Heating events in the quiet solar corona: multiwavelength correlations

Transcription

1 Astron. Astrophys. 341, (1999) ASTRONOMY AND ASTROPHYSICS Heating events in the quiet solar corona: multiwavelength correlations Arnold O. Benz and Säm Krucker Institute of Astronomy, ETH-Zentrum, CH-8092 Zürich, Switzerland Received 25 August 1998 / Accepted 28 September 1998 Abstract. Coronal, transition region and chromospheric lines and centimeter radio emission of the quiet Sun have been simultaneously observed by SoHO and the VLA. The corona above the magnetic network has a higher pressure and is more variable than above the interior of supergranular cells. The Fourier transform in time is found to have steeper spectra in the corona and upper chromosphere than in the transition region. The temporal sequence of brightenings has been determined by cross-correlations of identical picture elements in different emissions. The method allows to study statistically the faintest fluctuations in the corona and relate them to the layers below. The cross-correlations yield that (i) the first emissions to peak in time are O V and He I originating in the transition region and the upper chromosphere, respectively. (ii) The coronal line of Fe XII lags by about 5 minutes and Fe IX/X peaks a further half a minute later in the average, latest of all emissions. The interpretation of these lags follows readily from analogy with regular flares in active regions, where O V and He I correlate closely with hard X-rays emitted by beam electrons impinging on the chromosphere. The coronal iron lines are then emitted by the evaporating plasma expanding into the corona and cooling by conducting part of the energy to increase the emission in Fe IX. (iii) The radio emission peaks before the coronal emission measure, similar to the Neupert effect in flares, but shows considerable variation relative to O V. It is proposed that there are two emission processes at work radiating both thermal emission and non-thermal gyrosynchrotron emission at various fluxes. These statistical results show that the coronal heating events follow the properties of regular solar flares and thus may be interpreted as microflares or nanoflares. Key words: Sun: chromosphere Sun: corona Sun: radio radiation Sun: transition region Sun: UV radiation 1. Introduction The heating of the solar corona, and similarly of all stellar coronae, is a an enigma since the detection of the high temperature more than fifty years ago. Various heating mechanisms Send offprint requests to: A.O. Benz have been proposed (cf. reviews in Ulmschneider, Priest & Rosner 1991), including numerous small flares (microflares or nanoflares), waves and continuous currents. The time scales of these mechanisms are different: a few minutes for microflares, hours for waves and continuous currents. Variations of coronal emissions are thus important diagnostics for the heating process. Best suited for the observation of variability are sensitive hightemperature emission lines originating in the corona and soft X-ray continuum emission. Furthermore, thermal radio emission and Thompson scattered optical emission have been used in the past. It is very interesting to compare the variations of the corona also to variations in emissions from the transition region and chromosphere. These variations in the lower layers can either be the cause of the coronal changes or the result of them, or be unrelated. The dynamics of coronal phenomena is best known in active regions. Small variations with a duration of a few minutes have been found in soft X-rays (e.g. Shimizu 1995). They are accompanied by hard X-ray emission most possibly explained by precipitating electrons thermalizing in the chromosphere (Nitta 1997) and non-thermal radio emission in the rise phase presumably due to gyrosynchrotron emission of relativistic electrons (Gary et al. 1997). The delay of soft X-rays relative to centimeter radio emission and hard X-rays is between 1.5 and 6.4 minutes, similar to the well-known delay in regular impulsive flares (Neupert 1968). Thus the active region variations appear as small versions of regular flares. This Neupert effect is generally interpreted as flare energy release in the corona accompanied by accelerating particles, which propagate to the denser layer below where they deposit some of the flare energy. The chromospheric plasma is heated to coronal temperatures, expands, and fills up loops that reach into the corona (referred to as evaporation ). Considering the possibility of magnetic energy released in the chromosphere (e.g. Innes et al. 1997), we may add as a note of caution that we will refer in the following to any plasma hotter than 10 6 K as coronal, regardless of its altitude. Here we concentrate on quiet regions, having the advantage of a lower background emission. The variability of coronal heating has long been suspected from the variability of the transition region. The quiet Sun radio emissions at centimeter wavelength originate from the transition region and have been reported to vary at time scales of a few minutes (Kundu

2 A.O. Benz & S. Krucker: Heating events in the quiet solar corona 287 & Alissandrakis 1975; Butz et al. 1979; Benz & Fürst 1987). Low-temperature EUV lines, e.g. C IV, originating at temperatures of 10 5 K are known to exhibit turbulent events at a rate of about 800 s 1 averaged over the whole Sun (Brueckner & Bartoe 1983). Occasionly, high-velocity jets with velocities up to 400 km s 1 are observed. These brightenings generally lie above small bipoles of the photospheric and chromospheric magnetic network (Porter et al. 1987, Harrison 1997), but explosive events generally occur away from the larger concentrations of magnetic flux (Porter & Dere 1991). The relation between transition region activity to chromospheric and coronal processes is not yet understood, since the transition region is very sensitive to changes in the corona above, but also to variations originating from below. Dynamic phenomena in the corona can now also be studied directly. In quiet regions of the corona they have first been noticed in SXR as coronal bright points (Golub et al. 1974). About one of them appears per hour averaged over the whole Sun. They consist of several parallel loops, typically km long and 2000 km wide and have a mean lifetime of 8 hours. The rapid changes observed in the thermal radio emission of such loops suggest that the individual loops brighten and fade on time scales of a few minutes (Habbal and Harvey 1988). Evidence for reconnection in coronal bright point points has been presented by van Driel-Gesztelyi et al. (1996). The number of observed bright points increases with sensitivity. Sensitive observations in soft X-rays by Yohkoh/SXT have revealed a large number of microflares above the network of the magnetic field in quiet regions (Krucker et al. 1997a). They have a typical thermal energy content of erg per event and occur at a rate of of 1200 events per hour over the whole Sun. The energy was calculated from the thermal energy content assuming a filling factor of unity. For incomplete filling, the energy must be reduced by the square root of the filling factor. More recently, the coronal emission measure in quiet regions has been observed in EUV iron lines and was found to fluctuate locally at time scales of a few minutes in a large majority of pixels (Benz & Krucker 1998). The change in the content of coronal material in a given area suggests that the corona is not only heated, but plasma is frequently and impulsively injected from the chromosphere. Thus coronal heating may actively involve the chromosphere as a supplier of material. Berghmans, Clette & Moses (1998) report a steep power-law number distribution of these events vs. duration, continuing to increase down to 6 minutes. Krucker & Benz (1998) find a power-law distribution of such events with a slope 2.6 in energy, thus emphasizing the role of even smaller events. They estimate that the microflares exceeding a thermal energy input of erg constitute in the average about 16% of the radiation emitted from the same region. The power-law slope is steep enough that the equality of impulsive energy input by events below the 3σ limit and radiative plus connective loss cannot be excluded. In fact, a statistical analysis by Benz & Krucker (1998) of even smaller fluctuations of the emission measure suggests that, above the network, their energy input amounts to some 77% of the radiative loss observed from the quiet corona. If the observed power-law continues to smaller energies and the microflares inject all the heating energy, Krucker & Benz (1998) predict at least 28,000 microflares to start per second on the whole Sun. Multiwavelength observations have the potential to relate the various emissions and may indicate the causal order. Thus they have the potential to clarify the physics. First, spatial correlations of the various emissions must be investigated to select spatially coincident events. Enhanced emissions above the magnetic network have been reported previously, including centimeter radio emission (Kundu et al. 1979; Gary et al. 1990), transition region lines (Dere et al. 1984), as well as an enhanced coronal emission measure and thus an increased mass content of the corona (Benz et al. 1997). The latter authors also report a mean displacement from centimeter radio emission by 5 21 and of soft X-rays by 13, as measured by spatial cross-correlations. In this work we follow the strategy to first investigate the coronal variations and then compare them to changes at emissions originating from lower layers that cause the coronal dynamics or react to it. Thus we start with sensitive observations of high-temperature EUV lines and derive the coronal emission measure and a formal temperature. We concentrate on the enhancements of these parameters to localize and characterize the coronal energy input. Observations at other wavelengths are used to study the cause or effect of these changes. The paper first describes the observations and their properties at each wavelength, relating them spatially to both the magnetic network of the lower layers and to the coronal emission measure. In Sect. 3 the results of the observation at each individual wavelength are discussed and the different wavelengths are compared in location. The results from statistical investigations of the temporal correlations between wavelengths are presented in Sect. 4. The properties of fluctuations at the different wavelengths and in relation to each other are summarized and discussed in Sect. 5. Conclusions are given in Sect Instruments and observations The observations presented here aimed at imaging a small fraction of the quiet Sun with highest possible temporal resolution. Data from several instruments on board the Solar and Heliospheric Observatory (SoHO) are combined with observations from the Very Large Array (VLA). The joint observations imaged areas of several arcminute size of a quiet region in the center of the solar disk on July 12, The Extreme ultraviolet Imaging Telescope (EIT) on SoHO is a normal-incidence, multi-layered mirror instrument (Delaboudinière et al. 1995). It imaged a 7 7 area with a pixel size of 2.62 and a time resolution of s. The observing run lasted from 14:30 to 15:15 UT. Some results of these observations have been published by Benz & Krucker (1998) and Krucker & Benz (1998). EIT observed two wavelength bands, 171 Å and 195 Å, alternatively. They include emission lines of Fe IX/X and Fe XII, respectively, with diagnostic capabilities for temperatures in the range of K. These coronal lines dominate the observed parts of the EUV spectrum, and their large photon fluxes provide higher sensitivity than previ-

3 288 A.O. Benz & S. Krucker: Heating events in the quiet solar corona ous observations in soft X-rays. Using the two bands, formal values for the coronal emission measure and temperature have been determined for each pixel at each time. It may be noted here that in less than 1% of the pixels the line-ratio temperature is below K and in none of them below K. The emission measure, defined by the square of the electron density times the volume, is linearly proportional to the observed flux. The derived parameters are to be taken as formal values, representing weighted means over the sensitive temperature range. 2. The Coronal Diagnostic Spectrometer (CDS) on SoHO is a twin spectrometer applying normal and grazing incidence in the range Å (Harrison et al. 1997). A total of emission 6 lines were recorded from He I, O V, Si IX, Mg IX, and Si XII, covering a temperature range from below Kto K. The instrument observed from 14:00 to 23:42 UT with a pixel size of (East-West/North-South) in a field area of For both EIT and CDS, linear interpolation has been used to correct for solar rotation. The final accuracy of the coalignment is assumed to be better than ±5. 3. The Solar Ultraviolet Measurements of the Emitted Radiation (SUMER) instrument on SoHO is a normal incidence telescope and spectrometer (Wilhelm et al. 1995). It operated from 13:54 22:00 UT observing in two emission lines: C IV (1548 Å) and C II (1336 Å). Images in each line were recorded alternatively for approximately one hour. The pixel size in East-West direction was 1, separated by a gap of 3, thus the effective resolution was 4.Itwas2 in North-South direction. The field of view of each one hour observation was Itwas slightly shifted every hour such that the three images in each line could be merged into a single image extending A magnetogram observed at 14:28:05 UT by the Michelson Doppler Imager (MDI) on SoHO has been used as a reference to photospheric features. The instrument observed with a spatial resolution (pixel size) of 2.0 (Scherrer et al. 1995). 5. The VLA has observed from 14:30 to 23:00 UT in D configuration. The frequencies were 14.98, 8.45, and 4.87 GHz to which we refer by wavelengths as 2, 3.6, and 6 cm, respectively. The instrument observed at a single wavelength for 30s with 10s time resolution, and then changed to an adjacent wavelength. Wavelength pairs were observed alternating for 25 minutes, when the phase calibrations interrupted the observations for about 5 minutes. The field of view of the VLA is given by the single antenna (primary beam). It is circular and depends on wavelength. At 2.0, 3.6, and 6.0 cm the diameter of the field of view (FWHP) is 180, 240, and 648, respectively. For long integration times the spatial resolution (FWHP) is roughly circular and for 2.0, 3.6, 6.0 cm amounts to 4.5, 7.1, 12.5, respectively. The resolution decreases for snapshots. The radio data have been calibrated and cleaned as appropriate for solar observations. When especially noted in the analysis section, the same clean beam sizes of 10 to restore the image have been used at all three wavelengths for easier spatial comparisons. Fig. 1 gives an overview of the height where the various emissions originate. The line emissions observed here are indicated just by the height corresponding to the temperature of Fig. 1. a The temperature profile through the upper chromosphere, transition region and lower corona of the quiet Sun according to the FAL model C. b Differential contributions to the radio intensity vs. height above the photosphere: full: at 6.0 cm, dashed: at 3.6 cm, dotted: at 2.0 cm wavelength and a schematic indication of the origin of the emission in various spectral lines of interest as given by their temperature of maximum ion formation. peak formation of the given ion. The region of origin of the line emission is roughly a factor of two in temperature around this location, depending on density, abundance, and possibly excitation. The figure suggests that the lines of He I, C II, C IV, and O V originate very close to each other in the narrow transition region. The other lines, Fe IX XII, Si IX XII, and Mg IX, have coronal origin. The region of thermal bremsstrahlung (free-free) radio emission depends only on temperature and electron density and has been evaluated from FAL model C (average quiet Sun, Fontenla, Avrett & Loeser 1993). The model has been found to agree reasonably well with radio observations (Bastian et al. 1996). The most productive location at a given frequency ν is generally around unit optical depth τ, where in cgs units 0.137n 2 ds τ 1. (1) ν 2 T 3/2

4 A.O. Benz & S. Krucker: Heating events in the quiet solar corona 289 The peak contribution is normalized to unity in Fig. 1. The 6 and 3.6 cm emissions originate mostly in the transition region, and 2.0 cm has a considerable chromospheric contribution. 3. Single wavelength properties and spatial correlations Images originating from different altitudes in the solar atmosphere are overlaid in Fig. 2. The magnetogram (left) shows magnetic field strengths between 171 G and +112 G. In MDI resolution this is consistent with quiet Sun conditions throughout the field of view. The magnetic network is outlined by strong magnetic elements. The radio images are displayed by twelve contour levels in regular intervals between zero and the peak, which is about 30 Jy/beam at all wavelengths. The FWHP beam size for image reconstruction ( clean beam ) is chosen 10 at all wavelengths. The coronal emission measure in Fig. 2 (right) was derived from Fe IX/X and Fe XII line observations using standard EIT software. The values range from 1.6 to cm 5. The ion-ratio temperatures, derived from the same data, reach only up to K. It suggests that the plasma at temperatures beyond the sensitivity limit of K is a minor part and can be neglected for the coronal emission measure in the field of view. This result is consistant with Yohkoh SXR observations of quiet solar regions finding also no significant plasma with temperatures above 2 MK (Benz et al. 1997). When comparing the different instruments, it must be noted that the observing times were not identical: The magnetogram (Fig. 2, left) is a snapshot taken at 14:28:05 UT, the coronal emission measure (Fig. 2, right) is the average from 14:30 to 15:15 UT, and the radio contours of the transition region are synthesized over the time range from 14:30 to 23:00 UT to increase spatial resolution and the signal-to-noise ratio. Nevertheless, the spatial correlation between the different emissions is generally very good, in agreement with earlier reports by Kundu et al. (1979), Gary et al. (1990), Benz et al. (1997). Since thermal solar radio emission is optically thick, enhanced radiation indicates a higher temperature at an optical depth of approximately unity. Similarly, the emission measure in the corona above the radio sources is enhanced, indicating higher densities also in the corona above the magnetic network. These correlations suggest a generally enhanced plasma pressure above the magnetic network from the upper chromosphere to the corona. In particular, it is noted here for the first time that enhanced centimeter radio emission often originates close to magnetic elements (Fig. 2, left). The coronal material, on the other hand, is concentrated in between bipolar magnetic elements as previously noted by Benz et al. (1997), and Falconer et al. (1998). Some clear cases are marked with A, B, C, and D in Fig. 2. Thus the centimeter emission appears to be enhanced near footpoints of loops filled with plasma at coronal temperature. Fig. 3 displays all CDS and VLA data recorded (from 14:00 to 23:42 UT and 14:30 to 23:00 UT, respectively). Six EUV spectral lines indicated on the top by the emitting ion and the wavelength are shown. The temperatures of maximum ion formation range from below K for He I to K for Si XII (cf. Fig. 1), i.e. from the upper chromosphere to the corona. The spectral intensities have been integrated in wavelength over the line at half peak flux. Fig. 3 demonstrates the good correlation between emissions originating at different altitudes. However, even the crude representation in Fig. 3 by brightness shows that the ratio between ions varies considerably, indicating differences in temperature structure for different peaks. The centimeter radio intensities are shown by 16 contours equally spaced between the absolute minimum and maximum in the field at each wavelength. Negative values relative to the mean are shown by dashed curves. As in Fig. 2 the same clean beam sizes of 10 have been used for all wavelengths. There are significant differences between the three wavelengths. Note that sources E and F are missing at 6 cm. We have checked the data for incompleteness. Reducing the observing time to periods with simultaneous observations at 3.6 cm and 6 cm, these sources still only show at 3.6 cm. Most interesting is the topmost source in Fig. 3, referred to as source D in Fig. 2. It has a magnetic dipole structure (Fig. 2, left). He I and O V, originating from the transition region (cf. Fig. 1) and below show a binary structure, whereas the coronal lines, Si IX, Mg IX and Si XII, peak in between. Consistent with their common origin, the centimeter radio intensities also show a double structure, coinciding roughly with the transition region lines. In Fig. 4 only emissions from the upper chromosphere and transition region are compared. The grayscale lookup table is chosen logarithmic to enhance small brightenings. As indicated in Fig. 1, C II and C IV have maximum ion formation temperatures of K and 10 5 K, respectively. Fig. 4 combines all data recorded by SUMER and the VLA from 13:54 to 22:00 UT and 14:30 to 23:00 UT, respectively. The overlap in time is relatively good. Not surprisingly, the spatial coincidence is best of all. In particular source G, which not present in Fig. 2 (right) coincides with strong emissions at 3.6 and 6 cm. Source G appeared in radio waves only after the time when EIT was observing. Most remarkable are the three sources H 1, H 2, and H 3 seen in C II, C IV and 2 cm. At 3.6 cm only the two outer sources are present. At 6 cm, however, only the center source, possibly the top of a loop, is visible. If it is a stable loop having its peak temperature at the top, its temperature is not coronal. Indeed, Figs. 2 and 3 do not show it in the coronal lines. Thus the loops of the H complex are not part of the corona. 4. Temporal variations and correlations The temporal variations in each pixel have been characterized by the standard deviation σ as calculated from instrument calibrations (Tarbell 1996). In Fig. 5 (middle) pixels have been marked white if a positive enhancement larger than 3σ was found in at least one of the 2 minute time steps. Comparing Fig. 5 (middle) with the image of the coronal emission measure in Fig. 5 (left) shows immediately that enhanced emission measure often correlates with enhanced variations (in units of statistical significance) of it. Thus the corona above the magnetic network not

5 290 A.O. Benz & S. Krucker: Heating events in the quiet solar corona Fig. 2. Overview on the field of view in a quiet region near the center of the solar disk on July 12, left A magnetogram in grayscale showing the longitudinal magnetic field of the photosphere was observed by SoHO/MDI (white = positive, black = negative). The contours represent radio intensities emitted by the chromosphere and transition region as observed by the VLA (yellow = 2.0 cm, green = 3.6 cm, blue = 6.0 cm). right The same radio contours are overlaid to an image of the coronal emission measure in the K range as derived from SoHO/EIT Fe IX/X and Fe XII lines.

6 A.O. Benz & S. Krucker: Heating events in the quiet solar corona 291 Fig. 3. The SoHO/CDS viewed a field of , contained in the central part of the field shown in Fig. 2. The observations in 6 spectral lines are shown, representing different temperature regimes. They are presented in order of increasing nominal temperature from left up to right down. Each line is displayed thrice and overlaid with the same radio contours at 2, 3.6, and 6 cm wavelength from left to right. only appears to be brighter, but also more variable than above the interior of supergranular cells. There is a salient dark area in Fig. 5 (left) of low coronal emission measure. In the major part of it, the variations are not particularly low. The magnetogram shows a large region lacking magnetic features (Fig. 2, left), characteristic for the interior of network cells. The 6 cm radio flux, shown in the same figure, is also extremely low. Both iron lines and radio emission are consistent with low coronal pressure in this region. In Fig. 6 the power spectra of the temporal variations in the most prominent lines are shown. The flux of the line emission between the spectral half-power points has been Fourier transformed in each pixel over the available observing time. The power spectra of all pixels were then averaged and logarithmically displayed. The Fe XII and Fe IX/X lines were observed by EIT, O V and He I by CDS, and C IV and C II by SUMER. Except for Fe IX/X at high frequency, they seem not to be much affected by noise. The spectral slopes have been fitted by powerlaws of the form P ν γ, corresponding to a regression in logarithmic representation. The accuracy of the fit is not determined by statistics, but by the upper cutoff of the fitted frequency interval. The error given in the following defines the range of values resulting from different choices of the cutoff. (i) The coronal lines, Fe XII and Fe IX/X (low frequency part) have relatively steep power-law indices with γ = 1.78±0.03 and 1.61±0.05, respectively. Similarly, Moses et al. (1997) have reported γ =1.70±0.15 for Fe XII, and Benz & Krucker (1998) find γ =1.69 ± 0.08 for the coronal emission measure.

7 292 A.O. Benz & S. Krucker: Heating events in the quiet solar corona Fig. 4. SoHO/SUMER observed alternatively in C II and C IV lines. All data have been combined into one image in each line (cf. Sect. 2). The field of view is in the central part of Fig. 2. The radio observations are identical to Fig. 3. Each UV spectral line is displayed thrice and overlaid with the radio contours at 2, 3.6, and 6 cm wavelength from left to right. (ii) The typical transition region lines O V and C IV have significantly flatter spectra with γ = 1.31±0.05 and 1.06±0.02, respectively. (iii) At the bottom end of the temperature scale, the spectral slopes become steeper again. The C II line has a slope of 2.02±0.10 in the low-frequency part, and the chromospheric He I line has γ = 1.80±0.22. Moses et al. (1997) report γ = 1.55 ± 0.1 for He II. It is difficult to interpret power spectra of flux variations since such temporal changes may have several causes. Changes in emission measure or density at a given temperature are possible in the corona when new material is added from the chromosphere. Variations in the temperature gradient can also change the emission measure of a given ion. As temperature gradients in the transition region are steep and the emission regions are small, the time scales in the transition region are generally short. This may explain the relatively flat spectrum of O V and C IV. Common to all spectra is their flat slope with γ 2. It indicates that high-frequency changes dominate the integration over frequency and hints at the importance of short-time changes for the energetics. This is consistent with the energy distribution of microflares having a steep power-law index and thus giving dominant weight to the small events (cf. Sect. 1) Cross-correlations in time In Fig. 7 the different emissions are cross-correlated in time relative to Fe XII. Pixels have been combined so that identical

8 A.O. Benz & S. Krucker: Heating events in the quiet solar corona 293 Fig. 5. The distribution of the enhancements of the emission measure in the quiet corona. The field of view measures and was observed for 42 minutes. Left The coronal emission measure as displayed in Fig. 2 (right) is shown for comparison. Middle All pixels that have a > 3σ enhancement in at least one time step (2 minutes) are indicated white. Right All pixels that increase only < 2σ in all time steps are indicated white. Fig. 6. The temporal variations of line fluxes are Fourier transformed in each pixel and averaged over all pixels of the field of view given in Sect. 2. The spectra are ordered in increasing ion formation temperature and are increasingly offset relative to He I. The power-law slopes are given in the text. picture elements of two emissions with equal position and size could be analyzed. Similarly, the time series of picture elements have been interpolated to the same time resolution in each emission. Linear trends have been removed, which had however little effect on the final result. The cross-correlations have first been made for all picture elements in common and then averaged over the overlapping fields of view. In all data sets many crosscorrelations with different pixel selections were made to test the stability of the results. Fe IX/X and Fe XII (Fig. 7, top) are well correlated as indicated by the peak coefficient of This is not surprising as both lines originate in the corona. Fe IX/X lags Fe XII by about 23 seconds, as determined from interpolation by a spline fit. The lag is consistent with the observation that the line-ratio temperature peaks in the rise phase for large network flares (Benz & Krucker 1998). Thus the hotter line peaks first, which, according to Fig. 7, is also the case for the cross-correlation, where smaller events dominate. The peak correlation dramatically decreases when Fe XII is compared to transition region emission, such as radio waves and O V. The low maximum value of the correlation coefficient is consistent with the low spatial cross-correlation at zero spatial lag found by Benz et al. (1997) for the soft X-ray emission of the corona. It can be explained by the spatial displacement of the coronal emission from the associated transition region sources, as e.g. footpoints are displaced from loop tops. We cannot exclude that the different pixel sizes and temporal resolutions of the various observations as well as the uncertainties of the coalignment also have contributed to the lower correlation. The 6 cm emission precedes Fe XII by about one minute. We have tested the stability of this result by ignoring pixels below a given average radio flux in the cross-correlation. The result reveals considerable scatter in the peak lag of the crosscorrelation for different thresholds. Restricting to pixels having radio fluxes above the mean value, the peak lag is 86 s, for a cutoff at intermediate levels it decreases to 8 s, but increases again to 82 s for the brightest two radio sources. We conclude from this that the timing of the 6 cm radio emission relative to

9 294 A.O. Benz & S. Krucker: Heating events in the quiet solar corona Fig. 7. Cross-correlation of the temporal variations of various emissions in relation to the flux of the coronal Fe XII line as determined from EIT observations. Pixels were adjusted to the same size and time interval. Then the time profile of each pixel was cross-correlated. The result was averaged over all pixels in common. Negative lag indicates that Fe XII is delayed. Fe XII is not the same for all variations. At 3.6 cm wavelength no correlation was found at first. Restricting the correlated pixels to the ones with radio fluxes above the mean value yields a peak correlation of 0.05 and peak lags of about 2 minutes. He I and O V precede Fe XII by about 5 minutes. The crosscorrelation between the two lines (not shown in Fig. 7) suggests that O V is about 4 s earlier than He I. The cross-correlation coefficient between the two lines is relatively high and peaks at 0.55, suggestive of close proximity of the two emission regions. 5. Discussion This multiwavelength comparison of quiet Sun emissions finds good spatial correlations between enhanced radiations originating at temperatures from the chromosphere to the corona. Moreover, the temporal variations are also found to correlate in general, but with various shifts between the different emissions. The time lags between (i) coronal line fluxes is of the order of a few tens of seconds. It can most likely be interpreted as a temperature effect. The temperature of the hot material of microflares peaks in the rise phase and cools subsequently. The coolest coronal lines, Fe IX/X, have been found to peak latest of all emissions observed. (ii) The radio emissions precede the coronal brightenings, but scatter between a few seconds and more than one minute. (iii) The transition region line O V having a maximum ion formation temperature of K precedes the coronal variations by about 5 minutes. In the average it is the earliest emission of all studied here. (iv) The He I line originates mostly from plasma below K, thus from the transition region and the chromosphere. It is delayed relative to O V by a few seconds at most. The significance of this should not be overemphasized since such a small delay may also be caused by a systematic difference in the time profile of variations. In the transition region, the sequence of the brightenings in different emissions is more difficult to establish by crosscorrelations as the timing scatters considerably in different events. The data are observed by different instruments (VLA and CDS), thus amenable to alignment errors. More important may be the possibility that the radio emission is not entirely thermal, as assumed so far. In fact, Krucker et al. (1997a) have noted that some of the radio bursts associated with network flares are more polarized than can be explained by thermal bremsstrahlung radiation. In addition, Krucker, Benz & Delaboudinière (1997b) have published the spectrum of the radio emission associated with a network flare showing clearly a decrease with frequency. Such a spectrum is indicative of gyrosynchrotron emission. On the other hand, the background radio emission is of thermal origin and may well fluctuate. Some of the scatter in the radio peak time observed here in cross-correlations may therefore be due to the superposition of two radio emission processes: thermal and gyrosynchrotron. The actual process may be identified from the spectrum, but this is only possible for the largest events and will be the aim of future work. In normal, active region flares, O V enhancements have been reported in subsecond temporal correlation with hard X- rays (Woodgate et al. 1983). Cheng et al. (1988) find that O V (1371 Å) lags behind hard X-ray bremsstrahlung emission by only 0.3 to 0.7 seconds. They interpret the O V enhancement and the good temporal correlation with hard X-ray time profiles by energy deposition of the precipitating electron beam of flare particles. It heats the upper chromosphere to some 10 5 K and excites O V line emission by collisions. He I may be excited in a similar way (e.g. Porter et al. 1989). If microflares in the quiet Sun are similar phenomena, the O V and He I emission preceding the thermal coronal emission may be interpreted analogously by precipitating electrons accelerated in the corona. A test of this hypothesis would be a close temporal correlation of centimeter gyrosynchrotron emission, acting as a proxy for hard X-rays. 6. Conclusions Small scale structures of the quiet solar corona have been investigated in time. Significant statistical correlations have been

10 A.O. Benz & S. Krucker: Heating events in the quiet solar corona 295 found in multiwavelength observations of fluctuations in the quiet transition region and corona. The largest variations, both in absolute values and relative to the preexisting coronal emission measure have been found in regions of already enhanced coronal emission measure. They are generally situated above the magnetic network. Identical pixels observed in different wavelengths from radio waves to coronal Fe lines have been cross-correlated in time. The peak correlation coefficient is relatively small as expected from the spatial displacements between enhancements in the corona and the lower layers reported previously. At first sight it may be surprising that the flux enhancements are found to occur last in the coronal lines. Apparently the coronal heating as observed in Fe IX/X and Fe XII is preceded by activity in the transition region and chromosphere. The coronal line fluxes have also been transformed into the coronal emission measure representative of the coronal plasma column depth above the pixel area. The cross-correlations find the enhancements of the coronal emission measure delayed by 5 minutes relative to O V and He I originating in the transition region and chromosphere. Furthermore, the cooler coronal lines, Fe IX X, are delayed by 23 seconds relative to the hotter Fe XII line. An enhancement of the coronal emission measure is thus characterized by an early peak in temperature and cooling during peak phase. The above sequences in time may be interpreted as an impulsive heating of cold material in the chromosphere to coronal temperature and a subsequent cooling. The cooling is partially by conduction, bringing adjacent plasma above the one million degree threshold and thus increases the coronal emission measure during the small events. Future progress in the understanding of the energy input into the corona will be a combination of statistical methods as applied here and the study of individual events. The former approach reaches the weakest events, the second way is necessary to study the details of the processes and to estimate the actual energy input. Acknowledgements. We thank Markus J. Aschwanden, Jean-Pierre Delaboudinière, Manuel Güdel, Richard A. Harrison and Davina E. Innes for clarifying discussions, and Tim S. Bastian, Barbara J. Thompson and David Pike for help with the observations. SoHO is a joint project between the European Space Agency, ESA, and NASA. EIT was funded by CNES, NASA, and the Belgian SPPS. The Very Large Array is operated by Associated Universities, Inc. under contract with the US National Science Foundation. The work at ETH Zürich is financially supported by the Swiss National Science Foundation (grant No ). References Bastian T.S., Dulk G.A., Leblanc Y., 1996, ApJ 473, 539 Benz A.O., Fürst E., 1987, A&A 175, 282 Benz A.O., Krucker S., Acton L.W., Bastian T.S., 1997, A&A 320, 993 Benz A.O., Krucker S., 1998, Solar Phys., in press Berghmans D., Clette F., Moses D., 1998, A&A, in press Brueckner G.E., Bartoe J.-D.F., 1983, ApJ 272, 329 Butz M., Hirth W., Fürst E., 1979, A&A 72, 211 Cheng C.C., Vanderveen K., Orwig L.E., Tandberg-Hanssen E., 1988, ApJ 330, 480 Delaboudinière, J.-P., et al., 1995, Solar Phys. 162, 291 Dere K.P., Bartoe J.-D.F., Brueckner G., 1984, ApJ 281, 870 Falconer D.A., Moore R.L., Porter J.G., Hathaway D.H., 1998, ApJ 501, 386 Fontenla J.M., Avrett E.H., Loeser R., 1993, ApJ 406, 319 (FAL) Gary D.E., Zirin H., Wang H., 1990, ApJ 355, 321 Gary D.E., Hartle M.D., Shimizu T., 1997, ApJ 477, 958 Golub L., Krieger A.S., Silk J.K., Timothy A.F., Vaiana G.S., 1974, ApJ 189, L93 Habbal S.R., Harvey K.L., 1988, ApJ 326, 988 Harrison R.A., et al., 1997, Solar Phys. 170, 123 Innes D.E., Inhester B., Axford W.I., Wilhelm K., 1997, Nat 386, 811 Krucker S., Benz A.O., Acton L.W., Bastian T.S., 1997a, ApJ 488, 499 Krucker S., Benz A.O., Delaboudinière J.-P., 1997b, In: The Corona and Solar Wind Near Minimum Activity, ESA SP-404, 465 Krucker S., Benz A.O., 1998, ApJ 501, L213 Kundu M.R., Alissandrakis C.E., 1975, MNRAS 173, 65 Kundu M.R., Rao A.P., Erskine F.T., Bregman J.D., 1979, ApJ 234, 1122 Moses D., et al., 1997, Solar Phys. 175, 571 Nitta N., 1997, ApJ 491, 402 Neupert W.M., 1968, ApJ 153, L59 Porter J.G., et al., 1987, ApJ 323, 380 Porter J.G., Gebbie K.B, November L.J., 1989, Solar Phys. 120, 309 Porter J.G., Dere K.P., 1991, ApJ 370, 775 Scherrer P.H., et al., 1995, Solar Phys. 162, 129 Shimizu T., 1995, PASJ 47, 251 Tarbell T.D., 1996, personal communication Ulmschneider P., Rosner R., Priest, E.R. (eds.), 1991, Mechanisms of chromospheric and coronal heating. Springer-Verlag, Berlin Van Driel-Gesztelyi L., et al., 1996, Solar Phys. 163, 145 Woodgate B.E., Shine R.A., Poland A.I., Orwig L.E., 1983, ApJ 265, 530 Wilhelm K., et al., 1995, Solar Phys. 162, 189