retrieving the solar euv spectral irradiance from the observation of 6 lines
TRANSCRIPT
www.elsevier.com/locate/asr
Advances in Space Research 37 (2006) 341–346
Retrieving the solar EUV spectral irradiance from theobservation of 6 lines
M. Kretzschmar a,*, J. Lilensten b, J. Aboudarham c
a Istituto di Fisica dello Spazio Interplanetario, CNR, Via del Fosso del Cavaliere, 100, BP 53, 00133 Roma, Italyb LPG, Bat. D de physique, BP 53, 38041 Saint Martin d�Heres cedex, France
c LESIA, Observatoire de Paris, F-92190 Meudon, France
Received 25 October 2004; received in revised form 4 February 2005; accepted 14 February 2005
Abstract
We use recent solar extreme ultraviolet (EUV) irradiance data from the Solar EUV Experiment aboard the Thermosphere Ion-
osphere Mesosphere Energetics and Dynamics satellite to investigate the possibility to retrieve the whole solar EUV irradiance from
a minimum number of measurements. Computing a differential 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: Solar–terrestrial relationship; Solar EUV irradiance; Differential emission measure
1. Introduction
The extreme ultraviolet (EUV) solar irradiance is cer-
tainly amongst the most important parameters to mon-
itor and forecast space weather. It constitutes the first
and main source for the creation of the ionosphere
and also affects 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 first reference irradiance spectrum SC#21REF was
assembled from measurements performed by the Atmo-
sphere Explorer missions in July 1976 (the radio flux at
0273-1177/$30 � 2005 COSPAR. Published by Elsevier Ltd. All rights reser
doi:10.1016/j.asr.2005.02.029
* Corresponding author.
E-mail address: [email protected] (M. Kretzsch-
mar).
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-
ods of solar activity. Torr et al. (1979) and Torr and
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 II
core-to-wing (C/W) index for the coronal, transition re-
gion, and chromospheric emissions, respectively (Tob-
iska et al., 2000). Another model is EUVAC (Richards
et al., 1994). Its main difference with previous modelsis the reference flux chosen from a rocket observation,
and defines a modified F10.7 proxy named P10.7 that
is the average of the daily F10.7 and the 81-day
ved.
342 M. Kretzschmar et al. / Advances in Space Research 37 (2006) 341–346
smoothed 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 2–3 in the
0–20 nm range in order to match the photoelectron
observations. Warren and co-authors (Warren et al.,
1998, 2001) have undertaken a radically different 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 first 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 different 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 classification 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 differential 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
the 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 fluxes are averaged over all the mea-
surements of the day (typically 14–15 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 first 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:
Iðkij; h;/Þ ¼Z
Gðkij; T ÞfðT ; h;/Þ dT ; ð1Þ
where G(kij,T) is the contribution function of the line,
which depends on atomic parameters, and
fðT ; h;/Þ ¼ n2e
dlh;/dT is the differential 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. Defining the Full Sun DEM fx(T) by
Ix = �G(T)fx(T) dT, with Ix the mean solar intensity
at 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
f�ðT Þ ¼1
2p
Z p=2
0
dhZ p=2
�p=2
d/fðT ; h;/Þsin2h cos /: ð2Þ
Thus, the Full Sun DEM fx defined this way is simply
the sum over the half solar sphere of all the DEM�s 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
the intensity of all the others optically thin lines.
M. Kretzschmar et al. / Advances in Space Research 37 (2006) 341–346 343
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 Rothenflug (1985). The DEM
is represented by the exponential of a Chebyshev poly-
nomial, and we use a Levenberg–Marquardt 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 first day of observation are
shown in Fig. 1. Note that not all of the 5-lines subset
1018
1020
1022
1024
104 105 106 107
10-14
10-13
10-12
10-11
10-10
10-9
10-8
N II 108.5
C III 97.7O IV 55.5
Ne VII 46.5
Fe XVI 33.5
Temperature
DE
M G
( T
)
Fig. 1. (Top) Contribution functions for the 5 lines of the best set.
(Bottom) Full Sun DEM for the first day of observation (full line)
compared with the DEM for the ‘‘quiet Sun’’ region of Kretzschmar
et 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 IðkÞ ¼ Ih � expðk�khk0Þ, with
the 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 (Æk0æ = 57.46) and ratio (ÆIhæ/ILy d = 7.3) over all
the 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 different kinds of variation; however,
other factors might play a role in our method. In partic-
ular, the contribution function of the lines, whichstrongly influence the inversion of Eq. (1), and the math-
ematical procedure used to effectively 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 classification, 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
subset here selected, the N II emission may have coronal
10-5
10-4
344 M. Kretzschmar et al. / Advances in Space Research 37 (2006) 341–346
contribution 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.
1101051009590
959085807570
757065605550
10-6
10-6
10-5
10-4
10-6
10-5
10-4
10-6
10-5
10-4
555045403530
Wavelength (nm)
Flu
x (
W /
m2 /
nm
)
Fig. 2. For each panel, observed (dashed) and modeled (full line)
spectra vs wavelength for the first day of observation. The small upper
plot of each panel shows the relative deviation (Fmodel � Fobs)/Fobs
between �1 and 1, with a zero dashed line. The 5 lines used to compute
the 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.
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 profile 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 difference between observed and computed line pro-
files. 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 profile 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
thick emission dominates (i.e. the Lyman continuum,and above 90 nm) are also reasonably reproduced. The
relative deviation for the integrated irradiance over the
whole spectral range is �17% while the mean relative
deviation is �15%. Local disagreements for the lines
may 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 irradiance
of the 6 lines from the SEE spectrum, computes 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
our results with the original observed irradiance. Fig. 3
M. Kretzschmar et al. / Advances in Space Research 37 (2006) 341–346 345
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 30–35 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, the
O IV line at 78.9 nm is emitted in the solar transition re-
gion, and the 85–90 nm bin is dominated by the Lyman
continuum. These differences are well represented by the
1.2
1.0
0.8
0.6
0.4
0.2
1.2
1.0
0.8
0.6
1.2
1.1
1.0
0.9
0.8
0.7
1.2
1.0
0.8
0.61/1/041/1/031/2/02
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
80-85 nm
H I 102.5 nm
Fig. 3. Observed (dotted) and computed (dashed) variations for
several EUV bins. irradiance have been normalized to the first day.
Rms of the relative deviation (Icalc � Iobs)/Iobs between computed and
observed flux are, respectively (from top to bottom) 0.015, 0.016,
0.011, 0.003, and 0.011.
differences 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 effect and its
dependance on wavelengths are well reproduced, as visi-
ble for the strong irradiance enhancement at the end of
2003.
4. Conclusions
In this work, we have shown that the solar EUV irra-
diance and its variability may be reproduced with a
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 profitable 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.
Acknowledgments
We gratefully acknowledge Tom Woods (LASP,
Boulder) team for providing the SEE/EGS data and
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 NASA�s Office 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 Community�s Human PotentialProgram under contract HPRN-CT-2001-00314 ‘‘Tur-
bulent Boundary Layers in Geospace Plasmas’’.
346 M. Kretzschmar et al. / Advances in Space Research 37 (2006) 341–346
References
Arnaud, M., Raymond, J.C. Iron ionization and recombination rates
and ionization equilibrium. Astrophysical Journal 398, 394–406,
1992.
Arnaud, M., Rothenflug, R. An updated evaluation of recombination
and ionization rates. Astronomy and Astrophysics Supplement
Series 60, 425–457, 1985.
Brekke, P., Thompson, W.T., Woods, T.N., Eparvier, F.G. The
extreme-ultraviolet solar irradiance spectrum observed with the
coronal diagnostic spectrometer (CDS) on SOHO. Astrophysical
Journal 536, 959–970, 2000.
Craig, I.J., Brown, J.C. Inverse Problems in Astronomy: A Guide to
Inversion Strategies for Remotely Sensed Data (Research sup-
ported by SERC). Adam Hilger, Ltd., Bristol, England and
Boston, MA, 1986.
Dere, E., Landi, K.P., Young, P.R., Del Zanna, G. CHIANTI – an
atomic database for emission lines. IV. Extension to X-ray
wavelengths. Astronomy and Astrophysics Supplement Series
134, 331–354, 2001.
Hinteregger, H.E., Fukui, K., Gilson, B.R. Observational, reference
and model data on solar EUV, from measurements on AE-E.
Geophysical Research Letters 8, 1147, 1981.
Kretzschmar, M., Lilensten, J., Aboudarham, J. Variability of the
EUV quiet Sun emission and reference spectrum using summer.
Astronomy & Astrophysics 419, 345–356, 2004.
Mazzotta, P., Mazzitelli, G., Colafrancesco, S., Vittorio, N. Ionization
balance for optically thin plasmas: rate coefficients for all atoms
and ions of the elements H to NI. Astronomy and Astrophysics
Supplement 133, 403–409, 1998.
Meyer, J.-P. Solar–stellar outer atmospheres and energetic particles, and
galactic cosmic rays. Astrophysical Journal Supplement Series, 1985.
Richards, P.G., Fennelly, J.A., Torr, D.G. EUVAC: A solar EUV flux
model for aeronomic calculations. Journal of Geophysical
Research 99, 8981–8992, 1994.
Torr, M.R., Torr, D.G. Ionization frequencies for solar cycle 21 –
revised. Journal of Geophysical Research 90 (July), 6675, 1985.
Torr, M.R., Torr, D.G., Ong, R.A., Hinteregger, H.E. Ionization
frequencies for major thermospheric constituents as a function of
solar cycle 21. Geophysical Research Letters 6 (October), 771, 1979.
Tobiska, W.K. Revised solar extreme ultraviolet flux model. Journal of
Atmospheric and Terrestrial Physics 53, 1005, 1991.
Tobiska, W.K., Barth, A. A solar EUV flux model. Journal of
Geophysical Research 95, 8243, 1990.
Tobiska, W.K., Eparvier, F.G. EUV97: Improvements to EUV
irradiance modeling in the soft X-rays and FUV. Solar Physics
177, 147, 1998.
Tobiska, W.K., Woods, T., Eparvier, F., Viereck, R., Floyd, L.,
Bouwer, D., Rottman, G., White, O.R. The SOLAR2000 empirical
solar irradiance model and forecast tool. Journal of Atmospheric
and Terrestrial Physics 62, 1233–1250, 2000.
Warren, H.P., Mariska, J.T., Lean, J. A new reference spectrum for the
EUV irradiance of the quiet Sun 1. Emission measure formulation.
Journal of Geophysical Research 103, 12091–12102, 1998.
Warren, H.P., Mariska, J.T., Lean, J. A new model of solar EUV
irradiance variability: 1. Model formulation. Journal of Geophys-
ical Research 106, 15745–15758, 2001.
Woods, T.N., Bailey, S.M., Eparvier, F.G., et al. Timed solar EUV
experiment, in: Korendyke, Clarence M. (Ed.), Missions to the Sun
II. Proceedings of the SPIE, vol. 3442, 1998.