Solar Flares and Coronal Mass Ejections: A Statistically Determined Flare Flux – CME Mass Correlation

Abstract

In an effort to examine the relationship between flare flux and corresponding CME mass, we temporally and spatially correlate all X-ray flares and CMEs in the LASCO and GOES archives from 1996 to 2006. We cross-reference 6 733 CMEs having well-measured masses against 12 050 X-ray flares having position information as determined from their optical counterparts. For a given flare, we search in time for CMEs which occur 10-80 minutes afterward, and we further require the flare and CME to occur within ±45• in position angle on the solar disk. There are 826 CME/flare pairs which fit these criteria. Comparing the flare fluxes with CME masses of these paired events, we find CME mass increases with flare flux, following an approximately log-linear, broken relationship: in the limit of lower flare fluxes, log(CME mass) ∝ 0.68×log(flare flux), and in the limit of higher flare fluxes, log(CME mass) ∝ 0.33×log(flare flux). We show that this broken power-law, and in particular the flatter slope at higher flare fluxes, may be due to an observational bias against CMEs associated with the most energetic flares: halo CMEs. Correcting for this bias yields a single power-law relationship of the form log(CME mass) ∝ 0.70× log(flare flux). This function describes the relationship between CME mass and flare flux over at least 3 dex in flare flux, from ≈10 −7 −10 −4 W m −2 .

Mass Loss in Pre-Main-Sequence Stars via Coronal Mass Ejections and Implications for Angular Momentum Loss

“…Indeed, it is well established that not every flare is associated with a CME, and not every CME is associated with a flare. Aarnio et al (2011) found that 13% of CMEs are flare associated and ∼9% of flares are CME associated; this lack of correspondence is at least partially driven by observational biases, and any correction for over-or underestimating the number of CMEs associated with flares is likely less than approximately a factor of two. The most energetic solar flares, however, are the most likely to be CME-associated, and these CMEs are the most massive (Andrews 2003;Yashiro et al 2005Yashiro et al , 2006Aarnio et al 2011, to name but a few studies on the matter).…”

“…In Aarnio et al (2011), we cross-matched 10 years of solar flare and CME observations in order to determine, for associated flares and CMEs, whether there are correlations between flare and CME properties. Approximately 1000 solar flares and CMEs were found to be spatially and temporally associated.…”

“…We show the full rate distribution of reported CME masses (number of CMEs per year as a function of CME mass), including both well-constrained and highly uncertain CME masses, in Figure 2 (upper middle panel). We have included here the additional halo CMEs (those projected toward the Earth, or which are so wide as to appear as if they were) for which Aarnio et al (2011) estimated masses.…”

“…This value represents a lower limit to the mass loss rate via CMEs from the Sun, as just under half of the reported CMEs have measured masses and there may be CMEs that escape observation, especially at lower masses. Aarnio et al (2011) found 1,153 of the CMEs with measured masses to be associated with flares (the masses of these CMEs are also shown in Figure 2, upper middle panel); these CMEs were used to derive the relationship between flare energy and CME mass (eq. 2).…”

“…More generally, CMEs are expected from lowmass stars by analogy to the Sun as well as from basic escape velocity considerations for the flaring material; indeed, CMEs are believed to have been detected on M and K dwarfs from balmer line asymmetries, transient spectral line absorption components, and EUV dimmings (cf., Leitzinger et al 2011, and references therein). In particular, the extreme X-ray flares observed on PMS stars are expected to have associated extreme CMEs (e.g., Aarnio et al 2011), the ramifications of which-for the evolution of the star, for the protoplanetary environment, and for the star's angular momentum evolution-depend on the resulting mass-loss rate and the evolution of that mass loss over the course of the star's PMS evolution.…”