1 Introduction

Spectrometry is extremely useful for diagnosing solar atmosphere. Line profile analysis provides a significant information on the physical properties of the emission source, such as temperature, density, nonthermal velocities as well as the Doppler shifts. This kind of analysis helps us better understand the evolutions in the atmosphere. As is well known, the coronal atmosphere is composed of very high temperature plasma, above millions of degrees Kelvin. And there are numerous models which have been proposed to understand the puzzle although the ultimate solution of coronal heating remains unresolved. However, the spectral lines can provide a possible method to solve the problem.

The widths of optically thin emission lines formed in the upper chromosphere, transition region and corona generally are beyond the expected value. The physical essence of the extra width is still unknown. Parker (1988) thought it was attributed to the turbulence, caused by the magnetic reconnection. Furthermore, in the active regions with bulk flows, the line profiles can be decomposed into multiple components to explain the excess width of profiles. The multiple plasma flows lead to the enhancement of emission in the wings of profile, which was proposed by Kjeldseth-Moe et al. (1993, 1988). This case may be related to the mass motion between the chromosphere and the outer atmosphere of the Sun. To explain the line profiles observed, various scenarios have been assumed and studied in detail. The models of nanoflare-heating was applied by Patsourakos and Klimchuk (2006), and their results pointed out that hot plasma produced the high-temperature upflows and a weak additional component in the wing of line profiles with a blueshift. De Pontieu et al. (2009) pointed out that the profile asymmetry was caused by a high-velocity upflow in the blue wing. They interpreted the strong upflow are associated with type II spicules, and they thought the type II spicules played a substantial role of supplying mass into corona.

Most UV lines formed in the transition regions have a prevalence redshift (Doschek et al. 1976) in solar disk observation. The further research about the Doppler velocity and non-thermal width in the solar transition region was investigated in many works (e.g., Brekke et al. 1997; Chae et al. 1998a, 1998b). Pneuman and Kopp (1978) thought that the redshift was due to the return of the specular material. Moreover, McIntosh et al. (2012) found that the line profiles with low formation temperature contain both the redshift components and the blueshift components, and this was attributed to the plasma cycle in the solar atmosphere. And therein a lot of physical models have been established. As pointed out by McIntosh et al. (2012), the ensemble UV emission of the solar atmosphere was composed of three components: a fast and faint upflow generated in the lower atmosphere, a slow downflow of cooling plasma, and a nearly stationary background. These results would help us understand the persistent redshifts in transition region and the complex progress of the mass motion between chromosphere and corona. In addition, understanding the progress of cycle is vital to reveal the coronal heating and the acceleration of solar winds.

In order to accurately investigate the line profiles of solar atmosphere, the double Gaussian fit and even the triple Gaussian fit were applied in variety cases. Peter (2010) reported that the majority of profiles generated in the active regions could be best fitted by a narrow core component and a broad faint secondary component, and the double Gaussian fit could resolve the secondary component. It was proposed that the secondary component played an important role in the coronal heating and mass supply. De Pontieu et al. (2009) introduced the red-blue (RB) asymmetry analysis technique for the first time, and the method was developed and applied in numerous works (e.g., Tian et al. 2011a; 2011b; Bryans et al. 2010; Doschek 2012; Brooks and Warren 2012; Tripathi et al. 2013). The asymmetric profile was derived with the technique by comparing the intensity of the two wings at the same velocity range of the line profile. Undoubtedly, more detailed information of line profiles can be revealed by high resolution instruments and new analysis technique. And the improvements will help us deeply understand the dynamics and the loss in the process of energy transfer in the solar atmosphere.

One of important improvement is to utilize solar eclipse observations which minimizes the photospheric pollution and thus more accurate information can be obtained. Some measurements are being performed during the previous eclipse, like Guhathakurta et al. (1992) studied the eclipse data of white light to get the information on the coronal density and the temperature distribution. They found that both the electron density and the scale-height temperature are the function of the observation position angle. This kind of observation can present a large scale observation of solar atmosphere features from the transition region to hot corona.

In this paper, we analyze several data sets obtained by Fiber Arrayed Solar Optic Telescope (FASOT, Qu et al. 2014) around the Gabon total solar eclipse on November 3, 2013. Different from the former observations, the FASOT observation contained off-limb cool spectral emission lines forming in the upper solar chromosphere, including the neutral magnesium triplet as well as the numerous singly ionized iron lines. We apply the various techniques of spectral analysis, such as the single Gaussian fit and the double Gaussian fit to reveal the matter line-of-sight motion perpendicular to the local solar radius. Such investigation can add the line-of-sight motion component to those obtained by the on-disk observation where the line-of-sight shift is more directly related to the upflow and downflow of the matter involved, and thus more deeply reveal the motion patterns between the chromosphere and the corona.

The outline of this paper is as following. In Sect. 2, we introduce the instrument and observations which are the basis of our work. Then subsequently the data analysis are described and the physical properties of the emitting plasma are studied quantitatively in Sect. 3. Finally, we discuss our results and summarize some conclusions in the last section.

2 Instrument and observation

It is a common knowledge that the plasmas in the solar atmosphere are highly dynamic and the velocity distribution is highly structured. The 2-D observation is very important to research the total solar eclipse since the duration is generally of several minutes. A new telescope FASOT proposed by Qu et al. (2011) was utilized to observe the upper solar atmosphere during the total eclipse. The basic capability of FASOT is real time 2-D spectrography. This is realized by integral field unit (IFU) of size \(5\times 5\). Each fiber covers 2.0 arcseconds, thus the field of view (FOV) of the IFU reads as 10.0 arcseconds. Otherwise, FASOT was originally designed to carry out spectropolarimetry, and the corresponding images can be reconstructed according to the alignment of fibers of the IFU couple. The intensity profiles are easily obtained by summation from the couple of spectra at each wavelength point. The couple of spectra are produced by the same spatial point in the solar atmosphere but with opposite polarization states after the prism of the polarimeter. More detailed information about the instrument can be found from Qu et al. (2011, 2014) and Dun et al. (2013). The spectral resolution power reads as about 21,000 at 520 nm. The observational spectral band ranges from 516.3 nm to 532.5 nm.

The total eclipse took place on November 3, 2013, and the observation was executed at a small town Bifoun (E0° \(17'\,17''\) S10° \(29'\,24''\)) of Gabon. The total eclipse started at 13:56 UT and lasted only one minute. The field of view of the IFU was placed just above the north tip of crescent formed by lunar blocking the sun before the second contact and after the third contact, so that the off-limb upper atmospheres can be observed. The observational region where the data were acquired for following analysis are marked on an Atmospheric Imaging Assembly (AIA) image of the sun by a rectangle in Fig. 1. It is near the north pole of sun. The sample spectra used in this paper were acquired after the third contact. Fig. 2 presents one of such spectra, where the iron and magnesium lines are abundant within the band, and the strong lines are selected for the following analysis (listed in Table 1).

Fig. 1
figure 1

Spatial location of spectral acquisition, plotted with a small rectangle on the SDO image of the sun

Full size image
Fig. 2
figure 2

The sample spectral line profiles (from 516.4 to 532.5 nm) were obtained during the 2013 Gabon total solar eclipse

Full size image
Table 1 Emission lines used for analysis
Full size table

3 Data and analysis

Since we will focus on the plasma motion, six strong emission lines are chosen for this study, listed in Table 1. The corresponding line formation temperatures and the other atomic data are adopted from CHIANTI (version 7.1) atomic database.

In order to get the information on the motions, we carry out Gaussian fit. The basic Gaussian line profile is usually expressed as follow:

$$ I(\lambda )=I_{0} \exp\biggl(-\biggl(\frac{\lambda -\lambda_{0}}{\triangle \lambda _{D}} \biggr)^{2}\biggr)+I_{c} $$
(1)

where \(\lambda \), \(I_{0}\), and \(\lambda_{0}\) are the sample wavelength point, peak intensity and line center wavelength, respectively. \(\triangle \lambda_{D}\) is the Doppler width, \(I_{c}\) represents the background intensity. Once the electron and ion temperatures are assumed to be comparable for the ionization equilibrium, and the contribution of instrumental width is neglectable, the full width at half maximum can be expressed as (e.g. Mariska 1992).

$$ W=1.665 \frac{\lambda }{c}\sqrt{{\frac{2kT}{M}+\xi^{2}}} $$
(2)

where \(\lambda \) is the spectral line wavelength detected, \(c\) indicates the speed of light, \(k\) the Boltzman constant, \(T\) the temperature, \(M\) the ion mass, and \(\xi \) the nonthermal micro-turbulent velocity. Doschek (2007) pointed out that the width of line profile can be accurately measured if the resolution of instrument is high enough. We selected 100 line profiles in each spectrum and adopted an instrumental width of 0.004 nm. In the following analysis, we neglected the instrumental width whose value is much less than the total width.

The distribution maps of line parameters are obtained from different lines by the Gaussian fits. Examples of both Mg I 516.7 nm (upper panel) and Fe II 531.7 nm lines (bottom panel) are presented in Fig. 3. From left to right, the columns show the maps of the intensity, the Doppler width and the Doppler velocity, respectively. In our analysis, the intensity is derived by integrating over wavelength without background and velocity is obtained from the centroid of the single Gaussian fit. According to the results from Doschek et al. (2007), the largest widths do not occur in the highest intensity areas in the solar activity region, but seem to occur in their adjacent area where the lines also exhibit relative Doppler out flow. They also pointed out that this was caused by lower density in these regions. A similar trend is found in our work, as shown in Fig. 3, where the largest width is produced in a position different from the that yielding the greatest intensity for both the lines. And these emission lines are produced in different layers of solar atmosphere.

Fig. 3
figure 3

The spatial maps of the line intensity, width and Doppler velocity derived from the single Gaussian fit for Mg I 516.7 nm (upper) and Fe II 531.7 nm (bottom), respectively.

Full size image

For the line profiles discussed above, a single Gaussian fit of the emission lines would not be able to accurately describe the real physical process of the solar atmosphere. In order to compare the excess emission of the two wings, the double Gaussian fits of the line profiles are adopted extensively, while the red-blue (RB) asymmetry technique is applied to analyze the spectral lines and extract the second component information (2009). The purpose of this technique was to obtain the difference of two wings of line profile in the same velocity range. The RB asymmetry is influenced by the line center position, so it is very important to decide it as exactly as possible. A variety of methods have been proposed in this literature. Tian et al. (2011c) developed a technique. They determined the line centroid from the main component and used the double Gaussian fit to derive the RB asymmetry. Martínez-Sykora et al. (2011) found that the single Gaussian fit for all the line profiles could lead to a computed RB bias, so they fitted the line core only with a single Gaussian fit. Tripathi et al. (2013) used the central positions determined from the single Gaussian fits and the positions of peak intensity in spline interpolations respectively. Their results show that the small RB asymmetries are sensitive to the line center position. In this paper, we follow these researchers to adopt the double Gaussian fit to reproduce the asymmetric profiles.

Quantitatively the RB asymmetry for an offset velocity \(u_{c}\) can be given according to (De Pontieu et al. 2009; Martínez-Sykora et al. 2011):

$$ \mathit{RB}(u_{c})= \int_{u_{c}-\Delta u/2}^{u_{c}+\Delta u/2} I(u)du- \int_{-u_{c}-\Delta u/2}^{-u_{c}+\Delta u/2} I(u)du $$
(3)

where \(u_{c}\), \(\Delta u\), and \(I (u)\) are velocity derived by line centroid, the velocity range to compute RB asymmetry, and the spectral intensity, respectively. For comparison, the asymmetric profiles are determined by \(\mathrm{RB}_{P}\) and \(\mathrm{RB}_{D}\), developed and introduced by Tian et al. (2011c). These methods are different to determine the line centroid. For \(\mathrm{RB}_{P}\), the wavelength point corresponding to the peak intensity of the spectrum is identified as the line centroid. For \(\mathrm{RB}_{D}\), the line centroid is the primary component center, and the details can be seen from Tian et al. (2011c).

Figures 4 and 5 show the sample observational and the fitting line profiles (upper panels) of those lines listed in Table 1. The diamonds represent the observed profiles. The dashed lines are from the two Gaussian components. And the solid and dotted lines are the double Gaussian fits and the single Gaussian fit profiles in different spectral lines, respectively. It is clear that all spectral profiles can be decomposed into a primary component accounting for the main emission and a weaker secondary component representing the wing excess. By comparing the different fitting profiles with the observed profiles, we can clearly see a better result from the double Gaussian fit, while the results derived from the single Gaussian fit suffer from obvious deviations.

Fig. 4
figure 4

The line profiles (upper) and RB asymmetry profiles (bottom) of the Mg I 518.4 nm, Fe II 516.9 nm and Fe II 519.8 nm, respectively depicted in three columns. Upper panels: observational profiles (the diamonds) and single Gaussian fitting profiles (dotted lines), two components of double Gaussian fitting profiles (dashed lines) and the sum of the two components (solid lines). Bottom panels: \(\mathrm{RB}_{D}\) (dashed) and \(\mathrm{RB}_{p}\) (solid) profiles

Full size image
Fig. 5
figure 5

The line profiles (upper) and RB asymmetry profiles (bottom) of Fe II 523.4 nm, Fe II 527.6 nm, and Fe II 531.7 nm. The meanings of line styles are the same as in Fig. 4

Full size image

We then derive the parameters of the secondary component via double Gaussian fits. As an example, the profiles of Mg I 518.4 nm (upper panel in Fig. 4) show asymmetry and a secondary component locating in the red wing, and it is found to have a relative peak intensity around 0.226, a Doppler velocity of about \(40~\mbox{km}\,\mbox{s}^{-1}\) and a line width around 0.032 nm. The case seems to indicate that weaker but highly redshifted flows should exist. However, according to the results of single Gaussian fits (listed in Table 3), the overall behavior in Mg I 518.4 nm line is blueshifted and the velocity is judged to be about \(3.21~\mbox{km}\,\mbox{s}^{-1}\). The velocity difference of the plasma is most probably the reason causing the asymmetry. Similarly, the properties derived from other lines can be obtained and the details are shown in Table 2. We note that the profiles of Mg I 518.4 nm, Fe II 519.8 nm, Fe II 527.6 nm and Fe II 531.7 nm lines contain an extra component in the red wings, while the Fe II 516.9 nm and Fe II 523.5 nm contain a secondary component in the blue wings. In spite of their difference, the results show that these extra components contribute to the total line emission by an average of about 18%, and the relative velocity is in a narrow range of \(16\mbox{--}45~\mbox{km}\,\mbox{s}^{-1}\).

Table 2 Results of double Gaussian fitting
Full size table

The corresponding \(\mathrm{RB}_{P}\) and \(\mathrm{RB}_{D}\) asymmetric profiles are displayed in bottom panels of Fig. 4 and Fig. 5. It can be seen the RB asymmetric profiles depend on the distance from the line center, and the different emission between the two wings can be observed. According to the above definition of RB asymmetry, if the emission is enhanced in the red wing, the RB asymmetry should be a positive value, otherwise, the value becomes negative. As stated, the parameters shaping the secondary component like the peak intensity, the line width and velocity can be resolved from the asymmetry profiles (see details in Tian et al. 2011b). We find that the different asymmetric profiles show a similar tendency.

In addition, the effect of the instrumental profile can cause the line asymmetry. This factor can also be neglected in our work, because the instrumental profile should be the same to each case, and the emission enhancement in the line wing is roughly the same in the whole field view. However, the observed secondary components have different intensities, shifts and widths. According to the relative shifts between primary and secondary components (Table 2) is a clear result that the instrumental influence is not working.

In general, for spectral lines selected here, most of their profiles can be fitted well with the single Gaussian fit. Most line profiles analyzed in this paper are generally symmetric, and its examples with the single Gaussian fits are presented in Fig. 6 (upper panel) and Fig. 7 (upper panel). The line profiles do not show the excess component and the fits are approaching the observed. Even for those cases in which the double Gaussian fit is more suitable to be applied but the single Gaussian fit is executed, the peak intensity and width will have greater values for the asymmetric line profiles and the line centroid will be shifted compared with the primary profile.

Fig. 6
figure 6

Upper panels: the solid lines as the normalized profiles produced from the single Gaussian fit, and the dashed lines and asterisks represent the centroid of fits and the observed profiles, respectively. Bottom panels: the width versus line center position for the analyzed lines, and the parameters derived from the single Gaussian fit

Full size image
Fig. 7
figure 7

The single Gaussian fitting profiles (upper panels) and plots of width versus line center position relationships (lower panels) for the three lines, similar to Fig. 5 but for the different emission lines

Full size image

The relationships between the Doppler width and the line center position for the different lines are shown in bottom panels of Fig. 6 and Fig. 7. The solid line in each panel represents the linear fit, and the correlation coefficients \(r\) and the slope \(k\) are given in each panel, respectively.

The correlation of line centroid and widths contains valuable information on the dynamic style of the solar atmosphere and may reveal the physical insight into mass cycle. From their result, Peter (2010) suggested that a clear relation of broaden line width with high Doppler shift could indicate a heating process driving a flow. However, there is no clear relation found in our results. Probably the complicated factors for broadening line width can not be neglected.

For a better understanding of the solar plasma, the overall behavior of spectral lines was emphasized in the previous works. Raju et al. (2011) investigated the coronal green line profiles, which obtained by Fabry–Perot interferometers during the total solar eclipse on 2001 June 21. By studying the Doppler velocities of the lines, they found the evidence of the excess blueshift, and Raju et al. (2000) observed the similar result for the coronal red lines Fe X \(6274~{{\AA}}\). The result showed that the blueshift was generally more present than the redshift. Also, Tyagun (2010) found that 80% of the coronal red lines were asymmetric, and the fractions of the asymmetric lines with excess emission in the blue and red wings were 52% and 28%, respectively.

After executing the single Gaussian fit, we determined the velocities and the widths of both Mg I and Fe II spectral lines. The formation temperatures of these lines are shown in Table 1. In general, our results show that the widths and Doppler velocity as a function of wavelength, and the two examples of the different data sets are presented in top and middle panels of Fig. 8. With a polynomial fitting, we find that the deviation of width in Mg I lines is obvious to the fitting curves. This is not surprising, since the thermal width (\(\sqrt{2k T/M}\)) from massive ions would be much narrower than the lines from light ions if the ions temperature is approximately equal.

Fig. 8
figure 8

Width (left) and Doppler velocity (right) of various ions measured from FASOT as a function of the wavelength. The lines in every panel are the polynomial fitting results. Top and middle panels are two examples in different data sets, and the bottom panels are the results of average width and Doppler velocity

Full size image

To clearly see the relationship among the parameters, the average values over the available data are obtained for all selected lines. For instance, the relationships of the wavelength with width and Doppler velocity are presented respectively in the bottom panels of Fig. 8. The left panel shows the tendency of all emission lines (solid) and only Fe II lines (dashed) considered, respectively. From this panel, one can see that the behavior of the fitting curves is very similar. These indicate that the widths decrease with wavelength, reaching a minimal value at \(\lambda \approx 524~\mathrm{nm}\), and then increase towards larger wavelength. The right panel presents the characteristics of Doppler velocity. We can see that there is no significant difference between two kinds of lines. The fitting profiles show that the Doppler velocity reaches a minimum at \(\lambda\approx 525~\mbox{nm}\). All these results suggest that the average width and Doppler velocity are functions of wavelength, i.e., they are tightly related.

In order to see further the relationship among these line parameters, histograms of the centroid, the Doppler velocities and the widths of Fe II 531.6 nm lines are shown from top to bottom in Fig. 9, and all the parameters used for analysis here are derived by a single Gaussian fit. The mean values of parameters are also given in each case. The distributions of the doppler velocities and the centroid are similar because they have a highly positive correlation as is well known. All the histograms show a clear redshift.

Fig. 9
figure 9

The histograms of centroid, Doppler velocity and width (from top to bottom respectively). The dashed lines represent the single Gaussian fits

Full size image

Bottom panel in Fig. 9 shows the result of the widths. The width peak is around 0.02951 nm. Adopting the formation temperature of the spectral lines from the CHIANTI database (version 7.1), the nonthermal velocity can be calculated and it is found to be \(10~\mbox{km}\,\mbox{s}^{-1}\). However, it is well known that the nonthermal velocity plays a dominant role in the transition region and corona, in combination with the results of the other lines, the nonthermal velocity is evaluated to be about \(16~\mbox{km}\,\mbox{s}^{-1}\), and its contribution to the width is more than 90%. The observed value agrees well with previously reported results. Again, the single Gaussian fits are applied to the histograms. For examples, it is found that the centroid of width fit profiles are approximately located in a range of 0.0291–0.033 nm.

The derived line parameters are listed in Table 3 and the negative value represents a blueshift. It is worthy noting that all the widths are close to each other, although the Mg I line has a lower formation temperature. According to Eq. (2), this may mean that the turbulence is greater in the cooler plasma. Furthermore, the plasma motion with an average redshift velocity of \(1\mbox{--}6~\mbox{km}\,\mbox{s}^{-1}\) is also found in Fe II 516.9 nm and 531.7 nm emission lines, meanwhile the blueshift velocity of \(3\mbox{--}20~\mbox{km}\,\mbox{s}^{-1}\) is revealed in the other spectral lines.

Table 3 Parameters derived from the single Gaussian fit
Full size table

4 Conclusions

In this paper, we go into the details of spectral line profiles with a lower formation temperature (\({\sim}10^{4}~\mbox{K}\)) to investigate the dynamics of the solar atmosphere. We adopted a variety of techniques to analyze the spectral data. These analyses provide a clear evidence of excess mass flows, helpful to a better understanding of the dynamics in the solar upper atmosphere. The main results of the present study are listed as follows.

1. Based on these results obtained from the double Gaussian fits and the asymmetry analysis, several line profiles, which generated from the upper chromosphere and lower transition region, are composed of two components along the line-of-sight perpendicular to the local solar radius. It also remind us that the asymmetric profiles is very common in observations and the double Gaussian fits is a better method in some case;

2. The distributions of the centroid, the Doppler velocity and the width derived in Fe II 531.7 nm lines show that the plasma in observed region produced a redshift (\({\sim}1.33~\mbox{km}\,\mbox{s}^{-1}\)). The excess redshift components are more frequent than the blueshift components. We also find that the Doppler velocities of various lines with roughly the same formation temperature differ greatly, which may imply that the plasma motion in different lines are dominated by different cycle processes. Meanwhile, Doschek et al. (1976) found that the lines formed in the transition regions had a widespread redshift. Thus these combined observations reveal the complex dynamics pattern in the solar upper chromosphere and transition region;

3. After applying the single Gaussian fits to the data sets, the Doppler velocities of different emission lines show the complicated behavior of the plasma dynamics. Additionally, there is a clear correlation between line width and line wavelength in spectral lines, as well as Doppler velocity and line wavelength. It is a good choice to study the material motion in solar atmosphere by investigating the parameters of many lines, and further modeling is needed to explain the phenomenon if these observations can provide more detailed data.

According to the models proposed by McIntosh et al. (2012), a cooling downflow existed in the process of motion cycle. The above results have shown that the velocity component perpendicular to the local solar radius is not zero. This means the cycle is not directly along the local solar radius but has a complicated motion pattern; as mentioned before, the other researchers’ works show the existence of cycle of mass flow and the balance of energy in the solar atmosphere. The line profiles formed in the coronal region and transition region are composed of a primary component and a secondary blueshift component. Peter (2010) thought that the secondary component was identical to the type II spicules, which conveyed mass into corona. Raju et al. (2011) found that the velocities show a dependence on the position angle with maxima at the poles and minima at the equator. This was ascribed to the fast and slow solar wind flow. However, our observational region is close to the north pole and is the same in different spectrum, thus the motion revealed here cannot be completely ascribed to the solar wind flow but real motion component of the cycle perpendicular to the local solar radius. With the improvement of the resolution of the observation instruments, more accurate characteristics of the profiles can be measured, and the further investigation of the coronal heating and the mass cycle in the solar atmosphere can be studied.