High-resolution solar spectral irradiance from extreme ultraviolet to far infrared

Authors


Abstract

[1] This paper presents new extremely high-resolution solar spectral irradiance (SSI) calculations covering wavelengths from 0.12 nm to 100 micron obtained by the Solar Irradiance Physical Modeling (SRPM) system. Daily solar irradiance spectra were constructed for most of Solar Cycle 23 based on a set of physical models of the solar features and non-LTE calculations of their emitted spectra as function of viewing angle, and solar images specifying the distribution of features on the solar disk. Various observational tests are used to assess the quality of the spectra provided here. The present work emphasizes the effects on the SSI of the upper chromosphere and full-non-LTE radiative transfer calculation of level populations and ionizations that are essential for physically consistent results at UV wavelengths and for deep lines in the visible and IR. This paper also considers the photodissociation continuum opacity of molecular species, e.g., CH and OH, and proposes the consideration of NH photodissociation which can solve the puzzle of the missing near-UV opacity in the spectral range of the near-UV. Finally, this paper is based on physical models of the solar atmosphere and extends the previous lower-layer models into the upper-transition-region and coronal layers that are the dominant source of photons at wavelengths shorter than ∼50 nm (except for the He II 30.4 nm line, mainly formed in the lower-transition-region).

1. Introduction

[2] The solar spectral irradiance (SSI), i.e., the radiative flux incident at the top of the atmosphere, is an essential boundary condition to radiative transfer in the Earth's atmosphere and the main energy source that feeds the thermodynamics and dynamics of the Earth's atmosphere. The absorption of radiation by the atmosphere, ocean, and land, is wavelength dependent and in the case of the atmosphere it is sensitive to some high-resolution spectral details. Thus, it is important to accurately consider the solar irradiance spectrum at very high-resolution to make it possible to compute the effect of radiation on the various absorbing species. So far several irradiance spectra exist at various resolutions, absolute accuracy, and coverage. A complete, high-resolution, absolutely calibrated spectrum has not been reported from observations so far because of the difficulty of such measurement from space and the impossibility of accurately gathering and correcting ground-based data at all wavelengths.

[3] The Solar Irradiance Physical Modeling (SRPM) system is a set of tools for enabling physical models of the solar atmosphere to be devised and used for assessing the solar radiance (or emitted intensity) and irradiance spectra of the Sun and similar stars. In this paper, this system is applied to produce complete ultra-high resolution Solar Spectral Irradiance (SSI) computed for most of the last solar activity cycle.

[4] Here the radiance (i.e., emitted intensity) for ten observation angles is computed for seven “components” that correspond to the main features observed in medium-resolution, ∼2 arc sec, images of the solar disk. These components were defined in a previous paper by Fontenla et al. [2009, hereafter Paper III], and those physical models are somewhat modified here as described in a later section. The SSI is computed by adding the contributions of these components and using their distribution over the solar disk determined from the Precision Solar Photometric Telescope (PSPT) [Coulter and Kuhn, 1994] instrument at the Osservatorio Astronomico di Roma (OAR) [Ermolli et al., 1998, 2007] during most of the Solar Cycle 23. This paper describes the comparison of these spectra with various observations. A similar PSPT instrument operates at the Mauna Loa Solar Observatory (MLSO) [Rast et al., 1999], and differs only by minor hardware characteristics and operational strategies but the available well calibrated observations from MLSO do not extend over the period considered here. The PSPT telescopes achieve ∼0.1% pixel-to-pixel relative photometric precision and typically acquire full-disk solar images through a set of narrow-band interference filters, which includes two filters centered on the red continuum (607.09 nm with FWHM ∼0.46 nm) and the Ca II K line (393.41 nm with FWHM ∼0.27 nm).

[5] The OAR observations were processed for instrument calibration, re-sizing and alignment of the solar disk as described by Ermolli et al. [2010]. The images at the two wavelengths are obtained within minutes to allow good alignment of the various features that include sunspot umbra and penumbra (features S and R in Table 1) with the other features that for the present study include B, D, F, H, and P. The various solar features seen in each observation pair were singled out using the decomposition method described by Fontenla and Harder [2005]. Briefly, the method utilizes a contrast threshold scheme derived from partitioning intensity histograms constructed from the images as a function of heliocentric angle (an example of these histograms is shown by Fontenla et al. [2009]).

Table 1. Solar Features Designation and Corresponding Model Indices
FeatureDescriptionPhotosphere-Chromosphere Model IndexCorona Model Index
ADark quiet-Sun inter-network10001010
BQuiet-Sun inter-network10011011
DQuiet-Sun network lane10021012
FEnhanced network10031013
HPlage (that is not facula)10041014
PFacula (i.e., very bright plage)10051015
SSunspot umbra10061016
RSunspot penumbra10071017
QHot facula10081018

[6] Ground-based observations can achieve very high spectral resolution, e.g., using Fourier transform spectrometers (FTS) instruments, to discern detailed line profiles, continuum and densely packed lines. However, these data lack accurate absolute calibration and cannot provide intrinsic absolute intensity levels due to the effects of the Earth atmosphere, which include telluric lines and continuum scattering by aerosol particles. Attempts to correct for atmospheric effects have relied on variations due to zenith angle, but although these can correct for some effects they cannot be extremely precise because of atmospheric changes within the day. Moreover, at wavelengths shorter than ∼360 nm observations from the ground cannot be made because of the very heavy atmospheric absorption, and the same is true for several infrared bands.

[7] Space-based accurate observations are currently available [e.g., Thuillier et al., 2003; Harder et al., 2010], but only at limited spectral resolution and spectral ranges. Also, there are significant limitations that result from the observational techniques. In particular, at UV wavelengths instrument degradation is a very serious issue that results in significant uncertainties. Another limitation is the inability to discriminate the very rich spectral features in the violet and near-UV spectrum due to limited spectral resolution. In the FUV and EUV well calibrated comprehensive observations of the SSI from space have been published but again at limited resolution. Recently SSI variations over the part of the declining of the past solar cycle have been measured in the visible and infrared [Harder et al., 2009] and in the FUV [McClintock et al., 2005]. Also other EUV SSI observations have been obtained since 2002 [Woods et al., 2005, 2009].

[8] The goal of this paper is to present a complete and very high resolution SSI that can be used for current atmospheric calculations and that can be extended to historical periods. For this, the solar-feature atmospheric models described by Fontenla et al. [2009] were modified and complemented by the work described here. These physical models are used here to construct the complete solar spectra emitted by these physical models in each direction (corresponding to center-to-limb behavior) and ultimately weighted and added to construct the SSI during Solar Cycle 23. The resulting spectra permit comparison with the available SSI observations, inferring future SSI, understanding the role of various solar surface features, understanding the total solar irradiance (TSI) in terms of the various wavelength contributions, and evaluation of the effects of SSI change on the atmospheres of the Earth and other planets. In addition, the calculations in this paper permit comparison with the effects of different physical processes in the solar atmosphere and other stars of solar type. The data and results from the calculations described here are made available at http://www.digidyna.com/Results2010/ as much as practically possible, and interested persons are invited to request additional data from the first author of this paper.

[9] The present work uses the class of semi-empirical physical models of the solar atmosphere that are derived from observations and limited theory. Such models utilize the insight gained from the theory but mainly rely on observations and parametric descriptions of physical processes that are not well understood or cannot be computed in full detail. The reason for using these models is their capability to assimilate the observations and match them with high accuracy.

[10] Another class of models is based only on available quantitative theory of physical processes, much more limited observational constraints, and boundary conditions. The existing purely theoretical models of the solar atmosphere are not yet sufficiently precise because, while they use sophisticated time-dependent three-dimensional simulations, they must resort to highly simplified radiative transfer and suffer from the lack of understanding of the chromospheric and coronal heating mechanisms. Such atmospheric models, however, provide essential insight on the physical processes that determine the solar photosphere atmospheric structure and they are continuously improving. At some point it might be possible that these models will replace the semi-empirical ones, although the very large range of scales involved makes likely that parametric descriptions will still be needed even in a theoretical approach. Such a hybrid approach in which theory and observations complement each other is used in many fields including simulations of the Earth's atmosphere.

[11] As this paper shows, so far the radiance and irradiance spectra obtained from semi-empirical models are very successful at reproducing most of the observations relevant to SSI. The solar atmospheric models used here are highly simplified but in a different way from the theoretical ones. The present atmospheric models are very sophisticated in the treatment of radiation spectra and non-LTE (hereafter NLTE) effects but they assume a steady state one-dimensional structure, in which parametric quantities describe the important effects of the fine structure. These atmospheric models consider radiation-effective physical parameters averaged over the fine spatial and temporal structures, but they model the medium-resolution spatial scales of ∼2–3 arc sec and time scales of hours that are most relevant to the SSI. The effective physical parameters are established in order to satisfy the basic physical assumptions applicable to the solar atmosphere environment and for the emitted spectrum to match the well-understood observations at as many wavelengths as possible. Therefore, it is clear that these models can describe the observations that were used to construct them, which include the data shown in this paper, the additional auxiliary material, and other material not shown but published in the bibliography. Of course, the argument in favor of the semi-empirical models is a circular one, and only computation at all wavelengths and extensive comparison with observations can “validate” this type of models. Because the observations are incomplete or ambiguous there is always a margin of uncertainty. However, this margin is reduced when sufficient number of reliable and relevant observations is used even if there are inherent limitations to these observations.

[12] The atmospheric model set considered here is essentially that of Fontenla et al. [2009]. This and previous papers [Fontenla et al., 2006, 2007] describe model set designations and the way the models were constructed. For completeness these designations are repeated in Table 1 here where two new features are introduced, namely A and Q.

[13] The present paper describes the updates made to the physical models of the solar atmospheric features in the set, the calculations of the complete radiance (or emitted intensity) spectra for every solar feature, the results of the solar spectral irradiance (SSI) obtained by applying the synthesis method described by Fontenla and Harder [2005], and comparisons with observations.

[14] It is shown here that consideration of sufficient species and atomic levels, and full non-LTE calculations is very important and yields a good match to observations at essentially all wavelengths from the EUV to the far infrared. However, this paper points out some wavelengths at which the current calculations need improvement and proposes mechanisms to solve the main remaining issues.

2. Semi-empirical Atmospheric Models of Solar Features

[15] A few modifications to the photosphere of the plage models were carried out to assure a reasonable behavior of the spectrally integrated radiative losses and to better match the SORCE/SIM observations of solar irradiance variations over the decay of the last solar cycle. A separate paper (J. W. Harder et al., manuscript in preparation, 2011) will show the comparison of the calculated spectrum with the SORCE/SIM observations. Complete listings of the physical parameters of all the atmospheres in the present set can be found in this paper's electronic tables, or at the Website http://www.digidyna.com/Results2010/. A separate paper (J. M. Fontenla et al., manuscript in preparation, 2011) describes the methods used to adjust the transition region in the physical models that are a key part of the improvements to the 2009 models. These adjustments are based on the consideration of coronal loop foot points, but other adjustments are made in this paper to approximately describe the presence of chromospheric hot loops (8000 K < T < 40,000 K) that are needed for explaining some UV lines and continua.

[16] Figure 1 shows the temperature versus height for the current set of models (except for the sunspot umbra and penumbra). This figure include two new extreme models, model 1000 (feature A) for regions of very weak chromospheric enhancement, and model 1008 (feature Q) for very strong facula. The coronal part of the very strong facula, model 1018, reaches a coronal temperature of about 3 MK. These additional physical models are still under development and have not been used for the current SSI solar cycle synthesis. For these additional models detailed quantitative data is still been gathered and analyzed, and in addition reliable use of images to identify them is not yet implemented in SRPM. The identification of these features is in principle possible using SDO/AIA data and will be incorporated in the near future.

Figure 1.

Temperature vs. height for the solar atmospheric features. Dotted lines correspond to models of footpoints of coronal loops (see Section 5.5), and solid lines correspond to the final models adopted. (top left) The entire photosphere and chromosphere for the models representing various solar features as indicated in Table 1. (top right) The detail of the lower transition-region for the models representing various solar features as indicated in Table 1. (bottom left) The detail of the upper transition-region for the models representing various solar features as indicated in Table 1. (bottom right) The coronal portions of the models as indicated in Table 1.

[17] The coronal part of the models shows regions that are consistent with eclipse measurements at low altitude above the limb, height of ∼100 Mm corresponds to 1.15 solar radii, and show temperature values that are broadly consistent with the measurements by Guhathakurta et al. [1992] and Habbal et al. [2010] from forbidden lines of Fe at various ionization stages. The density values are not shown here but are also broadly consistent. Eclipse measurements are ambiguous for discerning the structure along the line of sight; STEREO observations are better positioned for that diagnostic but they are spectrally more ambiguous because of the broadness of the filters and uncertainties in atomic data.

[18] The SSI presented here for the low solar activity state in 2008–2009 is dominated by model 1001 (Internetwork, feature B) which covers most of the solar disk. However, another component, model 1002 (network, feature D) is also present in that solar state. This component differs little from the Internetwork and in this period only covers ∼19% of the solar disk area. Moreover, also a small relative area (∼1%) is occupied by model 1003 (active network, feature F) that has a higher contrast. Also, some activity features appear from time to time during that period.

[19] It is found here that, despite the relatively small contrasts of the network with respect to those of active regions, the relative areas of the network components are large and vary over the solar cycle. It is found that at some wavelengths the variations of the network contribute to the overall solar cycle change of the SSI about as much as the active region related features, but spectrally in a somewhat different way.

[20] In the following we designate as SRPM QS the spectra computed by assuming a uniform random pixels distribution over the solar disk of feature D covering 20% of the solar disk, and the rest covered by feature B. This case would correspond to a very low activity case, slightly lower than in 2009, but perhaps even lower could be possible if considering the dark inter-network feature A.

[21] Even for the lowest observed activity state, the overall solar atmosphere displays a temperature increase in its outer layers. The upper chromosphere, with T∼6300 K, and the corona, with T∼1.4 MK are diminished but still substantial at solar activity minimum. Of course, the chromosphere-corona transition region is also included in the models used here and these outer layers are very important for the EUV irradiance due to their abundant UV emission lines at wavelengths shorter than ∼160 nm.

[22] The temperature increase in the outer layers exists even in the quietest solar-type stars [e.g., Wilson and Bappu, 1957; Wilson, 1966; Jordan, 1969], and the emission lines produced are quite sensitive to solar activity. Speculation about the sources of the observed non-radiative chromospheric and coronal heating is abundant in the literature [see Fontenla et al., 2008, and references therein]. The models used here have a semi-empirically determined temperature versus height because the theoretical details of the heating mechanism are not critical for the present paper and so far theories have not been able to quantitatively reproduce the observations.

[23] Other important improvements to the previous calculations involve substantially improving the NLTE computations by including more frequencies in each line and continuum transition, and more species in the full-NLTE calculations.

[24] On the solar disk most lines at wavelengths longer than ∼200 nm are absorption lines formed in the photosphere and lower chromosphere. It is shown in eclipses that at the solar limb these lines turn into emission as the continuum intensity decreases faster than the line intensity for increasing height. Historically this property originated the designation of solar “photosphere” and “chromosphere.” In the temperature versus pressure plots there is no break between the photosphere and low chromosphere. The distinction between these layers indeed was not based on the temperature behavior but rather on the fact that the continuum visible opacity is very important in the photosphere but is insignificant in the chromosphere.

[25] The distinction between the lower and upper chromosphere is that, while in the lower chromosphere the temperature continues the outward decreasing trend of the photosphere, the upper chromosphere has a rise in the temperature to a plateau remaining mostly flat until the steep increase of the chromosphere-corona transition region occurs. The transition-region outward temperature rapid increase produces strong emission lines at FUV and EUV wavelengths.

[26] The absorption cores of the deep visible lines and the absorption lines at wavelengths shorter than ∼400 nm form in the lower chromosphere. But some of the deeper parts of very strong lines (e.g., Hα, Hβ, Na I D1 and 2, etc) are formed in the upper chromosphere and normally do not display emissions. This is also the case of many lines in the range 200–400 nm and a few in the infrared. If one were to compute these lines under the assumption of LTE a large central emission would be produced by the increased temperature of the upper chromosphere; however NLTE effects prevent such emission cores.

[27] In addition, the presence of the upper chromosphere produces UV back illumination on the lower chromosphere and thereby reduces (with respect to LTE) the amount of some neutral species in these layers. This effect is most important for species in which the first-ionization potential is lower than ∼6 eV (low-FIP elements). Because of this over-ionization effect the depth of many absorption lines from neutral low-FIP elements are reduced.

[28] These issues make it impossible to produce a reasonable SSI, or a solar-type stellar flux, assuming LTE. Of course, the problems with the LTE approximation described above produce a complete break-down at wavelengths shorter than ∼200 nm because they would produce huge unobserved emissions. Some computer codes resort to arbitrary “fixes” to avoid these emissions. In contrast, the present calculations do not suffer of these kinds of problems because they use full-non-LTE radiative transfer for the species listed in Table 2 and optically thin NLTE for others, and therefore does not resort to arbitrary fixes.

Table 2. Currently Computed Full NLTE Radiative Transfer
Ion (I)Levels (I)Ion (II)Levels (II)Ion (III)Levels (III)Abundance
H I25----1.0
He I20He II15--0.1
C I45C II27C III382.4e-4
N I26N II33N III390.9e-4
O I23O II31O III443.9e-4
Ne I80Ne II57--6.92e-5
Na I22Na II14Na III561.48e-6
Mg I26Mg II14Mg III543.39e-5
Al I18Al II14Al III322.34e-6
Si I35Si II14Si III603.24e-5
S I20S II30S III326.92e-6
Ar I48Ar II57--1.52e-6
K I10----1.20e-7
Ca I22Ca II24Ca III342.04e-6
Ti I10Ti II28--7.94e-8
V I10V II28--1.0e-8
Cr I10Cr II34--4.36e-7
Mn I10Mn II28--2.45e-7
Fe I120Fe II120Fe III902.82e-5
Co I10Co II28--8.32e-8
Ni I10Ni II28--1.70e-6

[29] Table 2 lists the species for which full-NLTE radiative transfer is carried out. In addition to these, also H-minus departure from LTE is computed in this way. In contrast to arbitrarily “fixed” LTE calculations, the SRPM calculations use a full-non-LTE procedure, with the only exception of molecular lines that are computed in LTE. Several species, e.g., B, Be, Li, P, F, are currently ignored because they have little importance for the SSI. As this table shows, currently the computations use 25 levels for the H atom; this is possible after a revision to the numerical method for computing H diffusion which is now different from the FAL procedure [Fontenla et al., 1993]. The increase in the number of H levels increases the number of lines near the ionization limit and partially closes the gap between the continuum and the lines. However, there is still a small gap between the lines and continuum even when consideration of 25 levels reaches the point where the lines merge into a quasi-continuum. Inclusion of more levels leads to a complicated quantum-mechanics problem, but a simple approach would be to fill the gap by extending the continuum.

[30] In the present calculations all ionization stages for which sufficient data is available are included. Higher ionization species than those listed in Table 2, i.e., charge larger than 2, are insignificant at chromospheric and photospheric temperatures and are only significant in the transition-region and corona. Therefore for these higher ionization stages a simpler “effectively optically thin NLTE” procedure is used. It was verified by Avrett [2007] that in these cases the results from full-NLTE do not significantly differ from those assuming effectively optically thin conditions in which the statistical equilibrium is formulated by neglecting radiative excitation and stimulated transitions and only considering the spontaneous transitions between all levels. Of course it is not always true that the optical depth along all of the lines of sight is small, but for the effectively thin approximation it is sufficient that over most of the raypaths the optical thickness of the lines and continua are small.

[31] The effectively optically thin ionization is first computed using published ionization/recombination rates given by Shull and Van Steenberg [1982], and Mazzotta et al. [1998]. After this, for each ion the full statistical equilibrium equations are simultaneously solved for all level populations considering spontaneous decay and collisional excitation/de-excitation (data is from CHIANTI 5.2 [Landi et al., 2006]). Approximate formulas, e.g., the two-level atom approximation, are not used but instead a full multilevel formulation is retained, and the statistical equilibrium equations are simultaneously solved for all levels using the Gauss-Jordan full pivoting method.

[32] The species for which the effective optically thin NLTE approach is used are all those present in the CHIANTI 5.2 database [Landi et al., 2006], and not listed in Table 2.

[33] At the moment the radiative excitation rates are not yet included, but in the low corona these are only important for a few coronal forbidden lines that are not discussed here. Inclusion of these radiative rates in SRPM is fairly simple and will be done when the coupling between the coronal and photospheric/chromospheric parts of the models is carried out.

3. Near-UV Opacity and Source Function

[34] It is not possible to completely separate the diagnosis of the semi-empirical solar model from the computation of its spectrum because that spectrum is the only diagnostic tool available. However, a very large amount of redundant information from the existing observations was used to construct a spectrum that matches them to the best of the present SRPM capabilities.

[35] The continuum opacity at visible and infrared wavelengths is mainly due to a few well known processes, namely H minus bound-free and free-free, and secondarily the bound-free transitions of a few other species. At these wavelengths, and because H minus is well known, the differences between various computations of the continuum mainly arise from different atmospheric models. However, in the near-UV a lack of continuum opacity is usually found in solar and cooler stars [e.g., Short and Lester, 1996]. Observations indicate that, although some lines are missing in the calculations shown here, there is important missing continuum opacity as well.

[36] The near-UV continuum opacity is partially due to free-bound absorption from the excited states of many low first-ionization potential elements (low-FIP elements, say with ionization energy less than 6 eV). The corresponding cross-sections are currently known mainly thanks to the work of TOPBASE and the OPACITY PROJECT [e.g., Seaton, 1987]. However, not all spectra computation codes are up-to-date on these extensive data. It is also critical that for realistic estimates of this opacity the full-NLTE calculations of these complex atoms are solved, since the level populations are involved and generally depart from LTE.

[37] Photodissociation of diatomic molecules is also a significant source of continuum opacity in the low chromosphere; at short wavelengths in which H minus opacity becomes small but long enough that the photo-ionization from the low-FIP elements is not too large. This was proposed by Tarafdar and Vardya [1972] and calculations were carried out by several authors. These continuum opacities are generally not very large but are quite significant and affect the SSI spectrum in the range ∼170–400 nm. In this range the emergent intensity originates in the low chromosphere where diatomic molecular species are abundant and other opacities are not large. Of course in this spectral range there are also many lines from the low FIP elements and also many lines of molecular origin.

[38] Much of the continuum opacity in the range 320–400 nm, in addition to H minus bound-free, can be explained by considering the CH photodissociation opacity. Also, OH opacity contributes significantly at wavelengths shorter than 240 nm.

[39] However, the published values of CH and OH opacities show an important decrease of the opacity in the range 240–320 nm which still leads to larger than observed SSI values in the gaps between lines. This gap would produce an intensity increase that is not observed, therefore leaving the observations in this range unexplained. This situation occurs in the neighborhood of the Mg II h and k lines where previous calculations showed a large continuum level in between lines that is not observed.

[40] It is proposed here that the photo-dissociation opacity of the diatomic molecule of NH may be an important contribution that “fills” the gap left by the decrease of CH opacity in the range 240–320 nm. This is suggested by the consideration that N is the next most abundant element after O and C, and by the calculations of Kirby and Goldfield [1991] that show a very large cross-section for NH photodissociation in that spectral range. These calculated cross-sections only considered the lowest vibrational state of the molecule and therefore are incomplete for solar conditions where higher vibrational states are important. For the present paper a very crude estimate of the cross-section including higher vibrational states was performed by just convolving the cross-section given in that paper with a distribution of shifted similar curves reduced by the exponential of Boltzmann (mimicking the populations of the higher vibrational levels). Of course there is only a weak physical basis for this approach and only full quantum-mechanical detailed analysis can provide reliable values of the photodissociation. Such calculations are being carried out by P. C. Stancil et al. (manuscript in preparation, 2011). Until those results are available, the present approximation is a numerical experiment to obtain a first guess of how significant NH photodissociation would be and whether it may explain the observations. Figure 2 shows the comparison of the NH photodissociation opacity with other opacities for one point of the atmosphere in one of the models.

Figure 2.

The opacity for model 1001 in the low chromosphere, at 75 km altitude (T = 5500 K). The total and its main components are shown. The NH proposed opacity is shown to be important in the range 210–320 nm, although other species are dominant.

[41] It is found that the present crude estimate of the NH photodissociation opacity fills the gap between the CH opacity and other opacities and significantly reduces the continuum intensity in the range 240–320 nm to levels compatible with the observed.

[42] In the present paper no additional or unknown opacity is considered. Formerly, Paper III dealt with a lack of continuum opacity because fewer species were considered. In the present paper it is found that consideration of the bound-free opacities due to the species shown in Table 2 and the NLTE in all of these, together with the molecular photodissociation opacities and the consideration of NH mentioned above, explain most of the continuum opacity and leaves very little unaccounted continuum opacity.

[43] Of course photo-dissociation of other diatomic molecular species may also have significant effects, such as SiH and MgH for which data has been published [Weck et al., 2003], and maybe also FeH for which photodissociation data has not been published but lines were observed. Other species that may be important are the ionized metal hydrides such as SiH+ [Stancil et al., 1997] and MgH+. Also CO could be significant at even shorter wavelengths because its infrared lines show it to be abundant in the low chromosphere.

[44] Changes in the low chromospheric temperature in different solar features can have large effects on the densities of very sensitive molecular species and thereby significantly affect the SSI variability in the 200–400 nm spectral region.

4. Computation of the Spectra

[45] The computation of the spectra by SRPM was described in several papers and the present paper does not repeat these details but refers to Fontenla et al. [2006, 2007, 2009, and references therein] (hereafter Papers I, II, and III). The accurate values of the photoionization cross-sections are one major issue for computing the solar spectrum with high accuracy because the available ab initio values are seldom verified experimentally, and because of a complete lack of data for some species.

[46] In particular, there is a continuum edge in the visible spectrum at 519.266 nm that is prominent in the full-resolution computed spectrum. This bound-free continuum is due to the photoionization from the Al I level number 3 (3s.3p2–4P) and is an important edge because of the relatively low level excitation energy (∼3.6 eV) and the very large photo-ionization cross-section (1.63e–15 cm−2 at the head). This spectral feature is usually obliterated in the high-resolution observations by their continuum normalization procedure, but is hinted in the SSI observations by Thuillier et al. [2003] (from SOLSPEC) and by Harder et al. [2010] (from SORCE/SIM). It is of course possible that the ab-initio TOPBASE computation used here may overestimate this cross-section; but there is no basis for dismissing this edge until such overestimate is demonstrated by other calculations or by absolutely calibrated high-spectral resolution observation.

[47] The emitted intensity (or radiance) is computed for photospheric-chromospheric layers assuming plane parallel geometry for 10 μ values from 1 to 0.1 (μ is the cosine of the observation angle with respect to the vertical). Verification was carried out using spherical geometry and very little differences were found at the lowest μ values.

[48] The upper transition-region/coronal portions of the models are stored independently but their bottoms are adjusted to match the top of the corresponding photosphere-chromosphere models. In the outer layers the NLTE level populations are computed in the effectively optically thin approach for all species (including H and He), but the calculation of the emitted intensity are carried out considering the opacity in addition to the emissivity. The lines are optically thin for most μ values but a few of the strongest lines have significant optical thickness when close to the limb. This makes significant differences in the limb brightening at some wavelengths, which is not as large as it would be if optical thickness was completely negligible. Also, because of the relatively large extension of the corona, the emitted intensity from these upper layers is computed using spherical symmetry. This is not perfect for active regions, which have a complex 3-dimesnional structure, but it is reasonably accurate when the horizontal dimensions are smaller than the radial dimension. The alternative is doing full 3-dimensional calculations with a fully 3-dimensional physical model. Some experiments of this sort were carried out but they are beyond the scope of the present work.

[49] The emitted intensity for both portions of the models, photosphere-chromosphere and transition-region-corona, are computed separately and added to form the total emitted intensity as prescribed by the radiative transfer equation. In this way the emitted intensity includes the contributions from all atmospheric layers.

[50] Presently, the irradiation of the photosphere-chromosphere by the coronal radiation is not included in the full-NLTE radiative transfer computation (although SRPM is able to include it) because some iteration is needed for full consistency. Because of this the He I ionization is probably underestimated in the upper chromosphere. However, the present approach allows for later including the downward radiation from the upper-transition-region/coronal model as an incident radiation onto the photosphere-chromosphere model. In this way the true effect of the coronal irradiation in the chromospheric NLTE will be gauged but it is not expected to be very important for the SSI.

[51] Figures 3 and 4 show the spectra obtained for the SRPM QS disk as defined above, and after smoothing with a 1 nm FWHM cos2 filter truncated at the first zero of the function. Figure 5 shows the usual brightness temperature that is computed by determining, for each wavelength, the temperature of a uniform solar disk that by emitting according to the Planck function would reproduce the irradiance data shown in Figure 4. This graph displays better the lines and the variations in temperature resulting from the solar atmospheric structure and opacity changes across the spectrum.

Figure 3.

The low-resolution (1 nm) EUV part of the irradiance spectrum computed for SRPM QS.

Figure 4.

The low-resolution (1 nm) visible and infrared part of the irradiance spectrum computed for SRPM QS.

Figure 5.

The low-resolution (1 nm) visible and infrared irradiance brightness temperature spectrum computed for SRPM QS.

[52] Calculations of daily SSI at 1 nm resolution were carried for the days within the period 2000–2009 in which PSPT images were available at the OAR and the spectra are shown in a compact graphical form in Figure 6. Despite the complicated behavior of the SSI as function of wavelength, this figure shows that, as solar activity decreased from 2002 to 2009, the calculations produce in general an energy flux decrease at wavelengths below ∼400 nm, but an increase at wavelengths longer than that. This compensating behavior is similar to that of the SORCE/SIM observations shown by Harder et al. [2009] and leads to the much smaller change of the TSI than the absolute changes in visible and UV.

Figure 6.

Graphical representation of the calculated SSI changes during Solar Cycle 23. The horizontal stripes correspond to rotational modulation events. The vertical stripes are due to spectral lines. The gray scale corresponds to the SSI differences (in W m−2 nm−1) on each day with respect to the SSI for the selected “low” activity day.

[53] Table 3 shows six days that were selected for computing representative high-resolution spectra. In this table FEUV designates the spectral band with wavelength shorter than 200 nm, NUV the band between 200 and 400 nm, and VIR the band with wavelengths longer than 400 nm. Figure 7 shows the masks of solar disk features for these days that include a low activity reference day and several cases where solar activity was present. Pairs of these cases (high2 and high1, and mid2 and mid1) correspond to similar epochs within the solar cycle but different SSI because of the different mix of sunspots and active regions in each case. The mid1 activity case on Jan 15 of 2005 corresponds to the decay of the cycle, but displayed a large sunspot group that hosted a powerful X-class flare.

Figure 7.

The chromospheric features on the solar disk for several days during Solar Cycle 23, i.e., various solar activity states. From left to right and top to bottom these are in chronological order.

Table 3. Selected Key Days
DayDesignationDelta FEUVDelta NUVDelta VIRDelta Total (SRPM)Delta TSI (PMOD TIM)Sunspot Relative Area
Nov 25 2000High28.9e-30.582 −0.681−0.0901.69753.4e-4
Dec 5 2000High15.5e-30.4700.1780.6541.82550.2e-4
Jan 17 2002Peak1.1e-20.716−0.774−0.0471.60412.4e-4
Jan 5 2005Mid22.3e-30.165−0.171−0.0080.5825 0.49280
Jan 15 2005Mid13.1e-3−0.127−2.103−2.233−1.5947 −1.6788.3e-4
Sep 15 2008Low000000

[54] Table 4 shows the relative areas covered by each of the features identified in Table 1 whose characterization for the PSPT images is currently implemented. Note that features A and Q have not yet been identified in the masks and the corresponding models (1000 and 1008 respectively) are not yet completed, thus in the following discussion it is merged A with B, and Q with P; this is indicated in the table. While this table contains important information, it does not contain all that is needed for spectral synthesis because it lacks the key information of the position on the disk for the features. The positions of the features have an important effect on their contribution to the SSI because of the large center-to-limb-variation of the features radiance at most wavelengths. This is not a serious problem for features B, D, and F, which we call the “quiet-Sun” features despite their variation over the solar cycle as displayed in the table, because they are more or less uniformly distributed on the disk and consequently do not produce rotational modulation. However, the effect of the other features, the “active region” ones, on the SSI depends critically on their position on the disk. These are not randomly distributed but instead occur predominantly at certain latitudes that are dependent on the phase of the solar cycle, and in addition produce the so-called rotational modulation of the SSI. For instance plage (feature H) has a tiny contrast with respect to internetwork (feature B) at visible continuum wavelengths (say at 800 nm) when near disk center, but close to the limb its contrast is significant. This combines with the fact that the radiance near the limb is still small (because of the decreasing radiance of both P and B toward the limb), so that a given contrast and area near the limb contributes less to the irradiance than it would do if the same values occurred at disk center. The same issue is valid for sunspots and goes beyond the simple foreshortening effect that makes areas smaller as they approach the limb.

Table 4. Relative Areas of Features for Selected Key Days
DayDesignationA+BDFHP+QSR
Nov 25 2000High20.7080.1870.0670.0324.5e-33.6e-41.9e-3
Dec 5 2000High10.7360.1910.0530.0182.2e-32.1e-54.5e-4
Jan 17 2002Peak0.7050.1770.0690.0397.8e-32.6e-42.2e-5
Jan 5 2005Mid20.7780.1860.0277.4e-31.2e-304.9e-5
Jan 15 2005Mid10.7760.1780.0270.0122.7e-38.8e-43.2e-3
Sep 15 2008Low0.8000.1890.0116.4e-5000

[55] All this shows that the proper way of doing the SSI synthesis is not the use of Table 4 but instead the use of the masks in Figure 7, together with the full angle dependent radiance spectra for each feature.

[56] Figures 8 and 9 show the variation of the calculated SSI for the active days indicated in Table 3 with respect to that of the low activity day. The variations are shown in irradiance units, and not ratios because it is irradiance that affects the Earth atmosphere. Large relative variations of very small absolute values only have small effects in comparison to other variations.

Figure 8.

The FUV and EUV SSI changes at low-resolution (1 nm) for the selected active days, with respect to the “low” activity day. Subtraction was performed, not a ratio, in order to show the actual power involved. The vertical axis units are W m−2 nm−1.

Figure 9.

The visible and infrared (bottom) brightness temperature and (top) SSI changes for the selected active days at low-resolution (1 nm), with respect to the “low” activity day. Note that subtraction was performed, and not a ratio, in order to show the actual power involved. The vertical axis units are W m−2 nm−1 and K for the irradiance and brightness temperature variations, respectively.

[57] Figure 8 shows that for all the active days the EUV SSI increases with respect to the “low” state, with the “peak” case having the largest increase. Instead, Figure 9 shows that in the visible and IR the behavior is much more complicated because of the very different, and at many wavelengths opposing, effects of sunspots and plage as well as the strongly wavelength-dependent center-to-limb behavior. In all cases the spikes correspond to deep spectral lines and some of the notable ones are Ca II H and K, Ca II infrared triplet, and CO bands with head at about 1.6 (delta.nu = 2), 2.1 (delta.nu = 1), and 4.5 (delta.nu = 0) micron. Generally the SSI in the lines is increased in all active cases with respect to the “low” activity case.

[58] The rotational modulation is displayed by the differences between “high2” and “high1,” and between “mid2” and “mid1.” This shows that solar activity does not present a representative spectrum but instead a significantly fluctuating one. Particularly notable is the case of the very large sunspot in the mid1 case (see Figure 7) which at all continuum wavelengths between ∼290 nm and 7 micron is darker than the “low” activity case. Only at the very strong lines even the mid1 case is still brighter then the “low” case.

[59] Apart from the effect of very large sunspots, the spectral regions for which the irradiance brightness temperature (see Figure 5) is smaller than the bolometric effective temperature (Teff = 5770 K) display increasing SSI with increasing solar activity. The calculations show that the SSI is produced mostly in the lower-chromosphere and photosphere and that the solar material is very opaque at these wavelengths. Instead, the spectral regions in which the solar material is less opaque, which are those for which the brightness temperature is larger than Teff, display decreasing SSI with increasing activity.

[60] These effects are due to the change of the photospheric/low-chromospheric temperature derivative with respect to pressure of the various feature models. In the current models this derivative is slightly shallower for increasing activity models (except for the sunspot ones), and the temperature versus pressure curves cross at pressures slightly lower than that where the optical depth at 500 nm is unity. A similar choice for the models was present in FAL models and in work by Fontenla et al. [1999] and corresponds to published observations that show a negative correlation of the continuum with magnetic field at some wavelengths [see Topka et al., 1997; Sobotka et al., 2000]. Further improvements were done in the models in order to better match the SORCE/SIM data shown by Harder et al. [2009] that covers more wavelengths.

[61] Around 1.6 micron the total continuum opacity per unit mass reaches a minimum when all the bound-free and free-free absorbers are accounted for. Around this wavelength the total opacity is due mainly to H minus bound-free decreasing opacity with increasing wavelength and H minus free-free increasing opacity with increasing wavelength. At these wavelengths active days show a decrease in irradiance. Nearly the same decrease occurs in “high2,” “peak,” and “mid1” cases but a much smaller decrease occurs in “high1” and “mid2” due to the relatively very small area of sunspots in these cases. A similar behavior occurs at around 450 nm where the total opacity is relatively small but not as small as at 1.6 micron.

[62] Longer than ∼4 micron (due to the increasing H minus free-free the opacity), and shorter than ∼400 nm (due to the molecular and metal bound-free opacities) the SSI is formed at lower pressures. For these wavelengths the effects of plage and facula are large and dominate over decreases by sunspots except in some extreme cases when very large sunspots occur. At these wavelength ranges active cases have a normally larger SSI than in the “low” state.

5. Comparison With Observed Spectra

[63] This section shows some of the many tests that were carried to evaluate the accuracy of the spectra computed and thereby the validity of the physical models. Some of the tests correspond to comparisons of SRPM calculations with very-high spectral-resolution radiance data spectral atlases. Other comparisons are with well calibrated absolute SSI observed from space but with limited resolution. Other comparisons were shown in previous papers (Papers I, II, and III). Also some comparisons between SRPM results and available solar variability observations are shown in this section.

5.1. Comparison With Some High-Spectral-Resolution Radiance Measurements

[64] A very detailed comparison was carried out of the SRPM results with the spectral atlas from the FTS instrument at Kitt Peak National Observatory (KPNO) by Wallace et al. [1998], the atlas by Delbouille et al. [1981], and the Farmer and Norton [1989] disk center spectra. These observations have very good spectral resolution but lack absolute calibration and instead use ad hoc continuum normalization. Also, these data do not resolve the solar surface features, not even at mid-resolution, but instead refer to an average of a region near the center of the “quiet-Sun.” Despite these limitations the observations are very important for the SRPM system to characterize the structure of the solar atmosphere. These data, and other published data on active region features, were considered in deriving the models as was described in Paper III, and the present model changes do not affect most of the previous statements and graphs that are not repeated here.

[65] Figures 10 to 13 show a few spectral lines for the SRPM QS mix described in Section 2. In all these figures the observations were normalized for the continuum to match the absolute values of such in the SRPM calculation, and the intensities units are erg cm−2 s−1 A−1 sr−1.

Figure 10.

One of the deepest CO lines in the high-resolution spectra from Farmer and Norton [1989] compared to the SRPM QS. The observed data do not have an absolute calibration and was scaled to match the continuum.

Figure 11.

The computed SRPM QS full-resolution Ca II H and K line profiles. The calculation and observed spectra, from the KPNO FTS Atlas by Wallace et al. [1998], correspond to disk center.

Figure 12.

High-resolution observed profile of the deepest line of the Ca II IR triplet, from Delbouille et al. [1981], compared to the SRPM QS. The observed data do not have an absolute calibration and was scaled to match the continuum.

Figure 13.

(top) High-resolution spectra of the Mg II h, and k lines, and the range including the Mg I resonance line, and (bottom) the detail of the h and k line cores from HRTS-9 by Morrill and Korendyke [2008] compared with the SRPM QS (after convolving the SRPM full-resolution data with a 0.08 A FWHM cos2 filter representing the HRTS data spectral smearing). The HRTS-9 data absolute calibration is its own and was not modified but its uncertainty maybe significant since these data were derived from a scan of a photographic plate. The more exposed portions at wavelengths longer than ∼282 nm have an envelope quite a bit larger than the SRPM calculated continuum, however, at the SSI lower resolution but much more reliable absolute calibration the agreement is good. It may be possible that the approximate NH continuum opacity used by SRPM is overestimated and that lines neglected in the present paper compensate for that continuum overestimate in such a way that the SSI measurements are still matched. However, the absolute calibration applied to the observation may be incorrect as well, and more observations that spatially resolve the solar disk, with high spectral resolution, low noise and accurate detectors, and providing absolute calibration are badly needed in the spectral range 200–400 nm.

[66] Figure 10 shows one of the deepest CO rotational lines and displays a slightly better agreement with the observed Farmer and Norton [1989] observations when the mix of inter-network and network is considered. However, it is apparent that the line broadening is somewhat overestimated for the CO lines at some layers near the base of the low chromosphere.

[67] The presently computed line profiles of the Ca II H and K lines and the IR triplet lines for the “quiet-Sun” are shown in Figures 11 and 12 and display a slightly better agreement with observations than in Paper III. However, the details of the line center of the H and K lines still do not display the richer variability and asymmetries that the observations show and the K3 and H3 cores are too deep. These details cannot be meaningfully reproduced by the 1-dimensional steady state models such as the present ones.

[68] The plots shown above show a common theme in that the broadening is too large in the Ca II line cores (all the IR triplet core and the H3 and K3). However, Paper III explains that the turbulent broadening velocity was selected in the SRPM models to match EUV chromospheric lines from lighter elements and that there seems to be an atomic mass dependence on the optimal values of this parameter.

[69] The Ca II K3 depth computed by SRPM is too low and the K2 peaks are too high but the K1 wings match the observed very well. The Mg II h and k lines also display h2 and k2 peaks that are larger than the observed, but the k3 features and the k1 intensities are close to the observed. The characteristics of the issues with h2 and k2 are similar to those with the Ca II H2 and K2.

[70] It is noted that in the present SRPM calculation the fine structure of the levels involved in these transitions (for both Ca II and Mg II) were not taken into account completely and the sublevels with different values of J were joined into a single level for the non-LTE calculation but then weighted according to the Boltzmann law for the purposes of computing the spectrum. It is possible that this approximation may not be good enough for the upper-chromospheric Ca II and Mg II line cores and it will be revised in future work.

[71] In any case, it is apparent that the details mentioned above for the upper-chromospheric line cores of Ca II and Mg II cannot be accurately addressed by the kind of models in this paper. The fluctuations in the temporal, spatial, and Doppler shift structure displayed in the high-resolution images show that the 1-dimensional steady state assumptions are not suitable for describing the asymmetries and details of the lines. Moreover, even in the lower-chromosphere and photosphere some fine details of the line profiles cannot be reproduced. For instance, most lines bisectors show a characteristic “C” shape that the kind of models discussed here cannot reasonably account for, but convection simulations explain.

[72] The details mentioned in the previous paragraph are not important for the overall SSI computations but they may be relevant for measurements of “indices” (e.g., Mg II or Ca II) that are sometimes used as proxies for SSI. More sophisticated calculations of 3-dimensional and non-steady models are needed in order to describe more realistically the structure of the upper-chromosphere. The models need to address the radiative interaction between the upper-chromospheric fine structures and requires full-NLTE radiative transfer in 3-dimensions.

5.2. High-Resolution UV Spectra

[73] High resolution observations of line profiles were carried out in the UV with SOHO/SUMER and were compared with the previous models (see Paper III). It is beyond the scope of the present paper to discuss the detailed radiance profiles of UV lines after the modifications to the atmospheric models that were introduced by the energy balance and the “cloud layer” introduced here.

[74] Summarizing the relevant aspects, it can be said that because of the modifications introduced by the actual energy balance in the chromosphere-corona transition-region, the line intensities have changed and generally become closer to the observed. However, some differences still remain in the detailed line profiles. In general the observed lines do not display central reversals, except for the Lyman alpha line and for the other Lyman lines to a much smaller extent.

[75] In the SRPM, currently 1-dimensional calculations, overall the upper-chromospheric and low transition-region strong lines, formed at temperatures of about < ∼40,000 K, show self-reversals that are not observed (except in Lyman alpha and smaller reversals in other Lyman lines). After performing some experiments it is concluded that changes in the model cannot fix all these issues but that most likely it is just a failure of the 1-dimensional steady state approach in the upper chromosphere. In this approach, plasma at different temperatures does not coexist spatially at the same height but is located either above or below. However, in a 3-dimensional approach material at various temperatures may be located side-by-side at the same height and each component may not absorb the observed radiation. These effects cannot be properly treated in an effectively optically thin approach because in the upper chromosphere there is very important radiation exchange between all structures, even if they are horizontally distributed.

[76] Most lines formed at temperatures above ∼40,000 K, instead, are somewhat overestimated by the present models, and would only be consistent with the observed lines if either the pressure was reduced or if the features occupied less than the full resolved area. The later explanation seems more likely because, although there are some low pressure regions on the disk, the measured pressure sensitive line ratios in most cases point to the values in the present models (see Paper III). Thus, it is proposed that only a fraction of the resolved area, at ∼2–3 arc sec, is covered by the foot points of coronal loops and the rest is covered by closed chromospheric loops that never reach coronal temperatures. The consideration of a “filling factor” value, which in the present calculations would be more or less temperature independent, could explain the observations.

[77] In the present understanding, the hot (in a relative sense) chromospheric loops have temperatures between ∼8,000 K and 40,000 K and can reach a wide range of altitudes that intermingle with coronal loops of apex temperatures of over 1 MK. There are no indications in the observations that could point to the existence of abundant loops at intermediate temperature in which the apex temperature could be between ∼40,000 K and coronal values. From the calculations performed the foot points of coronal loops can explain all observations except for transient dynamic loops that are occasionally observed and do not significantly contribute to the overall SSI. Calculations of radiative losses point to unstable (run-away) behavior in the transition-region temperature range that can only be stabilized by heat conduction when the apex temperature reaches coronal values.

5.3. Center-to-Limb-Variation

[78] Another useful type of available observations is the center-to-limb-variation (CLV) at various wavelengths, i.e., the ratio of emitted intensity at various angles with respect to that for the vertical. These were studied for the various features and compared with observations in Paper I, and it is verified that no significant differences occur in the present results. However, the published CLV data do not identify the quiet-Sun network components so they cannot be compared to a particular model within the present quiet-Sun features (B, D, or F).

[79] Some observations reported CLV behavior of active regions, but this is a difficult topic because active regions change very significantly over their passage on the visible disk. Consequently, the CLV of an individual active region cannot be directly observed from a single vantage point and while statistically it may be possible to derive some parameters, this is complicated by the large scatter between different active regions and even different locations within a single active region. Besides, there is a good possibility that some properties of active regions such as age, growing or decaying, timing within the solar cycle, latitude, field strength and orientation, etc, influence the CLV behavior. These properties are not included in our definitions shown in Table 1. Only if extensive statistical data existed and all these matters were clarified a comparison would be possible, however, we are not aware of such large statistical study publication.

[80] The “contrast CLV” of a feature is defined as the angular dependence of the intensity of the given feature relative to a reference feature. These angular variations indicate differences between the CLV of the various features. These quantities were compared with the observed in broadband images of the Ca II K line by Ermolli et al. [2010] for the Paper III models. The minor differences between the models calculated and the observed contrasts are probably due to the issues with the computed K2 and K3 spectral features that were discussed in the previous section and perhaps partially with instrumental issues.

[81] The overall continuum variation of the solar disk was measured at the KPNO and this paper examines the CLV and its solar-cycle expected variation. The observed changes in the network relative area imply that a certain change would occur in the CLV of the average “quiet-Sun” due to the different CLV of the network and inter-network. However, the SRPM computed variations are extremely small because the network and inter-network models are very close at photospheric layers. Moreover, even when small differences occur in the temperature versus height slope, these may not necessarily reflect observable intensities because the opacity is also different. These issues are discussed in more detail in a later section and here it is only necessary to note that the present SRPM calculations include all effects of radiative transfer and indicate which differences are expected from the models presented and the variations observed in the network over the solar cycle.

[82] Figure 14 shows the CLV at 445.1 nm for the quiet-Sun component in the present results for the “peak” and “low” cases. Also shown are the QS bounding curves from model 1003 (feature F, enhanced network) and model 1001 (feature B, inter-network) that indicate the magnitude of the irregularities in the “quiet-Sun” surface due to the presence of network and inter-network. These plots illustrate that there are tiny differences in CLV between the quiet-Sun component at the peak and low activity cases, because of different network statistics. However, the differences are very small and: 1) are much smaller than the fluctuations due to spatial scanning of the solar surface (e.g., network and inter-network) and temporal fluctuations (e.g., p-modes), and 2) the CLV change of the overall “quiet-Sun” is not detectable with current instrumentation.

Figure 14.

(top) The CLV and (bottom) the absolute brightness of the quiet-Sun component (network plus inter-network) expected from the present calculations over the solar cycle, in the continuum at 4451 A (but a very weak line is present). The extreme values of the irregularities in the solar surface are also plotted and result from presence of models 1003 (feature F) and 1001 (feature B). The values are computed only at 10 discrete values of μ and other angles are computed using spline interpolation as function of μ = sqrt(1 − r2) with r = sin(theta) and theta the angle between the radial direction and a line of sight.

[83] Also, the figure shows the absolute intensity as function of the heliocentric angle. This absolute value cannot be currently measured by the standard CLV measurement method because of lack of absolute calibration of the ground-based observations. The plot illustrates the larger vertical directivity of the radiation in the lower activity state, and that at certain angle all the network features have nearly the same absolute intensity but their contrast has opposite sign at disk center and near the limb.

5.4. Comparison With SSI Measurements From Space

[84] Figure 15 shows the current comparison of the SRPM results with the Composite 3 reference spectrum derived by Thuillier et al. [2003] from space-based observations. For the comparison the SRPM spectrum was degraded by convolution with a 1 nm FWHM cos2 type filter (having a shape not far from a Gaussian but easily truncated at the first zero and not requiring an additional truncation parameter). The comparison is very much better than that published in Paper III. The main reason for the improvement is the consideration of NLTE lines and photoionization of many species that were previously ignored or computed in LTE, e.g., Ti, V, Cr, Ni, Co, etc in the neutral and singly ionized state. Also, Al III, Na II, Ca III and Fe III were not computed in NLTE before.

Figure 15.

Comparison between the SRPM QS spectrum and the Thuillier et al. [2003] Composite 3 SSI spectrum. The data are shown (top) in standard SSI units (W m−2 nm−1) and (middle) in brightness temperature that highlights the differences. (bottom) Enlargements of sections of the graph.

[85] The present calculations consider the lines of all these elements as well as the bound-free transitions for the ground and excited levels. Although individually each of these is not large, the combined effects of many produce most of the improvements in the calculations shown in the Figure 15. There are also some effects due to the updates to the transition region carried out here, but these are minor in comparison. Additional differences with plots in Paper III are that before only model 1001 was compared with observations, while here we compare the SSI spectrum computed for the SRPM QS case. The Composite 3 spectrum is labeled as corresponding to a low activity day (although it was taken in Nov 1994 which is earlier than the minimum). Also, note that no normalization was applied to the SRPM spectrum while the Composite 3 was normalized to a given TSI (see Thuillier et al. [2003] for details).

[86] Figure 15 shows some differences in lines across the spectrum but although a few minor lines are still missing in the SRPM results, many other apparent differences are not real. The apparent differences in some line depths result from a mismatch between the Composite 3 actual resolution and the profile used to convolve the SRPM full-resolution data. A problem for the comparisons is that the Composite 3 data instrument profile is not well known and is likely variable. At most wavelengths it seems that the Composite 3 data has higher resolution than our 1 nm convolution and other trials were made but it was found that a single resolution does not match the entire Composite 3. For a very detailed comparison of lines the matching of instrument resolution and convolution profile is essential. As the next comparison shows (Figure 16) comparing data at the same convolution profile can save some serious misunderstandings.

Figure 16.

Comparison of the SRPM QS and the Thuillier et al. [2003] Composite 3 spectra with the SORCE/SIM ESR detector observation on 2004/4/21. Convolution of the SRPM and Composite 3 was made with the variable SIM instrument profile. (top) In standard SSI units and (bottom) in brightness temperature that highlights the differences.

[87] Figure 15 (bottom) shows enlargements of the range below and above 400 nm. Below 400 nm there are a few wavelengths in which the agreement of SRPM with observations is not as good. The main disagreements occur between 200 and 240 nm where the current SRPM estimate of the NH photodissociation opacity has a very significant effect that results in the SSI underestimation. However, if NH photoionization was completely disregarded an important overestimate of the SSI would occur at all wavelengths above 200 nm and below about 320 nm.

[88] Comparison was also carried out with the SORCE/SIM data by Harder et al. [2010] and for this the SRPM data was convolved down to the relatively coarse and variable resolution using the detailed instrument profile of the SORCE/SIM instrument. This instrument profile is a well characterized function for each wavelength and permits a useful comparison of the details. For reference also the Composite 3 spectrum was convolved in the same way. The comparison is shown in Figure 16. The irradiance panel in this figure shows better the slightly higher SRPM spectrum in the visible range, and the brightness temperature panel shows the slightly lower SRPM infrared tail.

[89] Figure 17 shows the comparison of the SRPM QS calculation with SORCE/SOLSTICE SSI observed on 10 April 2005. For this the SRPM data was convolved with a 1 A FWHM cos2 filter and although the resolution is similar the detailed convolution profile used may not perfectly match the SOLSTICE instrument profile. An overall agreement is shown but some differences exist that point to improvements in the SRPM NLTE or spectrum calculations. The C I lines computed for model 1001 are too strong and drive the QS spectrum lines higher than the observed. However, for the other models they are similar to the observed.

Figure 17.

Comparison of the SRPM QS spectra and the SORCE/SOLSTICE, after convolving the SRPM full-resolution spectrum with a 1 A FWHM cos2 filter. The SOLSTICE data shown corresponds to 10 April 2005.

[90] The present results partially use the formulation by Stehlé [1996] for all hydrogen lines Stark broadening. This is used here only in the computation of the spectra, and the complete implementation of the algorithm and application to the calculation of NLTE is still pending. It is not expected that there will be important changes when the formulation is also used to update the NLTE but some changes in the Ly alpha far wings may arise. The current calculation of the Ly alpha line uses partial-frequency-redistribution (PRD) for both, the NLTE and the emitted intensity, but with a truncation for large departures from line center.

[91] An issue in the SRPM calculation is the disagreement with the observations in the range between around 168 nm and 200 nm. In this range the calculated spectrum has larger values than the observed. This may be solved by the consideration of photo-dissociation continua from additional molecules (e.g., SiH, SiH+) that all have important cross-sections in this spectral range and could render this edge indiscernible. In any case these continua are not negligible and will be considered in future papers as we are able to gather and include these data.

[92] We do not consider as a viable alternative the suggestion by Kurucz [2011] of large numbers of very weak atomic and molecular lines in this region. Although we do not find in that paper or its references sufficient specific information about how the lines and continua were computed and their effect compared with the observations, we note that assuming LTE, as that paper does, is not a good approximation in general (see Paper III) and much less in this particular spectral range that is formed at chromospheric heights. The formation height is shown by our calculations that include important and well known continua, and is confirmed by the weak center-to-limb-behavior displayed in the observations.

[93] Many extremely weak transitions of course exist, but they have not been observed and have such low strength and opacity that we consider irrelevant (after trials we conducted in the past). Note that a million lines of gf = 10−6 would be equivalent to only one permitted transition of gf = 1.0 and only if all the weak transitions had identical wavelength. Thus, forbidden transitions from atomic or molecular levels of not very abundant species have negligible effects.

[94] The source of our lines from the neutral or weakly ionized atomic species is the NIST database [Ralchenko et al., 2011] that we consider one of the most reliable. This database contains sufficient information about not only the lines but the levels involved and permits us to compute the NLTE effects. We do so but only for the species and levels displayed in Table 2. From these results we compute the lines and continua that correspond to these levels only.

[95] However, the NIST database contains more levels and species that we have computed in detail so far. Using additional levels is not essential to the solar irradiance calculations in this paper, but is an ongoing task that will improve our results in some portions of the spectrum. These future improvements include the expansion of our NLTE calculations, e.g., expanding the Fe I current 120 levels to many more levels now available from NIST.

[96] We have carried offline experiments that are not shown here, and calculated all the lines and continua that were present in the NIST database of 2004 (now expanded [see Ralchenko et al., 2011]). These experiments again only used full-NLTE in the levels of Table 2, and considered two approximations for setting the additional level populations that are not computed in full-NLTE. One of the approximations used LTE with respect to the continuum and the other used the scheme described in Paper 3 in which the additional levels are assumed in LTE with respect to the topmost level computed in NLTE. In both approximations LTE was assumed in the additional species not included in Table 2.

[97] These experiments showed the lines and continua from these additional levels and species and we found that while some lines compare well with observations others do not. Also, these experiments showed that the lines neglected in this paper have some small effect on the SSI but are not critical. More importantly, these experiments showed that the photoionization continua from these extra species and levels have a small but clear effect on the blue and violet continuum and brings the computed spectrum into better agreement with the observed irradiance spectrum. Therefore, we believe the accumulation of continua from higher excited states may improve the SSI calculations because these photoionization cross-sections are often large and overlap over extended spectral ranges. However, the proper calculation of the levels populations would require including many more levels in the full-NLTE or at least a more sophisticated approach than we have tried so far.

[98] Figure 18 shows the comparison of the EUV spectrum computed by SRPM for April 2008 with the two SSI rocket observations by the SDO/EVE instrument that were used for calibration purposes. These observations were performed in April 2008 and in May 2010. Plots were made by enlarging sections of the spectra, but these are too lengthy to be discussed here and are included in the auxiliary material. These data show a generally good agreement but differences by a factor of less than two at some wavelengths. Underestimation by SRPM occurs at some wavelengths where no large lines are present that indicates lack of consideration of some weak lines that were not included in the CHIANTI 5.2 data. Also, overestimation of a few lines by factors of ∼2 occur and seem to be originated in a poor calculation of the ionization balance for a few species. The revision and more physically consistent treatment of dielectronic recombination by Dere [2007] has not yet been implemented in and will be included in future SRPM calculations.

Figure 18.

Comparison of the SRPM QS and the EVE instrument rocket flights spectra. For this comparison SRPM full-resolution spectrum was convolved with a 1 A FWHM cos2 filter.

[99] Another difference is that the SRPM spectrum does not display enough flux at the He I continuum, with head at 504 A, that is shown by both EVE spectra. Preliminary trials show that consideration of He I diffusion in the foot points of coronal loops (see FAL) can improve the agreement, but such has not been included in the SRPM calculations included in this paper. Also, time-dependent He II recombination/recombination in the “cloud layer” material and can have important effects on increasing this continuum.

5.5. Comparison of UV SSI Variability With Observational Data

[100] In the following a comparison is shown between the variability of the FUV and EUV SSI spectra computed by SRPM with the SORCE/SOLSTICE [McClintock et al., 2005] and with the TIMED/SEE data [Woods et al., 2005].

[101] The SORCE/SOLSTICE data started in the first half of 2003 and is still ongoing. The absolute calibration of this instrument relies on the observation of reference stars.

[102] Figure 19 shows the comparison of the SSI changes computed by SRPM and the observed by SORCE/SOLSTICE for the “mid2” and “mid1” days with respect to the “low” day. The SOLSTICE instrument has approximately 1 A wide band pass, but it were further convolved with a 1 A band pass cos2 filter to improve the signal-to-noise ratio at the very low continuum intensities. Therefore, for the comparison a 1 A band pass cos2 filter was applied twice to the SRPM data to mimic the resolution of the SOLSTICE data shown here.

Figure 19.

Comparison of the SRPM and the SORCE/SOLSTICE SSI changes for the “mid2” and “mid1” cases with respect to the “low” case (see Table 3). The changes shown are differences, not ratios, because it is the power involved what drives effects on the Earth's atmosphere.

[103] The TIMED/SEE data starts in early 2002 and although it does not cover the full period of the SRPM calculations it starts near the Solar Cycle 23 maximum. Absolute calibration of the TIMED/SEE instrument is carried out by rocket flights of similar instruments. These flights took place in Feb. 2002, Aug. 2003, Oct. 2004, Oct. 2006, Apr. 2008, and May 2010. However, the SEE data shown here have not yet been calibrated since 2006, and a new version will be produced in the future with the updated calibration.

[104] SEE Level 3 data are reported in 1 nm resolution bins. However, for wavelengths lower than 27 nm the observational data was obtained by broadband diodes (XPS instrument) and modeled to yield the bins data. At wavelengths in the range 27–190 nm the data was obtained by a spectrograph (EGS instrument) that has a resolution of 0.4 nm, and the published 1 nm bins data was produced from these.

[105] For the present comparison the SRPM full-resolution data was binned at 1 nm to mimic the published SEE/EGS Level 2 data. There may still be some minor differences between the adopted and the real EGS instrument profile. Also, the SEE data used for the comparison have obvious flares removed and the present SRPM calculations do not include flares.

[106] Trials performed showed that calculations using models based exclusively on the foot points of coronal loops and energy balance between energy downflow from the corona fail to account for the solar cycle and the rotational and solar cycle modulations of the SSI in the He II 30.4 nm and Ly alpha lines. A similar situation occurs with the 90.5 nm bin and shows that the H and He lines and continuum increased SSI with increased activity requires the consideration of an increase in the hot chromospheric loops for which satisfactory theory is yet unavailable. This is not an issue related to a particular line or continuum but rather is related to a range of formation temperature of the emissions.

[107] Also, analysis of the SRPM data and of SOHO/EIT and SDO/AIA He II 304 A images shows that the contrasts between the various features and the Internetwork (model 1001) are largely underestimated by SRPM calculations purely using the energy balance in coronal loop foot points. Furthermore, the Ly alpha contrasts computed from these coronal loop foot point theoretical models and the observed by the SMM/UVSP instrument [Fontenla et al., 1988] showed that the contrasts of the theoretical models were too small. Only the addition of material at temperatures in the range ∼8,000 to 40,000 K, that following Fontenla et al. [1988] is here called “cloud layer,” could produce contrasts such as the observed in network and active region features.

[108] The issue of “cloud layer” does not affect the 139.5 or 140.5 nm bands that are dominated by the Si IV lines, and also in the 155.5 nm bin that dominated by the C IV lines. It was also verified that the SEE observations of SSI variations at wavelength bins containing other transition region lines formed at higher temperatures are well reproduced by models exclusively based on foot points of coronal loops, and are not affected by including the “cloud layer” described above. Thus, the “cloud layer” is considered to vanish at the temperatures where the Si IV lines are formed and at higher temperatures.

[109] The wavelength region below 60.5 nm is dominated by coronal radiation, except for a few cases such as the 30.5 nm bin, and shows good agreement in the rotational modulation and also good agreement on the solar cycle trend between SRPM results and the TIMED/SEE observations.

[110] It is concluded that the foot points of coronal loops and the coronal models explain well the solar variability originating at temperatures larger than ∼40,000 K. The additional component needed below, i.e., the cloud layer, was determined from the observed contrasts and appears to be a relatively hot distribution of chromospheric loops that intermingle with loops at coronal temperatures and possibly even with the chromospheric loops at temperatures ∼6,000 K.

[111] Although such a situation cannot be fully described by a 1-dimensional approach, the finally adopted models include modifications in the vertical stratification in the temperature range 8,000–40,000 K that produce fairly good results from the SSI standpoint. These models are shown in the second panel Figure 1 by solid lines and the purely foot points of coronal loops are shown by dotted lines in that figure. The column of material involved is relatively small, less than 0.1 g m−2, but the radiative efficiency for emitting in the resonance H and He lines and continuum is very high.

[112] Figure 20 shows the final comparison of SRPM with the SEE/EGS data. Note that correction factors, of order unity, were applied to the SRPM data in order to approximately match the SEE data. These differences between SRPM and SEE are within the accuracy of the SEE data. For absolute comparisons of the SRPM results with observational data, the comparisons with SORCE/SOLSTICE and SDO/EVE data shown in Figures 17 and 18 are preferred because these observations have higher spectral resolution.

Figure 20.

Samples of the Solar Cycle 23 and the rotational modulation of the EUV and FUV comparison between TIMED/SEE ad the SRPM calculations. These wavelengths are dominated by chromospheric and low transition-region emissions.

[113] Generally the SRPM results have a bit less amplitude than were observed by TIMED/SEE. This may be due to several factors: 1) the lack of consideration of coronal holes in the present SRPM calculations, 2) the fact that SRPM is based on snapshot daily images (except for PSPT instrument downtime and bad weather) while the TIMED/SEE data are averages over some periods of time, 3) the SRPM calculations do not include flares but the TIMED/SEE data at times may contain emission from flares that were not fully eliminated.

5.6. Comparison With Variability Indices From KPNO Data

[114] Solar variability indices have been observed at KPNO for several solar cycles. The definition of the KPNO indices and background on them are given by Livingston et al. [2007]. Here some of these data are examined and compared with the synthetic index resulting from the SRPM calculations. The calculations of the corresponding SRPM indices performed here cannot be strictly identical because even when the same wavelengths and references are used, the continuum in the KP instrument has a shape different from the true solar continuum, and from that calculated by SRPM. This is because of the wavelength dependence of the KP instrument efficiency which is not absolutely and accurately known.

[115] Figure 21 shows the KP measurements compared to the computations of SRPM. The change of the computed Ca II K3 index is similar to the observed despite the detailed shape of K3 not being accurately reproduced by SRPM. However, the SRPM value has to be multiplied by a constant to compensate for the lower than observed intensity at K3.

Figure 21.

(top) The full-disk K3 index and (bottom) the CN equivalent width observed at KPNO during the last three cycles, and computed from SRPM for Solar Cycle 23.

[116] The CN equivalent width variation is somewhat overestimated by SRPM. This can be due to the Fe I line blend in the CN band head and the large uncertainties in the Fe I atomic data presently used by SRPM.

[117] It has been argued [Livingston et al., 2007] that other indices, namely the Ca II K quiet-Sun disk center and photospheric line equivalent widths, suggest the presence of a “basal” atmosphere that is not affected by the solar cycle. However, the PSPT observations of changing network areas do not agree with that view. Below we address separately the issues of whether the chromosphere and the photosphere change.

[118] KPNO observations of the K3 disk-center index for quiet-Sun, averaging over ∼2 arc min, have been carried out for several solar cycles. Part of the observations (1975–1982) was carried out by selecting the geometric disk-center regardless of possible presence of plage there and this shows a modulation of a bit less than ∼2% with some larger increases that may have resulted from presence of plage on the field of view. After the grating change [see Livingston et al., 2007], monitoring for the minimum K3 radiance was carried out and the target of the observation was moved to “a nearby area” showing the weakest K3 radiance. The later procedure minimizes any possibilities of detecting statistical changes such as those PSPT images find in the quiet-Sun. This is because this procedure selects the portions of the quiet-Sun where least network is present and where the presence of filaments may depress the K3 radiance to values even lower than those of the inter-network. Despite this, the KPNO record shows what is here regarded as a significant increase in the average K3 index even when the selection procedure used is minimizing any possible signal.

[119] For reference the SRPM expected change over Solar Cycle 23 of the K3 index in “average” of the so-called quiet-Sun at disk center was found to be very small and of the order of 2%. This value is of the order of the KPNO observed changes before the selection procedure was applied and somewhat larger than the observed changes after the selection of the lowest K3 radiance was started.

[120] Thus, given the selection procedure in the KPNO disk center K3 index, those observations, while not conclusive, are roughly consistent with the findings in this paper of a change in the average of the so-called “quiet-Sun” over the solar cycle. The change in the SRPM calculations of the K3 quiet-Sun disk-center index results simply from the increased network to inter-network ratio with increased activity observed by the PSPT instrument at OAR.

[121] The KPNO observations of the equivalent width of some photospheric lines, such as the C I 5381 A (in vacuum) line were also carried out and no significant changes were found with the solar cycle. From this, Livingston et al. [2007] concluded that the solar photosphere did not change with the solar cycle, but the present study does not support that conclusion although it confirms that changes of the C I line (and other photospheric lines) are insignificant. In the present models there are slightly different shapes of the photospheric temperature versus height curve between the Internetwork and the network models. This could be interpreted as to imply a smaller depth of the photospheric lines.

[122] However, this argument is flawed because the solar photosphere near optical depth unity in the continuum does not have a purely linear temperature gradient and the depth of the lines does not result exclusively from the temperature gradient but also the opacity plays a major role. Indeed the line depth depends on the change of the source function with respect to the optical depth. The physical reason for the temperature structure gradient in the photosphere is the energy balance and its dependence on the changing opacity. Therefore, as it occurs in the present models, while the overall photospheric temperature versus height decreases at high activity, the overall opacity also decreases at high activity too and the energy transported may not change. Similarly, these type of changes in the photospheric structure may not reflect in changes of line depths.

[123] The present SRPM calculations give an extremely small variation of the C I line equivalent width that is consistent with the KPNO observations, and the same is valid for other photospheric lines. This does not indicate presence of a basal solar photosphere but only that those line depths are expected to be insensitive to the photospheric temperature structure changes of the type studied here.

[124] Figure 22 shows the comparison between the H alpha line depth variations observed at KPNO and the calculated by SRPM.

Figure 22.

The H alpha line depth observed at KPNO compared to the SRPM computation for Solar Cycle 23.

[125] Trial calculations showed that the observed variation shown in Figure 22 cannot be explained by the foot points of coronal loops. The calculations with these only produced a practically flat H alpha line depth over the solar cycle and even a very slight trend opposite to the observed.

[126] However, the calculations including the “cloud layer” that was finally adopted provide the data in the figure which agrees with the observations. The effect of this layer on the H alpha line center depth is to decrease this line depth at maximum solar activity times in a similar way to the way it increases the Ly alpha line.

[127] This can be understood by considering the imaging observations in this line that show a very complicated structure of absorbing and emitting structures resembling loops, sometimes called fibrils or mottles. In the quiet-Sun these mostly surround the stronger magnetic field locations at the network. In active regions the long dark and bright fibrils are dominant and much extended. These observed H alpha structures correspond to upper chromospheric cool and warm loops (with temperatures between ∼6,000 and ∼20,000 K) which can be in absorption or emission depending on the relative populations of the hydrogen levels with n = 2 and 3. High-resolution H alpha images showing these structures and their dynamical character in the quiet-Sun were studied by Kneer and von Uexkull [1985].

6. The Bolometric Flux

[128] The daily variations in the SSI spectrum were integrated over all wavelengths to obtain the daily bolometric energy flux, equivalent to the TSI, but to distinguish the integrated SRPM SSI we will call it bolometric flux and reserve the term TSI for the observations. As it was stated above the bolometric flux value computed for the “low” activity case is 1379.909 W m−2 which is ∼1.1 and 1.4% larger than the value of 1365.1716 W m−2 reported by Fröhlich [2009], or 1360.7598 W m−2 reported by Kopp and Lean [2011], respectively.

[129] Figure 23 shows the comparison of the computed bolometric flux variations with the TSI composite reported by Fröhlich [2009]. For the purposes of the variations discussed here there is not an important difference between these and SORCE/TIM values.

Figure 23.

Comparison of the bolometric flux computed by SRPM with published TSI composite observations. (top) The full Solar Cycle 23 from the PMOD composite, and (bottom) an enlargement of the period 2003–2004 from SORCE/TIM. The short-lived large decreases of the TSI are due to large sunspot groups and particularly the drop around 2003 October 28 is due to the very large sunspot complex that produced the “Halloween” flare mentioned in Section 6.

[130] The observed TSI during cycle 23 is slightly increased at maximum times in between large sunspots, associated to active regions, passage over the disk, and increased more than the computed by SRPM. However, the observed enhancement is still small, ∼0.13%, and corresponds to an equivalent “apparent effective” temperature increase of only ∼1.9 K. Note, however, that this is the “apparent effective” temperature only when seen from Earth, which is a particular vantage point, in the ecliptic plane that has an angle of only ∼7 degrees with the solar equatorial plane. The changes in TSI, and thereby in the “apparent effective” temperature, may not correspond to changes in the astrophysical solar “effective” temperature that is a measure of the solar luminosity (i.e., the total radiative energy leaving the Sun in all directions). The relationship between the solar “effective” temperature and the “apparent effective” temperature depends on the particular directional characteristics of the overall solar output and it is currently unknown.

[131] Figure 23 (bottom) shows that SRPM matches well the rotational modulation observed in the TSI, and this was verified for the entire period 2000–2009 computed by SRPM, with Figure 21 illustrating only a part of this. However, as was said above, the SRPM overall Solar Cycle 23 bolometric flux has a significantly smaller solar cycle modulation. Therefore, some component of the solar cycle modulation occurs that is not directly related to the rotational modulation and is not captured by the present SRPM calculations, even when these calculations capture most details of the solar rotation which is due to the active regions. One factor that affects the solar-cycle trend of the bolometric flux but not its rotational modulation is the called “quiet-Sun” network change observed by the PSPT instruments and included in the present calculation. This effect is included though the mix of models 1001, 1002 and 1003 (features B, D and F, respectively).

[132] All the increasing activity models (except for sunspot umbra and penumbra) would have increasing bolometric flux if they were uniformly distributed over the solar disk. However, the active regions are never uniformly distributed and therefore it is not possible to use the relative areas in Table 4 for evaluating either the SSI or the bolometric flux. The results presented here always rely on the use of the solar disk masks like those shown in Figure 7.

[133] Simple analysis can only be carried out for the “quiet-Sun” network change because these features are roughly uniformly distributed over the solar disk. Therefore a corresponding bolometric flux for each component can be weighted with the areas in Table 4 and added to yield the change of the bolometric flux that is produced by the changes in the relative areas of the various “quiet-Sun” features. Such a simple study is of course not possible for the active region components whose distribution on the disk is far from uniform and greatly affects the contributions to the bolometric flux.

[134] At the “peak” state, the combined area of all active region features (H, P, S, and R, and models 1004 and above) reached ∼5% and of course at the “low” state the active region features relative area was practically 0.

[135] The fraction of the remaining “quiet Sun” area that was occupied by inter-network (feature B) was 75% at the peak and 80% at the low state. For network (feature D) it changed from 18.6 to 18.9%; and for the enhanced or active network (feature F) it changed from 7.2 to 1.1%. Therefore, feature B, became a larger part of the quiet Sun during the “low” state than during the “peak” state, and its increase was mostly at the expense of the active network, feature F.

[136] Considering the computed bolometric flux for each component, and assuming that the full disk was strictly composed in this same way, this change in the quiet Sun network would result in an increase of the bolometric flux of 0.854 W m−2 for the peak compared to the “low” state. This is a very substantial part of the observed solar cycle TSI changes but, as shown in Figure 23, it is compensated over the solar cycle by a similar decrease resulting from the active region features. Thus, it appears that an additional, and also non-rotationally modulated component, exists which is discussed in the next section.

[137] Considering the spectral contributions to the bolometric flux it is found that the SSI change due to the network is a slight decrease with increasing activity at visible wavelengths that is overcompensated by increases in the near-UV wavelengths (also increases in the FEUV but these have small absolute values). Qualitatively the behavior of the “quiet-Sun” features is not unlike that of active regions on average, but the quantitative details are different. In particular, the active network feature can be seen in the images mostly spread over the disk which enables its positive overall contribution to the bolometric flux. It has been observed that the enhanced network (feature F) results in part from the decaying parts of previous active regions, which spread out and generally migrate toward the poles [e.g., Bumba and Howard, 1965]. However, also part of this feature is unrelated to particular active regions and due to ephemeral magnetic regions emergence [e.g., Hagenaar et al., 2003] or just to randomly brighter areas of the network. It is not yet clear from observations if this random part of the enhanced network correlates or not to the solar cycle and more study is needed over several solar cycles.

[138] From the present calculations it is apparent that the net long-term effect of active regions, at least after the maximum time, is to slightly decrease the bolometric flux due to the preponderant visible decrease at wavelengths larger than ∼499 nm. However, plage and facula are very significantly brighter at wavelengths shorter than 400 nm, and in that way nearly balance the longer wavelengths active region deficit, except for the short periods where very large sunspots are not far from the center of the disk. These effects are shown in the Figure 23 displaying a moderate increase of the bolometric flux from SRPM at maximum solar activity times, in between sunspot decreases, which is just a bit smaller than the increase the network alone would produce. In examining Figure 23 the main evident effects of the solar activity cycle on the bolometric flux are the very substantial fluctuations up and down which are not present at the cycle minimum.

[139] The effects of active regions on the bolometric flux are very different from those of the enhanced network described above. This is in part due to the different radiance spectrum of these features, but it is also in part due to the fact that active regions are never uniformly distributed on the disk. During most of the cycle active regions only appear at relatively low latitudes and even at the beginning of the cycle they usually appear only at ∼50 degrees latitude or lower. Because of this, active regions spend most of the time at positions where their overall [plage+facula+sunspots) visible and infrared contribution to the bolometric flux is negative and cancels the positive UV contribution. At times when the result of the addition of all active regions contributions is positive, its absolute value is small because sunspots almost compensate or dominate the small positive flux from plage and facula. Thus on a temporal average the net effect of active regions is found to never increase the bolometric flux and only compensate for the positive effects of the changes in the quiet-Sun network (mostly the enhanced network) and spotless plage.

[140] The behavior in the SRPM SSI calculations mimics the observed by the SORCE/SIM instrument [Harder et al., 2009] and thereby the present models can be considered as a possible explanation of at least part of the observed SSI and TSI changes. However, unlike the present calculations, SORCE/SIM data matches the TSI observations of the solar cycle trend to a few hundreds of parts per million. This points to some component of the SSI solar cycle variations that is observed but is missing from the presently used 7 features and PSPT image analysis based SRPM calculations.

[141] Table 3 shows the few selected days and the bolometric energy fluxes computed by SRPM, as well as their breakout in FUV-EUV (wavelength < 200 nm), NUV (between 200 nm and 400 nm), and VIR (wavelength > 400 nm). This breakout is based on overall formation regions in the solar atmosphere (although spectral details are mixed) and on the consideration that variations in each of these ranges affect different parts of the Earth atmospheric layers.

[142] The variations in the FUV-EUV contribution result from plage and facula and sunspots which all contribute positively. However, the resulting increase of bolometric flux due to the FUV-EUV spectral range is small and does not have an important effect on the total as indicated in Table 3.

[143] It is shown in Table 3 that many times during the activity cycle “mid2,” the NUV increase practically compensates the decrease VIR giving a near zero bolometric flux change with respect to the “low” case, e.g., “high2,” “peak.” Occasionally big sunspots produce a large decrease in the VIR and a small decrease in the NUV resulting in decreased bolometric flux, e.g., “mid1.” Also occasionally predominance of facula and plage near the limb and low sunspot areas produce large NUV increases and small VIR increases that result in increased bolometric flux. However, these overall values include the bolometric changes produced by the changes in the network that were discussed above.

[144] Because there are very large fluctuations in the relationship between plage, facula, and sunspot umbra and penumbra, complicated fluctuations occur in the bolometric flux shown in Figure 23. There is little indication yet of how these features behave in different solar cycles or even at early and late times within the same cycle. A systematic study over many cycles would be very interesting but is difficult to do before the availability of good photometrically calibrated imaging data such as that from PSPT instruments at OAR and MLSO.

[145] Considering the changes of the bolometric flux with respect the “low” state, due to the network changes described above, the net effects of only active regions become more clear.

[146] When large sunspots are present, e.g., “mid1,” their large decreases in the VIR range and smaller decreases in the NUV largely overpower the “quiet-Sun” network increase. The net result is to reduce the net bolometric flux with respect to the “low” activity case. The particular case of “mid1” occurs during the decay of the cycle and when the network changes had already gone down. However, similar cases of large spots occurred earlier in the cycle, and the most notable one was the “Halloween” active region that produced a very large bolometric flux decrease in October 2003, in addition to an extremely large X flare [see, e.g., Tsurutani et al., 2005].

[147] At times when there is an even mix of sunspots and plage/facula on the disk, e.g., “high2” and “peak,” the NUV increases are insufficient to cancel the VIR decreases and a negative value of the bolometric flux change occurs due the active region. However, this is nearly canceled by the network increases and the net result is a slightly increased bolometric flux.

[148] When plage/facula near the limb dominates small sunspot area, e.g., “high1,” the net change due to active regions is near zero (or a small negative or positive value) because the NUV increase due to active regions cancels their VIR decreases. The net result is an increased bolometric flux because of the network increases.

[149] Yet another case is that of “mid2” during the decay of the cycle and in this case no sunspot umbrae, some penumbrae, and very little plage/faculae were observed. A small decrease occurs in VIR due to the combination of penumbrae and the darkness of plage/faculae on the disk away from the limb that SRPM modeling yields at some wavelengths. This is practically compensated by the small increase of network at that time and the net result is a bolometric irradiance similar to the “low” case.

[150] One problem in the analysis of Figure 23 and Table 3 values is that the TSI reported daily values are often averages of various measurements while the SRPM computation of the bolometric flux is based on a single snapshot. Intraday variations produce some expected differences, especially at times of flaring activity. This, together with the variable image quality, produces some noise in the computed bolometric flux values, but is not too serious as Figure 23 shows.

[151] The discussion in this section reveals clearly the main issues on interpretation of TSI observations. One such issue is the complicated nature of the solar features in which some compensate others and there is no simple relationship between each of the types of structure areas or positions on the disk. Of course active regions contain plage, facula, umbra, and penumbra, but there is no simple relationship between their areas and this produces a large variety of situations. Another issue is the spectral complexity since lines, continuum, and even different spectral regions of line and continuum, have different characteristics depending on the feature types and their center-to-limb variation. An issue with interpreting rotational modulation is that it is impossible to separate the effects of solar rotation and time dependence even if a single active region was present.

[152] Yet another issue is the change with the solar cycle that is observed in the “quiet-Sun” network that is not related to rotational modulation. This change is found in the PSPT mask data and is also obvious in Figure 7, and produces a change in the baseline on which the active region changes superimpose.

[153] The simple interpretation for the differences between the computed bolometric flux and the observed TSI is that there is another component that affects the bolometric flux but which is not yet considered by SRPM, and that this factor is not related to rotational modulation (in the same way the network changes do not reflect on this). The next section points to possible physical causes for the mismatch.

[154] Empirical ad hoc “corrections” could be attempted to match the observed TSI solar cycle trends. However, no such empirical “fix” is attempted in this paper.

7. The Quiet-Sun

[155] The comparison with the detailed observations by SORCE/SIM during the decay of Solar Cycle 23 indicates that SRPM is underestimating the SSI absolute changes at some wavelengths in the near-UV (increases at solar maximum), in the visible (decreases at solar maximum), and especially in the infrared at around 1.6 micron (decreases at solar maximum). However, the observed rotational modulation is well explained by SRPM as will be shown in separate papers (Harder et al., manuscript in preparation, 2011). Therefore, the same issue noted about the bolometric flux in the previous section also applies to the SSI.

[156] It is apparent that the mismatch between SRPM and SSI observations results from estimating the long-term trend that is not directly related to the passage of active regions that produce the rotational modulation. The following discussion shows several possibilities that individually, or in concert, may well explain these effects.

[157] SSI changes beyond those found here can be produced by solar cycle changes in the so-called “quiet-Sun” components which would still be consistent with the available observations and cannot be presently ruled out. This explanation is consistent with EUV observations that indicate an increase in FUV-EUV radiance of relatively quiet regions of the solar surface during maximum activity times [Schühle et al., 2000].

[158] That data analyzed in this paper show that there is no evidence supporting a “basal” portion of the solar surface that is completely unperturbed by the solar cycle. Rather to the contrary, it is found that at least changes in the so-called “quiet-Sun” network occur and that they have significant effect on the SSI and bolometric flux. These changes correspond to small spatial scales and magnetic field magnitudes that have been often overlooked in SSI and TSI studies.

[159] Also, it must be realized that the present SRPM method for constructing the SSI uses a feature discrimination scheme that relies purely in contrast levels with respect to the median brightness at each μ. This also applies to the so-called quiet-Sun features that have a small contrast in the PSPT Ca II image. There is no guarantee that this median could not change because of various effects. Moreover, a small change is expected due to the presence of 5% active region area at cycle maximum that offsets the median toward increased absolute intensity values. This effect could be minimized by a recursive iteration of the feature discrimination procedure, which in each iteration would mask out the known active region features when determining a new median for each annulus. A similar effect of shifting the median occurs due to the increasing enhanced network at cycle maximum. Again the previously mentioned method could be applied but this type of procedure, of excluding certain areas, destroys the statistical meaning of the median and could lead to a problem of small number statistics when too few “quiet-Sun” pixels remain.

[160] Also, a small change in the absolute intensity values of the median, or a split of the inter-network into features A and B, could have an important effect on the solar cycle trends of the SSI and the bolometric flux. Even at solar maximum the “quiet-Sun” features occupy 95% of the solar disk and a tiny change of only 0.1% in the spectral and total radiance of these features would affect the overall solar cycle trends by practically that same amount. Such a change would be undetectable with current spatially resolved instrumentation and would have no rotational modulation signature.

[161] The bottom line of these considerations is that using the median intensity as a reference in the features discrimination does not solve the lack of an absolute standard. (Of course the median is less affected than the mean but it is still sensitive to high-intensity pixels.) For an absolute standard to be sufficient in addressing the issues of SSI and bolometric flux it should be more precise than 0.1%. However, if imaging observations used were more sensitive to the causes of the radiance variations this constraint could be significantly loosened.

[162] It has been shown in this paper that differences between the physical models of the features that constitute the quiet-Sun produce different spectral and total radiance. This, together with the solar-cycle variation of the statistics of these features produces significant changes of the SSI and the bolometric flux.

[163] It has been also shown that the changes in these statistics do not produce measurable changes in the overall CLV, or in the equivalent width of photospheric lines. Only marginally observable changes would occur in the Ca II K3 “disk-center index” but this detectability depends critically on the observation setup and can be affected by subjective selection processes in trying to locate the quietest areas.

[164] Again, the use of observations that are more sensitive to the solar heating/cooling issues, and an absolute standard, could lead to much progress on these matters. It seems that Ca II K is the most sensitive spectral feature available from ground data, but that this line is not sensitive enough. From space may other possibilities are open.

[165] A source of uncertainties in the present calculations is the observational conditions of the PSPT instrument of the OAR. The changes in these conditions have little effect on the discrimination of active regions, but have a significant effect on the network components that have an intrinsic low contrast. The blurring by seeing effects during poor atmospheric conditions causes a reduction in network area. In particular the conditions in the winter season, corresponding to several of the cases reported in Table 3, are usually not very good. Images available from the PSPT instrument at MLSO are less affected by seeing changes but are only well calibrated for the period since 2005. Over the overlapping period the MLSO images show similar decay of the network with the Solar Cycle 23 decay.

[166] In addition to these issues, the effect of using discrete bins to characterize the continuous intensity distribution observed in the images can produce an underestimate of the changes in SSI and bolometric flux due to simply the observed changes of the “quiet-Sun” components. Analysis shows that the observed steepening at solar minimum of the shape of the PSPT data intensity distribution (see Paper III's Figure 1 for an example of this distribution), could keep almost unchanged the total number of pixels in the bin that characterizes feature E (network) but still would change its contribution to the SSI and bolometric flux. This occurs because within a bin the number of pixels corresponds to the zero-moment of the intensity distribution while the total radiance output is the first-moment. A shift of the pixels inside the bin toward larger intensities at cycle maximum does not change the zero moment but changes the first-moment, however, such change would not result in increased output in the SRPM scheme because only one physical model represents the entire bin.

[167] This problem could be minimized by increasing the number of bins, and models, but the current ground instrumentation is now at the limits of its capabilities in regard to the discrimination of features. Also, if the intensity discrimination is much increased several daily images would be needed to produce better statistics than a simple daily snapshot.

8. Sunspots

[168] In the present paper the sunspot umbra model used (1006, feature S) remains that of Paper I and has not been updated. The only modifications were done on the sunspot penumbra model (1007, feature R) for which energy balance in the coronal loop foot point was applied for the transition region and a cloud layer was added similarly to the facula model (1005, feature P).

[169] An important consideration is that although the sunspot umbra and penumbra contrast in the visible continuum is very large and well known, these features NUV contrast is not so well known. In particular, routine images in the Ca II K line show that for large sunspots and at relatively broad band pass of the PSPT instruments the dark area at the center of the spot is only a fraction of the dark area in images at visible wavelengths. Also, very small sunspots may be observed to be completely bright in Ca II K. In narrower band pass images well centered in the line the dark portion of sunspots become even smaller. Qualitatively similar but more pronounced effects occur in the Mg II line, and in Ly alpha [see Fontenla et al., 1988]. The detailed line profiles in all these lines are very different from those of the plage or facula around the sunspot. The umbra profiles show single emission peaks instead of the self-reversed peaks in the plage and facula. However, despite the very different shape, the integrated line emission, and the peak intensity, in the umbra is comparable to the surrounding emission.

[170] Experiments were carried out using NLTE calculations that showed that these effects cannot be explained by purely 1-dimensional models regardless of the temperature gradient adopted. Instead the single peaks can be easily explained by the sunspot umbra scattering of radiation received from the high raised edges around it (i.e., the Wilson depression walls). Because of these effects the sunspot contrast in UV lines is currently not accurately computed by SRPM and the dark sunspot umbra areas are overestimated in the UV. These 3-dimensional effects are most dramatic for small sunspots, such as those observed in the “high2” and “peak” cases, and can be responsible for a significantly higher increase in the NUV, and a stronger compensation of the VIR decrease, than is currently shown in Table 3 for these cases.

[171] Imaging observations at NUV wavelengths are very difficult from the ground because of the heavy atmospheric absorption. NUV images from space, with good photometrical quality, together with full 3-dimensional NLTE analysis of such observations could provide better constraints on the role of sunspots on the SSI in that spectral range.

[172] Also, the current SRPM scheme only uses the sunspot areas measured from red continuum images and without regard to their sizes or particular characteristics. Therefore, a modification to the method would be necessary to take into account the sunspot sizes and the apparent area reduction due to the effects described above.

[173] Particularly, the contributions by many small spots presently may result in SRPM calculating a decrease the NUV irradiance when in fact they may have the opposite effect. The sunspot sizes are, of course, easy to determine from good quality imaging observations but not from the standard sunspot index in which the individual sunspot areas and number of spots are inextricable mixed.

[174] In the PSPT images used here, of resolution normally not better than ∼2 arc sec, very small spots, i.e., pores, are blurred and consequently identified as penumbrae. Although this identification is not formally correct, it results in the net result of a small VIR decrease and an NUV increase which are essentially correct. Therefore this is not considered a serious problem.

[175] These matters about sunspots also affect some wavelengths of the EUV and FUV (e.g., He II 304 and Ly lines and continuum) in which the 1-dimensional SRPM computations of sunspots are also be problematic. However, this is probably not a problem for most of the EUV in which the emission can be computed by the effectively optically thin approach and only the un-occulted emitting volume is important.

9. Conclusions

[176] The present set of solar feature physical models and the spectral synthesis based on them, together with the areas and positions of these features determined from Ca II K PSPT images, explain very well the SSI and bolometric flux rotational modulation observed by SORCE and other instruments. The solar-cycle variations of the SSI and bolometric flux, however, are not completely explained at near-UV, visible, and IR ranges.

[177] However, the solar cycle trends of the observed optical indices are well explained by the current SRPM modeling. These indices are relative quantities that describe spectral line depths and therefore not based on absolute measurements.

[178] The present models and synthesis procedure explains well the FUV and EUV observed rotational and cycle variations, from nearly the maximum to the minimum of Solar Cycle 23. For this the models need to include a parameterization, that we call a “cloud layer” to describe a component of the upper chromosphere consisting in a distribution of loops at temperatures in the range ∼8,000–40,000 K that varies with the solar cycle. This distribution also affects the H alpha line depth in the visible and permits the SRPM calculations to match the observed H alpha index cycle variations.

[179] There is, however, a sharp step-like increase between 2002 and 2003 that SRPM calculations do not reproduce well. It is still not clear, but under analysis, whether an additional hotter feature (Q) atmospheric model (1008) can solve this issue. Also, a dimmer feature (A) is still under study for describing coronal holes.

[180] The consideration of the two additional features (A and Q) would somewhat increase the amplitude of the trends computed, but will not change the direction of these changes. Further analysis of historical images may yield a way to derive the distribution on the disk of these features in periods not covered by the present study.

[181] Because of what was said above in this section, the present SRPM computations should be regarded as providing slightly lower amplitude than observed SSI changes over the solar cycle, but it is an accurate representation of the rotational modulation changes. However, the present SSI estimates provide a very good basis for assessing the effects of SSI changes on the Earth and other planetary atmospheres. The current SRPM results provide very high resolution and wavelength coverage detail on the SSI and its changes in time scales of rotational modulation and solar cycle. The present spectra also provide a very good SSI reference for studies of the atmospheric transmission and heating rates that need such absolute and high-resolution input. At the same time, these data have been convolved and binned in different ways that make it suitable for direct use in most of the GCM and other calculations.

[182] The optically thin ionization calculation used here will be improved in future work by adopting the consistent formulation of the dielectronic recombination/ionization provided by Dere [2007]. Also, other atomic data will be updated in the future and this includes collisional rates, increase in the number of levels, consideration of lines from more species, and more photodissociation opacities. The SRPM use of these updates and the improved NH photodissociation opacity will likely improve the agreement with the observations for the few wavelengths where important differences still exist.

[183] Analysis of Solar Cycle 23 shows that a slowly variable solar-cycle network area in the computed solar masks produces significant SSI and bolometric flux variations. These are generally similar to the behavior of plage, but with smaller changes, and probably have similar causes from the magnetic fields. However, the network features are related to small-magnitude and spatial-scale magnetic fields. These abundant, but nearly homogeneously distributed brightenings, do not produce rotational modulation effects but are responsible for a large part of the solar cycle trend in the SRPM bolometric flux. The calculations presented here show that the lack of observable changes in the continuum CLV or the depths of photospheric lines do not imply an unchanging photosphere with the solar cycle. Rather, these are a natural consequence of the nature of the models considered here. This paper uses semi-empirical modeling and does not dwell more in the theory of how the models work, which require careful consideration of magneto-convective-radiative energy transport that are well beyond the present study using semi-empirical modeling.

[184] The current differences between SRPM SSI and bolometric flux and the corresponding observed quantities can be explained by very small changes in the “quiet-Sun” structure that are minute and practically undetectable by ground observations that lack precise absolute calibration. A related issue is that of the definition of “quiet-Sun.” This term originated in the early observations that showed the dichotomy between “active regions” where large-scale brightening and magnetic fields were observed and “quiet regions” where these were not observed. However, more recent observations have shown [e.g., Trujillo Bueno et al., 2004; Orozco Suárez et al., 2007] that there is abundant magnetic field in the “quiet-Sun” at small spatial-scales down to the granulation. Thus, a question arises as to whether the small-scale field changes over the solar cycle, and this affects the SSI and TSI. This question cannot be answered with the currently available data because there is not a sufficiently precise and statistically meaningful record of changes over a solar cycle in the small scale solar magnetic field. Only at intermediate scales is the magnetic network observed. Thus, it would be reasonable to think that a change may exist also at smaller scales. Observations from space at more sensitive wavelengths, e.g., images from SDO/AIA at 160 nm wavelength that display better the low intensity regions (that we attribute to model A) at the base of the upper chromosphere, may be able to answer these matters when a complete solar cycle is recorded.

[185] Another possibility for explaining the unaccounted part of the SSI and bolometric flux variations is that, irrespective of any small-scale magnetic field changes, the thermal structure of the solar atmosphere may change either related to a global magnetic field or not. In our view such can only be assessed by helioseismic tools after the details of how the observed p- and f-mode frequency changes over the solar cycle originate.

[186] While semi-empirical 1-dimensional models are suitable for SSI studies, they have problems for modeling the detailed profiles of many upper-chromospheric lines, e.g., the H, He I and II, Mg II and Ca II resonance lines. This is because of the highly inhomogeneous structure of the upper chromospheric and coronal layers in which material at very different temperature is interleaved at the same altitude range (and also at the same pressures). The mixture of coronal loops at around 1 MK with chromospheric loops in the range ∼8,000–40,000 K, i.e., what we call the “cloud layer,” creates a very complicated NLTE radiative transfer situation in these optically thick lines. This can only be properly solved in a full 3-dimensional NLTE radiative transfer scheme because the various adjacent structures illuminate each other and thereby affect the others source function.

[187] Moreover, the emitted radiation spectra are differently affected by various types of features. The foot points of coronal loops have been shown by FAL [Fontenla et al., 1993] to strongly affect the line centers and have too narrow near wings and relatively weak double peaks. Instead, a representation of the “cloud layer” consisting in a slab of material at chromospheric temperatures produces an emitted spectrum in which the line center is very weak but the peaks and near wings are very strong. An example of this is the Lyman alpha emission resulting from the VAL model [Vernazza et al., 1981]. The observed Lyman alpha profile matches neither of these extremes and shows a very significant line center and also large peaks and substantial near wings.

[188] In the mixed situation the foot points of coronal loops add their emitted radiation to the much deeper line center but stronger peaks of the chromospheric loops that share the same resolution element. The effects go further than this because the illumination of the coronal loops foot points by the chromospheric loops increases the source function and penetrates to deeper layers. This illumination strengthens the wings of the emission from the coronal loops foot points. In turn, the illumination of the chromospheric loops by the foot points of coronal loops produces an increase of the source function in the chromospheric loops. The result of these interactions cannot be simply guessed and is further complicated by the wavelength dependence and probably by PRD processes.

[189] The 1-dimensional physical models adopted here, like the FAL ones, cannot reproduce the observed line profiles very well. This is because, when adopting the 1-dimensional description of the upper chromosphere and the cloud layer used here the loops material stands solidly in the way of the physical linking between the transition region at the legs of the coronal loops and the chromosphere below. This does not allow for the steep temperature gradient driving the diffusion of hydrogen, helium, and probably other species, and absorbs too much at the line centers.

[190] In particular, for the Lyman alpha line the line center becomes too deep when including the cloud layer, but the peaks and near wings become too weak when omitting the cloud layer. In both cases the integrated line intensity is too small unless the pressure is increased for the case without cloud layer or the extension is increased in the case including the cloud layer.

[191] In the present paper we chose to represent the “cloud layer” in a way that explains the integrated intensities which are the most important quantities for SSI modeling, but may not represent well the details of the line profiles affected by this layer.

[192] This situation cannot be improved until full 3-dimensional radiative transfer is implemented in SRPM together with fully 3-dimensional physical models. This work is in progress.

Acknowledgments

[193] Juan Fontenla acknowledges support by NASA Living with the Star Program grants NNX07AO75G and NNX09AJ22G and by Air Force Office of Scientific Research (AFOSR) under grant FA9550-07-1-0565. J.H. acknowledges support by NASA NAS5–97045 (SORCE). We acknowledge I. Ermolli and S. Criscuoli for computing and providing us with the OAR PSPT daily features masks that made possible the present work. Also, we acknowledge C. Stehlé for providing us very detailed information and programs for computing the hydrogen line broadening. We acknowledge the PMOD/WRC, Davos, Switzerland for the TSI data from the VIRGO Experiment on the cooperative ESA/NASA SoHO Mission. We thank the anonymous reviewers of the manuscript for their comments that helped improving this paper.

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