Energy Budget

4 Energy Budget

Magnetohydrodynamic models suggest that reconnection releases magnetic energy into ohmic heating and fluid motion in about equal amounts (textbook by Priest and Forbes, 2000 ). At the level of kinetic plasma theory, ohmic heating may amount to accelerating particles to non-thermal energy distribution. The motion of the reconnection jet may involve waves and shocks, both are also capable of acceleration. Thus a flare releases energy initially into the forms of heat, non-thermal particles, waves, and motion.

In the past, the observed partition of energy in flares into the various forms has often changed with new instrumentation. The most complete estimate of the total flare energy is currently the measured enhancement in total solar irradiance. Woods et al. (2004 ) determined the total flare irradiance to exceed the soft X-ray emission ( $<$ 27 nm) by a factor of 5 in two well observed, large flares. The total irradiance enhancement is dominated by white light and infrared emission (77%). UV and soft X-ray emissions $<$ 200 nm amount to 23%.

Most of the white light originates in the chromosphere and upper photosphere (Neidig, 1989 ), but the excellent correlation with hard X-rays (Matthews et al., 2003 ; Metcalf et al., 2003 ; Hudson et al., 2006 ) suggests that the energy is deposited in the upper chromosphere and is transported to the deeper layers by radiation. The latter authors also point out that white light flares are not different from others, and that possibly all flares may be observed in white light with sufficient sensitivity. Not included in the total irradiance is the energy that leaves the corona in coronal mass ejections. Emslie et al. (2004a

) report that the kinetic energy of the CME exceeded the non-thermal electrons’ energy of the associated flare by about an order of magnitude in two major flares. However, taking into account the flare energy radiated at wavelengths other than X-rays, in particular in white light, brings the flare energy up to the CME energy or beyond (Table 1).

Table 1:

Energy budgets as reported by Saint-Hilaire and Benz (2005

) for M-class flares and by Emslie et al. (2005 ) for X-class flares. The non-thermal electron energy strongly depends on the low-energy turn-over of the electron distribution, which may be masked by thermal radiation. Thus the non-thermal electron energy is a lower limit. The total radiated energy includes the contributions of X-rays, UV, and optical emissions.


Energy mode	2002/11/10	2002/08/22	2002/04/21	2002/07/23
	M2.6	M7.8	X1.7	X5.1
	[erg]	[erg]	[erg]	[erg]

Non-thermal electrons	1.9 $×$ 10³⁰	6.5 $×$ 10³⁰	2.0 $×$ 10³¹	3.2 $×$ 10³¹
Non-thermal ions			$<$ 4.0 $×$ 10³¹	7.9 $×$ 10³¹
Thermal hot plasma	1.4 $×$ 10³⁰	2.6 $×$ 10³⁰	1.2 $×$ 10³¹	1.0 $×$ 10³¹
Total radiated			1.6 $×$ 10³²	1.6 $×$ 10³²

Kinetic CME			2.0 $×$ 10³²	1.0 $×$ 10³²
Gravitational CME			5.0 $×$ 10³⁰	1.6 $×$ 10³¹
Non-thermal CME			3.2 $×$ 10³¹	$<$ 10³⁰

Figure 23:

Overlays of RHESSI hard X-ray (orange) and white light difference (thick blue) image contours on a white-light image observed by the TRACE satellite. The thin white contours show white light contours as observed by MDI on SOHO; the accuracy of the pointing can be assessed by comparing the white light background observed by MDI and TRACE (Fletcher et al., 2007 ).