Soft X-ray emission in kink-unstable coronal loops

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Context

Solar flares liberate large amounts of magnetic energy in short periods of time, and are associated with intense soft X-ray emission generated by the heated coronal plasma. Strongly twisted magnetic flux-ropes are a key element of several flare scenarios, as they can store large amounts of energy in the corona, which can be released rapidly as a consequence of the development of magneto-hydrodynamical instabilities. We consider in this nugget twisted magnetic flux-ropes which are unstable with respect to the kink mode. Several properties of the kink instability make it a good candidate for explaining solar flares, even though flux-ropes with sufficiently high twist are rarely observed in the corona. We show and discuss here the properties of the thermal continuum X-ray emission produced by kink-unstable in coronal magnetic flux-ropes (temporal, spectral, and spatial evolution of the thermal continuum X-ray emission) based on a series of numerical simulations. In these, a highly twisted magnetic loop is embedded in a region of uniform and untwisted background coronal magnetic field. We let the kink instability develop and compute the evolution of the plasma properties in the loop (density and temperature), from which we deduce the continuum thermal X-ray emission from the loop (in the 1-25 keV range).

Magnetic twist: how much do we see and how much there is

Our simulations suggest that observations may underestimate the actual magnetic twist present in flaring coronal loops. This happens mainly for two reasons: 1) the magnetic threads which become “illuminated” at a given moment do not necessarily correspond to the most strongly twisted magnetic field-lines, 2) the flaring loops have already lost a large fraction of their initial twist when thermal emission by the heated plasma becomes strong enough to be observed. This is illustrated in Figure 1, which shows a few snapshots of the X-ray emissivity at 5 keV superposed over a sample of magnetic field-lines. Overall, the twist perceived directly from the continuum emission patterns is substantially lower than the highest magnetic twist in the flux-rope. During the saturation phase -- when the emitted flux is maximal -- the predominant emission patterns trace the large-scale arrangement of the thermal emission rather than actual magnetic field-lines. Individual field-lines are only clearly during the late phase of the instability. This is an important point: the lack of observational evidence of strongly twisted magnetic flux-ropes was seen as a major hurdle faced by flare scenarii relying on the kink instability.

Figure 1. Continuum emissivity at 5 keV and some magnetic field-lines from a kink-unstable twisted flux-rope.

X-ray emission after the onset of the kink instability

The growth of the kink instability leads to an episode of magnetic reconnection (between the twisted flux-rope and the background). Simultaneously, a burst of strong ohmic heating makes the flaring plasma strongly multi-thermal, with the hottest parcels of plasma reaching temperatures as high as 35 MK (the background temperature is of about 1.2 MK). Afterward, the system cools down globally under the action of thermal conduction, even though small sporadic heating events keep occurring. The plasma does not revert back to it's initial quasi-isothermal state. Figure 2 shows the X-ray thermal emission generated by the multi-thermal plasma in the flaring loop together with the total photon spectra at 1 AU at different stages of the simulated flare. The blue and yellow lines represent magnetic field lines belonging initially to the twisted flux-rope and to the background field, respectively. The green/cyan volumes represent the regions of the plasma emitting strongly at 10 keV. The plot to the right of the figure show the total photon spectra at 1 AU (with the gray lines representing preceding instants, with a time interval of 2.5 s between consecutive gray lines).

Figure 2. Continuum emissivity at 10 keV, magnetic field-lines from a kink-unstable twisted flux-rope, and photon flux spectra

Emission measures: how much hot plasma (and how dense)

The amount of heated plasma which is susceptible of emitting significantly in the soft X-ray range can be represented by the emission measure of the plasma above a certain temperature. Figure 3 shows the evolution of the emission measure of the plasma woth temperature between 1MK and 9 MK (“cold” component; dashed line) and of the plasma above 9 MK (“hot” component; continuous line) as a function of time. At the peak of emission, the emission measure of the hot plasma reaches a value of the order of 5 × 10^47 cm−3, which is one order of magnitude below what was measured by Sylwester et al. (2014) for an M -class flare. Figure 4 shows the distribution of the emission measure as a function of plasma temperature EM(T) at about the flare peak. The initial EM(T) distribution is narrow and centered at T = T0 = 1.2 MK, but extends into the higher temperature range as the flare proceeds with significant emission measures found for the plasma with temperature above 20 MK.

Figure 2a., 2b.

Conclusions

This nugget discusses the properties of soft X-ray emission in simulations kink-unstable coronal loops. Due to the development of the kink instability, the coronal plasma initially at 1.2 MK is heated up to temperatures between 10 and 30 MK. Significant emission measures arise for plasmas above 10 MK. Our simulations indicate that the morphology of the emission alone does not provide a good assessment of the magnetic field-line twist (which can be much higher that what the observations seem to indicate). Future work needs to consider more realistic magnetic configurations (e.g. curved loops) as well as the effects of the chromospheric layers on the evolution of the system. Particle acceleration in the reconnection sites (see e.g. Gordovskyy, Browning, et al) will also be taken into account to provide a combined view of the non-thermal and thermal X-ray emission during a flare.

References

Our paper Sylwester, et al, 2014 Gordovskyy, et al, 2014