Diagnostics of the Prominence Plasma from Hα and Mg ii Spectral Observations

The prominence was the target of an international campaign on 2017 March 30 with IRIS and ground-based instruments, e.g., the MSDP spectrograph (Figure 1). It was located on the northwest limb and extended along 120 arcsec with a maximum height of 30,000 km. IRIS provided high-resolution imaging and spectroscopic observations of this prominence. Details of these observations have been presented in Paper I.

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In the present paper, we use the coarse raster data obtained in the doublet of Mg ii h (2803.5 Å) and k (2796.4 Å) lines using 32 positions of the slit covering an area of 64'' × 120'' with a step of 2'' between two spectra and a pixel size of 033. Between 07:06 UT and 08:46 UT, six raster scans were recorded with a cadence of 15 minutes per raster, resulting in a total of 192 spectra (6 × 32).

Calibrated level-2 data are used in this study. Dark current subtraction, flat-field correction, and geometrical correction have been taken into account in the level-2 data (De Pontieu et al. 2014). Slit-jaw images (SJIs) in the broadband filter 2796 Å  with its large field of view (167'' × 175'') have been used for the coalignment. One example of a SJI is presented in Figure 1 left panel.

The MSDP operating on the solar tower in Meudon observed the same prominence in the Hα line. The entrance field stop of the spectrograph covers an elementary field of view of 60'' ×  450'' with a pixel size of 05. Using the MSDP technique (Mein 1977; Mein & Mein 1991; Mein 1991), the Hα image of the field of view is divided by wavelengths into nine channels covering the same channel field of view. The nine channels are recorded simultaneously on a CCD Princeton camera. In Figure 2 an example of observation of the disk with nine channels and the reconstruction of the profile using a point in each channel are shown. Each image is obtained in a different wavelength interval. The wavelength separation between the center wavelength of one channel image to the next is 0.3 Å. By interpolating using cubic spline functions between the observed intensity in these images, we are able to construct Hα profiles at each point of the observed field of view (Mein 1991).

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On 2017 March 30 three sequences of MSDP observations were obtained between 07:28:54 UT and 08:55:28 UT. We focus our study on the sequences covering the time interval of the IRIS observations. The exposure time was 100 ms for the first sequence and 150 ms for the next two sequences. A mean or reference disk profile is obtained by averaging over a quiet region of the disk in the vicinity of the prominence (in this case, at sin θ = 0.98). The photometric calibration is performed by comparing the reference profile with standard profiles for the quiet Sun (David 1961). Corrections of scattering effects are obtained by background subtractions from the nearby corona (see Paper I).

Each MSDP observing sequence is made of successive scans with a 30 s period. Each scan consists of five elementary fields of view, coaligned by cross-correlations between overlaps. In each MSDP pixel, an Hα line profile was obtained over a wavelength range of >±0.7 Å. Indeed, as can be seen in the bottom of Figure 2, profiles in the center of elementary fields can be obtained in the ±1.2 Å range. However, the wavelengths are moving across each channel from left to right so that in the full field of view the effective available spectral range is smaller. In this paper, we used a range of ±0.6 Å even for computing integrated intensities.

Fortunately, Hα profiles in quiescent prominences are narrow as compared with Hα profiles in the disk or in eruptive prominences (Li et al. 2004). It must be noted that the best way to measure Doppler velocities is through the use of a bisector method working with small spectral ranges. As in Paper I, Dopplershifts are computed with a bisector method for Δλ = 0.3 Å. We shall discuss later in more details problems concerning integrated intensities and widths of Hα line profiles (Section 3).

The coalignment of IRIS SJIs and MSDP maps has been achieved by a successive coalignment of a MSDP image with a Meudon full-disk spectroheliogram in the Caii K line and then the spectroheliogram with a IRIS SJI in 2796 Å. By doing so, we could fit the Mg ii SJI with the saturated MSDP image in Hα by overlapping the bright network visible in both. The accuracy of the coalignment is better than 2''. We note that the prominence in Mg ii is more extended than the prominence in Hα.

MSDP provides Hα spectra of the prominence inside the contour drawn in Figure 1. We divided the prominence visible in MSDP into two parts corresponding to two elementary fields of view (see Figure 3, right panel). The entrance window of the MSDP field of view is inclined by an angle of −20° toward the north–south direction. Therefore, we rotated both MSDP parts and coaligned them with a reconstructed map of the Mg ii raster (Figure 3, left and middle panels). We preferentially use the Doppler maps because the correspondence of the Dopplershifts are more straightforward as noted in Paper I . After this overlay, we select 75 pixels in the two MSDP parts (see the crosses in the right panel of Figure 3) and find the corresponding pixels in the individual spectra of IRIS with coordinates x, y (slit number and y position along the slit). We thus obtained a set of 75 Hα profiles and a set of 75 Mg ii profiles in overlaid pixels. We present a selection of typical profiles in Figures 4 and 5. We note that the Hα profiles in emission in the prominence (see Figure 4) are relatively narrow compared with those of the solar disk in absorption (see Figure 2, bottom panel). It confirmed other studies (Li et al. 2004). Therefore a wavelength range of ±0.6 Å used for MSDP observations seems reasonable to represent correctly the profiles.

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The integrated intensities of Mg ii h and k lines in each pixel of six rasters observed by IRIS between 07:06 UT, and 08:46 UT have been computed, encompassing a total of 192 spectra. To study the relationship between the Mg ii h and k line integrated intensities, we first selected the pixels which correspond to the prominence, and the disk in each spectra. We note that the maximum integrated intensity values of Mg ii k line (E_{Mg ii k}) are 35 × 10⁴ erg s⁻¹ cm⁻² sr⁻¹ in the disk, and only 8 × 10⁴ erg s⁻¹ cm⁻² sr⁻¹ in prominence. Because the first raster image data is noisy, we calculate the ratio of the integrated intensities between the Mg ii h and k lines only from the remaining five rasters. In Figure 6 we show the results for the disk and the prominence. The mean values of the Mg ii h and k integrated intensity ratios are 1.36, and 1.39, respectively, for the disk and the prominence. The ratio for the disk is slightly lower than for previous observations of the mean quiet Sun chromosphere (1.45 in Lemaire et al. 1984). They are nevertheless higher than flare ratios, which are around 1 (Lemaire 1984; Kerr et al. 2015). Recently, low Mg ii k/h ratio was found also in the region on the disk close to the limb, i.e., in spicules where the value is 1.22 ±0.04 (Alissandrakis et al. 2018). Such values indicate a relatively optically thick regime (Leenaarts et al. 2013). In the case of prominences, the value of 1.39 fits well with the ratio already found in different prominences (Schmieder et al. 2014b; Liu et al. 2015; Levens et al. 2017; Jejčič et al. 2018). In an optically thin regime far above the limb, the ratio could increase and reach 1.96 (Kerr et al. 2015; Alissandrakis et al. 2018).

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We separate the prominence into two areas, one visible in both Mg ii and Hα lines (Prominence 1) and one visible only in Mg ii lines (Prominence 2) (Figure 7). To do so, we use a mask defined by the contour of the Hα intensity above a minimum threshold (Figure 1). We explore the FWHM in these two areas. The FWHM is computed by two methods presented in Paper I: the FHWM obtained by fitting the line wings of Mg ii k line with a single Gaussian which is the common shape of the observed profiles and a proxy of the FWHM derived by the quartile method. In Paper I, only one raster has been studied and one example of comparison has been shown. In a first approximation, both methods give compatible results (Paper I). Here, we statistically compare results from five rasters using all spectra in the Prominences 1 and 2. Normalized histograms are presented in Figure 8 for both areas. We see a systematic shift in the histograms between the results of the two methods, of the order of 0.1 Å for Prominence 1 and even more around 0.15 Å for Prominence 2. The single Gaussian fit neglects the secondary peaks in the line profiles while the quartile method already captures them, which explains why the profiles seem larger with that method. In Prominence 1, where the Hα prominence is visible, the two histograms are symmetrical and very few profiles are narrow. On the contrary in Prominence 2 prominence contour the Gaussian fit detects a maximum of narrow profiles. The broad profiles could be either a result of the sum of profiles of unresolved structures with a large dispersion of LOS velocities as we have shown with a test in C ii lines (see Paper I) or due to the large optical thickness of the plasma along the LOS (Jejčič et al. 2018).

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We compute the integrated intensity of Mg ii lines k and h, respectively, in Prominence 1 and Prominence 2. Figure 9 presents the ratio between integrated intensities of Mg ii h and k line versus the integrated intensity of Mg ii k in Prominence 1 (left panels) and Prominence 2 (right panels).

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From this figure we can see that for Prominence 1 the integrated intensity values ${E}_{\mathrm{Mg}{\rm{II}}{\rm{k}}}$ are up to 8 × 10⁴ erg s⁻¹ cm⁻² sr⁻¹ with a mean value around 3.5 × 10⁴ erg s⁻¹ cm⁻² sr⁻¹. The optical thickness of Mg ii k for values around 3.5 × 10⁴ erg s⁻¹ cm⁻² sr⁻¹ is between 15 and 100 according to the Figure 16 in Jejčič et al. (2018). For a slightly higher value than the mean value (E_{Mg ii k} = 5×10⁴ erg s⁻¹ cm⁻² sr⁻¹), for which the optical thickness of Mg ii k may reach 1000 for a temperature of 6000 K. For Prominence 2 the mean integrated intensity values E_{Mg ii k} are around (2–2.8) × 10⁴ erg s⁻¹ cm⁻² sr⁻¹, for which the optical thickness of Mg ii is between 3 and 10. We summarized these values in Table 1. Similar results can be deduced from the theoretical study of 1D models with PCTR in Levens & Labrosse (2019). We conclude that there is a large difference of optical thickness for Mg ii k line between Prominence 1 visible also in Hα and Prominence 2 not visible in Hα.

In Figure 9 (left panels), the ratio between integrated intensities of Mg ii h and k shows a large dispersion of the values between 1.3 and 1.5 for Prominence 1. This is consistent with the mean value (1.39) obtained by considering all the points (see Section 3.1). It is also the typical variation that was presented for other observed prominences (Jejčič et al. 2018; Levens & Labrosse 2019). Besides, in Prominence 2 the cloud of the points has an enhancement for the low values of ${E}_{\mathrm{Mg}{\rm{II}}{\rm{k}}}$ reaching 1.8 then decreasing to the normal mean values. We put a threshold for the very low values (2 × 10³ erg s⁻¹ cm⁻² sr⁻¹) to eliminate the tail of the low ratios caused by the noise in the background. This decrease is found in the theoretical models (Jejčič et al. 2018). All of the values of the ratio of intensities of Mg ii h and k are consistent with the theoretical work of Jejčič et al. (2018), assuming a temperature in the prominence lower than 10,000 K. It will give a strong constraint for the conclusion of this paper (see Section 5).

The shape of the slope of the general distribution of the points in Figure 9 (right panels) corresponds to a microturbulence velocity of 5–8 km s⁻¹ according to the plots in Jejčič et al. (2018).

Here, we focus on the characteristics of the Hα and Mg ii line profiles in Prominence 1 visible in both lines.

The FWHM of Mg ii profiles has been presented in Section 3.2. Figure 10 presents the FWHM of Hα in normalized histograms. Here we use 67 positions, removing eight positions where FWHM is not computable. To compute FWHM of the Hα line, we correct it for the instrumental profiles (see Paper I). By using the grating at zero-order, it is possible to get directly images of the MSDP slits defining the channels after the first pass. The resulting instrumental profile is close to a rectangle with the width of 0.18 Å. However, to correct the Hα FWHM, we use at first approximation the assumption that the Hα profile and the instrumental profile are Gaussian functions, thus obtaining ${\mathrm{FWHM}}_{\mathrm{corrected}}={\sqrt{\mathrm{FWHM}}}_{\mathrm{observed}}^{2}-{0.18}^{2}$.

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We compute the integrated intensity E_Ha and E_{Mg ii k} for all 75 positions. From Figure 4 it is clear that the Hα profiles obtained by MSDP do not reach zero intensities in the wings. To assess the error due to the limited spectral range (±0.6 Å), we compare the obtained integrated intensities in two cases, the first one corresponds to the limited spectral range and the second to profiles with wings extrapolated to zero intensity. The differences between both integrated intensities is typically only 4 %.

The values of E_Ha corresponding to values of E_{Mg ii k} are presented in Figure 11 (red crosses). There is a certain relation between E_Ha and E_{Mg ii k}. E_{Mg ii k} is already saturated at around (2–3) × 10⁴ erg s⁻¹ cm⁻² sr⁻¹. E_Ha becomes saturated at values larger than 10⁵ erg s⁻¹ cm⁻² sr⁻¹ (Heinzel et al. 1994) because the Hα line is not so optically thick as the Mg ii k line. Therefore, the emission in Hα is due to the integration along the LOS of more structures than the Mg ii emission. In Section 4.2 we show the good correspondence of the observed variation E_Ha versus E_{Mg ii k} with the theoretical models.

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In this paper, we start with simplest 1D prominence-slab models (Labrosse et al. 2010; Heinzel 2015), where the prominence is represented by the slab of a finite thickness standing vertically above the solar surface. The slab is externally illuminated by the solar-disk radiation which sets the boundary conditions for the NLTE radiative transfer. We used the same NLTE code Multi-level Accelerated Lambda Iteration (MALI) as in Heinzel et al. (2014) and Jejčič et al. (2018). In this version of the code we used the diluted disk radiation incident on both sides of the vertical 1D slab for both Mg ii h and k lines, taken at a mean height of 13,000 km above the solar surface. The actual dilution factor (for the definition, see Jejčič & Heinzel 2009) is somewhat lower than 1/2 and only weakly dependent on the height. This height was derived from available prominence images. The input parameters of the 1D isothermal-isobaric slab are the kinetic temperature T, gas pressure p, geometrical (effective) thickness D, microturbulent velocity v_t and the height of the observed structural element above the solar surface. For a given microturbulent velocity we computed large grid of 294 models for temperature ranging between 6000 and 20,000 K, gas pressure between 0.01 and 0.5 dyn cm⁻², and a thickness between 200 and 5000 km. These ranges of values are commonly accepted for prominences (Labrosse et al. 2010). The MALI code solves the multi-level NLTE problem for a five-level plus continuum hydrogen atom and then for a five-level plus continuum model of Mg ii–Mg iii, using the partial redistribution approach for all resonance lines. The synthetic spectra are then obtained, among others, for the hydrogen Hα line and Mg ii h and k lines, to be compared with our observations. We use a common 1.5D inversion strategy, i.e., for each position (pixel) within a 2D prominence structure we try to fit the observed spectra using 1D slab models.

In Figure 11 we show the comparison between synthetic and observed integrated line intensities for both Mg ii k and Hα lines (note that here we show all 75 observed points as red triangles and all 294 models as blue dots). The fit between observed and computed intensities looks very promising and we find the following trend: while the Hα intensity increases, the Mg ii k one is more or less saturated in the range of observed intensities, indicating a large optical thickness of the Mg ii lines (see Table 2 in Heinzel et al. 2014). As shown by Gouttebroze et al. (1993) and Heinzel et al. (1994), Hα is optically thin for E(Hα) < 10⁵ erg s⁻¹ cm⁻² sr⁻¹, which is roughly the case of our observations. At larger intensities, Hα becomes optically thicker and starts to saturate. The computations were done for two distinct values of the microturbulent velocity, 8 and 16 km s⁻¹, for reasons discussed below.

As we see from the histogram of observed Hα line widths, the FWHM reach up to 0.75 Å, which is sensibly larger than the modeled values. On the other hand, typical microturbulence in quiescent prominences does not exceed 5–8 km s⁻¹ (see also Jejčič et al. 2018). Therefore, we first tried to fit the Hα line profiles and integrated intensities setting v_t = 8 km s⁻¹. Although the MSDP spectra have rather limited wavelength range of −0.6 Å to +0.6 Å on average, which leads to some uncertainties in determination of the FWHM and namely of the integrated intensity E(Hα), we used rather restrictive fitting criteria for Hα, and namely

$$\begin{eqnarray}&&\begin{array}{r}\displaystyle \frac{| E(\mathrm{obs})-E(\mathrm{mod})| }{E(\mathrm{obs})}\lt 0.1\\ \displaystyle \frac{| \mathrm{FWHM}(\mathrm{obs})-\mathrm{FWHM}(\mathrm{mod})| }{\mathrm{FWHM}(\mathrm{obs})}\lt 0.1.\end{array}\end{eqnarray} \tag{ 1 }$$

We tried to find the best fit for Hα alone within such an accuracy, using 75 observed positions (pixels) where both Hα and Mg ii lines were visible. As a result, about one third of pixels does not exhibit any reasonable fit, while the remaining ones show a good fit. For them we constructed a histogram of prominence temperatures shown in Figure 12, top panel. It is not very surprising that such a fitting of large FWHMs leads to a dominance of high temperatures, up to our considered limit 20,000 K where we get the maximum on the histogram. We made various tests to get lower temperatures, either by introducing a PCTR (so that the central temperature of the slab could be decreased), or a plane-of-sky filling factor which accounts for a lower spatial resolution of MSDP. However, the histograms of the temperature still exhibited a significant number of points with high temperatures reaching 20,000 K.

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Because such temperatures are not typical for quiescent prominences (e.g., Tandberg-Hanssen 1995), we looked for another possibility to enhance FWHM of Hα and still keep temperatures at reasonable values. A natural way is to consider random LOS motions of prominence fine structures as in 2D multi-thread models of Gunár et al. (2008) where the hydrogen lines were modeled. However, in case of Mg ii lines, the appropriate MALI2D code for multi-threads is not yet fully available and thus we used a rough approximation that the LOS random motions can be treated as an additional "turbulence." We therefore arbitrarily increased v_t to 16 km s⁻¹. Then fitting again the Hα line we obtained much better temperature distribution as shown in Figure 12 (bottom panel) where the kinetic temperature peaks around 8000 K. For the increased microturbulence, the synthetic integrated intensity of Mg ii is also somewhat increased as can be seen from Figure 11 (bottom panel). Mg ii line absorption profile is significantly broadened by the microturbulence (for heavy ions the thermal broadening is much smaller) and, as a consequence, more radiation is absorbed within the reversal of the solar incident profile. This enhances the line source function and thus also the synthetic intensity. The effect is negligible for Hα as also seen from the correlation plots. One way to escape from this problem would be to run the MALI codes with v_t = 8 km s⁻¹ to get more realistic line source functions and only at the end compute the synthetic profiles with higher microturbulence. This could better simulate expected random LOS velocities. However, our ultimate goal is to perform 2D multi-thread modeling as was done for hydrogen by Gunár et al. (2012).

The electron density which comes from hydrogen ionization (helium ionization is neglected here) and the gas pressure ranges are typical for quiescent prominences (Figure 13). Within the accuracy of 10%, the FWHMs and integrated intensities of Hα are also well reproduced (Figure 14). Next we show the distribution of the integrated Hα intensity as function of the Hα line-center optical thickness for fitted points (Figure 15). Nearly all such points have τ > 0.05 which seems reasonable for having a visible prominence in Hα. Only three points have τ lower and they correspond to low intensity profiles. Using these models we compute the optical thickness of Mg ii k and plot the integrated line intensities as function of τ (Figure 15). Comparing these values with the range that we derive in Section 3.3, using 1D models from Jejčič et al. (2018), we find a good agreement. Finally, the correlation plot between the line-center optical thickness of the k-line and that of Hα shows that the k-line can be up to a factor 100 thicker (Table 1).

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