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Science Journals RESEARCH ◥ whereas the dominant magnetic energy has only REPORT been estimated indirectly (20). Figure 1 shows context information for the flare, including SOLAR PHYSICS the microwave images that we observed using the Expanded Owens Valley Solar Array (EOVSA) Decay of the coronal magnetic field can release (21) in 26 microwave bands in the range of 3.4 to 15.9 GHz (13). sufficient energy to power a solar flare We produced magnetic field maps from these observations (13), examples of which are shown Gregory D. Fleishman1*, Dale E. Gary1, Bin Chen1, Natsuha Kuroda2,3, Sijie Yu1, Gelu M. Nita1 in Fig. 2. The full sequence is shown in movie S1. They show strong variation between maps, Solar flares are powered by a rapid release of energy in the solar corona, thought to be produced by demonstrating the fast evolution of the coro- the decay of the coronal magnetic field strength. Direct quantitative measurements of the evolving magnetic nal magnetic field strength B.Themagnetic field strength are required to test this. We report microwave observations of a solar flare, showing field strength decays quickly at the cusp re- spatial and temporal changes in the coronal magnetic field. The field decays at a rate of ~5 Gauss gion; away from that region, the field also per second for 2 minutes, as measured within a flare subvolume of ~1028 cubic centimeters. This fast decays but more slowly. rate of decay implies a sufficiently strong electric field to account for the particle acceleration that To quantify this decay, Fig. 3 shows the time produces the microwave emission. The decrease in stored magnetic energy is enough to power the solar evolution of the flaring coronal magnetic field flare, including the associated eruption, particle acceleration, and plasma heating. at two locations marked in Fig. 2. Both loca- tions exhibit a decay in the magnetic field strength but with different timing. One loca- Downloaded from he solar corona sometimes exhibits an tion approach does not allow the dynamic local tion shows a decay of the magnetic field from explosive release of the energy stored in changes of the magnetic field to be quantified ~600 to ~200 G over ~1 min, a magnetic field magnetized plasma, which drives pheno- at time scales short enough to characterize the decay rate of jBj≈6:6GsÀ1 . The decay ends T mena such as solar flares (1–5). The stan- flare energy release. at about 15:58 Coordinated Universal Time dard model of solar flares (6–9) posits that We report observations (13)ofalarge (UTC), after which the magnetic field at this they are powered by magnetic energy stored in solar flare—one of several that occurred in location remains roughly constant. By con- http://science.sciencemag.org/ the solar corona and released (dissipated into September 2017. The partially occulted eruptive trast, the location within a larger and higher other forms) through magnetic reconnection flare occurred in active region (AR) 12673, collapsing loop, marked in Fig. 1A, experiences (10)—a reconfiguration of the magnetic field at heliographic coordinates 9° south, 91° west a longer decay, until roughly 16:00 UTC. In this topology toward a state of lower magnetic en- (Fig.1A),on10September2017.Thiseventex- location, the magnetic field decays from ~900 ergy. Changes in the coronal magnetic field hibits the main ingredients of the standard flare to ~250 G over ~2 min, a rate of jBj ≈ 5:4GsÀ1. during a flare or other large-scale eruption have model, including a cusplike structure of nested The energy release suggested by this magnetic been quantified only indirectly, for example magnetic loops that evolves upward at a speed (11), from extrapolations of the magnetic field of ~30 km s−1 and an apparent current sheet — 14–16 1 measured at the photosphere the surface layer (Fig. 1A) ( ). This eruptive flare was widely Center for Solar Terrestrial Research, New Jersey Institute of the Sun seen in white light. Although this observed at many wavelengths (14–19). Esti- of Technology, University Heights, Newark, NJ 07102, USA. 2 on May 13, 2020 method can quantify the modest magnetic en- mates of the kinetic, thermal, and nonthermal University Corporation for Atmospheric Research, Boulder, CO 80307, USA. 3Space Science Division, Code 7684, Naval ergy transfer of ~10%, it is known to suffer energies released in the flare are available Research Laboratory, Washington, DC 20375, USA. from many shortcomings (12). The extrapola- from complementary approaches and datasets, *Corresponding author. Email: [email protected] Fig. 1. Multiwavelength observations of the class X8 flare on 10 September 2017. (A)An EUV image (193 Å) with inverted brightness overlain with contours outlining the thermal (red contours) and nonthermal (blue contours) hard x-ray (HXR) emission (16). The green and white lines are a schematic drawing of the plasma sheet (the current sheet, according to the standard solar flare model), closed and collapsing (newly reconnected) loops, and the cusp region, where the fastest evolution of the magnetic field takes place. Only one of the loop foot points (the southern one) is located on the visible side of the disk, whereas the other is located behind the limb (occulted by the Sun). The thin white curve shows the solar surface (photosphere). The dotted black lines indicate the solar coordinate grid marked at 5° intervals. X and Y are the Cartesian coordinates with the coordinate center adopted in the center of the solar disk. RHESSI, Reuven Ramaty High Energy Solar Spectroscopic Imager. (B) The same image as (A), overlain with the microwave observations taken with EOVSA. The colored regions indicate the ≥50% brightness areas corresponding to 26 frequencies from 3.4 to 15.9 GHz. The relationships among different data sources suggest that the microwave emission comes from the cusp region, outlining the newly reconnected collapsing field lines. The gray box outlines the region of corresponding magnetic field maps in Fig. 2. AIA, Atmospheric Imaging Assembly; Freq., frequency. Fleishman et al., Science 367, 278–280 (2020) 17 January 2020 1of3 RESEARCH | REPORT field decay ends around the time of the peak account for its enhanced temperature (15). The entering the induction equation is fluctuating microwave emission (16:00 UTC), which is magnetic-field–aligned component of our in- [turbulent-like (27)], rather than steady. Aver- consistent with the theoretical predictions ferred electric field should accelerate particles aging the induction equation over the random of microwave emission arising from a pop- as required to power the microwave emission velocity field results in a renormalization of ulation of trapped electrons (16). and could drive the observed enhanced heat- the magnetic diffusivity coefficient (26) such We compare these measurements of the de- ing at the cusp region (15). that n ∼ uR=3, where u is the typical turbu- caying coronal magnetic field with equilib- The decay in magnetic field strength implies lent velocity. Nonthermal turbulent velocities rium models that are based on extrapolation advection and/or diffusion of the magnetic of u ∼ 100 km sÀ1 were measured at the cusp of photospheric magnetic field measurements field, which can be estimated using the induc- region in this flare (15), which implies n ∼ uR= (11). The extrapolation requires corresponding tion equation, B ¼ ∇ ½v  Bþn∇2B,where 3 ∼ 1:2  1015 cm2 sÀ1 , in agreement with the photospheric vector magnetic field data, which v is the plasma velocity and n is the magnetic estimate obtained from B above. are not available for this partially occulted diffusivity. The advection term, ∇ ½v  B,can Figure 3B shows the evolution of the mean event. However, magnetic field models are easily account for the magnetic field variation magnetic energy density (13) in this region. available (22) for this AR a few days earlier, during the phase of apparent upward motion Over ~1.5 min, the magnetic energy density on 6 September 2017, when this AR could be of the arclike structures in the magnetic field decays at a rate of ~200 erg cm−3 s−1, losing seen more face-on. These models found that maps from 15:57:00 to 15:59:25 UTC (movie S1). ~80% of the magnetic energy available in this the strongest magnetic field in the corona at However, at later times these arclike struc- area. The net decrease of the magnetic energy the height of 30 Mm was ~200 G [figure 5 in tures fade without moving, which implies in the adopted nominal flare volume of 1028 cm3, (22)]. Our measurements at that height match dissipation of the magnetic field, not advec- which corresponds to a source with a linear this model value at the end of the time range tion. We estimate the magnetic diffusivity scale of ~20 Mm (Fig. 1), is ~2 × 1032 erg. analyzed, after the decay of the magnetic field n required to drive the apparent decay rate We compare this reduction in magnetic en- Downloaded from is over, which implies that the magnetic field ðjBj ≈ 5GsÀ1Þ of the magnetic field (B ≈ 600 G) ergy density with the energy density of non- in the flare evolves toward an equilibrium as n ∼ R2 B=B ∼ 1015 cm2 sÀ1. This value of n is thermal electrons (microwave diagnostics pro- state. However, the much stronger values ob- much larger than the magnetic diffusivity due vides the instantaneous electron and energy served earlier in the flare are several times as to Coulomb collisions (26). It can only be pro- densities, unlike x-ray diagnostics, which high as the equilibrium values. This indicates vided by turbulent magnetic diffusion, which provides electron and energy flux), which we that a dynamic, transient magnetic field was appears when a large fraction of the velocity v compute from the same data (13).
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