High resolution solar spectral irradiance from extreme ultraviolet to far infrared

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2011jd016032, 2011 High resolution solar spectral irradiance from extreme ultraviolet to far infrared J. M. Fontenla, 1 J. Harder, 1 W. Livingston, 2 M. Snow, 1 and T. Woods 1 Received 29 March 2011; revised 29 July 2011; accepted 1 August 2011; published 20 October [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). Citation: Fontenla, J. M., J. Harder, W. Livingston, M. Snow, and T. Woods (2011), High resolution solar spectral irradiance from extreme ultraviolet to far infrared, J. Geophys. Res., 116,, doi: /2011jd 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 groundbased 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 1 LASP, University of Colorado at Boulder, Boulder, Colorado, USA. 2 National Solar Observatory, Tucson, Arizona, USA. Copyright 2011 by the American Geophysical Union /11/2011JD 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 mediumresolution, 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 ( nm with 1of31

2 Table 1. Solar Features Designation and Corresponding Model Indices Feature Description Photosphere Chromosphere Model Index Corona Model Index A Dark quiet Sun inter network B Quiet Sun inter network D Quiet Sun network lane F Enhanced network H Plage (that is not facula) P Facula (i.e., very bright plage) S Sunspot umbra R Sunspot penumbra Q Hot facula FWHM 0.46 nm) and the Ca II K line ( 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]). [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 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 2of31

3 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. 1 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 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 1 Auxiliary materials are available in the HTML. doi: / 2011JD 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. [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 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 3of31

4 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. 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 4of31

5 Table 2. Currently Computed Full NLTE Radiative Transfer Ion (I) Levels (I) Ion (II) Levels (II) Ion (III) Levels (III) Abundance HI He I 20 He II C I 45 C II 27 C III e 4 N I 26 N II 33 N III e 4 O I 23 O II 31 O III e 4 Ne I 80 Ne II e 5 Na I 22 Na II 14 Na III e 6 Mg I 26 Mg II 14 Mg III e 5 Al I 18 Al II 14 Al III e 6 Si I 35 Si II 14 Si III e 5 S I 20 S II 30 S III e 6 Ar I 48 Ar II e 6 KI e 7 Ca I 22 Ca II 24 Ca III e 6 Ti I 10 Ti II e 8 VI 10 VII e 8 Cr I 10 Cr II e 7 Mn I 10 Mn II e 7 Fe I 120 Fe II 120 Fe III e 5 Co I 10 Co II e 8 Ni I 10 Ni II e 6 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., Ha, Hb, 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 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. [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 quantummechanics 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 5of31

6 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 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 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 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 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 crosssections 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. [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 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 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 nm that is prominent in the full 6of31

7 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 nm, although other species are dominant. 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 m values from 1 to 0.1 (m 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 m 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 photospherechromosphere 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 m 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 photospherechromosphere 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 photospherechromosphere 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 cos 2 filter truncated at the first zero of the 7of31

8 Figure 3. The low resolution (1 nm) EUV part of the irradiance spectrum computed for SRPM QS. 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. [52] Calculations of daily SSI at 1 nm resolution were carried for the days within the period 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. [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 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. 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. [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 socalled 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 8of31

9 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. the simple foreshortening effect that makes areas smaller as they approach the limb. [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. [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. Table 3. Selected Key Days Day Designation Delta FEUV Delta NUV Delta VIR Delta Total (SRPM) Delta TSI (PMOD TIM) Sunspot Relative Area Nov High2 8.9e e 4 Dec High1 5.5e e 4 Jan Peak 1.1e e 4 Jan Mid2 2.3e Jan Mid1 3.1e e 4 Sep Low of31

10 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. [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]. 10 of 31

11 Table 4. Relative Areas of Features for Selected Key Days Day Designation A+B D F H P+Q S R Nov High e 3 3.6e 4 1.9e 3 Dec High e 3 2.1e 5 4.5e 4 Jan Peak e 3 2.6e 4 2.2e 5 Jan Mid e 3 1.2e e 5 Jan Mid e 3 8.8e 4 3.2e 3 Sep Low e 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. 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 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 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 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 Wm 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 Wm 2 nm 1 and K for the irradiance and brightness temperature variations, respectively. 11 of 31

12 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. 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. [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. 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. 12 of 31