3.4 Temporal analysis

The solar corona is the site of a variety of transient phenomena. Coronal loops sometimes flare in active regions (see the review by Benz, 2008). However, most coronal loops are well-known to remain in a steady state for most of their life, much longer than the plasma characteristic cooling times (Rosner et al., 1978Jump To The Next Citation Point, see Section 4.1.1). This is taken as an indication that a heating mechanism must be on and steady long enough to bring the loop to an equilibrium condition, and keep it there for a long time. Nevertheless, the emission of coronal loops is found to vary significantly on various timescales, and the temporal analyses of coronal loop data have been used to obtain different kinds of information, and as a help to characterize the dynamics and heating mechanisms. The time variability of loop emission is generally not trivial to interpret. The problem is that the emission is very sensitive to density and less to temperature. Therefore, variations are not direct signatures of heating episodes, not even of local compressions, because the plasma is free to flow along the magnetic field lines. Variations must therefore be explained in the light of the evolution of the whole loop. This typically needs accurate modeling, or, at least, care must be paid to many relevant and concurrent effects.

Another important issue is the band in which we observe. The EUV bands of the normal incidence telescopes are quite narrow. Observations are then more sensitive to variations because cooling or heating plasma is seen to turn on and off rapidly as it crosses the band sensitivity. On the other hand, telescopes in the X-ray band detect hotter plasma which is expected to be more sensitive to heating and, therefore, to vary more promptly, but the bandwidths are large and do not take as much advantage of the temperature sensitivity as the narrow bands. Finally, spectroscopic observations are, in principle, very sensitive to temperature variations because they observe single lines, but their time cadence is typically low and able to follow variations only on large timescales. Time analysis studies can be classified to address two main classes of phenomena: temporal variability of steady structures and single transient events, such as flare-like brightenings.

In spite of limited time coverage, the instrument S-054 on-board Skylab already allowed for early studies of variability of hot X-ray loops. Decay times were studied by Krieger (1978) who found evidence of continued evaporation of coronal plasma in slowly-decaying structures. Sheeley Jr (1980) and Habbal et al. (1985) found timescales of moderate variability of a few hours over a substantial steadiness for observations of active region loops in 2 MK lines such as Fe xv and Si xii. Substantial (but non-flaring) temporal variability was reported by Haisch et al. (1988) in two active region loops observed with SMM in a few relatively hot X-ray lines (∼ 5 MK) on time scales of some minutes. Cooler loops (< 1 MK) first studied in detail by Foukal (1976Jump To The Next Citation Point) (see Section 3.5) were found to be more variable and dynamic (e.g., Kopp et al., 1985).

The high time coverage and resolution of Yohkoh triggered studies of brightenings on short time scales. The Yohkoh/SXT resolution and dynamic range allowed to study the interaction of differently bright hot loops and to show, for instance, that X-ray bright points often involve loops considerably larger than the bright points themselves, and that they vary on timescales from minutes to hours (Strong et al., 1992). The analysis of a large set (142) of macroscopic transient X-ray brightenings indicated that they derive from the interaction of multiple loops at their footpoints (Shimizu et al., 1994). Some other more specific loop variations were also observed, e.g., the shrinkage of large-scale non-flare loops (Wang et al., 1997). This was interpreted not as an apparent motion but as a real contraction of coronal loops that brighten due to heating at footpoints followed by gradual cooling. Fine-scale motions and brightness variations of the emission were found on timescales of 1 minute or less, with dark inclusions corresponding to jets of chromospheric plasma seen in the wings of Hα. Such small scale variations are associated with the fine structure and dynamics of the conductively heated upper transition region between the solar chromosphere and corona (Berger et al., 1999b).

Loop variability was specifically studied in several UV spectral lines observed with SoHO/CDS for about 3 hours by Di Giorgio et al. (2003Jump To The Next Citation Point). In the hottest lines, within the limited time resolution of about 10 minutes, a few brightenings of a hot loop (∼ 2 MK) were detected but they are minor perturbations over a steadily high emission level. The observation of the whole life of a cool loop (logT ∼ 5.3) on a time lapse of a few hours confirmed the highly transient nature of cool loops, probably linked to the presence of substantial flows (Section 3.5).

Variability analyses have been conducted also on warm loops present in TRACE data. The brightening of a single coronal loop was analyzed in detail by Reale et al. (2000bJump To The Next Citation Point) in an observation of more than 2 hours with a cadence of about 30 s. The loop evolves coherently in the rise phase and brightens from the footpoints to the top, allowing for detailed hydrodynamic modeling (Reale et al., 2000aJump To The Next Citation Point) (see also Section 4.4). Active region transient events, i.e., short-lived brightenings in small-scale loops, were observed with TRACE with a high cadence of 35 s over half an hour (Seaton et al., 2001). Several brightenings detected over a neutral line in a region of emerging flux were interpreted as reconnection events associated with flux emergence, possible EUV counterparts to active region transient brightenings. The fast evolution probably implies high speed flows and high coronal densities. Shimojo et al. (2002) noticed apparent shrinking and expansion of brightening warm loops and proposed heating and cooling of different concentric strands, leading to coronal rain visible in the Hα line. Plasma condensations in hot and warm loops were detected also in the analysis of line intensity and velocity in temporal series data from SOHO/CDS (O’Shea et al., 2007). Antiochos et al. (2003Jump To The Next Citation Point) found no significant variability of the moss regions observed with TRACE. This has been taken as part of the evidence toward steady coronal heating in active region cores (Warren et al., 2010Jump To The Next Citation Point, Section 4.4).

The analysis of temporal series from various missions has been used, more recently, to investigate the possible presence of continuous impulsive heating by nanoflares. The temporal evolution of hot coronal loops was studied in data taken with GOES Solar X-ray Imager (SXI), an instrument with moderate spatial resolution and spectral band similar to Yohkoh/SXT (López Fuentes et al., 2007). The durations and characteristic timescales of the emission rise, steady, and decay phases were found to be much longer than the cooling time and indicate that the loop-averaged heating rate increases slowly, reaches a maintenance level, and then decreases slowly (Figure 9View Image), not in contradiction with the early results of Skylab (Section 2). This slow evolution is taken as an indication of a single heating mechanism operating for the entire lifetime of the loop. If so, the timescale of the loop-averaged heating rate might be roughly proportional to the timescale of the observed intensity variations.

View Image

Figure 9: X-ray light curve observed with the SXI telescope on board GOES. The loop lifetime is much longer than the characteristic cooling times (courtesy of J.A. Klimchuk and M.C. Lòpez Fuentes).

Joint TRACE and SOHO/CDS observations allowed to study temperature as a function of time in active region loops (Cirtain et al., 2007). In many locations along the loops, the emission measure loci were found consistent with an isothermal structure, but the results also indicated significant changes in the loop temperature (between 1 and 2 MK) over the 6 h observing period. This was interpreted as one more indication of multistranded loops, substructured below the resolution of the imager and of the spectrometer. Further support to fine structuring comes from the analysis of the auto-correlation functions in SXT and TRACE loop observations (Sakamoto et al., 2008Jump To The Next Citation Point). The duration of the intensity fluctuations for the hot SXT loops was found to be relatively short because of the significant photon noise, but that for the warm TRACE loops agrees well with the characteristic cooling timescale. This may support loops to be continuously heated by impulsive nanoflares. The energy of nanoflares is estimated to be 1025 erg for SXT loops and 1023 erg for TRACE loops. The occurrence rate of nanoflares is about 0.4 and 30 nanoflares s–1 in a typical hot SXT loop and a typical warm TRACE loop, respectively.

A recent study on time series has been performed on data taken with the Hinode mission. Hinode’s Solar Optical Telescope (SOT) magnetograms and high-cadence EIS spectral data were taken to study the relationship between chromospheric, transition region, and coronal emission and the evolution of the magnetic field (Brooks et al., 2008). The data have allowed to distinguish hot, relatively steadily emitting warm coronal loops from isolated transient brightenings and to find that they are both associated with highly dynamic magnetic flux regions. Brightenings have been typically found in regions of flux collision and cancellation, while warm loops are generally rooted in magnetic field regions that are locally unipolar with unmixed flux. The authors suggest that the type of heating (transient vs. steady) is related to the structure of the magnetic field, and that the heating in transient events may be fundamentally different from that in warm coronal loops.

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