2.6 Masses and energies

CME mass calculations require a conversion from the coronagraph-observed intensity to electron (and therefore plasma) density using the physics of Thomson scattering. Most workers today follow the theory outlined in Billings (1966) (the necessary equations conveniently appear on a single page of this text) but more recent reviews of this theory, along with its adaption for heliospheric imaging appear in Howard and Tappin (2009Jump To The Next Citation Point), Howard (2011bJump To The Next Citation Point) and Howard and DeForest (2012bJump To The Next Citation Point). Masses and energy calculations of CMEs therefore require difficult instrument calibrations and have large uncertainties. The average mass of CMEs derived from the older coronagraph data (Skylab, SMM and Solwind) was a few times 1012 kg (see Table 1). LASCO calculations indicate a slightly lower average CME mass, 1.6 × 1012 kg (Figure 16View Image), likely because LASCO can measure smaller masses down to the order of 1010 kg (Vourlidas et al., 2002aJump To The Next Citation Point, 2010Jump To The Next Citation Point, 2011bJump To The Next Citation Point; Kahler, 2006Jump To The Next Citation Point). Studies using Helios (Webb et al., 1996) and LASCO (Vourlidas et al., 2000, 2010Jump To The Next Citation Point, 2011bJump To The Next Citation Point) data suggest that the older CME masses may have been underestimated because mass outflow may continue well after the CME’s leading edge leaves the instrument field of view. For example, Vourlidas et al. (2010Jump To The Next Citation Point) estimated that CME masses may be underestimated by a factor of two and CME kinetic energies by a factor of 8. LASCO results of the mass density of CMEs as a function of height suggest that this density rises until ∼ 7 R⊙, then levels off – Figure 17View Image). The implication is that CMEs with larger masses reach greater heights, and are more likely to escape the Sun. Indeed, there is a population with a mass peak < 7R ⊙; these CMEs are less massive and slower and may not reach IP space. This begs the question whether the outward motion of coronal mass that is not clearly “ejected” should be called a “CME” or something else. Downward motions of prominence material during eruptions are common, but similar downward motions of mass in white light CMEs are rare, though it has been reported (e.g., Tripathi et al., 2007).
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Figure 16: Histograms of LASCO CME mass distribution (upper left), kinetic energy (upper right), and total mechanical energy (bottom left) for 7668 events. Also shown are the histograms for events reaching maximum mass < 7R ⊙ (dashed lines) and events reaching maximum mass 7 R ⊙ (dash-double dot). Not all detected CMEs have been included because mass measurements require: (i) a good background image, (ii) three consecutive frames with CMEs, and (iii) CMEs well separated from preceding CMEs. Image adapted from Vourlidas et al. (2010Jump To The Next Citation Point, 2011bJump To The Next Citation Point), courtesy A. Vourlidas (2011).
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Figure 17: Top: scatter plot of the logarithm of maximum CME mass vs. the height where it was measured. Two populations are present: CMEs reaching maximum mass < 7 R ⊙ and CME with maximum mass > 7R ⊙. Bottom: scatter plot of the logarithm of CME surface density (e cm–2) vs. height. The CME density is constant above ∼ 10 R ⊙. A histogram with 1 R ⊙ bins is calculated and the average density (asterisks) and in each bin is overploted. Note the small spread of the CME density values above ∼ 10 R⊙. Its average value is shown on the plot. The height spread is mostly due to the noise and flatness of the mass measurements at those heights which tend to shift around the height of the maximum mass. Image adapted from Vourlidas et al. (2010Jump To The Next Citation Point, 2011bJump To The Next Citation Point), courtesy A. Vourlidas (2011).

Mass estimates of a few CMEs have also been made with radio (Gopalswamy and Kundu, 1993; Ramesh et al., 2003) and X-ray observations (e.g., Rust and Hildner, 1976; Hudson and Webb, 1997Jump To The Next Citation Point) and, more recently, in the EUV (e.g., Harrison et al., 2003Jump To The Next Citation Point; Aschwanden et al., 2009Jump To The Next Citation Point). Many X-ray and EUV measurements involve “coronal dimming” (Section 3.4) regions associated with a CME, and these estimates are usually lower than that of the equivalent white light masses. This is probably because the material leaving the coronal dimming region is only part of that comprised in the CME. The radio, X-ray, and EUV techniques provide an independent check on CME masses because their dependency is on the thermal properties of the plasma (density and temperature) vs only density in the white light observations. Likewise average CME kinetic energies measured by LASCO are less than previous measurements, 2.0 × 1030 erg (Vourlidas et al., 2010Jump To The Next Citation Point – Figure 16View Image). The CME kinetic energy distribution appears to have a power law index of –1 (Vourlidas et al., 2002a), different than that for flares (–2; Hudson, 1991; Yashiro et al., 2006Jump To The Next Citation Point).

Figure 18View Image shows plots of the solar-cycle dependence of the LASCO CME mass and kinetic energy (Vourlidas et al., 2010Jump To The Next Citation Point, 2011bJump To The Next Citation Point). The bottom panel shows the total CME mass per Carrington rotation. The mass, mass density, and kinetic energy all have minima in 2007 that are 2 – 4 times below the 1996 minimum and reflect the unusual extended activity in Solar Cycle 23. The total mass reaches a minimum in 2009 and is roughly equivalent to the 1996 minimum. MacQueen et al. (2001) found that the mass density variation between Solar Cycle 22 minimum and maximum varied by a factor 4 even in the background corona.

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Figure 18: Solar cycle dependence of the CME mass and kinetic energy. Top left: log CME mass. Top right: log CME mass density in g R–2. Middle left: log CME kinetic energy. Middle right: CME speed. All four plots show annual averages. Bottom panel: total CME mass per Carrington rotation. The data gaps in 1998 and the drop in 1999 are due to spacecraft emergencies. The plot is an update of Figures 14 and 1 in Vourlidas et al. (2010, 2011b) to include events to July 31, 2010, courtesy A. Vourlidas (2011).

Measuring CME masses and energies using white light images farther from the Sun has proven to be a difficult task (see Section 5.3), due to the lack of calibration information and the uncertainties imposed by the faintness of the CMEs compared to the background noise. Mass and energy estimates have also been made from 3-D density reconstructions of a few CMEs observed in the heliosphere by SMEI (Jackson et al., 2008a, 2010a). The mass estimates generally agree with the mass of the same CMEs as derived from LASCO data. Some attempts are currently being made using some highly developed processing techniques with the STEREO SECCHI images. DeForest et al. (2012Jump To The Next Citation Point) performed some mass measurements on a small disconnection event (i.e., not a CME) using photometric measurements and the theory of Thomson scattering. The technique is currently being applied to CME measurements.

The reader must note that as with the kinematical properties, mass calculations are based on coronagraph images and, therefore, subject to the same problems of projection and perspective. For example, the CME mass calculations in the CDAW catalog make the assumption that all of the CME mass is in the sky plane, as has always been the standard assumption. The Thomson scattering theory from which the density is derived includes a direction term χ, and so the direction of propagation is an integral component of the density calculations. Traditionally, auxiliary data such as solar flare or filament location have been used provide an estimate of CME direction but more recent work making use of the stereoscopic capabilities of STEREO have provided more accurate measurements (Colaninno and Vourlidas, 2009). Finally, the Thomson scattering theory provided by Billings differs somewhat from the initial treatment by Schuster (1879) and Minneart (1930). An alternative treatment of this theory and it applications to both coronagraphs and heliospheric imagers can be found in Howard and Tappin (2009Jump To The Next Citation Point), Howard (2011aJump To The Next Citation Point) and Howard and DeForest (2012b). This latest theory implies that the sky plane assumption may be more appropriate than has been previously assumed (see also van Houten, 1950).

A poorly understood topic is that of the energy budget available to the eruption of CMEs and associated solar activity. The next section discusses many of the phenomena that are known to be associated with CMEs and all of them require substantial quantities of energy. If we assume that the total energy arises from magnetic energy stored in the pre-launch corona then we may allocate an energy budget for the CME and its associated phenomena. Few studies have been conducted to address this topic, largely because of the difficulty in acquiring accurate measurements of both the available budget and the energies available from each associated phenomenon. These publications have revealed that the mechanical energy consumed by the launch and evolution of a CME is much greater than that of all the associated eruptive phenomena combined. Canfield et al. (1980Jump To The Next Citation Point), Webb et al. (1980Jump To The Next Citation Point), and Emslie et al. (2004Jump To The Next Citation Point) found the CME mechanical energy to be an order of magnitude greater than that of the associated flare and to consume the majority of energy available from the magnetic field. Ravindra and Howard (2010Jump To The Next Citation Point) found the mechanical energy of the CME was over an order of magnitude greater than that of the associated flare, and that half-to-all of the energy removed from the magnetic field during the eruption was consumed by the flare-CME-associated eruption combination. The uncertainties associated with the calculations in all of these studies, unfortunately, are too large to draw any firm conclusions.


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