Rapid intensity and velocity variations in solar transition region lines

Transcription

1 Astron. Astrophys. 360, (2000) ASTRONOMY AND ASTROPHYSICS Rapid intensity and velocity variations in solar transition region lines V.H. Hansteen 1, R. Betta 2, and M. Carlsson 1 1 Institute of Theoretical Astrophysics, P.O. Box 1029, Blindern, 0315 Oslo, Norway (viggoh@astro.uio.no) 2 University of Pisa, Physics Department, Piazza Torricelli 2, Pisa, Italy (betta@astr11pi.difi.unipi.it) Received 23 March 2000 / Accepted 9 May 2000 Abstract. We have obtained short exposure (3 s) time series of strong upper chromospheric and transition region emission lines from the quiet Sun with the SUMER instrument onboard SOHO during two 1 hour periods in With a Nyqvist frequency of 167 mhz and relatively high count rates the dataset is uniquely suited for searching for high frequency variations in intensity and Doppler velocity. From Monte-Carlo experiments taking into account the photon-counting statistics we estimate our detection limit to correspond to a wave-packet of four periods coherent over 3 with a Doppler-shift amplitude of 2.5km s 1 in the darkest internetwork areas observed in C iii. In the network the detection limit is estimated to be 1.5km s 1. Above 50 mhz we detect wave-packet amplitudes above 3km s 1 less than 0.5% of the time. Between 20 and 50 mhz we detect some wave-packets with a typical duration of four periods and amplitudes up to 8km s 1. At any given internetwork location these wave-packets are present 1% of the time. In the mhz range we see amplitudes above 3km s 1 12% of the time. At lower frequencies our dataset is consistent with other SUMER datasets reported in the literature. The chromospheric 3 7 mhz signal is discernible in the line emission. In the internetwork this is the dominant oscillation frequency but higher frequencies (7 10 mhz) are often present and appear coherent in Doppler velocity over large spatial regions ( 40 ). Wavelet analysis implies that these oscillations have typical durations of 1000s. The network emission also shows a 5 mhz signal but is dominated by low frequency variations (of < 4 mhz) in both intensity and velocity. The oscillations show less power in intensity than in velocity. We find that while both red and blue shifted emission is observed, the transition region lines are on average red shifted between 5 10km s 1 in the network. A net red shift is also found in the internetwork emission but it is smaller (< 4km s 1 ). The line widths do not differ much between the internetwork and network, the non-thermal line widths increase with increasing temperature of line formation from 30km s 1 for the C ii 1334 Å line to 45km s 1 for the O vi 1032 Å line. By constructing scatterplots of velocity versus intensity we find that in the network a mean redshift is correlated with a high mean intensity. In the Send offprint requests to: V. Hansteen internetwork regions we do not find any correlation between the intensity and the Doppler velocity. Key words: Sun: chromosphere Sun: transition region 1. Introduction The quiet Solar transition region between the chromosphere and the corona is dynamic and structured. Variations or oscillations in spectral lines formed in the UV may give important evidence on chromospheric, transition region and coronal dynamics and energetics. Such variations in spectral line intensity and in spectral line shift have been observed in many UV lines, also in the quiet Sun (e.g. Vernazza et al. 1975; Bruner & McWhirter 1979; Athay & White 1980; Dere et al. 1981, 1984; Rabin & Dowdy 1992). The SUMER instrument, described in Wilhelm et al. (1995), offers the opportunity to observe UV spectral lines as well as continuum emission formed in the upper chromosphere and in the transition region roughly covering a temperature range from Kto K. The instrument has high spatial resolution; Lemaire et al. (1997) report a spatial resolution of 1.2 across the slit and 2 along the slit. Furthermore the spectral resolving power (λ/ λ ) allows one, in principle, to determine plasma velocities with an accuracy of 1km s 1 using an integration time as short as 3 s(wilhelm et al. 1995). This improvement in observing capabilities over previous instrumentation allows us to investigate the structure and the dynamics of the transition region at smaller length and time scales than has been possible in the past. Observations made previous to SUMER seemed to exclude any evidence of periodic oscillations in the solar chromosphere and transition region (Mariska 1992, pp.60 62). Vernazza et al. (1975) found changes in intensity of up to 50% in times as short as 1 minute, but no periodic oscillations, while they assert to find some evidence of the presence of shock waves. However several recent studies with the SUMER instrument (e.g. Carlsson et al. 1997; Judge et al. 1997; Vial & Kaldeich-Schürmann 1999) have reported finding oscillations in the frequency range 3 7 mhz.

2 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines 743 These observations were made with cadences of 15 s or longer. In this paper we wish to extend these studies by looking for fairly rapid time variations in a number of bright chromospheric and transition region lines with the SUMER instrument at a 3.0 s cadence. 2. Observing program The SUMER instrument is a normal incidence spectrometer with spectral range Å( Å in first order and Å in second order). The grating is spherical in Wardsworth mounting. The spectral band covered is approximately 44 Å in first order and 22 Å in second order for a given incidence angle θ on the spherical grating. The entire wavelength range is covered by varying the incidence angle on the spherical grating (θ goes from to ). This operation is performed rotating the plane scan mirror positioned between the slit and the grating and adjusting the focal length which (weakly) depends on the angle of incidence. First and second order lines are both dispersed on one of the two two-dimensional detectors (A and B), which consist of multi-channel plates which are divided up into 1024 spectral 360 spatial pixels. Note that there are no physical pixels but the pixel position is determined by timing. The two detectors are very similar but detector B has been placed at a distance det =70.4 mm from the grating normal on the focal plane giving a slightly different wavelength range. Only one of the two detectors is in use at a given time, detector A was used throughout the observations reported here. The central part of each detector spectral pixels on detector A and spectral pixels on detector B has been covered with an opaque material (KBr). Depending on the wavelength, this increases the instrument efficiency compared to the bare part of the detector. The observations were made in a quiet region, centered on Sun center covering regions typical of both network and cell interior. The data were taken on September from 01:03:24 UT to 07:23:51 UT and on September from 13:16:52 UT to 19:37:15 UT. A total of five lines were observed; in order to allow for the desired cadence of 3 s, strong lines were chosen with the added requirement that the upper chromosphere (C ii 1334Å) and lower (C iii 977, 1175Å, Si iii 1206Å) to middle (O vi 1032Å) transition region be covered. The instrument observed each spectral line for 75 minutes before going on to the next line; the total time of the full program was therefore 6 hours and 15 minutes. Each spectral line was observed in four phases (or items in SUMER parlance): first a 5 minute exposure of the entire detector (120 spatial 1024 spectral pixels) is obtained. This exposure is used in order to derive an absolute wavelength calibration as described below. Thereafter, a spectroheliogram of an almost square region (approximately km 2 on the Sun) is rastered. Each exposure in the raster scan was set to 3.0 s so the spectroheliogram completes in approximately 8 minutes. With the slit centered in this region at Sun center for the series presented here a time series lasting roughly 1 hour is obtained. The time series uses a spectral window of 25 pixels and an exposure time of 3.0 s for all lines except the C iii 1175 Å multiplet (which required 50 spectral pixels and a corresponding exposure time of 6.0 s). After the time series completes another spectroheliogram is obtained. Due to programmer error, rotation compensation was not on during the time series. The Sun accordingly rotates roughly 10 during the 1 hour observation as shown in Fig. 1. In order to keep the projected number of counts in the linear range of the detector (which requires an average rate < 10 cts s 1 pixel 1 ) all the spectral lines except the C ii Å line were positioned on the bare part of the detector. For the same reason the narrow slit was used for the C ii Å line (which was on the KBr portion of the detector), for the O vi Å and the C iii Å lines. 3. Data reduction The data have been reduced in the following steps using IDL software developed by Mats Carlsson and Viggo Hansteen (this software is freely available at matsc/sumer/): 1. The FITS files produced by the SUMER instrument team are concatenated and organized into specific observation items (e.g. calibration spectrum, spectroheliogram, or time series). 2. A flat-field correction is applied. The sensitivity of the detector area is non uniform on several scales and varies on the order of 50%. In addition the AD converter introduces a pattern where every other spatial row has different sensitivity (Wilhelm et al. 1997). Excepting the pattern introduced by the AD converter the pixels also move in time (or total count number on the detector) as can be ascertained by viewing the full flat fields taken every month or so by the SUMER team. In order to correct for these nonuniformities we have divided the data by a flat-field taken on September 11, the same day of our first set of observations. Note that this flat field does not have as long an exposure time as the full monthly flat-fields; we find that, due to the evolution of the flat field with time, it is preferable to use a flat field taken close in time to the actual observations even though the signal to noise ratio is poorer than in the full monthly flat fields. 3. A geometric distortion correction is applied. All the images have been modified using the destretch routine written by Tom Moran (this routine, along with the other SUMER routines mentioned below may be found in the SOHO software tree in an attempt to eliminate the geometric distortion due to the detector. This distortion is present in both directions: spectral and spatial (Wilhelm et al. 1997). Note that this correction is based on calibration data taken on the ground before launch and at different epochs during the flight. The motion of the detector pixels is therefore not accounted for and may introduce an erroneous correction which could impact the wavelength calibration, see below.

3 744 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines 4. An absolute wavelength calibration is computed using the 5 minute reference spectra as described in Sect An absolute intensity calibration is computed. This calibration is obtained by using the radiometry procedure written by Klaus Wilhelm and Werner Curdt. The calibration itself is described in Wilhelm et al. (1997). 6. Moments (total line intensity, line shift, line width) of the line profiles are computed as described in Sect Wavelength calibration The wavelength calibration is often done by making a polynomial fit to certain reference lines. There are several draw-backs to this method: Firstly, there is no a priori reason to expect a higher order polynomial functionality between wavelength and pixel position. Secondly, a high order polynomial needs a large number of reference lines. Instead of this traditional approach we have used the actual grating equation to set up our wavelength calibration; we therefore describe the method in some detail below. As mentioned above the wavelength calibration is achieved by using the reference scan taken prior to each spectroheliogram/time series/spectroheliogram set: vital to the success of the method is that the reference pixel, or angle of incidence, is kept constant for all four items. Given the observed reference spectrum the calibration is made in two steps: first, the pixel positions of likely chromospheric lines with known laboratory wavelengths are identified in the reference spectrum, thereafter these pixel position/wavelength pairs are used to derive the angle of incidence used in the observation. The angle of incidence then allows us to make a correspondence between pixel position and wavelength. The calibration is based on lines formed in the chromosphere which have small average absolute shifts (Samain 1991) and therefore allow the determination of an absolute wavelength scale. Since the spectroheliograms and time-series that follow the calibration spectra are observed with a constant angle of incidence (θ) on the grating, the wavelength calibration established for the calibration spectrum should be valid for the latter items as well. However, we have previously found by comparing lines formed in different atmospheric regions observed simultaneously that there is a slow drift in the instrument (due to temperature variations in the spacecraft, Rybák et al. 1999) with a period of a few hours, causing a change in the wavelength calibration with an amplitude on the order of a few km s 1. There are also other possible sources of systematic errors inherent in our calibration which we describe below. The reference spectra used in line identification are constructed by averaging the calibration spectra along the slit. This spectrum is plotted along a preliminary wavelength scale using the original SUMER dispersion relation, which is good to a few pixels or so (a pixel corresponds to roughly 10km s 1 ). Lines are identified by overplotting the identification and laboratory wavelengths from a suitable linelist; we have used the compilation of Phil Judge (private communication) and the compilation found in the SUMER Redbook (Vernazza & Reeves 1978; Sandlin et al. 1986). Due to the presence of many blended lines a correct identification of chromospheric lines may be difficult and requires care. This is exacerbated by the fact that both first and second order wavelengths are prominent and overlap in the SUMER spectrum. Once an identification is made, the pixel position of the line is calculated by matching the observed line profile with a Gaussian fit. We have evaluated the error in the determination of the centroid of the line profile by using Monte Carlo simulations of the fitting process taking into account Poisson counting statistics. A 91% confidence level gives an error estimate of 0.1 pixels. We have assumed that any errors in the laboratory wavelengths are smaller than this error. There are generally candidate chromospheric lines in a given spectral window ( λ 40 Å in first order). Blends and difficulties in identifying a particular line complicate the identification; of these lines we find that a reliable identification can be made for perhaps Given a set of wavelength/pixel position pairs we may proceed to derive the angle of incidence (as well as pixel size) by considering the grating equation for the spherical grating used in the SUMER spectrograph (Wilhelm et al. 1995): mλ = d (sin θ + sin α) (1) where m is the order, λ is a particular wavelength, d is the grating spacing (d = Å), θ is the angle of incidence on the grating and α is the angle of reflection off the grating. The geometry of the SUMER spectrograph implies that the angle of reflection α is related to the measured pixel position on the detector by sin α (n 512) px + det (2) f λ where n is the pixel position of the particular line on the detector (512 is the central pixel position on the detector), px is the pixel size, f λ is the focal length and det is the distance of the center of the detector from the position where cos α =1. Detector A has det =0mm while detector B has det =70.4mm. The pixel size is nominally given by px =27.0mm/1024 = µm, we will henceforth assume it to be constant across the detector. The effective focal length depends on the angle of incidence θ such that r a f λ = (3) 1 + cos θ where r a = mm is the radius of spherical concave grating. Using the relations above we find λ(θ) = d [ sin θ + (n 512) ] px + (1 + cos θ) (4) m r a The least squares best fit is found by minimizing, with respect to θ and px, χ 2 (θ) = N [λ i λ(px i,θ, px )] 2 i=1 σ 2 i (5)

4 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines 745 Table 1. Data from the wavelength calibration procedure, the error in the wavelength calibration (σ λ or σ v) is determined with a Monte Carlo simulation as described in the text. Day Line λ lab θ px N lines σ λ σ v [Å] [µm] [Å] [km/s] 11 C ii C iii C iii O vi Si iii C ii C iii C iii O vi Si iii where λ i is the laboratory wavelength and px i is the measured position of the spectral lines used, σ i is the estimated measurement error given by the error from fitting of the chromospheric reference lines to Gaussian profiles and by errors in the laboratory wavelengths and which, as discussed above, we estimated to be on the order of 0.1 pixels. In order to find the final statistical error of the wavelength calibration we have carried out a Monte Carlo simulation of the calibration process. These estimates are reported in Table 1: the errors are well within ±2km s 1. Aside from statistical errors, systematic errors must also be considered. The SUMER detector does not have physical pixels but rather relies on the timing of signals to define pixel position and areas. We therefore believe that the major source of systematic error comes from our assumption that the pixel size is constant across the detector. There are indications that the pixel size may be a function of the epoch, geometrical correction and/or slit position: Tom Moran reports in the destretch routine that the correction has a wavelength σ of 0.1 pixels with maximum deviations from the mean of 0.25 pixels. In his estimate the variation with epoch is not taken into account. Difficulties in finding reasonable wavelengths for lines that are observed near the boundary between the bare and KBr part of the detector lead us to believe that the pixel size may change rapidly there. For the present set of observations the O vi 1032 Å line is observed close to the bare KBr boundary and may be susceptible to systematic errors. In any case: taking all sources of error into consideration, with the possible caveat of any irregularities introduced by the variation with epoch and position on the detector, we estimate that the error in the mean velocities should be on the order of better than ±2km s Determination of velocities and intensities The total line intensity, line shift and line width are computed from the zeroth, first and second moments of the line intensity with the continuum intensity subtracted. The observed line width is the sum of the instrumental contribution λ instr (as calculated in routines written by Klaus Wilhelm) and the Doppler width σ so that λ 2 = σ 2 + λ 2 instr (6) From this relationship we may derive non-thermal velocities ( c 2 ξ = λ 2 σ 2 2k ) 1/2 BT (7) 0 M where c is the speed of the light, λ 0 is laboratory wavelength of a particular line, k B is Boltzmann s constant, M is the emitting ion mass and the temperature T is the temperature of maximum ion concentration. 4. Line Formation In order to get a feeling for the significance of the measured absolute intensities and the difference between cell interior and network emission we have constructed a number of simple chromosphere and transition region models. The temperature structure in these models is a result of radiative equilibrium and a conductive heat flux F c from a corona at a temperature of 1 MK. This energy flux flows back into the chromosphere by thermal conduction forming the transition region interface between the corona and chromosphere. Varying F c will either move the transition region down towards higher densities if F c increases, or move it upwards towards lower densities if F c decreases as described by Rosner et al. (1978). Since the line intensities scale with the densities squared and the extent of the line forming region (proportional to the temperature gradient) varying F c will vary the transition region line intensities. Added to the model is incident radiation from the corona which is absorbed in the helium continua and which heats the upper chromosphere to about 10 kk. We find that the emission in the C ii 1334 Å line has about equal contributions from the upper chromosphere and the lower transition region. The majority of the emission from the Si iii 1206 Å line comes from the lower transition region where the Si iii ion has maximum abundance, at 30 kk. This line has also a small contribution from the cooler upper chromosphere but based on our models we do not believe that this contribution ever exceeds 20% of the total intensity in the line: when using the much simpler optically thin assumption in computing the line intensity, no significant differences were found. The emission from the other lines, C iii 977 Å and 1175 Å, and O vi 1032 Å, is found to be effectively thin and concentrated to the transition region roughly at temperatures of 80 kk and 320 kk. 5. Observations 5.1. Description of the surrounding region In Fig. 1 we display spectroheliograms taken in four different lines. We show the images taken before the time series on September 11. Spectroheliograms taken 3 days later, on September 14, do not reveal qualitative differences. The observations cover regions that can be characterized as network as well as regions that can be characterized as cell interiors. Rotation compensation was not operating during the observations so the raster images taken before and after each time series (phase 2 and 4 of the observation) show 10 shift. However, by comparing these spectroheliograms it is clear that the network pattern

5 746 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines Fig. 1. Spectroheliograms taken at different times in four different lines of increasing temperature: Cii 1334Å (T K), Siiii Å (T K), Ciii Å(T K), and Ovi Å (T K). The white solid line marks the position of the slit at the beginning of the time series, while the dashed line shows the position of the slit just after the time series is completed. remains fairly stable during the 1hr long time series. In fact, inspecting the images in Fig. 1 counterclockwise starting with C ii 1334 Å we can recognize the same patterns in all the images as they rotate across the disk. The images were obtained in the order C ii 1334 Å, C iii 1175 Å (not shown), C iii 977 Å, O vi 1032 Å, Si iii 1206 Å. Cell interiors as seen in C ii 1334 Å are roughly circular with dimensions on the order of The network emission in this line encircles the cell interiors. As the temperature of line formation increases this pattern is still apparent but the size of a typical cell interior decreases while the network emission seems to contain more small scale structures. Along with the general network/cell interior structure all the lines also show hot spots of enhanced network emission over regions that are roughly of size 5 5. Picking out typical cell interior and bright network regions from the September 11 images we find that the average brightness contrast between them decreases with increasing temperature: for C ii 1334 Å a ratio of 10 is found, for Si iii 1206 Å a ratio of 7, for C iii 977 Å a ratio of 5.5, and for O vi 1032 Å we find a ratio of brightest to darkest emission of 4.5. These ratios are constructed from averages over fairly large regions, if we pick smaller regions with dimensions on the order of a few arc seconds we typically find brightness ratios on the order of say 100. Note that the ratios are reported as a rough guide only; the observations on September 14 give slightly different results. The average values found for the absolute values of the intensities in various regions are shown in Table 2. Note that we see transition region emission at all locations, even in the internetwork.

6 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines 747 Table 2. Measured absolute intensities in the spectroheliograms. All intensities in W/m 2 /sr Day Line λ [Å] Max I Average intensity All Cell Network 11 C ii Si iii C iii O vi C ii Si iii C iii O vi Comparing the intensities of the transition region lines with our computed models we find that a conductive flux F c between 30 Wm 2 and > 1000 Wm 2 is required. The required energy flux is larger in the network and decreases with increasing line temperature for both network and internetwork. It has been known for some time (see e.g. Mariska 1992) that reproducing transition region emission in a manner that is consistent for all temperature ranges is very difficult without introducing local heating in order to stretch out the line forming region for the lines formed in the lower transition region Temporal variations Let us now consider the time series. The slit was kept in a fixed position, with no compensation for solar rotation, and exposures were made with a cadence of 3 s. We will concentrate most of our attention on the moments of the line profiles, but before we do so let us inspect the line profiles themselves at three positions, sampling typical internetwork and network emission. These line profile figures should be compared with the raster images (Fig. 1), the XT intensity and velocity time-series images (Figs. 4 and 5) and the wavelet images (Figs. 7 and 8) Line profiles Line profiles as functions of time of the two lines formed in the upper chromosphere/lower transition region are shown in Fig. 2. The C ii 1334 Å emission has contributions from both the upper chromosphere and from the lower transition region. The line profiles shown are taken from slit position 38, 60 and 105. Slit position 38 represents (weak) network emission while position 60 and 105 represent the internetwork. The Si iii 1206 Å line is formed in the lower transition region in plasma that has a temperature of roughly 30kK. The line profiles are taken from slit position 20, 61 and 70. While there are really no good examples of clean network or internetwork emission along the slit for this line (see Fig. 1) we will let slit position 20 represent network emission, slit position 71 internetwork while slit position 61 is a combination of the two. There are no obvious periodicities in the network line profiles; brightenings occur with timescales on the order of roughly s in both datasets, sometimes accompanied by line shifts with amplitudes of roughly 10km s 1 and line broadenings. There is also a longer period trend (brightening) especially evident in the C ii profile at slit position 38 which we believe is due to the rotation of a network element onto the slit. The Si iii line profile appears broader and also appears to experience larger amplitude modulations than the C ii profile. The internetwork emission, while exhibiting the same s brightenings seen in the network profiles, also shows clear evidence of periodic motions: the line profiles are shifted with periods on the order s. There is no clear intensity modulation associated with this periodic shift. We will discuss these periodic modulations in depth later in the paper. Notice that the Si iii emission from position 61, which represents weak network emission, also shows evidence of periodic modulations. We find that this may be typical: there appears to be a periodic variation at roughly 200s in the line profiles at all positions, except for regions of strong network emission. The C iii 977 Å and O vi 1032 Å lines are formed in the middle transition region at 80 kk and 320 kk respectively. Line profiles as functions of time are shown in Fig. 3. The slit positions chosen for C iii are 24, representing network emission, 38 representing the border between the network and the internetwork, and 58 which is internetwork emission. The first 700 s of emission at slit position 24 is dimmer than the rest and is probably from the internetwork. For the O vi line profiles we have chosen slit position 20 for network emission and position 73 for the internetwork while slit position 40 which is a mix of internetwork (during the first 1500 s) and network emission was chosen to show the two most violent events that we noted on either September 11 or September 14. The network emission for these lines seem similar to that of the upper chromospheric/lower transition region lines in that variations are mainly seen as brightenings with typical durations of s, sometimes accompanied by line broadenings and line shifts. It should be noted that the C iii line profile clearly becomes more red-shifted (positive velocity shift) after 700 s when a region more typical of the network rotates onto the slit, see Fig. 1. A similar phenomena can be seen in the O vi emission from position 15 in the period 1150 s to 1900 s where the line profile brightens while, at the same time, becoming noticibly more red-shifted. In the internetwork emission we again observe that the line profile oscillates with periods on the order s. There are no obvious brightenings associated with this periodic line shift. These periodic modulations appear to come in packets with durations on the order 1000 s as may be seen from inspection of the line profile at position 58 for the C iii line and (less clearly) position 73 of the O vi line. The line emission that comes from positions situated between the internetwork and network shows quite violent events in both lines: we see line shifts and broadenings with amplitudes > 50km s 1, in the case of the O vi line we see two events with amplitudes > 100km s 1, the first at 700 s has both a blue- and red-shifted component while the second at 1000 s is primarily blue-shifted. The variation in the C iii emission is from a region

7 748 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines Fig. 2. Line profiles as a function of time for C ii Å, and Si iii 1206Å at various positions along the slit. For C ii position 38 represents network emission while positions 60 and 105 represent the internetwork. For Si iii position 20 represents the network, 71 represents the internetwork while position 61 is a combination of the two. Negative velocities are blueshifts. that constitutes a true border between the network and internetwork and in vigorous motion during the entire observational series. On the other hand, the O vi events seem to jump out of the blue and occur in an otherwise quiescent internetwork region, the timescale of these events is close to or shorter than the exposure time of 3 s Low and intermediate frequency intensity and velocity variations In Figs. 4 and 5 we show intensity and line shifts moments, on the abscissa as functions of position along the slit, and on the ordinate as functions of time. The panels on the left show the intensity, high intensity is light. The panels on the right show the velocity such that blue-shifted (negative) velocities are light while red-shifted velocities are dark. Fig. 4 shows the chromospheric C ii 1334 Å and the lower transition region Si iii 1206 Å lines while Fig. 5 shows the transition region C iii 977 Å line and the upper transition region O vi 1032 Å line. The C ii 1334 Å panels show that slit position (see also Fig. 1) is brighter network emission, while slit position , except for a patch around position 80, is dimmer cell interior emission. The intensity moment varies in time both in the network and in the cell interior. The average internetwork intensity is only 0.4W m 2 sr 1 and it is from the figure difficult to see any variations in the

8 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines 749 Fig. 3. Line profiles as a function of time for, C iii 977Å, and O vi 1032Å at various positions along the slit. For C iii position 24 represents the network, 38 is on the border between network and internetwork, and 58 is internetwork emission. For O vi position 20 is network, position 73 is internetwork while position 40 is a mix of the two; the first 1500 s are internetwork emission. Negative velocities are blueshifts. intensity for this region. On the other hand, the velocity moment clearly shows oscillations with periods on the order of 3 minutes and amplitudes on the order of ±5km s 1. The oscillations seem coherent on a spatial scale of some 5 10 and are reminiscent of the oscillations reported by Carlsson et al. (1997) though the spatial scale for these oscillations may be somewhat larger. The network emission seems to consist of regions of scale 5 that vary irregularly in time on timescales of some hundreds of seconds. The velocity moment in the network varies on a similar spatial and temporal scale; correlations between variations in intensity and velocity occur, though sporadically. Notice that the velocity signal in the network portion of the slit is clearly red-shifted on average and that there are very few events that give rise to blue-shifted emission. The cell interior emission is more evenly balanced between red- and blue-shifts. The time series made of the Si iii 1206 Å line which is formed at a slightly higher temperature than C ii, shows an intensity and velocity signal very similar to the C ii 1334 Åline. Moving up in temperature into the lower transition region we have two C iii lines which are formed at roughly 80 kk. These lines are optically thin and should be somewhat simpler to model and to use diagnostically than the lines described above. Nevertheless, we find essentially the same pattern as for the C ii and Si iii line: a clear dichotomy between emission formed in the network and in the cell interiors. The C iii 977 Å line shown in the upper panels of Fig. 5 shows network emission that en-

9 750 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines Fig. 4. Total line intensities (left) and line shifts (right) for C ii 1334Å (top) and Si iii 1206Å (bottom) as a function of time (y-axis) measured along the slit (x-axis). Blueshifts are white while redshifts are black compasses slit positions and , the remainder of the slit shows cell interior emission. Again, there are no obvious periodicities in the intensity signal, but brightenings seem to occur on timescales of a few hundred seconds. The gradual disappearance of network emission at position 40 and the gradual appearance of network emission at position 75 are almost certainly due to solar rotation. Comparing the network intensity and velocity signal we note that some, but not all, of the intensity brightenings are accompanied by line shifts up to ±20km s 1 in either blue and red directions. The largest line shifts seem to occur in the network or in the border area between network and cell interior; for example following slit position 40, brightenings accompanied by both blue and redshifts are visible. It is difficult to see any variation in the internetwork intensity but

10 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines 751 Fig. 5. Total line intensities (left) and line shifts (right) for C iii 977Å (top), and O vi 1032Å (bottom) as a function of time (y-axis) measured along the slit (x-axis). Blueshifts are white while redshifts are black the velocity signal in the cell interiors shows a clear periodicity with a period of roughly 3 minutes or shorter and amplitude on the order of ±10km s 1. The spatial coherence of this oscillation seems to have increased from that seen in the C ii data to fill the entire supergranular cell and has a spatial scale of some It is hard to tell whether or not these oscillations extend into the network portion of the emission. The O vi 1032 Å line represents emission in the middle/upper transition region (i.e. above the minimum in traditional transition region emission measure curves). The lower panels of Fig. 5 presents the variation of the intensity and velocity moments of this line. Though this line is formed in a region where the typical electron temperatures are on the order of 320 kk the comments applied to the lines discussed previously

11 752 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines Fig. 6. Power spectra of the intensity and velocity signal for the C ii 1334 Å, C iii 977 Å, and O vi 1032 Å lines, averaged over typical internetwork (left panels) and network (right panels) regions. The velocity and intensity signals are averaged over the slit positions given in the figure and should be compared to Fig. 1. The dashed lines show our estimate of the noise level in these spectra derived using Monte Carlo simulations. also apply here: the network intensity shows brightenings with durations on the order of several hundred seconds or so, there are no obvious periodicities in the intensity variations while the (cell interior) velocity signal shows a clear periodicity on the order of 3 minutes. Notice that the coherence region for the oscillations in the O vi line is also large, at least on the order of 20. In addition to these phenomena the two violent events discussed in connection with Fig. 3 are clearly discernible at slit location 40 time 700 s and 1000 s. Further information on the variations in the intensity and velocity may be found by considering the power spectra of the moments in certain positions. The power spectra of the velocity signal and intensity signal in the September 11 data for the C ii, C iii 977Å, and O vi lines are shown in Fig. 6. In the figure the

12 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines 753 left hand panels show internetwork power while the righthand panels show network power. The intensity and velocity signals have been averaged over the slit positions designated in each panel. The intensity power is plotted in the first, third and fifth panels from the top while the velocity power is plotted in the second, fourth and sixth panels from the top. The signals have been treated with a Hann window in order to reduce the leakage of power across frequency bins. We did not find any appreciable difference between power spectra generated with the Hann window and the power spectra generated with a square window. The noise level plotted as dashed lines in all the panels of Fig. 6 was estimated by computing the power contained in random (Poisson), artificial data with the same average intensity as the real data at each spatial position. Displayed in the figure is the average of the estimated noise found at high frequencies. Power at frequencies below 2 mhz should be disregarded in these plots since the solar rotation will move new structures onto the slit on time scales corresponding to this frequency. Fig. 6, top left panel, shows the C ii intensity signal from internetwork emission. Evident are peaks at 3 and 6 mhz and a marginally significant peak around 10 mhz. We do not find any power above the noise level in the region mhz. By comparison, the network intensity signal for the same line shown in the top right panel displays a peak at 2.5 mhz and (weaker) peaks at 5 and 7 mhz. The C ii velocity signal for the internetwork and network are shown in the second panels from the top. In the internetwork we find power in a band from mhz with peaks at 3, 4, 6 mhz and another peak around 10 mhz. In the network we also find power in this range but there is less power than in the internetwork and the band is shifted towards lower frequencies, we find peaks at 4, 6 and perhaps 12 mhz. The power spectra of the velocity signal and intensity signal for the C iii 977 Å line is shown in the third (intensity) and fourth (velocity) rows of panels from the top in Fig. 6. The intensity signal shows a broad peak from 6 10 mhz along with a weaker peak at 12 mhz in the internetwork emission. The network intensity also has power in a band starting at 2 mhz with peaks at 4, 10 and perhaps 15 mhz. Aside from the high frequency peaks at 10 and 15 mhz, the power is located at lower frequencies in comparison with the internetwork emission. The internetwork velocity signal shown in the left panel has power in a band from 3 mhz to 12 mhz with a large peak at 6 mhz. The network velocity signal does not show the obvious peaks seen in the internetwork panels, but some power is visible at frequencies up to roughly 15 mhz. Again, aside from some high frequency peaks, the power spectrum seems shifted towards lower frequencies when compared with the power measured in the internetwork. The O vi line power spectra are shown in the fifth (intensity) and sixth (velocity) rows of panels from the top of Fig. 6. The intensity signal shows peaks at 3, 5, and 10 mhz both in the internetwork and in the network. We also find excess power in the velocity signal from both the internetwork and network in a band from 3 mhz to (at least) 10 mhz, though the data are noisier than for the C ii and C iii 977 Å lines. Observations/power spectra of the O vi 1032 Å line are also discussed in Wikstøl et al. (1998). Consideration of Figs. 2 5) shows that variations are often episodic, occuring only during part of the full time sequence. A power spectrum analysis will pick out the periods that are present during the whole sequence and smear out periods that are present only during parts of the sequence. We have therefore performed a wavelet analysis of the intensity and velocity signals. Figs. 7 and 8 show the wavelet power as function of time and frequency for the C ii and C iii line intensities (left panels) and line shift (right panels) for the same slit positions as in Figs The noise level in the wavelet analysis have been determined by random addition of Poisson counting statistics noise. Figs. 7 and 8 only show the power that is above this noise level. Fig. 7 displays the wavelet power for intensity (left) and velocity (right) of the C ii line. The network slit position 38 shows power at mhz in both intensity and velocity during the entire time series, there is also power at 4 mhz and, in intensity, near 5 mhz especially during the period from 500 s to 1500 s. There is also sporadic higher frequency power between 10 and 15 mhz evident in the intensity signal. The internetwork slit position 60 shows power at 3.5, 4.5 and 7 mhz, the latter most clearly in velocity. The internetwork slit position 105 shows power at 4 and 5.5 mhz in both velocity and intensity. There are instances of high frequency power at 10 mhz around 2000 s and 3000 s which are related to the brightenings obvious in Fig. 2. There is also high frequency power near 15 mhz in the velocity signal starting at 500 s, the source of this power is not obvious on inspecting the line profile in Fig. 2. Fig. 8 displays the wavelet power for intensity (left) and velocity (right) of the C iii 977Å line. The network slit position 24 shows significant power around 3 mhz, mainly visible in the intensity signal, towards the end of the sequence. There are also episodes with higher frequency power. The intermediate slit position 38 shows high frequency power close to t=2000 s and t=2400 s corresponding to the explosive events seen at those times in Fig. 3. The cell interior slit position 58 shows strong power close to 7 mhz close to the beginning and end of the time sequence. This is also evident in Fig. 3. In general, considering the Fourier power and wavelet transform spectra, we find there are clear differences between network and internetwork emission. The internetwork almost invariably shows power in a band between 3 and 10 mhz, this band usually contains at least two or three peaks but the exact location of these peaks varies with spatial location and time. We estimate the typical spatial scales of these variations to be on the order of 3 5 while the typical timescales are estimated to be close to 1000 s, though one should bear in mind that the observations are conducted for the comparatively short duration of one hour. In contrast, the network emission does not contain a maximum of oscillatory power between 5 7 mhz but rather at lower frequencies; since rotation compensation was turned off one cannot tell from this data set whether the maximum power in the network is concentrated close to 3 mhz or at even lower frequencies. This difference is visible in all lines

13 754 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines Fig. 7. Wavelet power as function of frequency and time for C ii 1334Å. The positions are the same as those shown in Fig. 2, slit position 38 represents (weak) network emission while position 60 and 105 represent the internetwork. observed here but is perhaps less pronounced in the hottest line O vi1032 Å. Discussing lines formed deeper in the chromosphere, Lites et al. (1993) reached similar conclusions with respect to the difference between network and internetwork emission High frequency intensity and velocity variations We have extended the wavelet analysis of the previous section to frequencies up to 150 mhz. At these higher frequencies the estimate of the noise level is crucial. We have estimated the noise caused by counting statistics through Monte-Carlo simulations. A Gaussian profile with position, width, maximum number of counts and continuum level taken from the observed profile was taken as a proxy for the real intensity profile. A large number of realizations were generated using Poisson-statistics. Each realization was treated in exactly the same way as the observations (running mean over three slit-positions, moment calculation, wavelet analysis). The noise level was chosen to be the level where 99.5% of all noise realizations had a lower wavelet amplitude. In order to give the noise level understandable units this level was compared with the wavelet amplitude generated from an artificial signal: We chose a wavepacket containing four periods oscillating with a frequency of 40 mhz. The noise levels reported below do not vary significantly with frequency nor with the characteristics of the artificial signal. For the C iii 977 Å line velocities we find that the noise level corresponds to a wavepacket amplitude of 2.4km s 1 for internetwork intensities and 1.5km s 1 for network intensities. The line velocities shows quite a bit of high frequency power in the internetwork. Fig. 9 shows the percentage of the signal that has wavelet power above the signal given by a 3.0km s 1 four period 40 mhz signal, comfortably above the derived detection limit. In the internetwork we find that more than 20% of the emission has significant wavelet power at 10 mhz, this falls to 5% of the emission at 20 mhz. Above 20 mhz the percentage of wavelet power falls rapidly towards the noise level, hovering around 1% of the observed emission. The percentage of high frequency emission in the network is lower, starting at 15% at 10 mhz and rapidly falling below the detection limit at 15 mhz. The figure was derived with data from September 11th. The dataset from September 14th gives very similar results. Inspection of the line profiles themselves show that the high frequency events often occur where complex, non-gaussian, line profiles

14 V.H. Hansteen et al.: Rapid intensity and velocity variations in solar transition region lines 755 Fig. 8. Wavelet power as function of frequency and time for C iii 977Å at various positions along the slit, position 24 represents the network, 38 is on the border between network and internetwork, and 58 is internetwork emission. containing several maxima are found. The variation of the line shift only gives a small hint of the possibly complex dynamics that underly these events. The positions where we find significant high frequency amplitudes in the internetwork is not randomly distributed but rather tends to concentrate in regions that lie close to the network. This behavior is illustrated in Fig. 10 where we show the total line intensity in the C iii 977 Å line plotted as a function of time and space overlayed the positions where the wavelet power in the frequency range mhz is significantly above the noise level. The C ii 1334 Å line has count rates very similar to those of the C iii line and also very similar wavelet noise levels. However, in contrast to that line we find very little high frequency wavelet power in the C ii line velocities both in the network and in the internetwork: Using a detection limit of 3km s 1 for the internetwork we find that less than 1% of the emission shows evidence of wavelet power even in the mhz range. The slit positions between (see Fig. 4) has internetwork emission with a somewhat higher countrate: in that region we may use a detection limit of 2km s 1, we still find that less than 2% of the C ii line velocities show any wavelet power above the noise. The wavelet amplitudes for the intensity signal of both carbon lines has also been extended to 150 mhz. We find results that are very similar to those reported for the line velocities: In the C iii line significant wavelet amplitudes are found above 10 mhz preferentially in the internetwork, but often tending to be close to the network boundary. Likewise, we find little wavelet signal above 10 mhz in the C ii line intensities (an exception can be found in Fig 7 position 105). For both lines the high frequency velocity and intensity wavelet amplitudes often coincide in time and space, though this is not always the case: Figs. 7 and 8 show examples of both coincident and noncoincident wavelet amplitudes. The O vi 1032 Å line has a lower count rate than the C ii and C iii lines, and interpretation of the wavelet power is correspondingly difficult. A wavelet analysis of the velocity and intensity signals seems to indicate that there is rather more high frequency power in this line than in the two cooler carbon lines, but the high noise level precludes us from making any definitive statements.