Magnetic Decay Index Profile and Coronal Mass Ejection Speed

TL;DR

The paper investigates how the ambient coronal magnetic-field profile, captured by the decay index $n(h)$, governs CME speeds through torus-instability-driven acceleration. It combines observational analysis of $n(h)$ profiles derived from potential-field extrapolations with a parametric MHD study of flux-rope eruptions in multipolar source regions to assess how dips in $n(h)$ affect acceleration. A striking result is that for very fast halo CMEs ($V_ ext{CME}\ge1500\,\mathrm{km\,s}^{-1}$), the slope of $n(h)$ above the TI onset height, $ig\langle n'(h)\big\bra_{\Delta h}$, correlates strongly with $V_ ext{CME}$, achieving $c\approx 0.81$ when outliers are excluded; dips in $n(h)$ can produce significant deceleration or confinement, reducing the correlation. These findings support TI as a principal driver of rapid CME acceleration and highlight the importance of coronal-field structure, particularly in multipolar regions, for forecasting CME speeds.

Abstract

We study the relationship between the speed of coronal mass ejections (CMEs) and the height profile of the ambient magnetic field, quantified by its decay index, n(h). Our sample is composed of 15 very fast CMEs (Vcme > 1500 km/s; all halo CMEs) and 22 halo CMEs below this speed limit from Solar Cycle 23. The very fast CMEs yield a high correlation of 0.81 between Vcme and the slope of n(h) in a height range above the onset height of the torus instability if one extremely fast outlier, which closely followed another very fast CME, is excluded. This is consistent with the hypothesis that the torus instability plays a decisive role in CME acceleration. The whole sample yields a weaker correlation, which is still significant if events with a broad torus-stable dip in n(h) are excluded. A parametric simulation study of flux-rope eruptions from quadrupolar and two-scale bipolar source regions confirms the decelerating effect of such dips. Very fast, moderate-velocity, and confined eruptions are found.

Figures (4)

• Figure 1: Decay index height profiles for the CMEs on 2005-01-15, 06:30 UT (left) and 2000-07-07, 10:26 UT (right). Each case has 6 sampling lines, and the average $n(h)$ is plotted in red. The height range $\Delta h$ used to compute $\langle n^\prime(h) \rangle_{{\Delta}h}$ is marked in blue.
• Figure 2: $V_\mathrm{CME}$ vs. $\langle n^\prime(h) \rangle_{{\Delta}h}$ for the parameters $n_\mathrm{cr}=1.5$ and $\delta=1$ that maximize the correlation coefficients for the very fast CMEs. The whole sample yields a correlation coefficient $c=0.13$ (left panel, black line is the linear fit). Excluding Event #11 and all 5 events with a strong dip in $n(h)$ (#19, 20, 32, 34, 35; open diamonds; see text), raises the correlation to $c=0.68$ (red fit line). Event #20 lies outside the range shown (see Table \ref{['t:sample']}). Results for the sub-sample of very fast CMEs are shown in the right panel.
• Figure 3: Decay index profiles $n(h)$ (left) and rise profiles of TD flux ropes, $h(t)/h_0$ and $v_z(t)/V_\mathrm{A}$, (right) in a line quadrupole with $B_\mathrm{et}=0$ for a range of source strength ratios $\epsilon=q_2/q_1$. Dotted profiles $n(h)$ are the exact profiles computed from $B_\mathrm{ep}$, which have a pole at the position of the null (X-) line, and the solid profiles are computed from the corresponding potential field. The rise profiles are dotted during the period when the flux rope apex closely approaches the closed upper boundary.
• Figure 4: Decay index and rise profiles for the two-scale bipole with $B_\mathrm{et}=0$ for a range of source strength ratios $\epsilon=q_2/q_1$ and two values of the scale ratio $\kappa=L_2/L_1$, displayed as in Fig. \ref{['f:n&cfl_all_quadrupole']}. The very different evolution times until considerable acceleration commences result from small differences of the initial equilibria from the exact marginal stability configurations.