2.6 Avalanche model and non-reconnection models

Observations revealed several interesting statistical properties of flares. First, the occurrence rate of flares decreases with the total energy from microflares to largest flares, following a power law (e.g., Lin et al., 1984; Dennis, 1985; Shimizu, 1995), as presented in Equation (4). The fact that the index of power-law is less than 2 suggests that microflares alone are insufficient to support the energy for coronal heating (Hudson, 1991), though the exact value of the power-law index is still controversial, especially for small events such as nanoflares (e.g., see Aschwanden, 2004). Even so, an universal power law seems to hold true for flares of various sizes suggests that there is a common physical mechanism operating in these different-scale flares.

It is well known that the occurrence rate of earthquakes and the avalanches of a sandhill against their magnitude also show power law-like distributions, and these phenomena can now be understood in terms of self-organized criticality (Bak et al., 1987). Lu and Hamilton (1991) proposed that the coronal magnetic field is in a self-organized critical state, and solar flare represents the avalanche of many small reconnection events, which is analogous to the avalanche in the sandpile model. They successfully explained the observed power-law distribution of the occurrence rate of flares. Although there is a big gap between the avalanche model for a group of events and the magnetohydrodynamic model focused on an individual event, the avalanche model is still useful for understanding the process of energy release in the system of the solar atmosphere. If you want to know the recent development of the avalanche model, see the review by Charbonneau et al. (2001).

There have also been proposed several models for flares where magnetic reconnection is not assumed. One of them is found at the Alfvén’s current disruption model (Alfvén and Carlqvist, 1967). The other models are proposed by Akasofu (1984), Uchida and Shibata (1988), Melrose (1997), and so on. Many of these models assume energy release inside a flaring loop, thus they are not consistent with those observations provided by Yohkoh, such as loop-top hard X-ray source and plasmoid ejection above a soft X-ray loop.

Table 1: Characteristics of flares and flare-like phenomena.
 LDE flares impulsive flares microflares cusp configuration yes1 no ? hot cusp loop yes1 ? ? slow shock (yes?)2 ? ? HXR loop-top source no yes6 ? reconnection jet no no? yes7 plasmoid ejection yes3 yes8 yes? downflow yes4 yes9 ? inflow yes5 ? ?
1 Tsuneta et al. (1992a), Tsuneta (1996), Forbes and Acton (1996).
2 Tsuneta (1996).
3 Hudson (1994), Yokoyama et al. (2001), Kim et al. (2005).
4 McKenzie and Hudson (1999), McKenzie (2000), Innes et al. (2003), Sui and Holman (2003).
5 Lin et al. (2005), Hara et al. (2006), Narukage and Shibata (2006).
6 Masuda (1994).
7 Wang et al. (2007).
8 Shibata et al. (1995), Tsuneta (1997), Ohyama and Shibata (1997, 1998), Kim et al. (2005).
9Asai et al. (2004), Linton and Longcope (2006), TanDokoro and Fujimoto (2005).

Table 2: Comparison of scales and associated mass ejection.
 size (L) time scale (t) energy associated ejection (104 km) (s) (erg) microflares 0.5 – 4 60 – 600 1026 – 1029 jet/surge (ARTBs) impulsive flares 1 – 10 60 – 3 × 103 1029 – 1032 X-ray/H filament eruption LDE flares 10 – 40 3 × 103 – 105 1030 – 1032 X-ray/H filament eruption large scale 30 – 100 104 – 2 × 105 1029 – 1032 X-ray/H arcade formation filament eruption

Table 3: Comparison of physical quantities.
 (G) (cm–3) (km s–1) (s) microflares 100 1010 3000 5 12 – 120 impulsive flares 100 1010 3000 10 6 – 300 LDE flares 30 2 × 109 2000 90 30 – 103 large scale 10 3 × 108 1500 400 25 – 500 arcade formation

Table 4: Unified view of flares and flare-like phenomena.
 mass ejections mass ejections (cool) (hot) giant arcades H filament CMEs eruptions LDE flares H filament X-ray plasmoid eruptions ejections/CMEs impulsive flares H sprays X-ray plasmoid ejections transient brightenings (microflares) H surges X-ray jets EUV microflares surges/spicules EUV jets facular points spicules (Alfvén waves) (nanoflares?)