Development of a Fast CME and Properties of a Related Interplanetary Transient

Abstract

We study the development of a coronal mass ejection (CME) caused by a prominence eruption on 24 February 2011 and properties of a related interplanetary CME (ICME). The prominence destabilized, accelerated, and produced an M3.5 flare, a fast CME, and a shock wave. The eruption at the east limb was observed in quadrature by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) and by the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) instrument suite on board the Solar-Terrestrial Relations Observatory (STEREO). The ICME produced by the SOL2011-02-24 event was measured in situ on STEREO-B two days later. The diagnostics made from multi-wavelength SDO/AIA images reveals a pre-eruptive heating of the prominence to about 7 MK and its subsequent heating during the eruption by flare-accelerated particles to about 10 MK. The hot plasma was detected in the related ICME as an enhancement in the ionic charge state of Fe, whose evolution was reproduced in the modeling. The analysis of the solar source region allows for predicting the variations of magnetic components in the ICME, while the flux-rope rotation by about $40^{\circ }$ was indicated by observations. The magnetic-cloud propagation appears to be ballistic.

Appendix: General Expectations for the Fe-ion Charge State

Figure 20 shows that the freeze-in process for the Fe-ion charge state starts within $1~\mathrm{R}_{\odot }$ for higher-charge ions and at $\gtrsim 2~\mathrm{R}_{\odot }$ for lower-charge ions. The freeze-in distance $r_{\mathrm{fr}}$ is determined by the kinematics and plasma parameters of a structure propagating through the corona. To derive an analytical expression for $r_{\mathrm{fr}}$ and its dependence on the parameters of an eruptive event, the plasma expansion timescale $\tau _{\mathrm{exp}}$ should be compared with recombination time $\tau _{\mathrm{rec}}$.

The expansion timescale is $\tau _{\mathrm{exp}} = n_{\mathrm{e}}/| \mathrm{d}n_{\mathrm{e}}/\mathrm{d}t|$, where $\mathrm{d}n_{ \mathrm{e}}/\mathrm{d}t = \partial n_{\mathrm{e}}/\partial t + ( \boldsymbol{{V}} \cdot \boldsymbol{\nabla })n_{\mathrm{e}}$. In stationary solar wind $\partial /\partial t = 0$. In our case $\partial /\partial t \neq 0$ and $\tau _{\mathrm{exp}}$ depends on deformation of the moving plasma volume. For self-similar expansion $n_{\mathrm{e}} = n_{0}(r_{0}/r)^{3}$, where $r$ is a distance from the eruption center that is located near the solar surface, and $r_{0}$ is a distance where the adiabatic regime starts. It follows from these expressions that $|\mathrm{d}n_{\mathrm{e}}/\mathrm{d}t| = n _{\mathrm{e}}(3V/r)$, where $V = \mathrm{d}r/\mathrm{d}t$ is the velocity of the leading edge of the erupting structure. For $r \ge r_{0}$, the velocity is assumed to be constant ($V = V_{0}$) and the expansion timescale is

$$ \tau _{\mathrm{exp}} = \tau _{0\,\mathrm{exp}}(r/r_{0}), \quad \text{where}\ \tau _{0\,\mathrm{exp}} = r_{0}/3V_{0}. $$

(4)

The total recombination rate for the ion with a charge $Z$ is $R_{Z} = R_{\mathrm{di}} + R_{\mathrm{rad}}$ ($\mbox{cm}^{3}\,\mbox{s}^{-1}$), where $R_{\mathrm{di}}$ and $R_{\mathrm{rad}}$ are the dielectronic and radiative recombination rates, respectively. To estimate the dependence $\tau _{\mathrm{rec}}(r)$ at temperatures of $(10^{6}\,\mbox{--}\,10^{8})~\mbox{K}$, we only consider the dielectronic recombination contribution $R_{\mathrm{di}}$, which usually prevails at high temperatures. With the plasma parameters in Figure 19, these temperatures correspond to the distances $r \leq 1~\mathrm{R}_{\odot }$. For the dielectronic recombination rate we use Equation 7 from Arnaud and Raymond (1992):

$$\begin{aligned} R_{\mathrm{di}}(T_{\mathrm{e}}) = T_{\mathrm{e}}^{-3/2}\sum c_{i} \exp (-E_{i}/kT_{\mathrm{e}})~\text{cm}^{3}\,\text{s}^{-1}, \end{aligned}$$

where $T_{\mathrm{e}}$ is in K, $kT_{\mathrm{e}}$ and $E_{i}$ are in eV, and $c_{i}$ is in $\text{cm}^{3}\,\text{s}^{-1}\,\text{K}^{1.5}$. The values of $E_{i}$ and $c_{i}$ are tabulated. The adiabatic plasma cooling for $r > r_{0}$ and $T_{\mathrm{e}}=T_{0}(n_{\mathrm{e}}/n_{0})^{\gamma -1}= T_{0}(r/r_{0})^{-3(\gamma -1)}$ results in a recombination time

$$\begin{aligned} \tau _{\mathrm{rec}}^{-1} \approx \tau _{\mathrm{di}}^{-1} = n_{ \mathrm{e}}R_{\mathrm{di}} = n_{0} T_{0}^{-3/2}(r/r_{0})^{4.5(\gamma -5/3)}\sum c_{i} (\varepsilon _{0\,i})^{f^{\prime \prime }}, \end{aligned}$$

where $\gamma$ is the adiabatic index, $\varepsilon _{0\,i} = \exp (-E _{i}/kT_{0})$, and $f^{\prime \prime } = (r/r_{0})^{3(\gamma -1)}$. The terms summed stand for atomic physics of the recombination process, and the product $n_{\mathrm{e}}T_{\mathrm{e}}^{-3/2}$ is proportional to the Coulomb collision frequency $\nu _{\mathrm{ie}}$ of an ion with thermal electrons. For $\gamma = 5/3$ we obtain

$$\begin{aligned} \tau _{\mathrm{di}}^{-1} = n_{0} T_{0}^{-3/2}\sum c_{i} (\varepsilon _{0\,i})^{f}, \quad f = (r/r_{0})^{2}. \end{aligned}$$

To estimate the recombination time $\tau _{\mathrm{di}}$, we consider the $\mbox{Fe}^{16+}$ ion that is one of the first ions undergoing the freeze-in process (Figure 20). For this ion the sum $\sum c_{i} (\varepsilon _{0\,i})^{f}$ is reduced to a single term $c_{1} = 1.23$, $E_{1} = 560~\text{eV}$, $\varepsilon _{01} = \exp (-560~\text{eV/kT}_{0})$ (Arnaud and Raymond, 1992). Thus,

$$ \tau _{\mathrm{di}} = \tau _{0\,\mathrm{di}}(\varepsilon _{01})^{1-f}, \quad \tau _{0\,\mathrm{di}} = T_{0}^{3/2}/(n_{0}c_{1}\varepsilon _{01}). $$

(5)

The freeze-in distance is determined by the competition between the expansion and recombination timescales that we characterize by a ratio $m = \tau _{\mathrm{rec}} / \tau _{\mathrm{exp}}$. The complete frozen-in situation corresponds to $m \gg 1$. To estimate the freeze-in distance $r_{\mathrm{fr}}$, we use the relation $m\tau _{\mathrm{exp}} = \tau _{\mathrm{rec}} \approx \tau _{\mathrm{di}}$ with $m = 3$. The usage of Equations 4 and 5 in this relation yields

$$ \mu ^{\mathrm{0.5}}\varepsilon _{01}^{\mu } = \varepsilon _{01}\, \tau _{0\,\mathrm{di}}/(m \tau _{0\,\mathrm{exp}}) = 3V_{0} T_{0}^{3/2}/(m r_{0} n_{0} c_{1}) \quad \text{with}\ \mu = (r_{\mathrm{fr}}/r_{0})^{2}. $$

(6)

We apply Equation 6 to our event, whose parameters are shown in Section 4.2. Taking the electron density and temperature at $r_{0} = 0.34~\mathrm{R}_{\odot }$ to be $n_{0} = 10^{9}~\mbox{cm}^{-3}$ and $T_{0} = 11.6\times 10^{6}~\text{K}$ ($kT_{0}= 1~\text{keV}$), and $V_{0} = 860~\text{km}\,\text{s} ^{-1}$, we get $\varepsilon _{01} = \exp (-0.56) = 0.67$ and $\tau _{0\,\mathrm{di}} = 46~\text{s}$. With $m = 3$, Equation 6 takes a form $\mu ^{0.5}0.67^{\mu } = 0.11$; thus, $\mu ^{0.5} = r_{ \mathrm{fr}}/r_{0} \approx 2.85$ and $r_{\mathrm{fr}} \approx 2.85r _{0} \approx 0.97~\mathrm{R}_{\odot }$. As follows from Section 4.2, $\mbox{Fe}^{16+}$ ions freeze-in earlier than the mean charge $\langle Q_{\mathrm{Fe}} \rangle$, whose variations are shown in Figure 19d. The main decrease in $\langle Q_{ \mathrm{Fe}} \rangle$ occurs within $r < r_{\mathrm{fr}}$. Note that the solutions of Equation 6 for $m = 2$ and $m = 1$ are the values $r_{\mathrm{fr}} \approx 2.6 r_{0} \approx 0.88~\mathrm{R} _{\odot }$ and $r_{\mathrm{fr}} \approx 2.15 r_{0} \approx 0.73~\mathrm{R}_{\odot }$, respectively. The latter value is not very different from $r \approx 0.5~\mathrm{R}_{\odot }$ where the curves $\tau _{\mathrm{exp}}$ and $\tau _{\mathrm{rec}}$ in Figure 20 calculated for $\mbox{Fe}^{16+}$ intersect. The results obtained from Equation 6 are reasonably close to the numerical calculations presented in Section 4.2.

For generalized estimates, Equation 6 can be simplified by replacing the $r_{0}/V_{0}$ ratio with $\tau _{\mathrm{acc}}/2$, where $\tau _{\mathrm{acc}}$ is a characteristic time, when an eruption moving with an effective constant acceleration [$a$] reaches the velocity $V_{0} = a\tau _{\mathrm{acc}}$; $r_{0} = a\tau _{\mathrm{acc}}^{2}/2$. This estimate of $r_{0}$ implies the plasma heating only at the acceleration stage of the erupting filament. For a typical $\tau _{\mathrm{acc}} \approx 300~\text{s}$ and $V_{0} \approx 10^{3}~\text{km}\,\text{s} ^{-1}$ in eruptions from active regions we estimate $r_{0} \approx 0.2~\mathrm{R}_{\odot }$, which is slightly different from $r_{0} \approx 0.34~\mathrm{R}_{\odot }$ obtained in the numerical modeling of the charge-state evolution in Section 4.2. With $m = 3$, Equation 6 transforms to the form

$$ \mu ^{\mathrm{0.5}}(\varepsilon _{01})^{\mu } \approx 2T_{0}^{3/2}/(c _{1} n_{0} \tau _{\mathrm{acc}}) \propto (\tau _{\mathrm{acc}} \nu _{0\,\mathrm{ie}})^{-1} \quad \text{with}\ \nu _{0\,\mathrm{ie}} = \nu _{\mathrm{ie}}\ (r = r_{0}). $$

(7)

The right part of this equation does not contain $r_{0}$, unlike Equation 6. Calculations show that an increase in the right parts of Equations 6 and 7 corresponds to a decrease in the $r_{\mathrm{fr}}/r_{0}$ ratio. Case studies of eruptions from active regions show that their temperatures at the acceleration stage reach ${\approx}\, 10^{7}~\text{K}$ ($kT_{0} \approx 1~\text{keV}$; e.g. Glesener et al., 2013; Grechnev et al., 2016). For $n_{0} = 10^{9}~\mbox{cm} ^{-3}$ Equation 7 yields $\mu ^{0.5}0.67^{\mu } \approx 0.22$, $r_{\mathrm{fr}}/r_{0} \approx 2.45$, and $r_{\mathrm{fr}} \approx 0.5~\mathrm{R}_{\odot }$. The dependence on $n_{0}$ is weak; with $n_{0} = 10^{10}~\mbox{cm}^{-3}$ and other parameters unchanged, $r_{\mathrm{fr}} \approx 0.7~\mathrm{R}_{\odot }$.

Thus, the high ionic charge states of iron are expected to form in fast CMEs near the Sun and not to change afterwards considerably. This conclusion is consistent with the results of the numerical calculations by Rodkin et al. (2017).