW18 – 23 approach assumes that the mass remains constant, we evaluate below whether this assumption holds for the two events. We estimate the CME mass and its number of electrons by means of the method described by Vourlidas et al. (2010), which is based on the scattering of photospheric light by coronal electrons. These masses are subsequently corrected to estimate the “true” mass evolution, by using the approach proposed by Bein et al. (2013). It proposes a fitting function that describes the mass evolution of the CME with height, taking into account the effect of the coronagraph occulter and the actual mass increase, due to the solar-wind mass piled up ahead of the CMEs and the mass supply by the outflow from the associated dimmings in the low corona (e.g. Aschwanden et al., 2009; Feng et al., 2015; López et al., 2017).

1.1 A.1 The CME on 16 June 2010

To estimate the mass in this event, we use STEREO-A images because the CME propagation angle with respect to the sky plane was ≈ 1^∘. The measured mass values are plotted in Figure 11a as black triangles, while the red dashed line and the blue solid line, respectively, represent the fitting function and the mass values corrected for the effects of the occulter after Bein et al. (2013). The resulting values for the initially ejected mass [$m_{\mathrm{0}}$], the real mass increase per height [$\Delta m$], and the effective occultation size [$h_{\mathrm{occ}}$] are shown to the bottom right of the plot area.

Figure 11

The Bein et al. (2013) fit and the curve accounting for the occulter effect are shown in red and blue, respectively. The inset shows the parameters arising from the aforementioned fit. (a): Mass measurements for E1. (b): Mass measurements for E2.

1.2 A.2 The CME on 14 June 2011

The propagation direction of this event was closest to the sky plane of STEREO-B, having an angle of ≈ 40^∘. Therefore, images from this vantage point were used for the mass estimates shown in Figure 11b (black triangles). Again, the blue solid line represents the corrected mass values.

Appendix B: Electron Density

We also calculate the density of electrons. The method used to calculate the masses (Vourlidas et al., 2010) also enables estimation of the number of electrons. To determine the volume of the CME, we use the method described by Holzknecht et al. (2018), which yields the volume of the GCS geometrical figure at different heights. Finally, the electron density arises from the corrected mass values (Appendix A) and the aforementioned volume.

In Figure 12, the electron density is plotted as red triangles connected by a red solid line. The electron densities resulting from the MW18 – 23 approach, using the $k_{7}$-value discussed in Section 4.1 are plotted as blue solid lines.

Figure 12

Comparison of the electron density as determined from the measurements (red triangles joined by solid line) and from the FRIS approach (blue solid line). (a) Electron density for E1. (b) Electron density for E2. In (b), the shaded bands represent the $95\%$ bootstrap confidence intervals and the central solid line is the median curve.

Appendix C: Energies

To characterize the events in terms of their energies, we estimate the potential and kinetic energy. The first is determined from the method of Vourlidas et al. (2000), while the kinetic energy is calculated from the corrected masses (Appendix A) and the speed profiles in Figures 3c and 5c.

These energies are, however, not considered by MW18 – 23, but they do estimate the relative changes of thermal [$E_{\mathrm{thermal}}$] and magnetic [$E_{\mathrm{m1}}$ and $E_{\mathrm{m2}}$] energies. $E_{\mathrm{m1}}$ and $E_{\mathrm{m2}}$ represent the magnetic energy associated with the toroidal and poloidal components of the magnetic field.

3.1 C.1 The CME on 16 June 2010

In Figure 13a, we can see the kinetic [$E_{\mathrm{k}}$, blue diamonds], potential [$E_{\mathrm{p}}$, red triangles], and total energies [$E_{ \mathrm{k}} + E_{\mathrm{p}}$, black squares]. Note that the kinetic energy is an order of magnitude smaller than the potential energy. Kinetic and potential energies gradually increase along with the propagation of the event in the mid-corona. In Figure 13c, we show the thermal [$E_{ \mathrm{thermal}}$, black solid line] and magnetic [$E_{\mathrm{m1}}$ and $E_{\mathrm{m2}}$, blue solid and dashed lines] energies arising from the MW18 – 23 approach, as relative changes with respect to their first value.

Figure 13

(a) and (b) display kinetic (blue diamonds), potential (red triangles), and total (black squares) energies. (c) and (d) are relative changes of energies from the FRIS approach. The black solid line represents the thermal energy $E_{\mathrm{thermal}}$, while blue lines are magnetic energies $E_{\mathrm{m1}}$ and $E_{\mathrm{m2}}$ (solid and dashed, respectively). The left panels correspond to E1, and the right panels to E2. In (d), the shaded bands represent the $95\%$ bootstrap confidence intervals and the central solid line is the median curve.

The magnetic energies $E_{\mathrm{m1}}$ and $E_{\mathrm{m2}}$ are identical for the three different fits to the values of height and radius vs. time. However, for $E_{\mathrm{thermal}}$ we chose to plot only the curve corresponding to the use of a cubic fit, to ease interpretation of the plot. The thermal energy shows a decrease of ≈ 40$\%$ at ≈ 7.5 R_⊙ and then slowly starts to increase. Both of the magnetic energies significantly decrease throughout the CME propagation.

3.2 C.2 The CME on 14 June 2011

Figure 13b shows the kinetic (blue diamonds), potential (red triangles), and total energies (black squares). For this event, the kinetic energy and the potential energy are similar in magnitude and both increase throughout the propagation. Figure 13d shows the relative change of thermal [$E_{\mathrm{thermal}}$, black solid line] and magnetic [$E_{ \mathrm{m1}}$ and $E_{\mathrm{m2}}$, blue solid and dashed lines] energies from the MW18 – 23 approach. The thermal energy shows a systematic decrease that reaches ≈ 70$\%$ by 10 R_⊙. The magnetic energies decrease significantly throughout the propagation.