Wave-like Formation of Hot Loop Arcades

Abstract

We present observations of hot arcades made with the Mg xii spectroheliograph onboard the CORONAS-F mission, which provides monochromatic images of hot plasma in the Mg xii 8.42 Å resonance line. The arcades were observed to form above the polarity inversion line between active regions NOAA 09847 and 09848 at four successive episodes: at 09:18, 14:13, and 22:28 UT on 28 February 2002, and at 00:40 UT on 1 March 2002. The evolution of the arcades can be described as: a) a small flare (precursor) appeared near the edge of the still invisible arcade, b) the arcade brightened in a wave-like manner – closer loops brightened earlier, and c) the arcade intensity gradually decreased in ${\approx}\,1~\mbox{h}$. The estimated wave speed was ${\approx}\,700~\mbox{km}\,\mbox{s}^{-1}$, and the distance between the hot loops was ${\approx}\,50~\mbox{Mm}$. The arcades formed without visible changes in their magnetic structure. The arcades were probably heated up by the instabilities of the current sheet above the arcade, which were caused by a magnetohydrodynamic wave excited by the precursor.

Appendix: Cooling Times

The loops of the arcade kept their high temperature for a long time (see Figure 6). This could be interpreted as a signature of the continuous loop heating. To verify this conclusion, we estimate the plasma cooling time in the absence of heating and compare it with the measured values.

There are two mechanisms of loop cooling: conductive and radiative. At high temperatures (${\approx}\,10~\mbox{MK}$), the conductive cooling dominates radiative cooling. To estimate the conductive cooling time ($\tau _{\mathrm{cond}}$), we use the formula (Culhane et al. 1994)

$$ \tau_{\mathrm{cond}} = \frac{21 n_{\mathrm{e}} k_{\mathrm{B}} L^{2}}{5 \kappa T^{5/2}}, $$

(4)

where $\kappa= 9.2 \times10^{-7}~\mbox{erg}\,\mbox{s}^{-1}\,\mbox{cm}^{-1}\,\mbox{K}^{-7/2}$ is the Spitzer conductivity, $n_{\mathrm{e}}$ is the electron density, $k_{\mathrm{B}}$ is the Boltzmann constant, $L$ is the loop length, and $T$ is the loop temperature.

To estimate the arcade temperature, we compared Mg xii and EIT 195 Å images. The EIT 195 Å channel is sensitive to 1 MK and 16 MK plasma (see Figure 10). The Mg xii spectroheliograph is sensitive to plasmas hotter than 5 MK (see Figure 10). Since we see the precursor structure in both EIT 195 Å and Mg xii channels, the precursor temperature should be about 15 MK. Since we were able to see the arcade in the Mg xii line but not in the EIT images, the loop temperature probably lies in the range of 5 – 10 MK.

Figure 10

Temperature response functions of the Mg xii spectroheliograph (solid line) and EIT 195 Å telescope (dashed line).

To estimate the precursor electron density, we estimated its temperature ($T$) and emission measure (EM) under isothermal approximation using the filter ratio method with EIT 195 Å and Mg xii fluxes. The result is $T \approx14~\mbox{MK}$ and $\mathrm{EM} \approx 8.8\times10^{46}~\mbox{cm}^{-3}$. The precursor structure had a length of $L \approx20~\mbox{Mm}$ and the width of the EIT pixel. However, since loops in the AIA images have the width of the AIA pixel ($r=0.44~\mbox{Mm}$), the AIA pixel size probably is a more reasonable estimate for the loop width than the EIT pixel size. Now, we can estimate the precursor electron density:

$$ {\mathrm{EM}} = n_{\mathrm{e}}^{2} \pi r^{2} L \quad \Rightarrow\quad n_{\mathrm{e}} = \sqrt{\frac{\mathrm{EM}}{\pi r^{2} L}} \approx8.6 \times 10^{10}~\mbox{cm}^{-3}. $$

(5)

Unfortunately, we have only Mg xii observations for the flaring loops, so that there is no way to measure the emission measure and temperature of their plasma separately using the filter ratio. However, we can estimate their electron density from

$$ I = G(T) n_{\mathrm{e}}^{2} \pi r^{2} L \leq G_{\mathrm{max}} n_{\mathrm{e}}^{2} \pi r^{2} L , $$

(6)

namely,

$$ n_{\mathrm{e}} \geq\sqrt{\frac{I}{G_{\mathrm{max}} \pi r^{2} L}} \approx1.8 \times 10^{10}~\mbox{cm}^{-3}, $$

(7)

where $I$ is the emission intensity of the loops on the Mg xii images, $G(T)$ is the temperature response function of the Mg xii spectroheliograph, and $G_{\mathrm{max}}$ is the maximum value of $G(T)$. For the sake of estimation, we used $n_{\mathrm{e}} = 10^{10}~\mbox{cm}^{-3}$ and $T= 10~\mbox{MK}$ for the loops of the arcade.

For the loops, we obtained $\tau_{\mathrm{cond}} = 100~\mbox{min}$ ($n_{\mathrm {e}} = 10^{10}~\mbox{cm}^{-3}$, $T= 10~\mbox{MK}$, and $L=170~\mbox{Mm}$). This is on the same order of magnitude as the measured values, 20 – 30 min. Furthermore, slight changes of the $n_{\mathrm{e}}$ and $T$ values can increase the agreement. This means that it is possible that the loop heating was impulsive and the long lifetime of the loops was due to their large size.

For the precursor, we obtained $\tau_{\mathrm{cond}} = 5~\mbox{min}$ ($n_{\mathrm{e}} = 8.6 \times10^{10}~\mbox{cm}^{-3}$, $T = 14~\mbox{MK}$, and $L = 20~\mbox{Mm}$), which coincides with the observed values. This means that it is possible that the heating of the precursor structure was impulsive.

It may be surprising that the long decay of the Mg xii light curves can be interpreted as pure cooling. However, our estimate is very rough; it is valid in the temperature range $6.8 < \log T < 7.3$, where the response function of Mg xii channel does not change much. Therefore, pure cooling is only a conjecture.

Furthermore, other mechanisms could decrease the loop intensity; for example by mass draining. The mass draining could play a significant role in the late phase of flare decay (Bradshaw and Cargill 2010). The draining will decrease the electron density, and therefore the loop intensity will decrease faster. In addition, according to Equation (4), the loops will cool faster. If the draining was present, then the hot loops would require continuous heating to support their long decay times.