Electron density and temperature

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. A5, PAGES , MAY 1, 1999 Electron density and temperature solar corona of the lower A. Fludra, G. Del Zanna, 2 D. Alexander, 3 and B. J. I. Bromage 2 Abstract. Off limb observations of the quiet Sun corona were made with the Coronal Diagnostic Spectrometer (CDS) on SOHO during the Whole Sun Month campaign in August Selected spectral lines in the Normal Incidence range were recorded up to 1.2 solar radii above the east and west limb and above the polar coronal holes. Intensities of the coronal lines covering the temperature range from 9 x 10 s to 2 x 10 e K have been measured and used to derive electron temperature and electron density as a function of the radial distance above the solar limb. Results from the east and west equatorial regions and polar coronal holes are compared. The temperature and density in the coronal holes is found to be lower than in the closed field regions. A density-sensitive line ratio of Si IX 350/342 is used to derive an averagelectron density which is found to decrease from 5 x 108 crn -3 near the limb to 1 x 108 cm -3 t 1.15Rs, in the equatorial region. Over the polar coronal holes, where polar plumes dominate the emission close to the limb, the density varies from 2 x 108 cm -3 at the limb to 6 x 107 cm -3 at 1.1Rs. The lowest density found inside the coronal hole on the disk is 9.9 x 107 crn -3. An increase in the quiet Sun temperature with the radial distance is found from the Si XII/Mg X and Si XII/Mg IX line ratios, and an increase in the coronal hole temperature is seen from the Mg X/Mg IX ratio. The Si XII/Mg X temperature varies from 1.1 x 10 e K at r- Rs to 1.4 x 10 e K at r- 1.2Rs in the equatorial regions. The EUV emission is compared with that of the soft X rays as measured by the Yohkoh SXT. The densities and temperatures determined from the SXT show a similar behavior to that determined from the CDS. Density and temperature, averaged over a position angle range of ø, show very little variation over a period of 20 days. 1. Introduction Modeling of the three-dimensional structure of the solar corona requires an accurate empirical description of the coronal plasma parameters (densities, temperatures, and velocities) for the coronal holes, coronal streamers, and the finer structures in the lower corona. Coronal holes are known as regions of low density, associated with open magnetic fields, and sources of the high-speed solar wind. The mechanism of coronal heating leading to the fast solar wind acceleration is still unknown. Various theoretical models, going beyond the thermally driven wind model by adding a direct deposition of momentum from MHD waves, have been investigated [e.g., Leer et al., 1982]. The models are sen- 1Space Science Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, United Kingdom. 2University of Central Lancashire, Preston, United Kingdom. 3Lockheed Martin Solar & Astrophysics Lab., Palo Alto, California. Copyright 1999 by the American Geophysical Union. Paper number 1998JA /99/1998JA sitive to the values of electron temperature and density at the base of the corona. Therefore density and temperature measurements above polar coronal holes can provide boundary conditions and constraints on theoretical mechanisms of heating the coronal plasma and accelerating the fast solar wind. Observations of closed-field regions give information on large-scale structure of coronal streamers and on smaller structures which make up the diffuse corona. The knowledge of radial temperature and density profiles provides information about where nonthermal energy is deposited and helps determine the coronal heating mechanism. Studies made near the solar minimum when the active regions are almost absent are particularly useful. The determination of the temperature-density structure of the solar corona, both in the regions of closed magnetic field and in coronal holes, has therefore been of considerable interest for many years. Early offlimb intensity studies were performed by Kastner et al. [1974] using OSO 7 observations of the quiet Sun in various iron lines. Skylab EUV intensity data were used by Mariska and Withbroe [1975], Mariska el al. [1978], and Feldman el al. [1979]. Coronal hole temperatures were discussed, for example, by Doschek and Feldman

2 9710 FLUDRA ET AL.: ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA [1978], and Itabbal et al. [1993]. Feldman et alo [1978] used a density-sensitive line ratio of S X lines to determine he density in the quie Sun and active region areas up o 40 arcsec above the limb. O her recent studies determined temperature and density s ructure of the solar corona from a combination of K-coronal brightness and polarization brightness (from eclipse or coronagraph observations), the green (Fe XIV ) and red (Fe X ) coronal for- bidden lines, and EUV images from a sounding rocke [e.g., Guhaihakurta et al., 1992, 1996]. Coronal temperatures from X-ray observations were derived by Foley e! al. [1997], $turrock et al. [1996], Wheatland e! al. [1997] and Alexander [ his issue]. However, none of he coronal hole density measurements a coronal temperatures made before the launch of SOHO used a density-sensitive line ratio. The Coronal Diagnostic Spectrometer (CDS) [Harrison et al., 1995] and SUMER spectrometers on SOHO contain several useful density-sensitive line pairs in their wavelength ranges and thanks to a very good sensitivity of these instruments, the density-sensitive lines record enough photons even inside the coronal holes to provide a measurement of electron densities. Doschek et al. [1997], Laming et al. [1997] and Warren [this issue] present densities from density-sensitive line ratios recorded by SUMER. Electron temperature above polar coronal hole has been derived from combined CDS/SUMER data by David et al. [1998]. Del Zanna and Bromage [this issue] present a detailed study of temperature and density obtained from on-disc CDS observations of a large equatorial coronal hole. In this paper, we describe above-the-limb observations of the quiet Sun made by the CDS in the closedfield regions in the equatorial plane and the open field regions above the polar coronal holes. CDS complements and allows many of the past results to be significantly improved in terms of spectral and spatial resolu- tion, and diagnostic capabilities [see Harrison and Fludra, 1995, Table 1.4]. In particular, it can provide electron density and temperature measurements both on the solar disk and above the limb up to 1.3Rs, includ- ing measurements very close to the limb, at distances unavailable from the white-light observations, which are usually restricted to heights greater than 1.15Rs. The CDS observes the Sun in the wavelength range were present, these areas were excluded from analysis, ]k, containing a number of coronal lines that provide and only the quiet part of the solar corona was analyzed. temperature and density diagnostics. The CDS mea- CDS data were processed by applying a standard insurements described in this paper use spectral lines from tensity calibration. CDS spectra were then spatially a Si IX ion which are not available in the wavelength averaged along concentric arcs at fixed heights above range of the SUMER instrument. the limb, usually in a position angle range of CDS observations made in August 1996, during the near the equator. This averaging is needed to improve Whole Sun Month campaign, provide the largest data the signal to noise in the weak lines of Si IX that provide set of electron density measurements from density- sensitive spectral lines. In this paper, 6 days of observations of equatorial regions and four observations of polar coronal holes made over a period of 3 weeks are compared to monitor spatial and temporal variability of electron temperatures and densities. CDS results from two selected days are compared to temperatures and densities derived from soft X-ray images recorded by the Soft X-ray Telescope (SXT) on Yohkoh. In a separate study, the electron densities derived in this paper will be combined for the first time with the white-light densities to produce an empirical model of a coronal streamer [Gibson et al., this issue ] and a polar coronal hole [Guhathakurta et al., this issue]. Observational data are discussed in section 2. The estimation of electron densities and temperatures is described in section 3. Section 4 describes a comparison of EUV and X-ray results. Conclusions are given in section Observations 2.1. Equatorial Regions Above the East/West Limb During the Whole Sun Month campaign in August 1996, CDS used a 4" x 240" slit and a 30 s exposure to build a 4 x 4 arcminute 2 raster. The following lines from the normal incidence range of CDS, covering temperatures from the chromosphere, transition region to the corona, were selected: He I 584, He II 304 (second order), O V 630, Mg IX 368, Mg X 625, Si XI 303 (second order), Si IX 342, Si IX 350, Si XII 521 ]k. The duration of one raster was 37 min. A mosaic of four rasters was made to cover a 4 x 16 arcminute 2 area. Figure 1 shows images made in the Mg X 625 and Si XII 520 ]k lines at the west limb on August 19, Observations like this were made regularly every few days from August 12 to September 6. From this larger data set, we have selected NIS data taken on 6 days for analysis in this paper. We selected three pairs of dates approximately half a solar rotation apart: August 12 and 27, August 15 and 30, and August 19 and September 3. This allows us to compare the same location viewed both on the east and west limb to check the time variability in the coronal structure. In addition, the dates of August 12 and 19 (and August 27, September 3) are 7 days apart, thus sampling different areas separated by 900 in longitude. All of the images taken on the above dates contain quiet Sun areas, in most cases free from any active region emission. In two cases where active region loops the density diagnostics. Gaussian profiles were fitted to such averaged spectra (including multiple Gaussians in the case of blended spectral lines). This gives a onedimensional, radial dependence of line intensities (Figure 2). Statistical errors of intensities were determined by the fitting routine.

3 ... ß.....:..... FLUDRA ET AL.' ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA M ":* :½ "'"' ";i1'" ' ::'3½.:: ½s :.::,:½4 ½.r :::L.:...:.:: ;...: :..... :::..:: :. :: :.. :.:!.[i;; :::::'; :.. ß -... : : ::::.. : :.: : :.:: Solar X Solar X Figure 1. A mosaic of four rasters taken by CDS on August 19, 1996, in Si XII (left panel) and Mg X line (right panel). The units of the X and Y axis are arcseconds. The total area in each panel is 4 x 16 arcminutes Polar Coronal Holes Observations of the north and south polar coronal holes were made on the following days: north coronal hole (August 16, 17, 24, 25, 31, September 7), south coronal hole (August 11, 18, September 1, 8). In this paper, we analyze north coronal hole observations from August 24 and 31, and September 7, and south coronal hole observations from August 18. Here the observed area was 16 x 4 arcminute 2, and the same spectral lines as in the observations in the previous section were recorded. Figure 3 shows the north coronal hole seen in the Mg IX 368 line on September 7, The Mg IX image shows the presence of polar plumes. Similarly to section 2.1, the data were spatially averaged in a range of position angle to provide a radial dependence of line intensities. 3. Results 3.1. Electron Temperature From Line Ratios Limb brightening curves for a number of EUV lines have been constructed from the observations described in the previous section. The limb brightening observed in the transition region lines up to 20" above the limb has been discussed by several authors, for example, Mariska and Withbroe [1975] and Mariska e! al. [1978]. The subtle details of transition region structures responsible for the emission up to 20" above the limb will not be addressed in this paper. We discuss the behaviour of coronal line intensities at larger distances, from the peak of the limb brightening up to 0.2 solar radii above the limb. Figure 2 shows intensities of several lines as a function of the radial distance, on August 19, The coro-

4 , FLUDRA ET AL.: ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA, [,,, ],,, i, [,,,, i,, i, (1) C) - \ x \ o 1 : 0,,,,,?: Rodiol Distonce [Rsun] leisure. Line intensities above the west limb on August 9, 996. From top to bottom (solid lines)' Mg IX 368 A, Mg X 6:25 A, and $i XI! 5:20 A. O ¾ 630 A is shown as a dashed line. The data have been averaged over a position angle range of 54 ø. nal lines (Mg IX 368, Mg X 625 ) show a nearly et al. (1992). In this approximation, the observed inexponential decay up to 0.2/ s above the limb. The tensity I(x) at height x above the limb is proportional transition region line of O V 630 is shown to demon- to E(x)x /2, where E(x)is the source function (i.e., strate the difference in the intensity gradient. In the a local intensity along the radial direction x) and x is analysis below, we assume that the instrumental scat- expressed in units of the solar radius. [ering can be neglected for the coronal lines at distances One way to determine the electron temperature of the up to 0.2 solar radii above the limb. corona is to use ratios of coronal emission lines whose The data analyzed in this paper consist of line inten- emissivities peak at differentemperatures. Among the sities, summed along the line of sight, as a function of lines available in the normal incidence range of CDS, height above the solar limb in the plane of the sky. To lines from the Mg IX, Mg X, Fe XII, A1 XI and Si XII obtain the so-called source function (i.e., the intensity ions are observed in the quiet Sun corona and cover per unit volume, as a function of the radial distance) one the temperature range from 0.9 x 10 e to 2 x 10 e K. The would need to perform an Abel inversion, assuming a data sets recorded during the Whole Sun Month contain spherically symmetric distribution of intensities. In this three of these lines: Mg IX 3683., Mg X 6253., and paper, we use an approximation given by Guhathakurta Si XII Mg IX ,A ; :; ;½;; ; - - ½., -... : :,,,.... :, <,,,,:,:,,. ß.....: ;½ ;... *?3 *:*aa:..'.[;.;'.;.'.?::'*4,? ß '...,,.,.,.. ::,,...,.-.,,: i Soiar igure 3. A mosaic of four Mg IX 368 rasters taken by CDS at the north coronal hole on September 7, The units of the X and Y axis are arcseconds. The total area is 16 x 4 arcminutes 2. X

5 ß FLUDRA ET AL.' ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA 9713 I I i oooo / 2 // 2 / : // i i / /I I I IOg o (Temperoture) Figure 4. Theoretical ratios of line intensities (photon cm-2 s- ster-1) as a function of electron temperature for isothermal plasma, derived from ADAS [Summers et al., 1996] and assuming Si/Mg abundancequal to 1.0: (Si XII 5203.)/(Mg IX 3683.), solid line, (Si XII 5203.)/(Mg X 6253.), dashed line, (Mg X 625 A)/(Mg IX 3683.), dotted line. Figure 4 shows theoretical ratios of Si XII/Mg X, Si XII/Mg IX, and Mg X/Mg IX as a function of temperature, calculated using the ADAS atomic data pack- age [Summers et al. 1996]. This calculation assumes that plasma is isothermal, has a Maxwellinn electron energy distribution, and is in ionization equilibrium. The relative silicon/magnesium abundance was taken equal to 1.0 based on the table from Fludra and $chmelz [1995]. Observed Si XII/Mg X, Si XII/Mg IX, and Mg X/Mg IX line ratios are then assigned a temperature scale by spline interpolation from the theoretical ratios. For an isothermal plasma, all three ratios should give the same temperature. Because of summing along the line of sight and spatial averaging in a range of position angles, the intensities at a given height x above the limb have contributions from plasma that were emitted at a range of temperatures. In this case, the three ratios will give different temperatures, and we will use the Si XII/Mg X temperature as the highest of the three values. The temperature scale in Figure 5 depends on the relative Si/Mg abundance ratio. A comparison of various measurements of Si and Mg abundances [Fludra and $chmelz 1995] shows that the relative Si/Mg coronal abundance can be taken as 1.0, with a deviation of 20%. To estimate the effect that a 30% error in abundance or intensity calibration would have on the derived temperature, we multiplied the intensity ratio by factors of 1.3 and 0.7, and obtained an offset of the temperature curve by 0.02 x 106 K and x 106 K, respectively. Thus we find that the temperature derived from the $i XII/Mg X ratio is quite robust. A similar analysis has been made for the coronal hole observations on August 18, 24, 31, and September 7. Here, however, we find that the $i XII line intensities above the polar coronal holes are unmeasurably small, thus making it di cult to use any ratio involving the Si XII line. Instead, we use the Mg X/Mg IX ratio which has a weaker temperature dependence than the other two ratios. Figure 5 shows the height dependence of temperatures derived from Si XII/Mg X and Si XII/Mg IX ratios on all 6 days of equatorial observations analyzed Figure 6 shows electron temperature derived from the ratio of Mg X and Mg IX line intensities measured above the north and south polar coroin this paper. On average, the temperature from the nal holes. Three observations of the north coronal hole Si XII/Mg X ratio rises from about 1.1 x 106 K at made 7 days apart show almost identical temperatures, r- 1.ORs to 1.4 x 106 K at r - 1.2Rs. Individual increasing with height from 7.5 x 10 s K at the limb differences between most of the observation dates are to 8.5 x 10 s K at 1.1 solar radii. The south coronal small, less than 0.05 x 106 K, with the exception of August 12, where the temperature is systematically higher by 0.1 x!06 K for r 1.05Rs. The temperatures dehole temperature is the same as above the north coronal hole. For comparison, the Mg X/Mg IX temperature, calrived from the Si XII/Mg IX ratio are systematically culated for the closed-field equatorial regions, is lower by 0.1 million K than the temperatures from the Si XII/Mg X ratio. This indicates that the plasma is not isothermal, for reasons explained above. 1.0 x 106 K between 1.0Rs and 1.1Rs. It can be seen that this temperature is lower in the coronal hole than in the closed-field regions. For the hotter plasmas in closed

6 9714 FLUDRA ET AL.' ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA 1.6x10 x, xl 0 1.2x10 1.0x Radial Distance [Rsun] Figure 5. The electron temperatures derived from the intensity ratio of Si XII 520 Ji to Mg X 624 Ji line for 6 days of observations of equatorial regions on August 12, 15, 19, 27, 30, and September 3 (solid lines). Dashed lines show temperatures from the Si XII 520 Ji to Mg IX 368 Ji line ratio. The line intensities were averaged over position angle range up to 540 containing only quiet Sun emission. The statistical errors of individual temperature points are 0.1-1%. field regions, the Mg X/Mg IX ratio is not a good measure of maximum coronal temperature though, because it is biased towards lower temperatures, giving temperature significantly lower than the temperature from the Si XII/Mg X ratio shown in Figure 5. For the coronal holes, however, the lack of Si XII emission shows that the average temperature in the coronal holes is lower than in the closed-field regions, and the Mg X/Mg IX ratio is a better representation of the peak temperature in this case. The temperature errors, estimated from 1.2x10 1.0xl 0 E 80x10 (1,) ' 6.0x Radial Distance [Rsun] Figure 6. A comparison of temperatures derived from Mg X 625 Ji to Mg IX 368 Ji intensity ratios measured above the north polar coronal hole on August 24, 31, September 7, and south coronal hole on August 18, The line intensities were averaged over a range of up to 200 of the position angle. The statistical errors of individual temperature points are i- 4%.

7 FLUDRA ET AL.' ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA 9715 line intensity errors, are very small' 0.1-1% in the equatorial regions and i- 4% above the polar coronal holes Density Diagnostics The wavelength range observed by the normal incidence part of CDS contains several line pairs whose ratio is density sensitive. A good diagnostic of the quiet Sun coronal densities is obtained from the Si IX 342/350 / line pair. These two Si IX lines were recordeduring the Whole Sun Month observations. The theoretical density dependence of the Si IX 342/ 350 / line ratio can be calculated from Dereet al. [1997]. However, the resonance contributions to the collision rates are not taken into account in this cal- culation. Laming e! al. [1997] included the resonance contribution for a number of ions and found that this could lower the derived electron density by 0.15 dex. This effect has also been found by P.R. Young (private communication, 1997). Therefore, in this paper we use the œaming et al. [1997] and P.R. Young (private communication, 1997) modification for the Si IX lines. Figure 7 summarizes the electron density measurements in the equatorial regions, giving a dependence of density with distance above the limb determined from the Si IX 342/350 ratio for the six dates: August 12, 15, 19, 27, 30, and September 3. The density curves fall Densities derived from the Si IX lines above the north and south coronal holes are compared in Figure 8. All four coronal hole measurements give the same densities. Close to the limb, they are a factor 2.5 lower than the densities in the equatorial region, decreasing from 2 x 10 s cm -a at r = 1.ORs to 6 x 107 cm -a at 1.1Rs. The density errors are between 2 and 15% in the equatorial regions, and between 10 and 50% in the polar coronal holes, being usually lowest near the limb and increasing with height. For example, Figure 9 shows the error bars for the density curve for August 19. The results above can be compared to several recent measurements of electron densities made with the SUMER instrument on SOHO: Laming e! al. [1997] derived densities in various regions above the West solar limb, using several densitysensitive line ratios of different ions. The density at the heights arcsec above the limb ranges from log(ne) to 9.5, with the spread being larger than the errors of individual measurements. This range of densities includes the CDS value of log(ne) = 8.5 at 1.03Rs in the equatorial plane obtained in this paper. Doschek e! al. [1997] derived electron densities above the polar coronal holes from a Si VIII line ratio. Their densities are systematically lower by about a factor of two than the CDS densities. However, Warren [this issue] derived density in the height range of arcsec along the same line, suggesting that the average density above the limb in a polar coronal hole using four line structure of the quiet Sun corona did not change during ratios, and their average value of log(ne)=8.3 agrees 20 days. Any local differences have disappeared because very well with our coronal hole measurement at this of averaging along the line of sight and an angular aver- height. age. The average density is 5 x 108 cm -a at r = 1.0Rs, The two main components contributing to the emisdecreasing to 1.0 x 108 cm -a at 1.15Rs. sion in the polar coronal holes are polar plumes (i.e., ,..., Rodiol Distonce [Rsun] Figure 7. The electron density (cm-3) of the quiet Sun corona derived from Si IX 342/3503. ratio measured in the equatorial region above the east or west limb for the same six dates as in Figure 5. The data represent an angular average over position angle range up to 540. Error bars of individual density values are 2-15%, as shown in the example in Figure 9.

8 9716 FLUDRA ET AL.' ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA " ½ I... 1.oo 1.o5 1.1o Radial Distance [Rsun] Figure 8. The electron density (cm-3) from the Si IX 342/3503. ratio measured above the north coronal hole on August 24, 31, and September 7, and the south coronal hole on August 18. The data represent an angular average over position angle up to 20 ø. The averaged area contains polar plumes. Statistical errors of individual density values are 10-50%. 1.1,5 ray-like structures aligned along open magnetic field lines) and the interplume region (which is the actual coronal hole). The emission in Mg IX and Mg X lines above the limb in coronal holes appears to be dominated by plumes. Although in this paper care has been taken to avoid the brightest plumes and bright points, any 20-deg range of position angle typically contains four or five plumes and thus our angularly averaged coronal hole spectra always include several plumes. We have found, however, two dark areas inside a coronal hole on the disk, on September 7, which appeared free from plumes or other brighter features. From a spa- 5.0x10 4.0x x x x Radial distance [Rsun] 1.20 Figure 9. Comparison of densities measured by the Coronal Diagnostic Spectrometer from the density-sensitive Si IX 342/3503` line ratio (solid line) and from the emission measure derived from the Mg X 6253` line (dashed line, arbitrarily scaled) on the west limb on August 19, The line intensities above the limb have been averaged along concentric arcs in a position angle range of 540.

9 FLUDRA ET AL.: ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA 9717 tial average we derive a Mg X/Mg IX temperature of x 105 K ( x 105 K) and an electron den- sity from the Si IX lines of 9 ß 9+} - x 107 (1' 2+ - '45.35 X l0 s) -3 cm. A comparison with Figures 6 and 8 shows that the temperature in the dark areas on the disk is greater by x 105 K than the temperature determined just above the limb, while the density is up to a factor of 2 lower than the density above the limb. Therefore we conclude that the results obtained by averaging the emission above the limb are significantly weighted by the plume material. Thus the density in Figure 8 is only an upper limit to the true coronal hole density. Fisher and Guhathakurta [1995] derive separately the plume and interplume densities and radial density gradients in the polar coronal holes from white light data. They obtain a scale-height temperature of 8 x 105 K for the interplume region and 1.0 x 10 K for plumes at distances up to 1.2Rs. A density-sensitive line ratio, for example, the Si IX 342/350 ratio used above, is the most direct way of measuring electron density. It is also possible to estimate the electron density from line intensities of other lines by calculating the emission measure and assuming the integration depth along the line of sight. For an isothermal plasma at temperature T, the intensity I of a collisionally excited spectral line is given by sity from the intensity of the Mg X 625 line, as described in the previous paragraph. The volume of plasma has been left as a free parameter to scale the density to match the density derived from the Si IX line ratio. Figure 9 shows a comparison of the Si IX line- ratio density with the density derived from Mg X 625 line for the equatorial region on August 19 and scaled to match the two curves. The slopes of the two curves agree well. A small difference in slope near 1.05Rs could indicate that the integration depth along the line of sight cannot be taken the same for all values of r due to local concentrations of magnetic structures. 4. X ray Observations From YOHKOH Two dates were selected for comparison between the CDS and SXT observations: August 19 and September 3. Since the west limb observation on August 19 and the east limb observation on September 3 are 15 days apart, they describe almost the same location on the Sun. On each of these 2 days the SXT obtained a series of full-disk image pairs in the two thinnest filters (the A l and A1/Mg/Mn filters) taken less than 128s apart and spanning some 23 hours. After a preselection based on exposure times, data completeness and spatial resolution, a number of viable filter pairs, suitable for temperature and emission measure analysis, remained: nine pairs for August 19 with total exposure times of 24 and 48 s in the A1 and A1/Mg/Mn filters, respectively, and ten pairs for September 3 (total exposure times of 27 and 53 s). It should be noted here that the SXT filters used are only sensitive to temperatures in excess of about 1 MK and have a nonlinear bias to higher temperatures up to around 6-10 MK. To increase the signal to noise all of the images for a particular filter on a particular day were coregistered and added together. Prior to the summation, the individual raw SXT data frames were corrected for back- ground, the presence of dark spikes, vignetting and scattered light [see Alexander, this issue]. After the correction and summation procedures the data were further summed along arcs corresponding to fixed heights above the solar limb. These arcs were chosen to correspond to the CDS rasters which resulted in a wedge off the west (east) limb on August 19 (September 3) with boundaries along radial lines corresponding approximately to (4-240 ) latitude. I = A ;G(T)N 2V, where A ; is the abundance of the element with respect to hydrogen, V is the volume of From the ratio of the summed images in each filter it is possible to derive a line-of-sight averaged temperature emitting plasma, and G(T) is a line emissivity which and emission measure in each summed pixel [Tsuneta includes the ion fraction and collisional excitation coef- et al., 1991]. The derived radial variation of temperaficients. Taking the temperature derived in section 3.1, it is possible to calculate the radial dependence of the ture found for the wedge on August 19 is shown by the dashed curve in Figure 10. The error bars indicate the emission measure EM = N 2V = I/A ;/G(T), and uncertainties derived from photon statistics and decomthen the density N if the volume V is assumed. We have multiplied the measured intensities by r-.5 to approximately remove the effect of the integration pression errors where these have been added in quadrature through the summation process. Figure 10 also compares electron temperatures derived from SXT filalong the line of sight and obtain a radial dependence ter ratio to temperatures from the CDS Si XII/Mg X of line intensities, following Guhathakurta et al. (1992). Next, we have calculated the emission measure and den- line ratio on August 19. The SXT temperatures are higher by about 0.2 x 10 s K than CDS temperatures, further demonstrating the multithermal nature of the coronal plasma. Both temperatures increase with distance above the limb. Figure 11 shows a comparison of SXT density with the CDS density from the Si IX line ratio. The SXT densities are derived from the SXT emission measure assuming a line-of-sight integration depth of l0 = 1.4 x 10 cm [cf. Yoshida and Tsuneta, 1995]. The agreement between the two instruments is very good for the August 19 data, where both densities decrease with the same slope. The same comparison made for the September 3 data, however, shows that while the SXT temperatures remain higher than CDS temperature, and the densities decrease with distance, the slope of the SXT temperatures and densities is different than that of the CDS temperature and density. Also, SXT fluxes are lower by a factor of 2 than on August 19, while the CDS line intensities are 10% higher than on August 19. Since SXT samples higher temperatures, we conclude that the structure of the hotter, X ray emitting coronal loops

10 9718 FLUDRA ET AL.' ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA 1.8x x10 1.4x10 1.2x10 1.0x Rodiol distonce [Rsun] Figure 10. Comparison of the electron temperature measured by the Coronal Diagnostic Spectrometer from the ratio of Si XII 520 Ji to Mg X 625 Ji (solid line), and the Soft X-ray Telescope (dashed line) on the west limb on 1996 August 19. The line intensities above the limb have been averaged along concentric arcs in a position angle range of 54 ø. changed significantly in 14 days, while the EUV emitting loops showed only 10% change in intensity, and almost no change in temperature and density. 5. Conclusions We have analyzed a series of EUV observations of the solar corona above the limb in equatorial regions and polar coronal holes. We have derived electron density from a density-sensitive line ratio and electron temperature up to 0.2Rs above the limb, using spectra averaged over up to 54-deg range of position angle. This is the largest data set of electron density measurements from a density-sensitive line ratio so far, allowing us to study the spatial and time variability of electron density distribution over a period of one month. Electron 5'0x108 ',, ',...,...,. 4.0x108 - :: 3.Ox x r i - ß -I--.t 1.0xl 08 L.d - :: - 0,,, I,, Rodiol distonce [Rsun] Figure 11. Comparison of the electron density measured by the Coronal Diagnostic Spectrometer from the Si IX 342/350 Ji ratio (solid line) and the Soft X-ray Telescope (dashed line) on the west limb on August 19, The line intensities above the limb have been averaged along concentric arcs in a position angle range of 54 ø.

11 FLUDRA ET AL.' ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA 9719 temperature derived from the ratio of Si XII and Mg X lines increases from 1.1 x 106 K at the limb to 1.4 x 106 K at 1.2Rs in the equatorial regions. Temperature derived from the ratio of Mg X 625 and Mg IX lines increases from 7.5 x 105 K at the limb to 8.5 x 105 K at 1.1Rs above the polar coronal holes. The density decreases exponentially from 5 x 108 cm -3 at 1.0Rs to 1.0 x 108 cm -3 at 1.15Rs in the equatorial region, and from 2 x 108 cm - at 1.0Rs to 6 x 107 cm - at 1.1Rs above the coronal holes. The coronal hole results above the limb are dominated by the plume material. The darkest areas, free from plumes, selected inside the coronal hole on the disk, had a temperature of about 8.2 x 105 K and density of about 1.2 x 108 cm -. These values can be used to provide boundary conditions for the modelling of the streamers and coronal holes from white light data on larger spatial scales. We find that EUV data spatimly averaged over a range of of the position angle show very little time variability in the quiet Sun temperatures and densities over a period of 20 days, both in the closed-field regions and above the coronal holes. These parameters are the same also when different spatial locations are seen on the limb as the Sun rotates. There can be somewhat greater differences among coronal holes due to the pres- ence of plumes, bright points, and the fact that the tops of magnetic loops consituting the coronal hole boundary may protrude into the coronal hole area from behind the limb. We have also compared the EUV results to the temperatures and densities derived from soft X-ray images. In the case of a typical quiet Sun streamer we find a very good agreement between the EUV and soft X-ray results. However, we find that the structures emitting soft X rays can significantly change over a period of 15 days. Acknowledgments. The CDS instrument was built and is operated by an international consortium led by the Rutherford Appleton Laboratory. We would like to thank the many members of the hardware groups at the Rutherford Appleton Laboratory and Mullard Space Science Laboratory in the United Kingdom, Max-Planck-Institut flit Extraterrestrische Physik and PhysicMisch-Technische Bundesanstalt in Germany, the Goddard Space Flight Center in the USA, and the University of Oslo, in Norway. This work was supported by the United Kingdom PPARC. SOHO is a project of international cooperation between ESA and NASA. Yohkoh is a mission of the Japanese Institute for Space and Astronautical Science. DA is supported by NASA under contract NAS BJIB and GDZ used Starlink data analysis facilities at U CLAN. We thank M. Laming and P.R. Young for providing theoretical intensities of Si IX lines. The Editor thanks Alexander Panasyuk and another referee for their assistance in evaluating this paper. References Alexander, D., Temperature structure of the quiet Sun X- ray corona, J. Geophys. Res., this issue. David, C., A.H. Gabriel, F. Bely-Dubau, A. Fludra, P. Lemaire, and K. Wilhelm, Measurement of the electron temperature gradient in solar coronal holes, A stron. A s- trophys., 336, 90, Del Zanna, G., and B.J.I. Bromage, The elephant's trunk: Spectroscopic diagnostics applied to SOHO/CDS observations of the August 1996 equatorial coronal hole, J. Geophys. Res., this issue. Dere, K.P., E. Landi, H.E. Mason, B.C. Monsignori Fossi, and P.R. Young, CHIANTI- An atomic database for emission lines, Astron. Astrophys. Suppl. Ser., 125, 149, Doschek, G.A., and U. Feldman, The coronal temperature and nonthermal motions in a coronal hole compared with other solar regions, Astrophys. J., 212, L143, Doschek, G.A., P. Warren, J.M. Laming, J.T. Mariska, K. Wilhelm, P. Lemaire, U. Schiihle, and T.G. Moran, Electron densities in the solar polar coronal holes from density sensitive line ratios of Si VIII and Si X, A strophys. J. Left., 482, L109, Feldman, U., G.A. Doschek, J.T. Mariska, A.K. Bhatia, and H.E. Mason, Electron densities in the solar corona from density-sensitive line ratios in the N I isoelectronic sequence, Astrophys. J., 226, 674, Feldman, U., G.A. Doschek, and J.T. Mariska, On the structure of the solar transition zone and lower corona, A strophys. J., 229, 369, Fisher, R., and M. Guhathakurta, Physical properties of polar coronal rays and holes as observed with the SPARTAN coronagraph, Astrophys. J., 447, L139, Foley, C.R., J.L. Culhane, and L.W. Acton, Yohkoh soft X- ray determination of plasma parameters in a polar coronal hole, Astrophys. J., 491,933, Fludra, A., and J.T. Schmelz, Absolute abundances of flaring coronal plasma derived from SMM spectral observations, Astrophys. J., 4{47, 936, Fludra, A., G. Del Zanna, B.J.I. Bromage and R. Thomas, EUV line intensities above the limb measured by the CDS, Proceedings of the 5th SOHO Workshop, Eur. Space Agency Spec. Publ., ESA SP-JOJ, 385, Gibson, S.E., A. Fludra, F. Bagenal, D. Biesecker, G. Del Zanna, and B.J.I. Bromage, Solar minimum streamer densities and temperatures using the Whole Sun Month coordinated data sets, J. Geophys. Res., this issue. Guhathakurta, M., G.J. Rottman, R.R. Fisher, F.Q. Orfall, and R.C. Altrock, Coronal density and temperature structure from coordinated observations associated with the total solar eclipse of March 18, 1988, A strophys. J., 388, 633, Guhathakurta, M., T.E. Holzer, and R.M. MacQueen, The large-scale density structure of the solar corona and the heliospheric current sheet, Astrophys. J., J58, 817, Guhathakurta, M., A. Fludra, S.E. Gibson, D. Biesecker, and R.R. Fisher, Physical properties of a coronal hole from CDS, Mark III and LASCO observations during the Whole Sun Month, J. Geophys. Res., this issue. Habbal, S.R., R. Esser, and M.B. Arndt, How reliable are coronal hole temperatures deduced from observations, Asfrophys. J., 413, 435, Harrison, R.A., et M., The Coronal Diagnostic Spectrometer for SOHO, Sol. Phys., 162, 233, Harrison, R.A., and A. Fludra, (Eds), The Coronal Diagnostic Spectrometer for the Solar and Hellospheric Observatory, Tech. Rep. RAL-SN , Rutherford Appleton Lab., Chilton, Oxfordshire, Kastner, S.O., E.D. Rothe, and W.M. Neupert, Limb brightening observations from the OSO 7 satellite, A stron. A s- frophys., 37, 339, Laming, J.M., U. Feldman, U. Schiihle, P. LemMre, W. Curdt, and K. Wilhelm, Electron density diagnostics for the solar upper atmosphere from spectra obtained by SUMER/SOHO, Astrophys. J., 485, 911, Leer, E., T.E. Holzer, and T. Fla, Acceleration of the solar wind, Space Sci. Rev., 33(1-2), 161, 1982.

12 9720 FLUDRA ET AL.: ELECTRON DENSITY AND TEMPERATURE OF THE SOLAR CORONA Mariska, J.T., U. Feldman, and Doschek, G.A., Measurements of extreme ultraviolet emission line profiles near the solar limb A strophys. J., œœ6, 698, Mariska, J.T., and G.L. Withbroe, Analysis of EUV limbbrightening observations from ATM, Sol. Phys., 44, 55, Sturrock, P.A., M.S. Wheatland, and L.W. Acton, YOHKOH Soft X-ray Telescope images of the diffuse solar corona, Astrophys. J., 461, Ll15, Summers, H.P., D.H. Brooks, T.J. Hammond, A.C. Lanzafame, and J. Lang, Atomic Data and Analysis Structure - User Manual, Tech. Rep. RAL- TR , Rutherford Appleton Lab., Chilton, Oxfordshire, Tsuneta, S., The Soft X-ray Telescope for the Solar-A mission, Sol. Phys., 156, 37, Warren, H., The density structure of a solar polar coronal hole, J. Geophys. Res., this issue. Wheatland, M.S., P.A. Sturrock, and L.W. Acton, Coronal heating and the vertical temperature structure of the quiet corona, Astrophys. J., 8œ, 510, Yoshida, T., and S. Tsuneta, Temperature structure of solar active regions, Astrophys. J., 5t9, 342, D. Alexander, Lockheed Martin Solar & Astrophysics Lab., Org. Hl-12, B252, 3251 Hanover St, Palo Alto, CA (alexande@sag.space.lockheed.com) B.J.I. Bromage and G. Del Zanna, Centre for Astrophysics, University of Central Lancashire, Preston, PR1 2HE, United Kingdom. (b.j.i.bromage@uclan.ac.uk, g. del-z ann a@uclan. ac. uk) A. Fludra, Space Science Dep., Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OXll 0QX, United Kingdom. (fludra@cds8.nascom.nasa.gov) (Received April 3, 1998; revised July 28, 1998; accepted September 11, 1998.)