th

4 (Virtual) Thermospheric/Ionospheric Geospheric Research (TIGER) Symposium

Variability of the solar EUV emission and implication for modeling the solar EUV irradiance. Kretzschmar, M. (1) , Lilensten, J. (1), Aboudarham, J.(2) (1) (2)

Laboratoire de Planétologie de Grenoble, UJF/CNRS/UJF DASOP/LPSH, Observatoire de Meudon

Abstract. As far as Solar-Terrestrial relationships are concerned, and in particular in the space weather context, the solar EUV flux plays a major role since it is the principal source for the diurnal ionosphere. It is unfortunately badly known. Although several models exist, very few measurements were available on its variability before SOHO (ESA/NASA) and TIMED (NASA). Our study aims at building a new solar EUV flux model, based on a method proposed by Warren et al. (1996,1998). They propose to estimate the typical spectra for solar regions with various types of activity and then to correlate ground-based solar images with the different fractions of the sun covered by these regions. This allows to try to synthesize the solar EUV irradiance from ground-based observations. We processed about 750 data files of the SUMER instrument onboard SOHO, and computed spectral radiances for about 30 EUV lines ranging from 70 nm to 110 nm and covering a temperature range from 2.104 K to 1.106 K. Data were split into different characteristic areas (quiet sun, coronal hole, and active region) using the simultaneous measurements of the EIT telescope .In this work, we analysed the variability of quiet sun emission against solar cycle. We defined typical radiances for this region and computed the differential emission measures.

1. Introduction The extreme ultraviolet (EUV) solar flux is energetic enough to ionise the upper atmosphere. It constitutes the major source of the diurnal ionosphere. The rapid growing of space weather makes it necessary to determine it precisely and in absolute values. Warren and co-authors (1996,1998) have proposed to model the solar EUV flux by combining a spectral emission line database, solar emission measure distributions, and estimates from ground-based solar images of the fraction of the Sun covered by the various types of activity to synthesise the irradiance. The goal was to give a way to estimate the irradiance from EUV line emission formed in the upper chromosphere and lower transition region from the Ca II K-line through the model. Based on this approach, they could derive the emission measure from a spectrum of a portion of the quiet solar disk measured with the Harvard instrument onboard Skylab and compilations of atomic data. This last method reveals to be very promising. It rises new questions, which are the variability of the EUV spectrum versus specific solar zones (quiet sun, coronal hole, and active region) and, in a single zone, versus time and solar activity. We address part of these questions using data from the SUMER instrument onboard SOHO (Wilhelm et al, 1995). We have selected about 750 SUMER files, ranging from 1996 to 2001 and from 750 Å to 1100 Å. We developed an automatic procedure to compute the radiances of several spectral lines formed at different temperature. All the SUMER data used are in the public domain and can be accessed via the web (http://www.medoc-ias.u-psud.fr), and most of them were a part of specific science studies. The emission region for each file was identified using the coordinated image of EIT (Delaboudinière et al., 1995). Section 2 describes the processing of SUMER data and section 3 presents results on the variability of the radiance and the computed differential emission measure (DEM). 1

2. Instrumentation and data reduction 2.1. SUMER spectrometer. The SOHO/SUMER instrument is a normal incidence spectrometer with two alternate detectors working in UV wavelength, from 50 nm to 161 nm. The two photon-counting detectors ('A' and 'B') have 1024 spectral and 360 spatial pixels; they have two different photocathode areas and a Lyman α attenuator on the edge. Several slits are available, some of them with angular dimensions of 4''x300'', 1''x300'''and 1''x120''. Spatial and spectral resolutions of each pixel are respectively about 1'' and 0.044 Å (in first order). Data files are in FITS format and structured as follows: a principal header with general information about all the file, a secondary header with a detailed description of the data, and finally, the three dimensions (spectral, spatial, temporal) data arrays. All the characteristics of the telescope can be found in Wilhelm et al (1995). 2.2. Data reduction. In this section, we outline how line radiances are computed from the data. The description and procedure of the radiometric calibration and corrections of SUMER data are available at http://www.linmpi.mpg.de/english/projekte/sumer/text/radcal.html. We corrected data from instrumental effects using these procedures. We converted count rates in radiance (in photon number/cm2/s/sr/ Å) using the RADIOMETRY procedure. The two detectors available on-board SUMER were used to record these data. In this study, we did not take into account spectral pixels on the attenuated part of the detector. Spectra were averaged in time and space according to the following procedure: for each file, we summed the different expositions of the SUMER detector and divided by the number of exposures. When the solar emission is recorded from the same zone of the sun during the entire file, this averages the data in time (usually over about 30 minutes). When the pointing of the SUMER instrument changes between each image, this averages the data both in time and space. Finally, we also averaged the spectrum over the total observed zone, either 120 or 300 arcseconds depending of the slit used by SUMER for the observations. To achieve the wavelength calibration of each file, we developed the following procedure: for 8 reference files covering the whole wavelength range (750 Å - 1100 Å), we calibrated the wavelength using chromospheric lines identified in the literature and re-computing the best spectral resolution (wavelength step between 2 pixels). Then during the automatic procedure, all other files were correlated with these calibrated spectra over its spectral range. The wavelength calibration achieved by correlation gives good results, as indicated by the high value of the correlation coefficients, which are often superior to 0.9. However, aspect of a spectrum recorded over the limb is different from a spectrum recorded on the solar disk; indeed, for an off-limb spectrum, emission lines from the chromosphere and the thin transition region may be less bright or even totally absent, depending on the height of the instrument pointing. Then, the correlation of an « over limb » spectrum with the reference spectra recorded on the disk does not give good results. For this reason, only spectra recorded principally on the solar disk are only presents in our results. Line identification is based on Feldman et al. (1997) and Curdt et al. (1997). Very recently, Curdt et al. (2001) published an up to date line list from SUMER data. Our identification is in total agreement with their work.

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Line profiles were fitted automatically with a Gaussian profile plus a constant continuum. The fits were achieved over a fixed distance from the pic of the lines. Total intensity of the lines were computed from the gaussian parameters. Because most of the EUV emission lines are optically thin, the radiances for these wavelengths are expected to vary as 1/cos(θ) from solar center to the limb, where θ is the heliocentric angle. The center to limb variation was studied by Withbroe (1970). He compares theoretical center to limb curves with OSO-IV observation and found a good agreement for lines emitted by Lithium-like ion. Spectral lines with optical depth near unity have a lower variation. Withbroe notes the possible absorbing effects of spicules that extend up into the chromospheric-coronal transition region. More recently, Wilhelm et al. (1998) reported SUMER observations of center to limb variation for several lines emitted by the chromosphere, the transition region and the corona. For most of the lines emitted in the transition region and the corona, they found a good agreement with Figure 1: Radiance (in photons/cm2/s/sr) for 4 lines a variation as 1/cos(θ). For against the decimetric index F10.7. Both values corrected chromospheric lines (such as (x) and non-corrected ( ) from the center to limb variation hydrogen lines), no variation was are shown. found. However, they reported that both the value and position of the maximum center to limb variation change for different lines and different activities of the emitting areas. For the line at 770.41 Å emitted by Ne VIII, a variation smaller than 1/cos(θ) was found. According to this and to the observed variation in our results, we applied 3 kinds of center to limb variation. No variation was applied for the lines emitted by the ions H I, He I, O I, N I, which are emitted in the deep chromosphere. For the other lines, we applied center to limb variation as 1/cos(θ) such that 1/cos(θ)=2 at the limb or such that θ=90° at 20 arc second above the limb depending on the optical depth of the line and on our observations. To allow the comparison between radiance, intensities were then reported to the center of the solar disk.

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3. Results and discussion 3.1. EUV radiances variability Because of the difficulties related to space mission, no data set from the same instrument until now allow to address the question of the variability of the solar emission along the ascending phase of the solar cycle. Vernazza and Reeves (1978) addressed this question by comparing the average quiet sun emission from the ATM ultraviolet spectrometer on SKYLAB, measured near the minimum of the solar cycle 21 to the quiet sun measured by OSO 6 near the pic of solar cycle 20. With an accuracy of +/- 85%, they found a relatively little change in the EUV quiet-Sun spectral radiance. In this section, we investigate this question for EUV emission measured by the SUMER instrument and arising in solar zone identified as “quiet sun” zone. This label refers to an area where there is no magnetic activity, and which is not a coronal hole; this name was largely used in the literatures, and we achieve the identification of the emitting area by looking at the EIT images. However, several others features are known to be included in the so called “quiet” area; these features can be the network and the intra network for the chromosphere and the lower transition region, as well as the bright points. It is important to note that all these features contribute to our results. Moreover, the center to limb variation adds to the dispersion of the results. We show on figure 1 all the radiances used to compute the average quiet sun intensities for 4 lines: C II at 904.10 Å, N III at 763.34 Å, Ne VI at 1005.84 Å, and Ne VIII at 770.41 Å. These lines are used to compute the Differential Emission Measure in the next section. The symbol "x" refers to radiances which are not corrected from the center to limb variation, while symbol " " refers to radiances computed at the center of the solar disk. We first note that there is a high variability of the emission for a single value of F10.7; this variability can come from the variability of the sub-structure (network and bright points) of the quiet zone. Vernazza and Reeves (1978) have already found a change of the specific intensity of the quiet Sun approaching 20% during a period of 9 month near the minimum of solar cycle 21; they have also noted time variations shorter than 3.5 minutes. Because the SUMER instrument is very sensitive, there are only few measurements on the solar disk near the solar maximum. We can see that the determination of the variation of our data with the solar cycle is strongly dependent of the applied correction; it is notably the case for the C II and Ne VI lines. λ (Å) 904.10 775.96 763.34 764.36 765.15 759.44 762.00 1005.84 780.33 770.41 769.38 776.37

Table 1: Lines used for the inversion. Ic Ion ∆I n Iav C II 30.0% 33 7.48 E+11 6.76 e+11 N II 27.7% 53 5.01 E+10 5.19 e+10 N III 22.4% 55 9.41 E+10 9.62 e+10 N III 20.5% 57 1.84 E+11 1.87 e+11 N IV 16.6% 76 2.26 E+12 2.21 e+12 OV 21.3% 55 1.39 E+11 1.42 E+11 OV 23.7% 55 1.77 E+11 1.75 E+11 Ne VI 23.2% 25 3.96 E+10 3.94 e+10 Ne VIII 23.5% 54 1.05 E+12 1.11 e+12 Ne VIII 23.9% 70 2.27 E+12 2.19 e+12 Mg VIII 36.2% 23 1.48 E+10 1.44 e+10 SX 30.5% 39 2.92 E+10 2.84 e+10

Ratio 0.9 1.03 1.02 0.98 0.98 1.02 0.99 0.99 1.06 0.96 0.97 0.97

∆I = mean absolute deviation of the SUMER intensity to the averaged value. n = sample number used to compute the averaged intensity; Iav = averaged intensity; Ic = computed intensity; Ratio = 2 Ic/Iav Intensity are in photons/cm /s/sr.

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However, for the N III and Ne VIII lines, most of the measures needed only a small correction and it is then possible to judge the availability of the correction. The two biggest correction for these lines were applied to data with F10.7~140 and F10.7~160; the corrected values agree very well with the other ones, even at higher solar activity. This is also the case for all the other lines in the spectral range 760-790 Å, which come nearly from the same data files. Then, we believe that the variation of the radiances is well represented by their corrected values. For all the lines used to compute the DEM (see next section and table 1), it was not possible to find an evidence for a correlation between the average quiet sun intensity at the center of the solar disk and the decimetric index. 3.2. Implication on solar EUV model using dem The modelling of the solar EUV flux from the knowledge of the contributing area of the quiet sun regions, the active regions, and the coronal hole supposed that we can define one typical spectra for each of these regions. Because there is a variability of the intensities measured in quiet sun areas, we used the average quiet sun radiances from the SUMER data to compute a differential emission measure. One of the main difficulties in the computation of a correct Differential Emission Measure is the choice of the lines used. McIntosh et al. (2000) have studied the influence of several emission lines in the spectral range of the SUMER and CDS instrument. They showed that more than individual lines, one can find good sets of lines for this inversion problem. Several sets of lines can be chosen for the inversion in our study. The first criterion is that they must cover a broad range of temperatures in order to determine the emission measure both for the solar transition region and the corona. The lines must be optically thin so that there is no interference with important processes such as opacity or interactions with the solar radiation field. In our data set, we can rely on several tens of such lines, which leave us with thousands of possible sets. However, from Judge et al. (1995), emission lines from Liand Na-like ions should be excluded from the DEM computation. The reasons can be the lack of atomic data or that one or more hypotheses used are false for these lines. For each line of a given set, we first compute its contribution function; this was achieved with the abundance from Feldman et al. (1992) and ionisation equilibrium computed by Arnaud and Rothenflug (1985), and the facilities offered by the CHIANTI database. Then, to compute the DEM from the contribution functions, we have systematically tested two inversion methods, a non-linear least squared fit assuming the DEM varying as an exponential of a Chebyshev polynomial and a method of direct inversion plus a smoothing condition (see for instance Press et al (1986)). Finally, from the DEM, it is possible to re-compute the intensities of the emission lines. In order to choose between the multiple possible sets, we have computed the chi square value between observed and computed intensities. As suspected, we found that the O VI lines Figure 2: upper panel: contribution function of the lines used to compute the DEM against give bad results. The selected set of temperature. Lower panel: The DEM computed emission lines is the one which have given in this work (labeled SUMER) is shown with the smallest Chi square value. This value is two others DEM presented in the text. 0.16 and is reached with the regularised 5

solution. This is the best result in Table 2 : comparison of computed radiance and the hundreds of sets that we have average SUMER radiance. tested. The result has also been Ic Ratio λ (Å) Ion Iav systematically better with this 758.68 OV 1.80 E+11 1.83 E+11 1.02 method than with the polynomial 779.90 O IV 8.27 E+10 5.92 E+10 0.72 method. 787.70 O IV 1.66 E+12 3.02 E+12 1.82 This “best” set of line (best in view 790.22 O IV 3.38 E+12 5.48 E+12 1.62 of this criterion) is made of 12 895.17 Ne VII 1.51 E+11 1.02 E+11 0.67 lines. They are shown in table 1. 916.71 Ne II 3.24 E+11 1.02 E+11 0.31 Columns 1 and 2 show wavelength 922.02 N IV 1.88 E+11 1.26 E+11 0.67 and ion; column 3 shows the mean 933.41 S VI 1.00 E+12 1.79 E+11 1.79 absolute deviation of the SUMER 977.02 C III 4.70 E+13 1.20 E+13 0.25 intensities to the averaged value. 989.80 N III 9.72 E+11 5.32 E+11 0.55 Column 4 shows the number of 991.51 N III 1.88 E+12 1.02 E+12 0.54 measure used to compute the 996.00 S II 6.34 E+10 1.89 E+09 0.03 averaged value. Column 5 and 6 997.40 Si III 5.86 E+10 4.05 E+10 0.69 show respectively the averaged 999.29 Ne VI 6.85 E+10 6.63 E+10 0.97 and computed intensities. This set 1031.93 O VI 1.60 E+13 7.03 E+12 0.44 covers a wide range of 1036.32 C II 2.40 E+12 2.09 E+11 0.12 temperatures as seen in figure 2 (upper panel), which shows their 1037.02 C II 2.83 E+12 4.19 E+11 0.15 contribution function. The 1037.60 O VI 7.15 E+12 3.52 E+12 0.49 temperature goes from about 1062.64 S IV 2.95 E+11 1.63 E+11 0.55 1.5104 K to 5.106 K. The main 1066.64 Si IV 1.35 E+11 3.13 E+09 0.02 contribution at low temperature comes from C II. Around 1.6 105 K, it comes from N IV and from Ne VIII at high temperature. Some lines are generated by the same ion and are close to each other. The result of the emission measure distribution is shown in figure 2 (lower panel). It represents a DEM for the quiet sun averaged over a full solar cycle. For each line, we also show the ratio of the observed intensity to the computed intensity times the differential emission measure at the temperature of the formation of the line. This temperature is chosen as the one that maximises the product of the contribution function of the considered line and the DEM. The agreement is excellent. The observed and computed intensities are given in table 1. Their ratios range between 0.09 and 1.06. In the same figure, we compare our results with Warren et al. (1996) (labelled NRLEUV) and with Landi et al. (1998) (labelled CDS), computed respectively with ATM and CDS data. There are strong discrepancies at high and low temperatures. This is a common problem with determining a DEM, and it becomes more uncertain at these temperatures. In fact, the assumption made fail at low temperature, and it is not possible to retrieve the maximum temperature (the one above which the DEM is nul) in the line of sight. Moreover, in our case, the DEM above about 1.3 106 K essentially comes from the wings of the contribution functions. The NRLEUV model stands for quiet sun conditions. It should therefore be close to our DEM, whatever the set of lines. This is not fully the case. The methods of inversion, relative abundance, and ionisation equilibrium are different (iterative method in the NRLEUV case) and but most important is the fact that the average is not made on a set of lines covering the full solar cycle. This may be the main explanation for the discrepancies. The differences with the CDS differential emission measure are somehow less surprising because they used data taken on a single observation. From the DEM, it is then possible to compute radiance for every optically thin emission line. In table 2, we show the comparison between averaged radiances measured from this work and radiances computed from the DEM. There is a very good agreement for emission lines of O V and Ne VI ions. Emission lines from these ions have been used to compute the DEM. However, there is a bad agreement with S II and C II lines. The computed values are 6

systematically lower than the observed one. This can indicate that our DEM has too small value at low temperature. There is a very different behaviour for O IV lines. Two of them have a larger computed value than the observed one while one has a smaller value. This could indicate an error in atomic data or limitations in differential emission measure diagnostic. Inconsistency for O VI lines is not surprising since O VI ion is a Li-like ion. The C III line at 977.02 A could fail with assumptions. There is a general agreement for the other line inside a factor 2. Next, we have converted radiance to irradiance at 1 AU by integration of the computed intensity over the solar disk. We assumed a center to limb variation as 1/cos(θ), which leads to F=2.I.Ω,

λ (Å) 315.02 319.84 328.25 332.78 334.17 341.15 345.10 347.40 368.06 525.80 543.88 550.05 554.51 554.08 558.60 558.60 561.72 572.31 574.05 580.90 585.69 609.79 609.83 629.74 770.41 786.47 787.72 933.39 944.52 977.02

Table 3 : comparison of Irradiance. Ion Irradiance Irradiance This work SUMER Mg VIII 1.36 E+08 Si VIII 1.43 E+08 Al VIII 0.82 E+07 Al X 4.12 E+07 Fe XIV 2.27 E+08 Fe XI 1.55 E+07 Si IX 7.28 E+07 Si X 1.50 E+08 Mg IX 4.15 E+08 O III 7.50 E+07 Ne IV 2.73 E+07 Al XI 5.03 E+07 O IV 7.94 E+08 Ne VI Ne VII Ne VII Ne V Ca X Si XI Ar VII Mg X O IV OV Ne VIII SV O IV S VI S VI C III

Irradiance CDS 1.14 E+08 1.14 E+08 1.72 E+07 5.65 E+07 3.20 E+07 3.75 E+07 1.03 E+08 1.11 E+08 4.93 E+08 4.07 E+07 1.90 E+07 1.43 E+07 3.56 E+08

2.85 E+07

2.68 E+07

0.83 E+07 2.62 E+07 0.57 E+07 2.16 E+07 0.73 E+07 7.93 E+08

1.36 E+07 2.29 E+07 2.20 E+07 2.14 E+07 1.33 E+07 3.45 E+08

1.21 E+09 2.98 E+08 9.15 E+07 4.11 E+08 2.43 E+07 1.23 E+07 1.63 E+09

1.00 E+09* 8.65 E +08 3.20 E+08* 1.03 E+08 1.94 E+08* 1.08 E+08 6.54 E+07 5.63 E+09

2

Irradiances are in photons/cm /s. For SUMER value, * design an irradiance averaged over 2 or 3 values.

where Ω is the solid angle of the sun at 1 AU, I is the computed intensity, and F is the irradiance or total solar flux of the line at 1 AU. We compare these values with measurements of the CDS and SUMER instrument in table 3. Column1 and 2 show wavelength and ion of emission lines. Column3 shows irradiance from this work, column4 shows irradiance measure by SUMER (Wilhelm et al, 1998), and column 5 shows irradiance measured by CDS (Brekke et al., 2000). Once again, there is a good agreement for lines emitted by ions used to compute the DEM: O V, Ne VI, Ne VIII, and Mg VIII. However, there is a bad agreement for some lines formed at high temperature (such as Fe XIV at 334,17 and Ca X at 574.05) and for lines emitted by Na-like ion (S VI). For the two lines emitted by O IV ion (at 554.5 and 787.72), there is a different tendency; the former has a larger irradiance value than the observed one, while the latter has a smaller value. Finally, there is a general good agreement for other ions.

4. Conclusion We have processed about 750 data file of the SUMER instrument, and computed intensities in quiet sun area for about 30 EUV emission lines and from the minimum to the pic of the current solar cycle. On most of the lines, we could not find evidence for a variation of the quiet sun emission with the solar activity represented by the decimetric index. Using these 7

measurements, we computed an averaged quiet sun radiance for all the lines observed. We then determined a quiet sun DEM from a set of 12 emission lines. This set was chosen on a minimum chi squared basis from hundreds of possible sets; two inversion methods were also tested, and we found that a regularised solution gives the better results. Finally, we compared radiance and irradiance values computed from this DEM with other values from this work and measured by the SUMER and CDS instruments. We found a good general agreement. These results support the concept proposed by Warren et al (1996) to model the solar EUV flux. They show that the SUMER instrument provides very useful observations to model the solar EUV flux.

Reference Arnaud M., and Rothenflug R., A&AS, Vol. 60, 425, 1985. Delaboudinière J.-P., and 27 co-authors, Sol. Phys., Vol. 162, 291-312, 1995. Brekke P., Thomson W.T., Woods T.N., and Eparvier F.G., ApJ, Vol. 536, 950-970, 2000. Curdt W., Feldman U., Lamong J.M., Wilhelm K., Schuhle U., and Lemaire P., A&AS, Vol. 126, 281296, 1997. Curdt W., Brekke P., Feldman U., Wilhelm K., Dwivedi B.N., Schühle U., Lemaire P., A&A, Vol 375, 591-613, 2001. Dere K.P., Landi E., Mason H.E., Monsignori Fossi B.C., Young P.R., A&AS, Vol. 125, 149-173, 1997. Feldman U., Mandelbaum P., Seely J.L., Doschek G.A., Gursky H., ApJSS, Vol. 81, 387, 1992. Feldman U., Behring W.E., Curdt W., Schuhle U., Wilhelm K., Lemaire P, and Moran T.M.,ApJSS, Vol. 113, 195-219,1997. Judge P.G., Woods T.N., Brekke P., and Rottman G.J., ApJ, Vol. 445, L85-L88, 1995. Landi E., and Landini M., A&A, Vol. 340, 265-276, 1998. McIntosh S.W., Charbonneau P., and Brown J.C., ApJ, Vol. 529, 1115-1130, 2000. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T., Numerical recipies, Cambridge univ. press, 1986. Vernazza J.E., and Reeves E.M., ApJSS, Vol. 37, 485-513, 1978. Warren H.P., Mariska J.T., Lean J., Marquette W. and A. Johannesson, Geoph. Res. Lett., Vol. 23, 2207-2210, 1996. Warren H.P., Mariska and J.T., Lean J., Journal Geoph. Res., Vol. 103, 12077-12089, 1998 Wilhelm K., and 15 co-authors, Sol. Phys., Vol. 162, 189-231, 1995. Wilhelm K., Lemaire P., Dammasch I.E., Hollandt J., Schüle U., Curdt W., Kucera T., Hassler D.M., Huber M.C.E., A&A , Vol. 334, 685-702, 1998. Withbroe G.L., Sol. Phys., Vol 11, 42-58, 1970. Withbroe G.L., Sol. Phys., Vol 11, 208-221, 1970.

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