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

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    osphere Mesosphere Energetics and Dynamics satellite to investigate the possibility to retrieve the whole solar EUV irradiance from

    tainly amongst the most important parameters to mon-

    sphere Explorer missions in July 1976 (the radio ux at

    ods of solar activity. Torr et al. (1979) and Torr and

    iska et al., 2000). Another model is EUVAC (Richards

    et al., 1994). Its main dierence with previous modelsis the reference ux chosen from a rocket observation,

    and denes a modied F10.7 proxy named P10.7 that

    is the average of the daily F10.7 and the 81-day

    reserved.

    * Corresponding author.

    E-mail address: mkretzschmar@solar.stanford.edu (M. Kretzsch-

    mar).

    Advances in Space Research 370273-1177/$30 2005 COSPAR. Published by Elsevier Ltd. All rightsitor and forecast space weather. It constitutes the rst

    and main source for the creation of the ionosphere

    and also aects the thermosphere. The EUV emission

    is strongly variable in all time scale, from minutes (erup-

    tive phenomena) to years (solar cycle) and more.

    In order to reach a better understanding of thesepoints, it is necessary to have real time solar EUV irra-

    diance with the best possible radiometric accuracy. Sev-

    eral solar EUV irradiance models have been developed

    since the 1970s to compensate the lack of observations.

    A rst reference irradiance spectrum SC#21REF was

    assembled from measurements performed by the Atmo-

    Torr (1985) proposed two reference irradiance spectra

    for aeronomy called F79050N (F10.7 = 243) and

    SC#REFW (F10.7 = 68). The UV spectrum was divided

    in 37 bins. Tobiska and co-authors (Tobiska and Barth,

    1990; Tobiska, 1991; Tobiska and Eparvier, 1998) devel-

    oped a model called EUV97, which takes data fromother sources into account. This model takes into ac-

    count the solar emission zone (i.e. chromosphere, coro-

    na) of each line. A new version, SOLAR2000, has been

    recently developed and uses F10.7, Lyman-a, and Mg IIcore-to-wing (C/W) index for the coronal, transition re-

    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

    and using a sixth line to model optically thick emission, we are able to reproduce with a good agreement the variability of the whole

    solar EUV irradiance.

    2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

    Keywords: Solarterrestrial relationship; Solar EUV irradiance; Dierential emission measure

    1. Introduction

    The extreme ultraviolet (EUV) solar irradiance is cer-

    10.7 cm F10.7 was 70), and given in 1659 wavelengths.

    An extrapolation model (SERF1, Hinteregger et al.,1981) allows estimating the irradiance during other peri-Retrieving the solar EUVobservatio

    M. Kretzschmar a,*, J. L

    a Istituto di Fisica dello Spazio Interplanetario, CNR,b LPG, Bat. D de physique, BP 53, 3

    c LESIA, Observatoire de

    Received 25 October 2004; received in revised

    Abstract

    We use recent solar extreme ultraviolet (EUV) irradiance dadoi:10.1016/j.asr.2005.02.029ectral irradiance from theof 6 lines

    sten b, J. Aboudarham c

    l Fosso del Cavaliere, 100, BP 53, 00133 Roma, Italy

    Saint Martin dHe`res cedex, FranceF-92190 Meudon, France

    4 February 2005; accepted 14 February 2005

    om the Solar EUV Experiment aboard the Thermosphere Ion-

    www.elsevier.com/locate/asr

    (2006) 341346

  • in Spsmoothed F10.7. An important improvement to the EU-

    VAC model was the increase of the solar irradiance, as

    compared to earlier models, by a factor of 23 in the

    020 nm range in order to match the photoelectron

    observations. Warren and co-authors (Warren et al.,

    1998, 2001) have undertaken a radically dierent ap-proach. They combined a spectral emission line data-

    base, solar emission measure distributions, and

    estimates from ground-based solar images of the frac-

    tion of the Sun covered by the various types of activity

    to synthesize the irradiance. One can thus distinguish

    two class of model: the rst one is based on a reference

    irradiance spectrum and its extrapolation using proxies,

    while the second one is based on a combination of refer-ence radiance spectra for the dierent features of the so-

    lar atmosphere.

    All of these solar irradiance models are very impor-

    tant for aeronomic computation and as input for atmo-

    spheric models. However, until 2002 there has been no

    permanent monitoring of the solar EUV irradiance,

    and the lack of data has prevented accurate enough

    modeling of the solar EUV irradiance. Yet, thermo-sphere/ionosphere (T/I) models often make use of prox-

    ies such as F10.7 or the Mg index (Mg II h and k

    emission lines core to wing ratio). Their correlation with

    the solar EUV/UV irradiance is not accurate enough for

    the demanding space weather operation requirement to

    know the solar EUV irradiance with a relative accuracy

    of 10% or better. In December 2001, a new instrument

    devoted to the observation of this part of the solar spec-trum has been launched to space, onboard the Thermo-

    sphere Ionosphere Mesosphere Energetics and

    Dynamics (TIMED) (NASA) spacecraft. The Solar

    EUV Experiment (SEE) (Woods et al., 1998) is com-

    prised of a spectrometer and a suite of photometers de-

    signed to measure solar ultraviolet radiation. In this

    paper, we use TIMED SEE data version 7 of the EUV

    Grating Spectrograph (EGS) to investigate the possibil-ity to retrieve the solar EUV irradiance with spectral res-

    olution from a minimum set of line irradiance

    measurements; this approach is supported by a statisti-

    cal analysis of the solar EUV spectrum, based on clus-

    tering analysis and dendogram classication which

    shows that at least 6 classes of equivalence could be

    drawn in the solar spectrum (Dudok de Wit, personal

    communication).In detail, we succeed in reproducing the solar EUV

    irradiance and its variability from the measurements of

    6 lines. The spectrum reconstruction makes use of a pre-

    vious work aiming at building a quiet Sun reference

    spectrum using dierential emission measure (DEM)

    (Kretzschmar et al., 2004); the optically thin part of

    the spectrum, i.e. the part which escapes freely from

    the Solar atmosphere, is computed using a Full SunDEM, while the optically thick part is deduced from

    342 M. Kretzschmar et al. / Advancesthe measurement of the H I Ly d line at 95 nm.2. EUV irradiance spectrum modeling

    The TIMED SEE EGS consists of two instruments to

    measure the solar vacuum ultraviolet (VUV) spectral

    irradiance from 0.1 nm to 195 nm (Woods et al.,

    1998). The EUV Grating Spectrograph (EGS) is a nor-mal incidence Rowland circle spectrograph that has a

    spectral range of 26 to 195 nm. The SEE level 2 EGS

    data product consists of a spectrum from 26 to 195

    nm per day. The uxes are averaged over all the mea-

    surements of the day (typically 1415 recording se-

    quences of about 3 min) and corrected to one

    astronomical unit. Flare contribution is removed. In this

    work, we use the data from 8 February 2002 to 1 Febru-ary 2004.

    To reproduce the whole EUV spectrum from a min-

    imum number of emission lines, we distinguish between

    optically thin and optically thick emission: the latter is

    assumed to be composed of the continua of C I, H I,

    He I, and He II, some lines emitted between 91 and

    110 nm by low-ionized elements, and the blue wing

    of the H I Ly a line. Contrary to the optically thinlines, optically thick lines cannot be deduced from a

    DEM. We rst describe the procedure for optically

    thin lines.

    2.1. Optically thin emission

    Assuming that a EUV line is optically thin, its inten-

    sity may be computed from the following equation:

    Ikij; h;/ Z

    Gkij; T fT ; h;/ dT ; 1

    where G(kij,T) is the contribution function of the line,which depends on atomic parameters, and

    fT ; h;/ n2e dlh;/dT is the dierential emission measure(DEM) for which the dependance with the foot point

    position of the line of sight has been made explicit.

    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-

    ment, it can then be easily shown that the Full Sun

    DEM is linked to the local DEMs by

    fT 1

    2p

    Z p=20

    dhZ p=2p=2

    d/fT ; h;/sin2h cos/: 2

    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

    geometry and the change of emitting plasma state. Note

    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

    lines. Once the DEM computed, one is able to compute

    ace Research 37 (2006) 341346the intensity of all the others optically thin lines.

  • The inversion of Eq. (1) involves the computation of

    the contribution functions of the lines, and an adapted

    mathematical procedure. We compute the contribution

    functions using the CHIANTI database (Dere et al.,

    2001), solar abundances from Meyer (1985), and ioniza-

    tion equilibria computed by Arnaud and Raymond(1992) and Arnaud and Rothenug (1985). The DEM

    is represented by the exponential of a Chebyshev poly-

    nomial, and we use a LevenbergMarquardt algorithm

    to compute it.

    The computation of the DEM is a very (and well-

    known, see Craig and Brown, 1986) ill-posed mathemat-

    ical problem, and our main criterion for the choice of

    the lines is simply the success of the computation, as wellas its reproducibility; to this purpose, note that the more

    recent ionization equilibria computed by Mazzotta et al.

    (1998) lead to less stable computation of the DEM.

    While the reason is unclear, this explains while we use

    older computations. Starting with 30 intense lines and

    using a try and test approach to select the subset,

    we found that the lowest number of lines which leads

    to a good agreement is 5. The contribution functionsof the 5 lines forming the best subset and the computed

    DEM obtained for the rst day of observation are

    shown in Fig. 1. Note that not all of the 5-lines subset

    -9

    10-8C III 97.7

    O IV 55.5 Fe XVI 33.5

    M. Kretzschmar et al. / Advances in Sp1018

    1020

    1022

    1024

    104 105 106 107

    10-14

    10-13

    10-12

    10-11

    10-10

    10

    N II 108.5Ne VII 46.5

    Temperature

    DEM

    G

    ( T)

    Fig. 1. (Top) Contribution functions for the 5 lines of the best set.

    (Bottom) Full Sun DEM for the rst day of observation (full line)

    compared with the DEM for the quiet Sun region of Kretzschmaret al. (2004) (dotted).allows to compute the DEM; in fact, only some lines

    of the set of Fig. 1 may be changed (such that using an-

    other Fe XVI line), and the results obtained in these case

    were found to be less satisfying.

    2.2. Optically thick emission

    Optically thick emission can not be modeled using the

    DEM approach. These continua and lines are empiri-

    cally deduced from the measurement of one of them.

    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

    choice is motivated by the relative isolated spectral posi-

    tion of this line, which makes it easier to measure. Thespectral evolution of the continua and of the blue wing

    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

    intensity Ih of each continuum are assumed to be pro-

    portional to the H I Ly d intensity. Ratio values are ta-ken from two averaged quiet Sun spectra previously

    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-

    ionized elements between 91 nm and 120 nm, come from

    Kretzschmar et al. (2004). However, neither of the two

    published values for the Lyman continuum was in agree-

    ment with the observation, and we then use the average

    slope (k0 = 57.46) and ratio (Ih/ILy d = 7.3) over allthe samples at our disposition.

    2.3. Discussion on the best subset of lines

    The best subset of lines that we found in that study

    should include the emission lines which are the most rep-

    resentative of the dierent kinds of variation; however,

    other factors might play a role in our method. In partic-

    ular, the contribution function of the lines, whichstrongly inuence the inversion of Eq. (1), and the math-

    ematical procedure used to eectively inverse this equa-

    tion might restrict the capacity of this method to identify

    unambiguously the most representative lines. To tackle

    this problem, we have started a statistical analysis of

    the solar EUV spectrum, based on clustering analysis

    and dendogram classication, which allows to identify

    rigorously other valuable set of lines; results from thisanalysis will be published elsewhere (Dudok de Wit, per-

    sonal communication) and the method presented here

    will then be adapted to the other relevant set of lines.

    This will allow to address instrument issues on this mod-

    eling approach and discuss in more detail its technical

    feasibility. Possible instrument issues include spectral

    resolution, higher grating order corrections, and degra-

    dation with time. Spectral resolution is important in or-der to remove contributions from other lines. For the

    ace Research 37 (2006) 341346 343subset here selected, the N II emission may have coronal

  • thick emission dominates (i.e. the Lyman continuum,and above 90 nm) are also reasonably reproduced. The

    DEM, the optically thin and the optically thick parts

    of the modeled spectrum. For each day, we can thus

    reconstruct the spectrum as shown in Fig. 2 and compare

    1101051009590

    959085807570

    757065605550

    10-6

    10-5

    10-4

    10-6

    10-5

    10-4

    10-6

    10-5

    10-4

    10-6

    10-5

    10-4

    555045403530

    Wavelength (nm)

    Fl

    ux ( W

    / m2

    / n

    m )

    Fig. 2. For each panel, observed (dashed) and modeled (full line)

    spectra vs wavelength for the rst day of observation. The small upper

    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,

    while the line used to determinate the optically thick part is highlighted

    with an oval.

    in Space Research 37 (2006) 341346relative deviation for the integrated irradiance over the

    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

    and/or errors in the atomic parameters.

    It is also interesting to check the capacity of our model

    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

    97.7 nm is very intense, detector degradation in time

    should also be taken into account. As optically thick

    emission is computed using a constant ratio between

    these lines, all optically thick line should give the same

    results. However the H I ly d line is quite spectrally iso-lated and then should be easier to measure. An alterna-

    tive solution could be the strong He I line at 58.4 nm.

    3. Results

    The spectral range of the modeled spectra here pre-

    sented is 26 nm 6 k 6 110 nm. The lower limit corre-sponds to the lower bound of the EGS spectrum while

    the upper limit corresponds to the usual upper limit in

    the EUV irradiance models. We plan to extend the

    model output in the XUV range; a preliminary analysis

    suggest that the model underestimates the irradiance at

    short wavelength and that we must add other emission

    lines and/or emission mechanisms. Fig. 2 shows the

    TIMED-SEE spectrum measured on 8 February 2002,with the one deduced from the 6 lines; the lines of the

    computed spectrum have been convoluted with a Gauss-

    ian prole with a 3 A width. The background emission

    in the computed spectrum is generally 60% lower below

    70 nm; a part of this disagreement can be explained by

    the dierence between observed and computed line pro-

    les. As can be seen from the plots of the relative devi-

    ation, the distribution of the photons in the core and thefar wings of the prole is badly reproduced while the

    integrated irradiance is in better agreement (see for

    example the line at 58 nm). However, this alone can-not explain the whole disagreement and it is yet not clear

    if this lower computed irradiance is due to the lack of

    numerous low intensity emission lines in our model, or

    if other emission processes have to be included. Another

    possibility is that the correction for grating scatteredlight might not be large enough in the EGS data at these

    shorter wavelengths. Brekke et al. (2000) show higher

    wing results for the rocket EGS data as compared

    to the higher spectral resolution measurements by

    SOHO CDS.

    All the observed intense EUV lines appear in our

    model and the parts of the spectrum where optically

    344 M. Kretzschmar et al. / Advancesof the 6 lines from the SEE spectrum, computes the our results with the original observed irradiance. Fig. 3

  • shows this comparison for 5 wavelength bins in the for-

    mat generally used by T/I modelers (Torr et al., 1979).

    The irradiance of the 3035 nm bin is dominated by coro-

    nal lines near 1 MK (the contribution from the He II line

    at 30.34 nm is subtracted and the emission is then dom-

    inated by lines Mg VIII, Si VIII, Al VIII, Al X and theblue wing of a Fe XIV line), the He I line at 58.43 nm

    and H I Ly b line at 102.5 nm are optically thick, theO IV line at 78.9 nm is emitted in the solar transition re-

    gion, and the 8590 nm bin is dominated by the Lyman

    continuum. These dierences are well represented by the

    In this work, we have shown that the solar EUV irra-

    diance and its variability may be reproduced with a

    We gratefully acknowledge Tom Woods (LASP,

    Boulder) team for providing the SEE/EGS data and

    1.21.00.80.60.40.21.2

    1.0

    0.8

    0.6

    1.21.11.00.90.80.7

    Rel

    ativ

    e V

    aria

    tion

    1.2

    1.0

    0.8

    0.6

    30-35 nm

    He I 58.43 nm

    O IV 78.9 nm

    H I 102.5 nm

    M. Kretzschmar et al. / Advances in Sp1.2

    1.0

    0.8

    0.61/1/041/1/031/2/02

    80-85 nm

    Fig. 3. Observed (dotted) and computed (dashed) variations for

    several EUV bins. irradiance have been normalized to the rst day.

    Rms of the relative deviation (Icalc Iobs)/Iobs between computed andobserved ux are, respectively (from top to bottom) 0.015, 0.016,0.011, 0.003, and 0.011.Thierry Dudok de Wit (LPCE, Orleans) for useful dis-cussions. The TIMED spacecraft was developed by the

    Johns Hopkins University Applied Physics Laboratory.

    The TIMED mission, including the SEE instrument, is

    sponsored by NASAs Oce of Space Science. CHI-ANTI is a collaborative project involving the NRL

    (USA), RAL (UK), and the Universities of Florence

    (Italy) and Cambridge (UK). MK acknowledges sup-

    port by the European Communitys Human PotentialProgram under contract HPRN-CT-2001-00314 Tur-good precision from the observation of 6 lines. In partic-

    ular, the mid-term variability has been recovered suc-

    cessfully by this method which, in our opinion, may be

    a good candidate to model the solar EUV irradiance

    variability at shorter time scale, where eruptions take

    place.In order to investigate furthermore the possibility to

    retrieve the solar EUV irradiance from the observation

    of a few lines, we refer to a statistical analysis in progress

    of the solar EUV spectrum which aims at identifying

    other relevant subset of lines (Dudok de Wit, personal

    communication). The method to reconstruct the EUV

    spectrum presented here will then be adapted to these

    other subsets, with protable comparison of the results,and more instrument oriented discussion.

    This method relies on the direct observation of 6 solar

    EUV lines without spatial resolution and has good po-

    tential to predict the solar irradiance at all EUV wave-

    lengths at possibly a lower instrument cost than a

    spectrograph that observes over the full EUV range.

    However, the good results obtained here through the

    Full Sun DEM computation can be of interests for otherexperiments, such as those for solar imaging.

    Acknowledgmentsdierences in the amplitude of the irradiance variations

    for these bins in Fig. 3. As seen from the closed vicinity

    of the curves for each boxes, our model is able to repro-

    duce with a good precision the long term (decrease due to

    the descending phase of the solar cycle) and mid term

    (solar rotation with period of 27 days) variations. More-over, the amplitude of the solar rotation eect and its

    dependance on wavelengths are well reproduced, as visi-

    ble for the strong irradiance enhancement at the end of

    2003.

    4. Conclusions

    ace Research 37 (2006) 341346 345bulent Boundary Layers in Geospace Plasmas.

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    346 M. Kretzschmar et al. / Advances in Space Research 37 (2006) 341346

    Retrieving the solar EUV spectral irradiance from the observation of 6 linesIntroductionEUV irradiance spectrum modelingOptically thin emissionOptically thick emissionDiscussion on the best subset of lines

    ResultsConclusionsAcknowledgmentsReferences

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