A&A 385, 1073-1077 (2002)
S. Patsourakos1,2 - J.-C. Vial3
1 - US Naval Research Laboratory, Space Science Division, Washington, DC 20375, USA
2 - Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK
3 - Institut d'Astrophysique Spatiale, Université Paris XI - CNRS, Bât. 121, 91405 Orsay Cedex, France
Received 12 June 2001 / Accepted 24 January 2002
We present an analysis of light-curves obtained in the O IV and Ne VIII transition region and low corona lines, that were simultaneously recorded in a quiet Sun region by SUMER/SOHO. By using the flatness spectrum of the observed light-curves we searched for intermittency signatures. It was found that a significant proportion of points in the observed area exhibit clear indications of intermittency, irrespectively of their intrinsic intensity. Our findings give favor to an impulsively heated transition region and corona via intermittent-type MHD turbulence.
Key words: Sun: corona - Sun: transition region - Sun: UV radiation
It is indeed the aim of the present paper to search for signatures of intermittency in high temporal and spatial resolution time-series of transition region and lower corona spectral lines intensities. This paper is organized as follows: in Sect. 2 we describe our observations and data while Sect. 3 is dedicated to a description of the tools used to search for intermittency signatures. Finally, in Sect. 4 we discuss our results and give our conclusions.
|Figure 1: Time-"solar-y'' diagrams for a) the O IV intensity (top panel, logarithmic scaling in intensity) b) the O IV intensity which has been normalized by the minimum value of the light-curve at each spatial pixel (middle panel, linear scaling in intensity) and c) O IV sample light-curve for spatial pixel 100 along the slit (bottom panel).
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We first applied standard corrections to the raw data including flat-fielding, destretching, removal of the local gain depression and correction for non-linearities in the instrument response in order to get rid of a number of instrumental peculiarities (Wilhelm et al. 1997). By integrating over the line profiles (after a background was subtracted) we produced light-curves for each point along the slit. For our analysis we focus on the O IV and Ne VIII lines at 790.2 and 770.4 Å since they are brighter than the other O IV and Ne VIII lines, for ensuring an exploitable signal-to-noise ratio. These two lines offer a good temperature coverage of the transition region and the lower corona since they have formation temperatures of and K correspondingly. For our analysis we use a 235 pixels long portion of the slit.
An example of the obtained light-curves is given in Fig. 1 for O IV. Along the slit one can observe (Fig. 1, top panel) an alternation of bright and dark portions reminiscent of network and cell elements which roughly speaking preserve their identity during the duration of our observations. We can note the existence of intensity bursts that are unevenly spaced in time. The above remark can be better evidenced in the middle panel of Fig. 1 where we plot the light-curves normalized to their minimum values in order to better visualize such bursts irrespectively to their intrinsic intensity. It can be seen that these bursts seem to occur both in dark and bright regions. Finally, we show (bottom panel of Fig. 1) a sample light-curve at a point selected randomnly alon the slit. We can readily note the existence of spikes in the above time-series all over its duration. The above behavior is indicative of intermittency with switches between bursts and quiescent phases taking place randomly in time.
The flatness spectrum analysis, as a probe of intermittent behavior both in space and time, has been extensively used in a great number of problems including turbulent flows (e.g., Frisch 1995 and references within), solar sunspot number (Lawrence et al. 1995), photospheric flow fields (Lawrence et al. 1999) magnetic and kinetic energy as well as the dissipation rate of modeled coronal loops (Dmitruk et al. 1998), and solar wind magnetic field and velocity fluctuations (Bruno et al. 1999).
|Figure 2: Temporal flatness spectrum of the O IV line intensity along the slit (top panel-logarithmic scaling). The horizontal color-bar corresponds to the logarithm of the flatness. The overplotted contours indicate points with flatness below 3. Time-averaged O IV intensity along the slit (bottom panel).
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|Figure 3: Spatially averaged temporal flatness spectra for O IV (continuous line) and for Ne VIII (dashed line).
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The main result of this work is that intermittent activity is quite ubiquitous throughout the TR of the quiet Sun and in fact increases when the time scales under consideration get smaller and smaller. This lends considerable support to a series of theoretic models of coronal heating (see the references in the introduction) which find their route to the Parker's nanoflare heated corona via MHD turbulence. All these models lead to an intermittent behavior in the time-variation of a number of physical parameters including the dissipated energy. The radiative losses are related to the dissipated energy since one part of it is lost as radiation. Thus, we should expect a correlation between the observed line intensities and the dissipated energy and consequently intermittent bursts in the observed light-curves, even though a smoothing may be expected in the observed light-curves due to the limited (and not infinitely small) time it takes a plasma to react to modifications of its thermodynamic properties by radiation. Such bursts could be related to well-known types of transient events such as explosive events (e.g., Dere et al. 1987; Innes et al. 1997; Patsourakos Vial 2001), microflares (e.g., Porter et al. 1987), blinkers (e.g., Harrison 1997) etc., with however the above events been presumably just the "tip of the iceberg'' of a whole hierarchy of events (e.g., Parker 1988) that are currently non-resolved by our instrumentation, given also the fact that such events are not too numerous to account for the almost omni-present observed intermittency. Another point which deserves some comment here is the fact that the models above are originally intended to model large scale coronal loops. However we can assert that they could be applied also to the quiet Sun, via the interaction of small loops in the frame of the "magnetic carpet'' concept (Schrijver et al. 1997) for example (see also the relevant discussion in Aletti et al. 2000). It is just the macroscopic spatial scales of the structures involved which are different: the underlying physical processes could be the same. It is very tempting to draw a link between these small loops and the spikes observed in the flatness spectrum. What it is really needed from MHD turbulence models is that they could be able to cope with the plasma local thermodynamics, in order to reproduce the spectral emission of the plasma which provides a common ground for comparisons between observations and models. We note that most of MHD turbulence simulations assume incompressibility which by definition does not cater for variations of local thermodynamic parameters (i.e., density and temperature) which are essential elements for determining the radiative signatures of the plasma. Some first steps trying to reconcile this deficiency, have been taken for a number of simplistic cases by Walsh Galtier (2000). Very interestingly these authors found, that for some of the cases they considered, bursts appear in both the plasma temperature and density as it was anticipated above. These bursts result from intermittent energy release followed by its dissipation. To note here that the bursts in the dissipated energy are by far more stronger in magnitude than the bursts in density and temperature, which may make feasible the observational detection only for the stronger among them.
Our results are broadly consistent with the work of Aletti et al. (2000). These authors found that the intensity distributions of the quiet Sun coronal snapshot images they analyzed, show departures from Gaussianity at large intensities even with a degraded spatial resolution. They interpreted the above findings as suggestive of a forced turbulent system characterized by an intermittent behavior, having dissipation scales much more smaller than the spatial resolution. The relevance of an MHD turbulence regime in the quiet Sun has also been demonstrated in two recent articles by Berghmans et al. (1998) and by Chae et al. (1998) by totally independent means than ours. They analyzed respectively temporal/spatial intensity power spectra and non-thermal velocities in the quiet Sun and found that they are consistent with predictions from MHD turbulence theory. As a matter of fact, our findings in favor of intermittent MHD turbulence could have a significant bearing on the way that observational data are investigated for scaling properties (e.g., exponents) of MHD turbulence. Higher order than 2 (power spectrum) moments may need to be considered.
What is clearly needed for the future is on the one hand a more realistic coupling between heating and the hydrodynamics and on the other hand an extension of our study to other structures (e.g. active regions) and to bi-dimensional spatial fields seeking for spatio-temporal intermittency in 2-D.
S. Patsourakos acknowledges post-doctoral support by the PPARC. The research of S. Patsourakos was supported in part by NASA and ONR. We would like to thank the referee, Dr. L. Milano for his comments/suggestions that helped to improve this paper. The authors wish to thank S. Galtier, M. Georgoulis, U. Frisch, P. Lemaire, A. Mangeney and M. Velli for very useful and enlightening discussions during the course of this work. The SUMER project is financially supported by DLR, CNES, NASA and the ESA Prodex programme (Swiss contribution). SOHO is a mission of international cooperation between ESA and NASA. Wavelet software was provided by C. Torrence and G. Compo, and is available at URL: http://paos.colorado.edu/research/wavelets.