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Register a new userStatistical Study of the Reconnection Rate in Solar Flares Observed with YOHKOH/SXT
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Authors
Kaori Nagashima
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We report a statistical study of flares observed with the Soft X-ray Telescope (SXT) onboard Yohkoh in the year of 2000. We measure physical parameters of 77 flares, such as the temporal scale, the size, and the magnetic flux density and find that the sizes of flares tend to be distributed more broadly as the GOES class becomes weaker and that there is a lower limit of magnetic flux density that depends on the GOES class. We also examine the relationship between these parameters and find weak correlation between temporal and spatial scales of flares. We estimate reconnection inflow velocity, coronal Alfven velocity, and reconnection rate using above observed values. The inflow velocities are distributed from a few km/s to several tens km/s and the Alfven velocities in the corona are in the range from 10^3 to 10^4 km/s. Hence the reconnection rate is 10^-3 - 10^-2. We find that the reconnection rate in a flare tends to decrease as the GOES class of the flare increases. This value is within one order of magnitude from the theoretical maximum value predicted by the Petschek model, although the dependence of the reconnection rate on the magnetic Reynolds number tends to be stronger than that in the Petschek model.
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Using a recently developed analytical procedure, we determine the rate of magnetic reconnection in the standard model of eruptive solar flares. During the late phase, the neutral line is located near the lower tip of the reconnection current sheet, and the upper region of the current sheet is bifurcated into a pair of Petschek-type shocks. Despite the presence of these shocks, the reconnection rate remains slow if the resistivity is uniform and the flow is laminar. Fast reconnection is achieved only if there is some additional mechanism that can shorten the length of the diffusion region at the neutral line. Observations of plasma flows by the X-Ray Telescope (XRT) on Hinode imply that the diffusion region is in fact quite short. Two possible mechanisms for reducing the length of the diffusion region are localized resistivity and MHD turbulence.
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.
The plasmoid-induced-reconnection model explaining solar flares based on bursty reconnection produced by an ejecting plasmoid suggests a possible relation between the ejection velocity of a plasmoid and the rate of magnetic reconnection. In this study, we focus on the quantitative description of this relation. We performed magnetohydrodynamic (MHD) simulations of solar flares by changing the values of resistivity and the plasmoid velocity. The plasmoid velocity has been changed by applying an additional force to the plasmoid to see how the plasmoid velocity affects the reconnection rate. An important result is that the reconnection rate has a positive correlation with the plasmoid velocity, which is consistent with the plasmoid-induced-reconnection model for solar flares. We also discuss an observational result supporting this positive correlation.
Recently, many superflares on solar-type stars were discovered as white-light flares (WLFs). A correlation between the energies (E) and durations (t) of superflares is derived as $tpropto E^{0.39}$, and this can be theoretically explained by magnetic reconnection ($tpropto E^{1/3}$). In this study, we carried out a statistical research on 50 solar WLFs with SDO/HMI to examine the t-E relation. As a result, the t-E relation on solar WLFs ($tpropto E^{0.38}$) is quite similar stellar superflares, but the durations of stellar superflares are much shorter than those extrapolated from solar WLFs. We present the following two interpretations; (1) in solar flares, the cooling timescale of WL emission may be longer than the reconnection one, and the decay time can be determined by the cooling timescale; (2) the distribution can be understood by applying a scaling law $tpropto E^{1/3}B^{-5/3}$ derived from the magnetic reconnection theory.
This paper reports the results of a survey of Doppler shift oscillations measured during solar flares in emission lines of S XV and Ca XIX with the Bragg Crystal Spectrometer (BCS) on Yohkoh. Data from 20 flares that show oscillatory behavior in the measured Doppler shifts have been fitted to determine the properties of the oscillations. Results from both BCS channels show average oscillation periods of 5.5 +/- 2.7 minutes, decay times of 5.0 +/-2.5 minutes, amplitudes of 17.1 +/- 17.0 km/s, and inferred displacements of 1070 +/- 1710 km, where the listed errors are the standard deviations of the sample means. For some of the flares, intensity fluctuations are also observed. These lag the Doppler shift oscillations by 1/4 period, strongly suggesting that the oscillations are standing slow mode waves. The relationship between the oscillation period and the decay time is consistent with conductive damping of the oscillations.
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