Quiet-Sun Mg ii h and k Line Profiles Derived from IRIS Full-Sun Mosaics. I. Reference Profiles and Center-to-limb Variation

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Published 2021 July 19 © 2021. The American Astronomical Society. All rights reserved.
, , Citation Stanislav Gunár et al 2021 ApJS 255 16 DOI 10.3847/1538-4365/ac07ab

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Abstract

We derived high-precision reference profiles of the Mg ii h and k lines that represent the quiet Sun during a minimum of the solar activity. To do so, we used the broad catalog of full-Sun mosaics obtained by the Interface Region Imaging Spectrograph (IRIS). To minimize the influence of the local variations due to the on-disk solar features and to achieve low levels of uncertainties, we used 12 IRIS full-Sun mosaics without sunspots or other significant signs of solar activity. These mosaics were obtained between 2019 April and 2020 September in the near-ultraviolet spectral range. In this paper, we present the disk-averaged reference profiles of Mg ii h and Mg ii k lines, together with a series of reference profiles spanning the distance between the disk center and the solar limb. These series of profiles offer a detailed representation of the center-to-limb variation of both Mg ii h and Mg ii k lines. The reference Mg ii h and k line profiles provided in this paper can be used as the incident radiation boundary condition for radiative-transfer modeling of prominences, spicules, and other coronal and chromospheric structures.

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1. Introduction

The resonance Mg ii h and k lines at 2803.53 Å (Mg ii h) and 2796.35 Å (Mg ii k) are among the most prominent spectral lines observed on the solar disk. As such, they represent a significant source of illumination for chromospheric and coronal structures, such as chromospheric fibrils, spicules, or prominences. Mg ii h and k lines also provide a good diagnostic tool for these structures. This was demonstrated by, for example, Leenaarts et al. (2013a, 2013b) and Pereira et al. (2013) in the solar atmosphere, Heinzel et al. (2014), Vial et al. (2016, 2019), or Ruan et al. (2018, 2019) in prominences, and Alissandrakis et al. (2018) or Tei et al. (2020) in spicules. Moreover, the Mg ii h and k doublet plays an important role in the radiative losses and thus the energy balance of the chromosphere, where the cores of these lines are formed. To fully utilize the diagnostic potential of Mg ii h and k lines, it is essential to have a detailed, up-to-date knowledge of the radiation emerging from the solar disk in these lines. In the present work, we use the extensive data set of full-Sun mosaics obtained by the Interface Region Imaging Spectrograph (IRIS; De Pontieu et al. 2014) to derive state-of-the-art quiet-Sun reference spectra of Mg ii h and k lines. These are complementary to our previous work on the quiet-Sun reference Lyα line profiles presented in Gunár et al. (2020).

Owing to its near-ultraviolet (NUV) wavelength range inaccessible to ground-based instruments, the Mg ii h and k doublet was observed relatively infrequently prior to the launch of IRIS. The first Mg ii h and k spectra from the solar disk were obtained by a spectrograph borne by a V-2 rocket (Durand et al. 1949). Other sounding-rocket spectrographs (e.g., Bonnet et al. 1967; Bates et al. 1969; Kohl & Parkinson 1976; Allen & McAllister 1978) and high-altitude balloon experiments (e.g., Lemaire 1969; Lemaire & Skumanich 1973) followed. In orbit, Mg ii h and k spectral profiles were obtained by the spectrograph on board Skylab (Doschek & Feldman 1977) and by the Laboratoire de Physique Stellaire et Planétaire (LPSP; Artzner et al. 1977; Bonnet et al. 1978, or Lemaire et al. 1981) on board the Orbiting Solar Observatory (OSO-8). Later, high-spectral-resolution Mg ii h and k observations were obtained by the balloon-borne spectrograph RASOLBA (Staath & Lemaire 1995) and by the sounding-rocket-flown High-Resolution Telescope and Spectrograph (HRTS; Morrill et al. 2001). Spectropolarimetric observations of the Mg ii h and k lines were obtained by the Ultraviolet Spectrometer and Polarimeter (UVSP; Woodgate et al. 1980) on board the Solar Maximum Mission (Vial 1984) and by the Solar Ultraviolet Magnetograph Investigation (SUMI; West et al. 2011) and Chromospheric Layer Spectropolarimeter-2 (CLASP-2; Ishikawa et al. 2021) sounding-rocket experiments. The number of available Mg ii h and k observations has increased dramatically with the advent of IRIS. Since its launch in 2013, this space-borne spectrograph obtained a wide set of NUV and far-ultraviolet (FUV) spectra of various solar phenomena. IRIS also periodically produces full-Sun mosaics composed of raster scans that cover the entire solar disk.

The Mg ii h and k spectral observations provide not only a diagnostic tool for analyses of solar plasmas but also an important boundary condition—the incident radiation from the solar disk—for generations of models of prominences, spicules, etc. For example, Bocchialini & Vial (1994) used OSO-8/LPSP observations to derive the disk-center quiet-Sun spectral profiles of Mg ii h and k lines. The disk-center averaged spectrum of the core of the Mg ii line (including h and k lines) was derived from the RASOLBA observations by Staath & Lemaire (1995). This quiet-Sun Mg ii spectrum was compared with a spectrum obtained by IRIS in the work of Liu et al. (2015). Therein, the authors derived a sample of quiet-Sun Mg ii h and k spectra by averaging over a part of IRIS raster observations obtained not far from the disk center (μ = 0.83). The incident radiation in the Mg ii h and k lines for the modeling of prominences was derived from the IRIS full-Sun mosaics by Vial et al. (2019).

The Mg ii h and k intensities observed on the solar disk vary considerably, not only with different observed structures but also with the distance from the disk center. Such center-to-limb variation was shown already by, for example, Bonnet et al. (1967) and Kohl & Parkinson (1976). Both the Mg ii h and k profiles averaged over the solar disk and their center-to-limb variation derived previously were based on a relatively sparse number of observations. These were typically limited to a few slit exposures within a short period. For example, Kohl & Parkinson (1976) observed two locations on the solar disk (μ ∼ 1.0 and 0.23) during several minutes offered by a sounding-rocket flight. Staath & Lemaire (1995) used RASOLBA disk-center and near-limb observations obtained by 10 and 8 exposures, respectively. The slit of the RASOLBA spectrograph had a length of 30''. The limb-darkening curve for Mg ii h and k lines provided in Staath & Lemaire (1995) is mostly based on the doctoral thesis of Greve (1978). Morrill & Korendyke (2008) derived the curve of the center-to-limb variation for the Mg ii line core from observations by the HRTS sounding-rocket experiment. These data had a factual spectral resolution of 0.2 Å and incorporated a plage region. Using a much broader data set provided by IRIS full-Sun mosaics, Schmit et al. (2015) studied the variability of the Mg ii h line emerging from different on-disk magnetic structures. These authors also studied the center-to-limb variation of this line. Later, Vial et al. (2019) used center-to-limb variation curves derived from the IRIS full-Sun mosaic observations to construct the Mg ii h and k incident radiation profiles for the modeling of prominences.

The Mg ii h and k radiation from the solar disk is not constant over time but varies considerably with the solar cycle. This variation is continuously monitored by a succession of instruments—for example, the Solar Ultraviolet Spectral Irradiance Monitor (SUSIM; Floyd et al. 2003) and the SOLar-STellar InterComparison Experiment (SOLSTICE; Rottman et al. 1993; Rottman & Woods 1994) on board the Upper Atmosphere Research Satellite (UARS; Reber et al. 1993), the Ozone Monitoring Instrument (OMI; Levelt et al. 2006) on board the Aura satellite, or the redeployed SOLSTICE II instrument (McClintock et al. 2005a, 2005b) on board the Solar Radiation and Climate Experiment (SORCE; Anderson & Cahalan 2005). We will investigate this variation in a follow-up paper.

In the present work, we use a series of 12 IRIS full-Sun mosaics obtained during a period of a minimum of solar activity (see Section 2). We derive high-precision reference spectra of Mg ii h and k lines (Section 3) and map the variation of these lines with the position on the solar disk (Section 4). We also provide the disk-averaged profiles which represent the solar spectral irradiance in the Mg ii h and k lines during a solar minimum. The reference profiles mapping the center-to-limb variation in both Mg ii h and Mg ii k lines are provided in tabulated form in the Appendix and in machine-readable format online (Tables 36).

2. Observations

2.1. IRIS Full-Sun Mosaics

Since its launch, IRIS commenced a quasi-regular acquisition of maps of the entire solar disk in both NUV and FUV spectral ranges. The main purpose of these full-Sun mosaics is to track the changes of the instrument sensitivity over its lifetime. This is achieved by the comparison with cotemporal measurements by SORCE/SOLSTICE II or the Solar EUV Experiment (SEE; Woods et al. 2005) on board the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) spacecraft—for more information see Wülser et al. (2018). To generate an IRIS full-Sun mosaic, 184 different raster scans are needed to cover the entire solar disk. Each raster scan consists of 64 positions of the IRIS 175'' long slit. Each step in a raster covers a distance of 2'', yielding a raster area of 128'' × 175'' (Schmit et al. 2015). At the time of writing, the archive of the IRIS full-Sun mosaics 3 contained 91 observations spanning the period from 2013 September 30 to 2020 October 19. Some of these mosaics are constructed from less than 184 rasters, leaving gaps in the full-disk coverage. All mosaics are affected by spikes due to cosmic rays, which are not removed by default. We used the function de_spiker.pro available in the SolarSoft package (SSW; Freeland & Handy 1998) for removing the spikes from the mosaic images and the SSW function despike_gen.pro for processing the spectral data. In the following, we summarize the observational characteristics of 91 available NUV mosaics which cover two spectral windows of ±1.75 Å centered at 2803.53 Å (Mg ii h) and 2796.35 Å (Mg ii k). The mosaics were taken with exposure times of 1 s (16 mosaics), 2 s (63), 4 s (3), and 8 s (9). The spectra along the slit were binned with the binning factors of 2 (76 mosaics) and 4 (15). The spectra along the dispersion (i.e., along the wavelength range) were binned with factors of 2 (76 mosaics) and 4 (15). All mosaics are given in data number units (DN) and have a uniform spectral sampling of 0.035 Å.

2.2. Reference Mosaics

To derive high-precision quiet-Sun reference profiles of Mg ii h and k lines, we use 12 IRIS NUV mosaics obtained around the minimum of solar cycle 24. With a help of the magnetograms and continuum images obtained by the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012; Schou et al. 2012) on board the Solar Dynamics Observatory (SDO; Pesnell et al. 2012), we identified the following mosaics which represent days without sunspots or other significant signs of solar activity: 2019 April 21, May 27, July 27, September 12, 22, and October 20; 2020 March 2, 23, April 22, June 21, August 23, and September 6. All 12 selected mosaics were constructed from 184 individual rasters. Nine mosaics were taken with an exposure time of 2 s and three mosaics (2019 September 12, 2020 April 22, and 2020 September 6) with an exposure time of 8 s. All mosaics have a uniform spatial and spectral binning of 2. In Figure 7 in the Appendix, we show all 12 mosaics in the line center of Mg ii k. Hereafter, we refer to the 12 selected mosaics and days as the reference mosaics and the reference days.

2.3. Radiometric Calibration and Uncertainties

To convert DN units into the radiometric units of W m−2 sr−1 Å−1, we followed IRIS Technical Note 26 (ITN26) 4 —see also Liu et al. (2015, Equation (1)). The input calibration parameters for each mosaic were obtained by the SSW function iris_get_response.pro and from headers of the mosaic FITS files. One of the parameters provided by the IRIS team via the up-to-date iris_get_response.pro function is the current best estimate of the instrument effective area Aeff as a function of wavelength and time (Wülser et al. 2018). The temporal changes of the IRIS effective area are caused by the aging of the instrument. The change in the FUV spectral range is significant, with Aeff declining by over 80% during 5 yr of IRIS operations (see Figure 24 of Wülser et al. 2018). However, the same figure shows that Aeff in the NUV range, which contains the Mg ii h and k lines, is more stable. In this range, Aeff declined by only around 20% during 5 yr of operations. As is described in detail in Section 8.1 of Wülser et al. (2018), the determination of the IRIS Aeff is to a large extent based on the cross calibration with the measurements of the SORCE/SOLSTICE instrument. In the NUV range, the cross calibration between IRIS and SORCE/SOLSTICE is based on averaging within six spectral windows indicated in Figure 23 of Wülser et al. (2018). This figure also shows that the effective area changes only slightly over the IRIS NUV spectral range. As a function of wavelength, Aeff varies only by about 10% between the maximum and minimum values. The iris_get_response.pro function does not provide Aeff uncertainties. However, the Aeff values obtained by cross calibration with SORCE/SOLSTICE likely depend on its absolute calibration, which is estimated to be around 5% (Snow et al. 2005). Another source of Aeff uncertainties might be the small differences between the values interpolated from six spectral windows (Figure 23 of Wülser et al. 2018) and the actual Aeff values at a specific wavelength. We address this issue in more detail in Section 2.4. Because the potential sources of the Aeff uncertainties appear to be small (within 5%) and the IRIS effective area in the NUV range is quite stable, and because the actual values of the Aeff uncertainties are not provided by iris_get_response.pro, we do not consider them in the present paper.

According to ITN26, the value of the solid angle Ω subtended by an IRIS pixel is obtained as:

Equation (1)

Here, Nsp is the spatial binning factor, dynom is the nominal IRIS spatial scale along the slit of 0farcs167 per pixel, and wslit is the nominal slit width of 0farcs33 (De Pontieu et al. 2014, Table 1). Taking into account the fact that plate scales DYhead provided in the headers of the mosaic FITS files already include the spatial binning Nsp, we customized Equation (1) for the actual plate scales and slit width as follows:

Equation (2)

This yields a solid angle smaller by about 1.5% compared to Equation (1).

Assuming that uncertainty of calibrated intensity is a linear combination of Poisson photon noise and constant readout noise σRON (Schmit et al. 2015, also D. Schmit 2021, private communication), we estimated the uncertainty σ(λ) in the units of W m−2 sr−1 Å−1 for a given day by the equation:

Equation (3)

Here, C is the calibration coefficient in W m−2 sr−1 Å−1 DN−1 (see ITN26), Q is the camera gain in photon DN−1, n(λ) is the observed intensity in DN, and σRON is the readout noise in DN. The camera gain Q is provided by the function iris_get_response.pro. It has the same value of 18 photons DN−1 for all NUV mosaics. The readout noise σRON of 3 DN is also constant (Schmit et al. 2015). The calibration coefficient C in Equation (3) scales with the exposure time as $C\approx 1/{t}_{\exp }$ (see ITN26). Therefore, assuming that $n(\lambda )\sim {t}_{\exp }$, the uncertainty of calibrated intensity σ(λ) scales with ${t}_{\exp }$ as:

Equation (4)

The uncertainties of the specific intensities σ(λ) in individual IRIS full-Sun mosaics are relatively large. This is mainly due to the short exposure times (typically 2 s) used to record the raster scans constituting the mosaics. To reduce the uncertainty of the reference Mg ii h and k profiles provided in this paper, we used an average over 12 reference mosaics. The uncertainty σref(λ) of the derived quiet-Sun Mg ii h and k reference profiles is then given by the error propagation formula:

Equation (5)

where N = 12 and σi (λ) are uncertainties of disk-average Mg ii h and k profiles from individual reference mosaics. Owing to the averaging over 12 mosaics, the reference Mg ii h and k spectra provided here have estimated uncertainties as low as 2% in the line peaks (3% in the case of Mg ii h) and typically below 10% in the wings of each line.

2.4. Comparison with SORCE/SOLSTICE

In this subsection, we provide a comparison between the calibrated data from the IRIS full-Sun mosaics and SORCE/SOLSTICE data obtained from the LISIRD database. 5 We focus specifically on a 3.5 Å wide spectral window covering the Mg ii k line. Using all 91 available NUV mosaics, we computed disk-averaged profiles for every mosaic using the disk-center coordinates and plate scales provided in the headers of the mosaic FITS files. We then used the SSW function get_sun.pro to derive the solar angular radius for each mosaic. From the disk-averaged Mg ii k profiles we computed the spectral irradiance at the reference distance of 1 au by multiplying them with a factor $\pi {({R}_{\odot }^{{\rm{N}}})}^{2}/{(1\mathrm{au})}^{2}$, where ${R}_{\odot }^{{\rm{N}}}$ is the nominal solar radius. In Figure 1, we compare the irradiance of the Mg ii k line obtained by IRIS (black line) and SORCE/SOLSTICE (red dots). In the upper panel, we show the variation of the spectral irradiance integrated over a 3.5 Å wavelength range. In the lower panel, we show an example of Mg ii k spectral-irradiance profiles from both instruments in the 3.5 Å wide spectral window. In both panels, the uncertainties of the IRIS spectral irradiance are indicated by gray areas. In the integrated spectral irradiance, the uncertainties of individual IRIS mosaics reach up to 20% (less for mosaics taken with an exposure time of 8 s). The absolute calibration of the SORCE/SOLSTICE instrument, which is estimated to be around 5% (Snow et al. 2005), is indicated by light-red area. The comparison in Figure 1 shows, that while the measured IRIS spectral irradiance in the Mg ii k line is systematically lower than the measurements by SORCE/SOLSTICE, the difference is well within the uncertainty range of the IRIS data. The systematic difference between the IRIS and SORCE/SOLSTICE data might be due to the fact that the emission from off-limb chromospheric structures and prominences is not included in the spectral irradiance obtained from the IRIS full-Sun mosaics, but contributes to the Sun-as-a-star observations by SORCE/SOLSTICE. Another contributing factor might be the difference between the instrument effective area values provided by the iris_get_response.pro function, which are obtained by interpolation from selected spectral windows that do not contain Mg ii h or k lines (see Figure 23 of Wülser et al. 2018), and the actual Aeff values at the Mg ii k wavelengths.

Figure 1.

Figure 1. Top panel: the black line indicates the IRIS Mg ii k spectral irradiance integrated over 3.5 Å wide wavelength range. Red dots represent the SORCE/SOLSTICE measurements. The gray areas indicate the uncertainties in individual IRIS mosaics. Bottom panel: an example of cotemporal Mg ii k spectral-irradiance profiles obtained by IRIS (black) and SORCE/SOLSTICE (red) on 2019 October 20. The gray and light-red areas indicate the uncertainties of the respective instruments.

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To confirm the values of the spectral irradiance integrated over the 3.5 Å wavelength range (Figure 1, top) which we derived by averaging over individual IRIS mosaics, we used the center-to-limb variation curves presented in Section 4 of this paper (see Figure 6). Adapting Equation (3.72) of Hubeny & Mihalas (2014), we obtained a formula for the spectral irradiance in the Mg ii k line integrated over the 3.5 Å wide spectral window (fk〈3.5〉):

Equation (6)

Here, Ek〈3.5〉(μ) is the function of the intensity of the Mg ii k line integrated over the 3.5 Å wide spectral window (shown in Figure 6) which depends on the directional cosine μ. Equation (6) yields the value of 19.8 mW m−2, which is consistent with the IRIS Mg ii k integrated spectral irradiance of around 20 mW m−2 obtained in the years 2019–2020 (see Figure 1, top).

3. Reference Mg ii h and k Profiles

The goal of this paper is to provide high-precision reference quiet-Sun Mg ii h and k profiles well representing the entire solar disk. We thus need to take into account the significant variation of the Mg ii h and k spectra with the position on the solar disk. The limb darkening—a progressive decrease of intensity with the shortening distance from the solar limb—in Mg ii h and k lines is a well-known fact (see, e.g., Kohl & Parkinson 1976; Morrill & Korendyke 2008). Therefore, alongside the reference Mg ii h and k profiles averaged over the entire disk, we also derived a sequence of reference profiles that follow the center-to-limb intensity variations.

To properly characterize these variations, we divided IRIS full-Sun mosaics into 10 zones (aj) consisting of concentric rings with an equal area—see the example in Figure 2. The outer radius ri of an ith zone is given by the equation

Equation (7)

where R is the angular radius of the Sun, N is the number of zones, and i = 1, 2, 3...N. The directional cosine μi corresponding to ri is given by the equation

Equation (8)

The μi values for the inner and outer radii of the zones aj are listed in Table 1. We chose the size of the zones both to minimize the influence of the local variations of Mg ii h and k intensities and at the same time to achieve a sufficiently detailed description of the center-to-limb variation.

Figure 2.

Figure 2. The IRIS full-Sun mosaic obtained on 2019 October 20, in the Mg ii k line center. Overlaid circles are the boundaries of 10 equal area zones labeled aj. The diameters of the zones are listed in Table 1. The x- and y-axes give the solar X and solar Y coordinates in arcseconds.

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Table 1. List of the Inner and Outer Diameters of the Equal Area Zones aj from Figure 2

  a b c d e f g h i j
μin 1.000.950.890.840.770.710.630.550.450.32
μout 0.950.890.840.770.710.630.550.450.320.00
rout 303429526607679743803858910960

Note. The first two rows give the diameters in values of directional cosines μ. The last row lists the outer diameter rout of each zone in arcseconds.

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As is clear from Section 2.3, averaging over several mosaics—in our case over 12 mosaics—significantly diminishes the uncertainties in the observed data. Therefore, to derive the reference Mg ii h and k profiles representing the center-to-limb variation, we averaged the observed data first within each zone in a mosaic and then over the 12 reference mosaics. Doing so, we further decreased the influence of the local variations—such as filaments or enhanced network regions—on the resulting reference profiles. This is because the on-disk structures are present at different locations on different days, and thus in different zones in different reference mosaics.

The reference Mg ii h and k profiles obtained in individual zones are shown in Figure 3. In this figure, we plot both Mg ii k and Mg ii h lines in the entire 3.5 Å wide wavelength range covered in the IRIS full-Sun mosaics. Thanks to the averaging over 12 mosaics, the estimated uncertainties are as low as 2% in the peaks of the Mg ii k line (3% in the case of Mg ii h) and typically less than 10% in the wings of each line. The intensities of these reference profiles are tabulated in the Appendix (Tables 3 and 4). In the machine-readable tables we provide the intensities in units of W m−2 sr−1 Å−1 and erg s−1 cm−2 sr−1 Hz−1, together with the estimated uncertainties.

Figure 3.

Figure 3. Reference profiles of Mg ii k (blue) and Mg ii h (red) lines in individual zones aj (see Figure 2). The estimated uncertainties are as low as 2% in the peaks (3% in the case of Mg ii h) and typically below 10% in the wings of each line. Tables 3 and 4 containing these reference profiles can be found in the Appendix.

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The disk-averaged reference profiles were obtained by first averaging over entire disk in each mosaic and then averaging over all reference mosaics. The resulting Mg ii h and k profiles are shown in Figure 4. The estimated uncertainties are the same as in the case of the reference profiles in individual zones. The intensities of the disk-averaged reference profiles are tabulated in the Appendix (Tables 5 and 6). We provide the intensities in units of W m−2 sr−1 Å−1 and erg s−1 cm−2 sr−1 Hz−1, the spectral-irradiance values in units of mW m−2 Å−1, and the estimated uncertainties.

Figure 4.

Figure 4. Disk-averaged reference profiles of Mg ii k (left) and Mg ii h (right) lines. The estimated uncertainties are as low as 2% in the peaks (3% in the case of Mg ii h) and typically below 10% in the wings of each line. Tables 5 and 6 containing these reference profiles can be found in the Appendix.

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4. Center-to-limb Variation

To better visualize the amplitude of the limb darkening in the Mg ii h and k lines, we plot the reference Mg ii k profiles from individual zones in Figure 5 side by side. This composite plot clearly shows the gradual decrease of the intensities going from the disk-center zone a to the near-limb zone j. The figure also indicates that the shape of the Mg ii k profiles varies with the distance from the disk center. The peaks appear to be less asymmetric and the width of the profiles is larger closer to the limb. We will investigate these characteristics in detail in a follow-up paper.

Figure 5.

Figure 5. A composite image showing the reference profiles of the Mg ii k line from individual zones aj side by side. The area and location of the zones are shown in Figure 2. The reference Mg ii k profiles used here are plotted in the full spectral range in Figure 3. The x-axis gives Δλ in Å and its 0 value corresponds to the Mg ii k line center. The y-axis gives the specific intensity in W m−2 sr−1 Å−1.

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In Figure 6, we show the integrated intensities of the Mg ii h and Mg ii k lines as a function of distance from the disk center. The upper pair of step functions in this plot shows the intensities integrated over the entire 3.5 Å wide wavelength range covered in the IRIS full-Sun mosaics. The lower pair shows the intensities integrated over 1.0 Å wide wavelength range centered at the rest wavelength λ0 of each line. The same wavelength range is used in Figure 5. Both sets of the integrated-intensity values are listed in Table 2. While the center-to-limb variation curves obtained by integration over the 3.5 Å wide spectral window are very similar to each other, the curves corresponding to the emission parts of the Mg ii h and Mg ii k lines (those integrated over 1.0 Å range) differ. The integrated intensities of Mg ii h (1.0 Å) are lower by about 20% than those of Mg ii k (1.0 Å). The amplitude of the limb darkening is also different depending on the wavelength range used for the integration. In the case of 3.5 Å wide range, the intensities in the near-limb zone j are lower by about 35% than those in the disk-center zone a. The difference in the case of 1.0 Å wide range is around 23%. In both cases, the drop in the Mg ii h intensities is slightly steeper.

Figure 6.

Figure 6. Center-to-limb variation of the integrated intensities of the reference Mg ii h and Mg ii k profiles (Figure 3) from individual zones aj (see Figure 2). The upper pair of the step functions corresponds to integration over the wavelength range of 3.5 Å while the lower pair corresponds to the integration over 1.0 Å.

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Table 2. Integrated Intensities (in Units of W m−2 sr−1) of Mg ii h and Mg ii k Lines in Individual Equal Area Zones aj (See Figure 2)

  a b c d e f g h i j
k〈3.5〉 334328322315306297287275257226
h〈3.5〉 337330324316307296285271252216
k〈1.0〉 165163162160157153150146140129
h〈1.0〉 132131129127125122119115110100

Note. In the table, k〈3.5〉, h〈3.5〉 and k〈1.0〉, h〈1.0〉 correspond to the Mg ii k and Mg ii h lines integrated over either the 3.5 Å wide or 1.0 Å wide wavelength range. Both wavelength ranges are centered at the rest wavelength λ0 of the respective lines.

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5. Discussion and Conclusions

The Mg ii h and k lines are some of the most prominent spectral lines observed on the solar disk. The radiation emitted in these lines thus significantly contributes to the illumination of chromospheric and coronal structures. As such, Mg ii h and k lines represent a valuable diagnostics tool for the investigation of these structures. However, utilization of the full diagnostic potential of these spectral lines requires detailed knowledge of the Mg ii h and k spectra emerging from the solar disk.

In this paper, we present high-precision reference Mg ii h and k line profiles representing the quiet Sun during a minimum of the solar activity. To derive these reference profiles, we used 12 NUV full-Sun mosaics from the extensive catalog provided by IRIS. These reference mosaics obtained between 2019 April and 2020 September correspond to days without clear signs of solar activity—see Section 2 for more details. The use of 12 mosaics allowed us to limit the influence of the local variations caused by the presence of on-disk structures, such as filaments or enhanced network regions. Moreover, averaging over the reference mosaics minimizes the uncertainties of the observed data. In Section 3, we provide the disk-averaged reference profiles of both Mg ii h and Mg ii k lines, together with a series of reference profiles describing the center-to-limb variation in these lines. This series of profiles corresponds to the radiation emerging from 10 zones covering the solar disk in concentric rings with an equal area—see Figure 2. Both the reference profiles from the individual zones (Figure 3) and the disk-averaged profiles (Figure 4) are available in tabulated form in the Appendix (Tables 36).

The reference Mg ii h and k line profiles provided in this paper can be used as the incident radiation boundary condition for radiative-transfer modeling of, for example, prominences or spicules. In providing these incident radiation data, we joined several previous studies, such as Bocchialini & Vial (1994), Staath & Lemaire (1995), and Vial et al. (2019). A quick comparison between these studies shows considerable differences reaching up to a factor of 2. This variability is likely related to the differences between the used instruments, their radiometric calibrations, and also the cyclic variations of the Mg ii h and k lines. We note that the radiation from the solar disk in these lines can vary significantly while the reference profiles presented here correspond to a minimum of the solar activity. We will address the issue of the Mg ii h and k cyclical variability and its impact on the results of the radiative-transfer models in the follow-up studies. However, to obtain highly accurate incident radiation data for modeling isolated structures like prominences, one may use cotemporal IRIS observations of both the solar disk and the modeled structures. Such observations will naturally have identical radiometric calibration. This was done, for example, by Vial et al. (2019) using the IRIS observations of a prominence and the solar disk observations of Zhang et al. (2019). Such use of cotemporal observations of the solar disk and the modeled structures, in particular the low-lying structures, is critical especially during periods of high solar activity when nearby active regions can significantly affect the illumination conditions.

S.G., P.H., and P.S. acknowledge support from the grant Nos. 19-16890S and 19-17102S of the Czech Science Foundation (GAČR). S.G. acknowledges support from the grant No. 19-20632S of the Czech Science Foundation (GAČR). J.K. and P.S. acknowledge the project VEGA 2/0048/20. S.G., P.S., P.H., and J.K. acknowledge support from the Joint Mobility Project SAV-18-03 of the Academy of Sciences of the Czech Republic and Slovak Academy of Sciences. S.G., P.H., and W.L. thank the support from project RVO:67985815 of the Astronomical Institute of the Czech Academy of Sciences. J.K. thanks the support from the grant No. 19-17102S of the Czech Science Foundation (GAČR). The authors thank J. C. Vial and N. Labrosse for valuable discussions and suggestions.

IRIS is a NASA small explorer mission developed and operated by LMSAL with mission operations executed at NASA Ames Research Center and major contributions to downlink communications funded by ESA and the Norwegian Space Center. IRIS full-Sun mosaics are available at iris.lmsal.com/mosaic.html. We acknowledge the use of data obtained from the LASP Interactive Solar Irradiance Data Center available at lasp.colorado.edu/lisird. This research has made use of NASA's Astrophysics Data System.

Facilities: IRIS - , SORCE/SOLSTICE. -

Appendix A: Reference Mosaics

Figure 7 provides all 12 IRIS full-Sun mosaics used in the paper. Mosaics are shown in the line center of the Mg ii k line.

Figure 7.

Figure 7. Mg ii k line-center images of all 12 IRIS reference mosaics used in the paper.

Standard image High-resolution image

Appendix B: Reference Profile Tables

Tables 3 and 4 provide the Mg ii k and Mg ii h reference profiles in individual zones aj from Figure 2. Tables 5 and 6 provide the disk-averaged Mg ii k and Mg ii h reference profiles.

Table 3. Mg ii k Reference Profiles in Individual Zones aj (see Figure 2)

Δλ (Å) a b c d e f g h i j
  I σ I σ I σ I σ I σ I σ I σ I σ I σ I σ
  $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ %
−1.750945925905876846816776727657539
−1.715905886866836806776746707647529
−1.680846826806786766736707667618509
−1.645796786766746727697667637588489
−1.610816796786756736707677647588489
−1.575846826806786756727697657598489
−1.540856826806786756727697657598479
−1.5058368167967767467176876375784610
−1.4708267967767567276976676275684510
−1.4357967767567367076776476085484410
−1.4007767567367076876576275885394310
−1.3657667467277076776476185785294211
−1.3307667467277076776576185785294211
−1.2957667467276976776476185785194211
−1.2607467367176876676376085685194111
−1.2257367176976776576275985585094011
−1.1907277076876676376185885484994011
−1.1557176976776576276085785394893911
−1.12069767765763761858855852947103812
−1.08568766764762760857854851946103712
−1.05066765763761859856853950945103612
−1.01565763762859857855852949944103612
−0.98064762760858856854851948943103512
−0.945627608598578558529509461042113413
−0.910608588568548529509479441040113213
−0.87555853952950948946104310411137123014
−0.84050948947104510431041113911371233132716
−0.8054610441043104111401138123612331330142517
−0.7704011391137123612351333133114291526162120
−0.7353213311430142915281526162517231821201724
−0.7003214311430142915281526162517231821201824
−0.6653911381237123512341332133114291526162120
−0.6304510441043104111401138123612341330142617
−0.5954610441043104211401138113712341331142716
−0.5604310421141113911381236123513331331142815
−0.5254211401139113811371236123413331331143014
−0.4904510441043104211411139113811371236123712
−0.45551950949948947104610451045104510489
−0.420588588578578568558558558568647
−0.385707707707707707707707726756876
−0.35089590590591591592594597510251174
−0.3151184119412141224123412441274132413841523
−0.2801623164316531673168317031733178318331863
−0.2452163217321932203221222222232225222422083
−0.2102722272227322722271226922672262225022123
−0.1753102308230623022297229022812268224521933
−0.1403162311230522982288227722632245221731663
−0.1052892282227422652253224022252206318131414
−0.0702422236222822193209319731853171315331254
−0.0352043199319331863178316931613151313841174
0.0001843180317631713164315831513143413241144
0.0351873184318031753169316231563148413641174
0.0702103207320331973191318331753165315031254
0.1052412238223422292222221432053193317431404
0.1402652263226022562250224322352223220331613
0.1752582258225722552251224722432236222121843
0.2102262227222822272226222522252223221831953
0.2451793181318231833183318431863189319331903
0.2801354137413841394139414041434147315431663
0.3151005101510251035103510351065109511741344
0.3507667767767767767667868068561025
0.385637637627627618608618627647766
0.420558548548539529519509509519588
0.455519509499489471045104410431043104510
0.4904994894794610441043104111401138113811
0.52549948946104510431042114011381136123413
0.56049948947104510431042114011381235123114
0.5955094994794610441042114011381235123014
0.6305195094894710451043104111391135123014
0.665539519499489461044104211401136123014
0.70054852951949947945104310401137123014
0.73555853852950948946104410411137123114
0.7705685585395194994794510421038113114
0.8055885685485295094894610431039113213
0.840598578568548529499479441040113313
0.875618598578558539519489451041113313
0.910627608588568548529499461042113413
0.94563761860858855853950947943103512
0.98065763761859857854852948944103612
1.01566764762760858855853949944103612
1.05067765763761859856854850946103712
1.08568766765762760858855851947103811
1.1207076876676476175985685394893911
1.1557176976776576376085785484994011
1.1907367176976776476175985585094011
1.2257467277076876576276085685194111
1.2607567367176976676376085785194211
1.2957467267076876676376085685194211
1.3307467277076876676376085685194211
1.3657767467267076876576275885394310
1.4008067867667467176876576175684610
1.435846816796776756727697657598509
1.470866846826806786756736697647558
1.505895876856836816786766726687598
1.540915885876846826796776736687588
1.575905885866846816786756717657548
1.610895876856826796766736697627519
1.645895876856826796766736687627509
1.680905885856836806776736697627509
1.715925895876846816786746707637519
1.750935905885856826796766717647529

Note. The wavelength range is given in Δλ (Å) centered at the rest wavelength λ0 of the line. The specific intensity I is in units of W m−2 sr−1 Å−1 and the uncertainties σ are given in % of I.

A machine-readable version of the table is available.

Download table as:  DataTypeset images: 1 2 3

Table 4. Mg ii h Reference Profiles in Individual Zones aj (see Figure 2)

Δλ (Å) a b c d e f g h i j
  I σ I σ I σ I σ I σ I σ I σ I σ I σ I σ
  $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ % $\tfrac{{\rm{W}}}{{{\rm{m}}}^{2}\,\mathrm{sr}\,\mathring{\rm A} }$ %
−1.75011441114108510551015985935875796637
−1.715935915885856826796756707637509
−1.68070768766764762759856852946103612
−1.645489461045104310411139113712341231142417
−1.6105194994894610441042104011371233132616
−1.57571669767765762759856852946103612
−1.540905885866836806766736687617489
−1.505975945925895866826786736667538
−1.470985955935905875836796746687548
−1.435975945925895866836796746677548
−1.400965945915885856826786736667548
−1.365955925905875846816776726667538
−1.330935915895866836806766717657529
−1.295925905885856826796756707647529
−1.260915895866846816786746697637519
−1.225895875856826796766736687627509
−1.190885866846816786756716677618499
−1.155865846826806776746707667598489
−1.120856836806786756726697647588479
−1.0858368167967667467176776375784610
−1.0508267967767567266976676275684510
−1.0158067867667367176876576175584410
−0.9807867667467266976776375985484310
−0.9457767567367176876576275885294310
−0.9107567367166976776476175785194210
−0.8757367167076776576275985585094111
−0.8407267076876676376175885484994011
−0.8057076876676476275985685394893911
−0.77068766764762760857855851946103811
−0.73566765763761759856853850945103712
−0.70065763761759857854852948944103612
−0.66563761759857855853850947943103512
−0.630617598588568548519499461041113412
−0.595598588568548529509489451041113413
−0.560588568558538519499469431040113413
−0.5255685585385195094894510431039113412
−0.4905585485295194994794510431040113612
−0.4555585385295194994894610441042104011
−0.420568558548538519509499489469489
−0.385617608598598588568568558568617
−0.350707707707697697687687697716806
−0.3158758758758858758858959159551055
−0.2801164116411741184118411941214124412841354
−0.2451553156315731583159316031613163316531593
−0.2102033203320432043203320332023200319431703
−0.1752422241224022382234223022252216320031603
−0.1402582254225022442237222922192204318231394
−0.1052422237223022232213320231893173315231174
−0.0702043198319231843175316531553142412741035
−0.035170316531603154314731404132412341124955
0.000151314831444140413441294123411641075935
0.035155315231493145413941344128412141114955
0.0701763173316931653159315331463137412441035
0.1052003198319531903185317931713161314531164
0.1402133211321032073203319831923183316831354
0.1751983198319731963194319231893185317731503
0.2101653166316731673166316631663166316531543
0.2451274128412941294130413041324134413841424
0.2809759859859859859851005102510751184
0.315766766766766756756756766806925
0.350637637627617607598598598617697
0.385568558548538529509509499489538
0.42051950949948946945104310421040114210
0.4554994894794510441042104011381136123512
0.490519509489479451043104111391136123313
0.52555853852950948946104410411138113313
0.5605885685485385194894610431040113413
0.595608588578558538519489451041103512
0.63062761759857855853850947943103612
0.66565763761759857855852949945103712
0.7006776576476275985785585194793911
0.7357076876676476276085785484994111
0.7707267076876676476175985585094210
0.8057367176976776476275985585094110
0.8407267076876676476175885585094111
0.8757176976776576376085785484994011
0.9107176976776576376085885484994011
0.9457567367166976776476175785294210
0.9807967767567367076776476085484410
1.0158268067867567367076776275684610
1.050846826806776756726687647588479
1.085865836816796766736707657598489
1.120875856836806786756716677607499
1.155885865846816796766726687617509
1.190905875856836806776736697627519
1.225915895875846826796756717647538
1.260945925905885856826786746687568
1.295975955935905885856816776716608
1.330985965945915895865826786726617
1.365985965945915885856826776717598
1.400995965945925895856826776707578
1.4351015985965935905875836786716578
1.47010351005985955925885846796726588
1.50510451025995965935895866806736598
1.540106510351005975945915875826746607
1.575107510451025995965925885836766617
1.6101094106510451015985945905856786637
1.6451114108410651035995965925865796647
1.68011241094107510451005975925875796647
1.7151114109410651035995965915865786637
1.7501094107510451015985945905846776617

Note. The wavelength range is given in Δλ (Å) centered at the rest wavelength λ0 of the line. The specific intensity I is in units of W m−2 sr−1 Å−1 and the uncertainties σ are given in % of I.

A machine-readable version of the table is available.

Download table as:  DataTypeset images: 1 2 3

Table 5. The Disk-averaged Mg ii k Reference Profile

Δλ I I Ee σ
(Å)(W m−2 sr−1 Å−1)(10−7 erg s−1 cm−2 sr−1 Hz−1)(mW m−2 Å−1)(%)
−1.750802.085.416
−1.715761.995.196
−1.680721.884.917
−1.645681.784.657
−1.610691.814.727
−1.575711.864.857
−1.540711.864.847
−1.505701.834.767
−1.470681.794.667
−1.435661.734.517
−1.400641.684.377
−1.365641.664.337
−1.330641.664.337
−1.295631.654.307
−1.260621.624.247
−1.225611.604.168
−1.190601.574.098
−1.155591.544.018
−1.120581.503.928
−1.085561.473.848
−1.050551.443.778
−1.015541.413.698
−0.980531.383.619
−0.945521.353.519
−0.910491.293.359
−0.875451.183.0810
−0.840411.072.7911
−0.805380.982.5612
−0.770330.852.2213
−0.735260.691.7916
−0.700260.691.7916
−0.665320.842.1813
−0.630380.982.5512
−0.595381.002.6011
−0.560370.952.4812
−0.525360.942.4512
−0.490401.052.7311
−0.455471.233.229
−0.420571.493.888
−0.385721.894.926
−0.350952.486.475
−0.3151283.338.684
−0.2801724.4811.673
−0.2452195.7314.933
−0.2102626.8417.822
−0.1752807.3119.052
−0.1402697.0118.282
−0.1052366.1516.032
−0.0701975.1313.373
−0.0351704.4211.543
0.0001574.1010.703
0.0351614.2110.973
0.0701814.7112.293
0.1052095.4514.213
0.1402366.1516.032
0.1752416.2816.372
0.2102225.7915.102
0.2451854.8312.593
0.2801443.759.774
0.3151082.817.335
0.350812.105.486
0.385631.654.317
0.420531.383.599
0.455471.213.1610
0.490441.142.9610
0.525421.102.8710
0.560421.092.8411
0.595421.102.8610
0.630431.122.9110
0.665441.142.9810
0.700451.173.0510
0.735461.203.1210
0.770471.223.1910
0.805481.253.269
0.840491.283.349
0.875501.313.429
0.910511.343.509
0.945531.373.579
0.980541.403.658
1.015551.433.728
1.050561.463.808
1.085571.493.888
1.120581.523.968
1.155601.554.058
1.190611.594.138
1.225621.614.217
1.260631.644.267
1.295621.634.247
1.330621.624.237
1.365641.674.377
1.400681.774.607
1.435711.854.837
1.470751.955.086
1.505782.035.306
1.540792.055.356
1.575772.015.256
1.610751.975.136
1.645751.965.106
1.680761.985.156
1.715772.015.236
1.750782.045.316

Note. The wavelength range is given in Δλ (Å) centered at the rest wavelength λ0 of the line. The specific intensity I is in units of W m−2 sr−1 Å−1 and 10−7 erg s−1 cm−2 sr−1 Hz−1, the spectral irradiance Ee is in units of mW m−2 Å−1, and the uncertainties σ are given in percent.

A machine-readable version of the table is available.

Download table as:  DataTypeset images: 1 2

Table 6. The Disk-averaged Mg ii h Reference Profile

Δλ I I Ee σ
(Å)(W m−2 sr−1 Å−1)(10−7 erg s−1 cm−2 sr−1 Hz−1)(mW m−2 Å−1)(%)
−1.750962.516.525
−1.715782.045.296
−1.680581.523.938
−1.645391.022.6511
−1.610411.092.8111
−1.575581.533.988
−1.540751.975.126
−1.505812.135.526
−1.470822.155.596
−1.435822.145.556
−1.400812.125.506
−1.365802.095.436
−1.330792.065.356
−1.295782.035.276
−1.260762.005.206
−1.225751.975.116
−1.190741.945.026
−1.155731.904.946
−1.120711.864.847
−1.085701.834.747
−1.050681.794.657
−1.015671.764.567
−0.980661.724.477
−0.945641.694.387
−0.910631.654.287
−0.875611.614.177
−0.840601.574.078
−0.805581.533.978
−0.770571.493.878
−0.735551.453.778
−0.700541.413.668
−0.665521.373.559
−0.630511.333.469
−0.595501.303.379
−0.560481.273.299
−0.525471.243.239
−0.490471.243.219
−0.455481.263.269
−0.420511.343.479
−0.385581.523.958
−0.350701.854.797
−0.315902.376.145
−0.2801213.188.254
−0.2451594.1810.843
−0.2101995.2113.503
−0.1752235.8415.142
−0.1402225.8115.072
−0.1051985.1913.463
−0.0701644.3111.183
−0.0351403.679.524
0.0001293.378.754
0.0351333.499.044
0.0701513.9510.243
0.1051744.5611.843
0.1401925.0313.053
0.1751884.9212.763
0.2101654.3311.223
0.2451323.468.974
0.2801012.666.895
0.315782.045.296
0.350621.614.197
0.385521.363.549
0.420461.203.1010
0.455421.112.8810
0.490431.132.9410
0.525461.203.1110
0.560481.263.289
0.595501.323.439
0.630521.373.578
0.665541.423.698
0.700571.483.848
0.735591.554.028
0.770611.594.137
0.805611.604.157
0.840601.584.117
0.875591.564.048
0.910601.564.058
0.945631.654.297
0.980661.744.527
1.015691.804.687
1.050711.854.807
1.085721.894.916
1.120731.935.006
1.155741.955.076
1.190761.985.146
1.225782.035.276
1.260812.125.496
1.295842.195.696
1.330852.225.766
1.365842.205.716
1.400842.205.726
1.435852.245.806
1.470872.285.915
1.505882.316.005
1.540892.346.085
1.575912.386.185
1.610932.436.315
1.645942.476.415
1.680952.506.475
1.715942.476.415
1.750932.436.295

Note. The wavelength range is given in Δλ (Å) centered at the rest wavelength λ0 of the line. The specific intensity I is in units of W m−2 sr−1 Å−1 and 10−7 erg s−1 cm−2 sr−1 Hz−1, the spectral irradiance Ee is in units of mW m−2 Å−1, and the uncertainties σ are given in percent.

A machine-readable version of the table is available.

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Footnotes

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10.3847/1538-4365/ac07ab