Retrieving the solar EUV spectral irradiance from the observation of 6 lines

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<ul><li><p>spn</p><p>ilen</p><p>Via de</p><p>8041</p><p>Paris,</p><p>form</p><p>ta fr</p><p>osphere Mesosphere Energetics and Dynamics satellite to investigate the possibility to retrieve the whole solar EUV irradiance from</p><p>tainly amongst the most important parameters to mon-</p><p>sphere Explorer missions in July 1976 (the radio ux at</p><p>ods of solar activity. Torr et al. (1979) and Torr and</p><p>iska et al., 2000). Another model is EUVAC (Richards</p><p>et al., 1994). Its main dierence with previous modelsis the reference ux chosen from a rocket observation,</p><p>and denes a modied F10.7 proxy named P10.7 that</p><p>is the average of the daily F10.7 and the 81-day</p><p>reserved.</p><p>* Corresponding author.</p><p>E-mail address: (M. Kretzsch-</p><p>mar).</p><p>Advances in Space Research 370273-1177/$30 2005 COSPAR. Published by Elsevier Ltd. All rightsitor and forecast space weather. It constitutes the rst</p><p>and main source for the creation of the ionosphere</p><p>and also aects the thermosphere. The EUV emission</p><p>is strongly variable in all time scale, from minutes (erup-</p><p>tive phenomena) to years (solar cycle) and more.</p><p>In order to reach a better understanding of thesepoints, it is necessary to have real time solar EUV irra-</p><p>diance with the best possible radiometric accuracy. Sev-</p><p>eral solar EUV irradiance models have been developed</p><p>since the 1970s to compensate the lack of observations.</p><p>A rst reference irradiance spectrum SC#21REF was</p><p>assembled from measurements performed by the Atmo-</p><p>Torr (1985) proposed two reference irradiance spectra</p><p>for aeronomy called F79050N (F10.7 = 243) and</p><p>SC#REFW (F10.7 = 68). The UV spectrum was divided</p><p>in 37 bins. Tobiska and co-authors (Tobiska and Barth,</p><p>1990; Tobiska, 1991; Tobiska and Eparvier, 1998) devel-</p><p>oped a model called EUV97, which takes data fromother sources into account. This model takes into ac-</p><p>count the solar emission zone (i.e. chromosphere, coro-</p><p>na) of each line. A new version, SOLAR2000, has been</p><p>recently developed and uses F10.7, Lyman-a, and Mg IIcore-to-wing (C/W) index for the coronal, transition re-</p><p>gion, and chromospheric emissions, respectively (Tob-a minimum number of measurements. Computing a dierential emission measure for the whole Sun from the irradiances of 5 lines</p><p>and using a sixth line to model optically thick emission, we are able to reproduce with a good agreement the variability of the whole</p><p>solar EUV irradiance.</p><p> 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.</p><p>Keywords: Solarterrestrial relationship; Solar EUV irradiance; Dierential emission measure</p><p>1. Introduction</p><p>The extreme ultraviolet (EUV) solar irradiance is cer-</p><p>10.7 cm F10.7 was 70), and given in 1659 wavelengths.</p><p>An extrapolation model (SERF1, Hinteregger et al.,1981) allows estimating the irradiance during other peri-Retrieving the solar EUVobservatio</p><p>M. Kretzschmar a,*, J. L</p><p>a Istituto di Fisica dello Spazio Interplanetario, CNR,b LPG, Bat. D de physique, BP 53, 3</p><p>c LESIA, Observatoire de</p><p>Received 25 October 2004; received in revised</p><p>Abstract</p><p>We use recent solar extreme ultraviolet (EUV) irradiance dadoi:10.1016/j.asr.2005.02.029ectral irradiance from theof 6 lines</p><p>sten b, J. Aboudarham c</p><p>l Fosso del Cavaliere, 100, BP 53, 00133 Roma, Italy</p><p>Saint Martin dHe`res cedex, FranceF-92190 Meudon, France</p><p>4 February 2005; accepted 14 February 2005</p><p>om the Solar EUV Experiment aboard the Thermosphere Ion-</p><p></p><p>(2006) 341346</p></li><li><p>in Spsmoothed F10.7. An important improvement to the EU-</p><p>VAC model was the increase of the solar irradiance, as</p><p>compared to earlier models, by a factor of 23 in the</p><p>020 nm range in order to match the photoelectron</p><p>observations. Warren and co-authors (Warren et al.,</p><p>1998, 2001) have undertaken a radically dierent ap-proach. They combined a spectral emission line data-</p><p>base, solar emission measure distributions, and</p><p>estimates from ground-based solar images of the frac-</p><p>tion of the Sun covered by the various types of activity</p><p>to synthesize the irradiance. One can thus distinguish</p><p>two class of model: the rst one is based on a reference</p><p>irradiance spectrum and its extrapolation using proxies,</p><p>while the second one is based on a combination of refer-ence radiance spectra for the dierent features of the so-</p><p>lar atmosphere.</p><p>All of these solar irradiance models are very impor-</p><p>tant for aeronomic computation and as input for atmo-</p><p>spheric models. However, until 2002 there has been no</p><p>permanent monitoring of the solar EUV irradiance,</p><p>and the lack of data has prevented accurate enough</p><p>modeling of the solar EUV irradiance. Yet, thermo-sphere/ionosphere (T/I) models often make use of prox-</p><p>ies such as F10.7 or the Mg index (Mg II h and k</p><p>emission lines core to wing ratio). Their correlation with</p><p>the solar EUV/UV irradiance is not accurate enough for</p><p>the demanding space weather operation requirement to</p><p>know the solar EUV irradiance with a relative accuracy</p><p>of 10% or better. In December 2001, a new instrument</p><p>devoted to the observation of this part of the solar spec-trum has been launched to space, onboard the Thermo-</p><p>sphere Ionosphere Mesosphere Energetics and</p><p>Dynamics (TIMED) (NASA) spacecraft. The Solar</p><p>EUV Experiment (SEE) (Woods et al., 1998) is com-</p><p>prised of a spectrometer and a suite of photometers de-</p><p>signed to measure solar ultraviolet radiation. In this</p><p>paper, we use TIMED SEE data version 7 of the EUV</p><p>Grating Spectrograph (EGS) to investigate the possibil-ity to retrieve the solar EUV irradiance with spectral res-</p><p>olution from a minimum set of line irradiance</p><p>measurements; this approach is supported by a statisti-</p><p>cal analysis of the solar EUV spectrum, based on clus-</p><p>tering analysis and dendogram classication which</p><p>shows that at least 6 classes of equivalence could be</p><p>drawn in the solar spectrum (Dudok de Wit, personal</p><p>communication).In detail, we succeed in reproducing the solar EUV</p><p>irradiance and its variability from the measurements of</p><p>6 lines. The spectrum reconstruction makes use of a pre-</p><p>vious work aiming at building a quiet Sun reference</p><p>spectrum using dierential emission measure (DEM)</p><p>(Kretzschmar et al., 2004); the optically thin part of</p><p>the spectrum, i.e. the part which escapes freely from</p><p>the Solar atmosphere, is computed using a Full SunDEM, while the optically thick part is deduced from</p><p>342 M. Kretzschmar et al. / Advancesthe measurement of the H I Ly d line at 95 nm.2. EUV irradiance spectrum modeling</p><p>The TIMED SEE EGS consists of two instruments to</p><p>measure the solar vacuum ultraviolet (VUV) spectral</p><p>irradiance from 0.1 nm to 195 nm (Woods et al.,</p><p>1998). The EUV Grating Spectrograph (EGS) is a nor-mal incidence Rowland circle spectrograph that has a</p><p>spectral range of 26 to 195 nm. The SEE level 2 EGS</p><p>data product consists of a spectrum from 26 to 195</p><p>nm per day. The uxes are averaged over all the mea-</p><p>surements of the day (typically 1415 recording se-</p><p>quences of about 3 min) and corrected to one</p><p>astronomical unit. Flare contribution is removed. In this</p><p>work, we use the data from 8 February 2002 to 1 Febru-ary 2004.</p><p>To reproduce the whole EUV spectrum from a min-</p><p>imum number of emission lines, we distinguish between</p><p>optically thin and optically thick emission: the latter is</p><p>assumed to be composed of the continua of C I, H I,</p><p>He I, and He II, some lines emitted between 91 and</p><p>110 nm by low-ionized elements, and the blue wing</p><p>of the H I Ly a line. Contrary to the optically thinlines, optically thick lines cannot be deduced from a</p><p>DEM. We rst describe the procedure for optically</p><p>thin lines.</p><p>2.1. Optically thin emission</p><p>Assuming that a EUV line is optically thin, its inten-</p><p>sity may be computed from the following equation:</p><p>Ikij; h;/ Z</p><p>Gkij; T fT ; h;/ dT ; 1</p><p>where G(kij,T) is the contribution function of the line,which depends on atomic parameters, and</p><p>fT ; h;/ n2e dlh;/dT is the dierential emission measure(DEM) for which the dependance with the foot point</p><p>position of the line of sight has been made explicit.</p><p>The extension of Eq. (1) to the whole Sun is quietstraightforward. Dening the Full Sun DEM fx(T) byIx = G(T)fx(T) dT, with Ix the mean solar intensityat disk center deduced from the line irradiance measure-</p><p>ment, it can then be easily shown that the Full Sun</p><p>DEM is linked to the local DEMs by</p><p>fT 1</p><p>2p</p><p>Z p=20</p><p>dhZ p=2p=2</p><p>d/fT ; h;/sin2h cos/: 2</p><p>Thus, the Full Sun DEM fx dened this way is simplythe sum over the half solar sphere of all the DEMs asso-ciated with each surface element, taking into account the</p><p>geometry and the change of emitting plasma state. Note</p><p>that one cannot retrieve information on the spatial dis-tribution of the emission measure from fx. Eq. (1) al-lows us to compute the DEM from a set of observed</p><p>lines. Once the DEM computed, one is able to compute</p><p>ace Research 37 (2006) 341346the intensity of all the others optically thin lines.</p></li><li><p>The inversion of Eq. (1) involves the computation of</p><p>the contribution functions of the lines, and an adapted</p><p>mathematical procedure. We compute the contribution</p><p>functions using the CHIANTI database (Dere et al.,</p><p>2001), solar abundances from Meyer (1985), and ioniza-</p><p>tion equilibria computed by Arnaud and Raymond(1992) and Arnaud and Rothenug (1985). The DEM</p><p>is represented by the exponential of a Chebyshev poly-</p><p>nomial, and we use a LevenbergMarquardt algorithm</p><p>to compute it.</p><p>The computation of the DEM is a very (and well-</p><p>known, see Craig and Brown, 1986) ill-posed mathemat-</p><p>ical problem, and our main criterion for the choice of</p><p>the lines is simply the success of the computation, as wellas its reproducibility; to this purpose, note that the more</p><p>recent ionization equilibria computed by Mazzotta et al.</p><p>(1998) lead to less stable computation of the DEM.</p><p>While the reason is unclear, this explains while we use</p><p>older computations. Starting with 30 intense lines and</p><p>using a try and test approach to select the subset,</p><p>we found that the lowest number of lines which leads</p><p>to a good agreement is 5. The contribution functionsof the 5 lines forming the best subset and the computed</p><p>DEM obtained for the rst day of observation are</p><p>shown in Fig. 1. Note that not all of the 5-lines subset</p><p>-9</p><p>10-8C III 97.7</p><p>O IV 55.5 Fe XVI 33.5</p><p>M. Kretzschmar et al. / Advances in Sp1018</p><p>1020</p><p>1022</p><p>1024</p><p>104 105 106 107</p><p>10-14</p><p>10-13</p><p>10-12</p><p>10-11</p><p>10-10</p><p>10</p><p>N II 108.5Ne VII 46.5</p><p> Temperature</p><p>DEM</p><p> G</p><p> ( T) </p><p>Fig. 1. (Top) Contribution functions for the 5 lines of the best set.</p><p>(Bottom) Full Sun DEM for the rst day of observation (full line)</p><p>compared with the DEM for the quiet Sun region of Kretzschmaret al. (2004) (dotted).allows to compute the DEM; in fact, only some lines</p><p>of the set of Fig. 1 may be changed (such that using an-</p><p>other Fe XVI line), and the results obtained in these case</p><p>were found to be less satisfying.</p><p>2.2. Optically thick emission</p><p>Optically thick emission can not be modeled using the</p><p>DEM approach. These continua and lines are empiri-</p><p>cally deduced from the measurement of one of them.</p><p>We chose the H I Ly d line at 95 nm as our observed in-dex, its value coming directly from the EGS data; this</p><p>choice is motivated by the relative isolated spectral posi-</p><p>tion of this line, which makes it easier to measure. Thespectral evolution of the continua and of the blue wing</p><p>of the Ly a line is modeled as Ik Ih expkkhk0 , withthe decay values kh assumed constant for each contin-uum. The optically thick lines intensities and the peak</p><p>intensity Ih of each continuum are assumed to be pro-</p><p>portional to the H I Ly d intensity. Ratio values are ta-ken from two averaged quiet Sun spectra previously</p><p>published; in detail, values for the emission of He I,He II, and Ly a are taken from Warren et al. (1998)while the others values, including several lines of low-</p><p>ionized elements between 91 nm and 120 nm, come from</p><p>Kretzschmar et al. (2004). However, neither of the two</p><p>published values for the Lyman continuum was in agree-</p><p>ment with the observation, and we then use the average</p><p>slope (k0 = 57.46) and ratio (Ih/ILy d = 7.3) over allthe samples at our disposition.</p><p>2.3. Discussion on the best subset of lines</p><p>The best subset of lines that we found in that study</p><p>should include the emission lines which are the most rep-</p><p>resentative of the dierent kinds of variation; however,</p><p>other factors might play a role in our method. In partic-</p><p>ular, the contribution function of the lines, whichstrongly inuence the inversion of Eq. (1), and the math-</p><p>ematical procedure used to eectively inverse this equa-</p><p>tion might restrict the capacity of this method to identify</p><p>unambiguously the most representative lines. To tackle</p><p>this problem, we have started a statistical analysis of</p><p>the solar EUV spectrum, based on clustering analysis</p><p>and dendogram classication, which allows to identify</p><p>rigorously other valuable set of lines; results from thisanalysis will be published elsewhere (Dudok de Wit, per-</p><p>sonal communication) and the method presented here</p><p>will then be adapted to the other relevant set of lines.</p><p>This will allow to address instrument issues on this mod-</p><p>eling approach and discuss in more detail its technical</p><p>feasibility. Possible instrument issues include spectral</p><p>resolution, higher grating order corrections, and degra-</p><p>dation with time. Spectral resolution is important in or-der to remove contributions from other lines. For the</p><p>ace Research 37 (2006) 341346 343subset here selected, the N II emission may have coronal</p></li><li><p>thick emission dominates (i.e. the Lyman continuum,and above 90 nm) are also reasonably reproduced. The</p><p>DEM, the optically thin and the optically thick parts</p><p>of the modeled spectrum. For each day, we can thus</p><p>reconstruct the spectrum as shown in Fig. 2 and compare</p><p>1101051009590</p><p>959085807570</p><p>757065605550</p><p>10-6</p><p>10-5</p><p>10-4</p><p>10-6</p><p>10-5</p><p>10-4</p><p>10-6</p><p>10-5</p><p>10-4</p><p>10-6</p><p>10-5</p><p>10-4</p><p>555045403530</p><p>Wavelength (nm)</p><p> Fl</p><p>ux ( W</p><p> / m2 </p><p> / n</p><p>m )</p><p>Fig. 2. For each panel, observed (dashed) and modeled (full line)</p><p>spectra vs wavelength for the rst day of observation. The small upper</p><p>plot of each panel shows the relative deviation (Fmodel Fobs)/Fobsbetween 1 and 1, with a zero dashed line. The 5 lines used to computethe optically thin part of the spectrum are highlighted with a rectangle,</p><p>while the line used to determinate the optically thick part is highlighted</p><p>with an oval.</p><p>in Space Research 37 (2006) 341346relative deviation for the integrated irradiance over the</p><p>whole spectral range is 17% while the mean relativedeviation is 15%. Local disagreements for the linesmay come from one or more failures of the hypothesis</p><p>and/or errors in the atomic parameters.</p><p>It is also interesting to check the capacity of our model</p><p>to reproduce the solar EUV variability time series. Weuse an automatic procedure which extracts the irradiancecontribution from higher order. Since the C III line at</p><p>97.7 nm is very intense, detector degradation in time</p><p>should also be taken into account. As optically thick</p><p>emission is computed using a constant ratio between</p><p>these lines, all optically thick line should give the same</p><p>results. However the H I ly d line is quite spectrally iso-lated and then should be easier to measure. An alterna-</p><p>tive solution could be the strong He I line at 58....</p></li></ul>