Modelling the radiative signature of turbulent heating in coronal loops. S. Parenti 1, E. Buchlin 2, S. Galtier 1 and J-C. Vial 1, P. J. Cargill 3 1. IAS, Université Paris Sud - CNRS, FR; 2. University of Florence, IT 3. Space and Atmospheric Physics, Blackett Laboratory, Imperial College, UK Introduction In this work we investigate the statistical properties of a cooling coronal loop subject to a turbulent heating along the lines of Cargill (1994) work. We are interested to see if the statistical properties of the injected energy are conserved by the radiation produced during the cooling phase. The potentiality of this kind of study is in the direct connection between the theory adopted for the coronal heating and the real data available from the observations. We model a coronal loop as composed by n unresolved identical threads. Each elemental thread has a half length L, a section area A and at each time t it is described by one temperature T and one density N. We simulate the heating-cooling cycle of each thread and we calculate its radiative losses. We use this quantity to built synthetic spectra that we will compare with instrumental observations, such as SOHO/EIT and SolarB/EIS. The heating model We use the Buchlin et al (2003) model to simulate the injection of energy in the loop system in the corona. This energy originates from turbulent fluctuations in the photosphere and propagates in the corona through Alfvén waves.The dissipation is done through instantaneous nanoflare events ( = ergs) during a period of about 10 5 s. The Probability Distribution Function (PDF) of this energy (Q) is a power law function with index  = Individual events with energy Q are randomly distributed in space. The cooling model The elemental strand that is instantaneously heated, cools through conduction and radiation (Cargill ’94). These processes are governed by their characteristic time scales  C and  R. T is the plasma temperature, N is the density, L is the half length of the loop,  (T) is the loss function calculated assuming Mazzotta et al. ’98 ionisation equilibrium and coronal abundances (CHIANTI v. 4.2). The histories of the plasma parameters T, N during the time of the simulations are then used for statistical studies. Some general properties of the radiative emission of a loop subject to a power law heating function have been anticipated in Cargill & Klimchuk ’04  C  N L 2 / T 5/2 ;  R  T 1-  / N  ;  (T) =  T  Conclusions The results of this work show that the properties of the PDF of the energy given as input for our loop model are partially conserved during the radiation phase. The power law distribution of the intensity is better conserved when we assume small and thin strands. The index of the power law changes with the assumed fine structure of the loop. Smaller and thinner are the strands, more the index gets closer to that of the heating distribution. Higher is the temperature of the line we synthesize, more similar to the heating function is the PDF of the intensity. We have shown here that the coronal plasma response to the heating depends on the unresolved fine structure. To understand the plasma behavior is an important issue in order to properly associate the plasma heating properties with those derived from the observations (i.e. Aschwanden et al, 2000, Aletti et al. 2000). Our work shows that it is important to direct the attention to the very hot lines. These are emitted just after the heating injection. Here we may find direct information on the heating. The SolarB/EIS instrument, with its high resolution and large wavelength bands, which include high temperature lines, will be an important source of information for studying the nanoflare case.References Aletti, V et al., 2000, ApJ, 544, 550Cargill, P.J. & Klimchuk, J.A., 2004, ApJ, 605, 911 Buchlin, E. et al., 2003, A&A, 406, 1061Mazzotta, P. et al., 1998, A&AS, 133, 403 Aschwanden, M.J. et al., 2000, ApJ, 541, 1059Young, P.R. et al., 2003, ApJS, 144, 135 Cargill, P.J., 1994, ApJ, 422, 381 Some results Fit: -3.9 Figure 3 Figure 3 shows the loop system total intensity emitted by the Fe XV 284 Å (log(T) = 6.3) line as function of time. This line is now observed by SOHO/EIT and it will be one of the strongest line on SolarB/EIS. The intensity shown in figure 3 is calculated by considering the total variation of the N and T parameters in the loop system during the simulation, and using the CHIANTI (Young et al. 2003) atomic database. The signature of the impulsive heating is still recognised by the rapid variation of the intensity. These fluctuations can be studied statistically. FIGURE 3 FIGURE 4 Figure 4 Figure 3 Figure 4 shows the Probability Distribution Function for the intensities of Figure 3. The simulations show that this distribution follows a power law similar to the heating function. This means that part of the information on the heating is still present. However, the intensities are distributed over only about one decade, contrary to the distribution of the heating. The index of the power law has changed. For this simulation we have assumed A = 8·10 13 cm 2 and L = 10 9 cm. Parameter L Figure 5 Figure 4 ( We tested the intensity behaviour when changing the geometrical parameters of the elemental strands. These parameters affect the way the strands cool down and imply a change in the DEM profile. Figure 5 shows an example where we have decreased the loop length L with respect to Figure 4 (L=2·10 8 cm, A = 8·10 13 cm 2 ). The index of the power law decreases. FIGURE 5 Parameter A Figure 6 Figure 4 In Figure 6 we have increased the strand section A with respect to Figure 4 (L = 1·10 9 cm and A = 8·10 14 cm 2 ). In this case a power law does not represent any more the intensity distribution. Fit =-2.0 FIGURE 6 FIGURE 7 The temperature parameter Because we are interested in the heating signature, Figure 7 Figure 8 we have calculated the intensity PDF for lines emitted at higher temperatures. Figure 7 shows the example for Fe XIX 1118 Å (SOHO/SUMER, logT =7) and Figure 8 for Fe XXI 188 Å (SolarB/EIS, logT=7.1). Note the change in the index of the power law that gets closer to that of the heating function for the hottest line. At each instant t, if  R >  c conduction is the dominant process, whereas if  R <  C radiation dominates. Fit =-1.53 FIGURE 8 Figure 2 Figure 2 shows the logarithm of N 2 as function of the logarithm of temperature, integrated in the entire loop system and the simulation time. This quantity is proportional to the Differential Emission Measure (DEM), which gives the amount of material at a given temperature. From this curve we can establish that most of the emission of the loop system happens between 10 6 and 10 7 K. Using this result and an atomic database, we can calculate the synthetic emission of the loop system at such a temperature. FIGURE 2