One of the important features of the Petschek-type reconnection is the formation of a pair of slow MHD shocks extending from a diffusion region. The role of the slow shocks was first considered in Cargill and Priest (1982). A pair of the slow shocks guide a reconnection jet, and the angle between these shocks is very narrow, of the order of . In the adiabatic case, the temperature of coronal plasma increases across a slow shock up to (Vršnak and Skender, 2005)et al., 1989; Yokoyama and Shibata, 1997).
Yokoyama and Shibata (1997) first carried out a self-consistent MHD simulation of magnetic reconnection that includes thermal conduction (see the top panels in Figure 44). They confirmed that an adiabatic slow shock is split into a conduction front and an isothermal slow shock, as predicted by Forbes and Malherbe (1986). Yokoyama and Shibata (1997) further explained the structure of a cusp-shaped flare observed by Yohkoh (Tsuneta et al., 1992a), where the evaporation of chromospheric plasma heated by the conduction front is reproduced (Yokoyama and Shibata, 1998, see the bottom panels in Figure 44). Typically, the conduction time is estimated to be
On the other hand, the Alfvén transit time is
The radiative cooling time of plasma is written aset al., 1976). In a typical SXR loop, the temperature is about 107 K and electron density is about n = 1010 cm–3, so the radiative cooling time becomes of the order 104 s, which is much longer than both the conduction time and the Alfvén transit time. Hence, the radiative cooling could be neglected at least in the very early phase of a flare.
Assuming that cooling via thermal conduction () is balanced by heating via magnetic reconnection ( erg cm–3 s–1) in an SXR loop with the size of , the temperature in this loop is given by (Fisher and Hawley, 1990)
Combining Equation (35) and (36), we obtainet al., 1989; Yokoyama and Shibata, 1998, 2001). The temperature of 107 K is comparable to the one observed in the superhot region formed at the top of an SXR loop (Masuda, 1994; Kosugi et al., 1994; Tsuneta, 1996; Nitta and Yaji, 1997). Note that this value is smaller than the value obtained from adiabatic MHD simulations, in which the temperature becomes of the order 108 K as mentioned before.
It should be noted that the conduction could be strongly reduced due to a large difference in the magnetic field strength in inflow and outflow region, as well as due to thermal flux saturation and the flow/field geometry (for details see Vršnak et al., 2006, and references therein).
During a flare, the chromospheric evaporation (i.e., ablation of chromospheric plasma) plays a fundamental role in creating an SXR loop via the injection of hot plasma into a loop (Hirayama, 1974). The evaporation occurs when the heat flux coming from the corona overcomes radiative cooling rate in the chromosphere. That heat flux then increases the gas pressure in the upper chromosphere significantly to produce an upflow toward the corona against gravity (called evaporation flow Antonucci et al., 1982, 1984) as well as downflow (Ichimoto and Kurokawa, 1984; Canfield et al., 1990) to the lower chromosphere. In a steady state, the heat flux of thermal conduction from the corona is balanced by the enthalpy flux of evaporation, such as
Nagai (1980) first performed a one-dimensional hydrodynamic simulation of chromospheric evaporation. Since then, similar one-dimensional hydrodynamic simulations have been performed extensively (Somov et al., 1981; Nagai and Emslie, 1984; Peres et al., 1987; MacNeice et al., 1984; Mariska et al., 1989; Fisher and Hawley, 1990; Gan et al., 1991), which qualitatively explained the blue shift of Bragg Crystal Spectrometer (BCS) lines observed by Yohkoh as well as the red shift of H line observed during the impulsive phase of a flare (Ichimoto and Kurokawa, 1984). Investigations into the quantitative agreement between one-dimensional models and observations are still in progress. Later, pseudo two-dimensional models have been developed, reported by several authors (Hori et al., 1997; Warren et al., 2003). Yokoyama and Shibata (1998) performed a two-dimensional MHD simulation reproducing the chromospheric evaporation driven by thermal conduction (see the bottom panels in Figure 44). By combining magnetic reconnection, thermal conduction and radiative cooling, they derived a scaling law about the temperature observed in a loop filled with evaporated plasma, as shown in Equation (38). Later, Shibata and Yokoyama (1999) applied this scaling law to stellar flares (see Section 6).
A fast MHD shock is formed by the downward reconnection jet colliding with the top of an SXR loop (Forbes and Priest, 1983; Ugai, 1987; Magara et al., 1996; Aurass et al., 2002) where high-energy electrons are possibly produced (see Figure 42). In the adiabatic case, the temperature just behind the fast shock becomes
A fast shock could also be formed at the bottom of an ejecting plasmoid when it moves much slowly compared to the local Alfvén velocity (Magara et al., 1997, 2000).
Living Rev. Solar Phys. 8, (2011), 6
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