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Register a new userGlobal Energetics of Solar Flares. XI. Flare Magnitude Predictions of the GOES-Class
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Markus J. Aschwanden
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In this study we determine scaling relationships of observed solar flares that can be used to predict upper limits of the GOES-class magnitude of solar flares. The flare prediction scheme is based on the scaling of the slowly-varying potential energy $E_p(t)$, which is extrapolated in time over an interval of $Delta t le$ 24 hrs. The observed scaling of the dissipated energy $E_{diss}$ scales with the potential field energy as $E_{diss} propto E_p^{1.32}$. In addition, the observed scaling relationship of the flare volume, $V propto E_{diss}^{1.17}$, the multi-thermal energy, $E_{th} propto V^{0.76}$, the flare emission measure $EM propto E_{th}^{0.79}$, the EM-weighted temperature $T_{w}$, and the GOES flux, $F_8(t) propto E_p(t)^{0.92}$, allows us then to predict an upper limit of the GOES-class flare magnitude in the extrapolated time window. We find a good correlation (CCC$approx 0.7$) between the observed and predicted GOES-class flare magnitudes (in 172 X and M-class events). This is the first algorithm that employs observed scaling laws of physical flare parameters to predict GOES flux upper limits, an important capability that complements previous flare prediction methods based on machine-learning algorithms used in space weather forecasting.
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In this study we test 30 variants of 5 physical scaling laws that describe different aspects of solar flares. We express scaling laws in terms of the magnetic potential field energy $E_p$, the mean potential field strength $B_p$, the free energy $E_{free}$, the dissipated magnetic flare energy $E_{diss}$, the mean loop length scale $L$, the mean helically twisted flux tube radius $R$, the sunspot radius $r$, the emission measure-weighted flare temperature $T_w$, the electron density $n_e$, and the total emission measure $EM$, measured from a data set of $lapprox 400$ GOES M- and X-class flare events. The 5 categories of physical scaling laws include (i) a scaling law of the potential-field energy, (ii) a scaling law for helical twisting, (iii) a scaling law for Petschek-type magnetic reconnection, (iv) the Rosner-Tucker-Vaiana scaling law, and (v) the Shibata-Yokoyama scaling law. We test the self-consistency of these theoretical scaling laws with observed parameters by requiring two conditions: a cross-corrleation coefficient of CCC$>$0.5 between the observed and theoretically predicted scaling laws, and a linear regression fit with a slope of $alpha approx 1$. With these two criteria we find that 10 out of the 30 tested scaling law variants are consistent with the observed data, which strongly corroborates the existence and validity of the tested flare scaling laws.
In this study we synthesize the results of four previous studies on the global energetics of solar flares and associated coronal mass ejections (CMEs), which include magnetic, thermal, nonthermal, and CME energies in 399 solar M and X-class flare events observed during the first 3.5 years of the Solar Dynamics Observatory (SDO) mission. Our findings are: (1) The sum of the mean nonthermal energy of flare-accelerated particles ($E_{mathrm{nt}}$), the energy of direct heating ($E_{mathrm{dir}}$), and the energy in coronal mass ejections ($E_{mathrm{CME}}$), which are the primary energy dissipation processes in a flare, is found to have a ratio of $(E_{mathrm{nt}}+E_{mathrm{dir}}+ E_{mathrm{CME}})/E_{mathrm{mag}} = 0.87 pm 0.18$, compared with the dissipated magnetic free energy $E_{mathrm{mag}}$, which confirms energy closure within the measurement uncertainties and corroborates the magnetic origin of flares and CMEs; (2) The energy partition of the dissipated magnetic free energy is: $0.51pm0.17$ in nonthermal energy of $ge 6$ keV electrons, $0.17pm0.17$ in nonthermal $ge 1$ MeV ions, $0.07pm0.14$ in CMEs, and $0.07pm0.17$ in direct heating; (3) The thermal energy is almost always less than the nonthermal energy, which is consistent with the thick-target model; (4) The bolometric luminosity in white-light flares is comparable with the thermal energy in soft X-rays (SXR); (5) Solar Energetic Particle (SEP) events carry a fraction $approx 0.03$ of the CME energy, which is consistent with CME-driven shock acceleration; and (6) The warm-target model predicts a lower limit of the low-energy cutoff at $e_c approx 6$ keV, based on the mean differential emission measure (DEM) peak temperature of $T_e=8.6$ MK during flares. This work represents the first statistical study that establishes energy closure in solar flare/CME events.
We present an analysis of soft X-ray (SXR) and extreme-ultraviolet (EUV) observations of solar flares with an approximate C8 GOES class. Our constraint on peak GOES SXR flux allows for the investigation of correlations between various flare parameters. We show that the the duration of the decay phase of a flare is proportional to the duration of its rise phase. Additionally, we show significant correlations between the radiation emitted in the flare rise and decay phases. These results suggest that the total radiated energy of a given flare is proportional to the energy radiated during the rise phase alone. This partitioning of radiated energy between the rise and decay phases is observed in both SXR and EUV wavelengths. Though observations from the EVE show significant variation in the behavior of individual EUV spectral lines during different C8 events, this work suggests that broadband EUV emission is well constrained. Furthermore, GOES and AIA data, allow us to determine several thermal parameters (e.g. temperature, volume, density, and emission measure) for the flares within our sample. Analysis of these parameters demonstrate that, within this constrained GOES class, the longer duration solar flares are cooler events with larger volumes capable of emitting vast amounts of radiation. The shortest C8 flares are typically the hottest events, smaller in physical size, and have lower associated total energies. These relationships are directly comparable with several scaling laws and flare loop models.
We investigate physical scaling laws for magnetic energy dissipation in solar flares, in the framework of the Sweet-Parker model and the Petschek model. We find that the total dissipated magnetic energy $E_{diss}$ in a flare depends on the mean magnetic field component $B_f$ associated with the free energy $E_f$, the length scale $L$ of the magnetic area, the hydrostatic density scale height $lambda$ of the solar corona, the Alfven Mach number $M_A=v_1/v_A$ (the ratio of the inflow speed $v_1$ to the Alfvenic outflow speed $v_A$), and the flare duration $tau_f$, i.e., $E_{diss} = (1/4pi) B_f^2 L lambda v_A M_A tau_f$, where the Alfven speed depends on the nonpotential field strength $B_{np}$ and the mean electron density $n_e$ in the reconnection outflow. Using MDI/SDO and AIA/SDO observations and 3-D magnetic field solutions obtained with the vertical-current approximation nonlinear force-free field code (VCA-NLFFF) we measure all physical parameters necessary to test scaling laws, which represents a new method to measure Alfven Mach numbers $M_A$, the reconnection rate, and the total free energy dissipated in solar flares.
Small amplitude quasi-periodic pulsations (QPPs) detected in soft X-ray emission are commonplace in many flares. To date, the underpinning processes resulting in the QPPs are unknown. In this paper, we attempt to constrain the prevalence of textit{stationary} QPPs in the largest statistical study to date, including a study of the relationship of QPP periods to the properties of the flaring active region, flare ribbons, and CME affiliation. We build upon the work of cite{inglis2016} and use a model comparison test to search for significant power in the Fourier spectra of lightcurves of the GOES 1--8~AA channel. We analyze all X-, M- and C- class flares of the past solar cycle, a total of 5519 flares, and search for periodicity in the 6-300~s timescale range. Approximately 46% of X-class, 29% of M-class and 7% of C-class flares show evidence of stationary QPPs, with periods that follow a log-normal distribution peaked at 20~s. The QPP periods were found to be independent of flare magnitude, however a positive correlation was found between QPP period and flare duration. No dependence of the QPP periods to the global active region properties was identified. A positive correlation was found between QPPs and ribbon properties including unsigned magnetic flux, ribbon area and ribbon separation distance. We found that both flares with and without an associated CME can host QPPs. Furthermore, we demonstrate that for X- and M- class flares, decay phase QPPs have statistically longer periods than impulsive phase QPPs.
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