1 Introduction

The transition region and the solar corona are widely explored for their several intriguing features. The dynamics of the flows and mass motions, the multiple component line profiles, line shifts and their dominance, nonthermal velocities and intensity variations at different regions are a few topics that are widely discussed. Most studies of these topics aimed at determining whether they can provide any insight into coronal heating and the solar wind acceleration. The solar corona has been an interesting region: it has a very low density of the order of \(10^{8\,\text{--}\,9}~\mbox{cm}^{-3}\) and a temperature of the order of 2 MK. Many theories such as nanoflare heating, type-II spicules, magnetic reconnection, and Alfvén waves have been proposed to explain this high temperature (Sakurai, 2017). The study continues in search of nonthermal energy sources that might cause coronal heating and the solar wind acceleration. Studying the solar coronal line profiles is one such method, where we can gain information about the physical parameters of the solar corona.

Asymmetries have generally been reported in spectral lines from the transition region and the solar corona. Mass motions in the corona have been reported by Delone and Makarova (1969, 1975), Delone, Makarova, and Yakunina (1988) and Chandrasekhar et al. (1991). Multiple components with excess blueshifts have been reported by Raju et al. (1993). Brynildsen, Kjeldseth-Moe, and Maltby (1995) described the increasing fraction of redshifts in the transition region. Brekke, Hassler, and Wilhelm (1997) and Teriaca et al. (1999) reported that the transition region comprises redshifts. Chae, Yun, and Poland (1998) and Peter and Judge (1999) also found excess blueshifts through Solar Ultraviolet Measurements of Emitted Radiation (SUMER) observations. Raju (1999) showed the existence of multiple components in the line profiles. Dadashi, Teriaca, and Solanki (2011) also found excess blueshifted profiles in the corona. Patsourakos and Klimchuk (2006) explained these emissions in terms of nanoflare heating, and De Pontieu et al. (2009) related them to type-II spicules. Brooks and Warren (2012) explained these asymmetries as signatures of chromospheric jets that provide mass and energy to the corona.

Furthermore, the results regarding the variation in nonthermal velocity and line width with height were different. The line width of the red line was reported to increase with height above the limb by Singh et al. (2006). Prasad, Singh, and Banerjee (2013) presented a negative gradient of the green line width with height. Raouafi and Solanki (2004) reported an anisotropy of the velocity distribution in this region. The nature of the variation in line profile parameters is still unclear, and in this paper, we aim to study it in more detail.

In this context, we have focused on the physical parameters of the solar corona, such as Doppler velocity, half-width, centroid, and asymmetry and their correlations at various points away from the limb by analyzing a set of Fabry–Perot interferograms. We have primarily focused on the variation in Doppler velocity and centroid of the line widths of the line profiles. This work is a continuation of our earlier work (Prabhakar, Raju, and Chandrasekhar, 2013), which mainly focused on the shifts and asymmetries of the line profiles. Section 2 gives details of the instrument used and of the analysis and data reduction methods involved in our study. In Section 3 we describe the results we found in our study and discuss them in comparison to the earlier results. Section 4 gives the conclusion of our study.

2 Analysis and Data Reduction

Our study involves the analysis of 14 Fabry–Perot interferograms. These were taken during the total solar eclipse that occurred in Lusaka, Zambia, on 21 June 2001. It had a magnitude of 1.0495 and lasted for 3 min 37 sec when the Sun was at \(31^{\circ}\) elevation above the northwest horizon. From the data, we have obtained the intensity, Doppler velocity, half-width, centroid, and asymmetry at different points in the corona. The centroid is defined as the wavelength point that divides the area of the line profile into two (Raju, Chandrasekhar, and Ashok, 2011). To calculate the asymmetry, strips of equal width (0.5 Å) at equal distances (0.1 Å) from the peak wavelength were considered in the red (\(R\)) and blue (\(B\)) regions. The asymmetry was then calculated using the relation \((R-B)/(R+B)\). The observation was made in the coronal green line Fe XIV 5302.86 Å, which was chosen because its formation temperature (2 MK) is close to the average inner coronal temperature. This means that the results yield more accurate information about the corona.

The Fabry–Perot interferometer we used is the one used in Chandrasekhar et al. (1984). However, during the 21 June 2001 eclipse, a CCD was used as the detector. The interferometer has a free spectral range of 4.75 Å, an instrumental width of 0.2 Å, a spectral resolution of 26,000 for the coronal green line, and a pixel resolution of 3.4 arcsec. The instrumental details are given in Table 1. The line profiles were extracted in the angular range of \(240^{\circ}\). The original plan of the experiment was to obtain a time-sequence of Fabry–Perot interferograms of the solar corona during the total solar eclipse. The aim was to study the temporal changes in the physical properties of the solar corona. However, as a result of a minor tracking error that happened during the observation, it was later noted that the interferograms were not cospatial. Hence, we could not study the temporal variations. However, this enabled us to study the corona at more spatial locations than was originally planned.

Table 1 Instrumental features of the Fabry–Perot interferometer.
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In a Fabry–Perot interferogram, the region between two adjacent fringe minima constitutes a line profile. The spatial resolution in an imaging Fabry–Perot interferometer is therefore generally low. It is about \(0.2~\text{R}_{\odot}\) in our observation. The tracking error in the observation will shift an interferogram with respect to the previous one, leading to the formation of a new fringe pattern in the gap. This will give line profiles from new locations, but with some boxcar averaging of the nearby spatial points. The angular coverage therefore remains the same (\(240^{\circ}\)) as in a single interferogram, but we obtain more line profiles from the intermediate regions. Part of the data obtained during this particular eclipse was used by Raju, Chandrasekhar, and Ashok (2011) and Prabhakar, Raju, and Chandrasekhar (2013).

The analysis was made by first locating the fringe center position in the interferograms. Then the radial scans from the fringe center were made to obtain the line profiles. The wavelength was calibrated as in Raju et al. (1993). In order to reduce the noise, a \(2\times2\) pixel averaging was made at the outset. It was also noted that the line profiles close to the limb were slightly contaminated by the scattered light in some interferograms. Therefore we considered only line profiles beyond \(1.1~\text{R}_{\odot}\). Single Gaussian curves were fit to all the line profiles and the parameters were obtained. We selected only line profiles whose signal-to-noise ratio was \({\geq}\,15\) in order to obtain good Gaussian fits. A set of line profiles fitted with Gaussian curves is shown in Figure 1. The estimated errors in the fitting are about 5% in intensity, \(2~\mbox{km}\,\mbox{s}^{-1}\) in velocity, and 0.03 Å in width. Interactive Data Language (IDL) was used for computation purposes. All the spatial locations of the line profiles obtained are plotted on an Extreme ultraviolet Imaging Telescope (EIT) image of the Sun obtained at the same time as that of the eclipse, which is shown in Figure 2.

Figure 1
figure 1

Example of line profiles fitted with Gaussian curves. The upper two line profiles represent single component profiles, and the lower two represent blueshifted (left) and redshifted (right) line profiles.

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Figure 2
figure 2

EIT image of the Sun on 21 June 2001 at time 13:48:13, showing the spatial locations of all the line profiles we analyzed.

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3 Results and Discussion

We obtained 1295 line profiles in all by removing the noisy profiles. We found that 59% of them are blueshifted, 7% are redshifted, and 34% are single components. Single components are those that fall in the asymmetry range of \(-0.08\,\mbox{--}\,0.08~{\mathring{\mathrm{A}}}\), corresponding to the Doppler velocity range of \(-2\,\mbox{--}\,2~\mbox{km}\,\mbox{s}^{-1}\). It is interesting to see that the percentages of the single components, blueshifts, and redshifts are different from what was observed in Raju, Chandrasekhar, and Ashok (2011) and Prabhakar, Raju, and Chandrasekhar (2013). Note that the above works considered almost 300 line profiles. In this work, the improved statistics give a better reliability (a factor of about 2) to our results than in the works mentioned above.

This work is primarily focused on the variations in Doppler velocity, half-width, centroid, and asymmetry and their interrelationships. The gross properties of a large number of line profiles fitted with a single Gaussian were obtained. By examining the interrelationships between the quantities, we expect to receive information on the nature of the multiple components without requiring complex multiple Gaussian fitting. Raju, Chandrasekhar, and Ashok (2011) obtained line profiles from a single interferogram and the nature of the secondary component, obtained by subtracting the red from the blue wing, was studied in detail. Prabhakar, Raju, and Chandrasekhar (2013) primarily studied the asymmetry of the multiple components.

The number of line profiles observed in different asymmetry ranges is given in Table 2. The line profiles with the greatest asymmetry are found in the blue wing (96 line profiles). Thus, our results agree well with the works by Raju et al. (1993), Raju (1999), Dadashi, Teriaca, and Solanki (2011), Chae, Yun, and Poland (1998), and Peter and Judge (1999) regarding the presence of the multiple components and dominance of the blueshifts, but the percentage is found to be on the higher side. The redshifts are seen to be very less, with a contribution of just 7%.

Table 2 Number of line profiles observed in different ranges of asymmetry.
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The normalized histograms of Doppler velocity, centroid, and asymmetry of the line profiles are shown in Figure 3. All of them show the domination of the blueshifts, which does not agree with McIntosh et al. (2012), who reported a weak emission component in the blue wing that contributes a very low percentage of the emission line profiles. The multiple components with blueshifts are found to have a maximum Doppler velocity of \(-18~\mbox{km}\,\mbox{s}^{-1}\), and those with redshifts are found to have a maximum Doppler velocity of \(11~\mbox{km}\,\mbox{s}^{-1}\). It is to be noted that these values are taken from the composite line profiles, and when the Gaussian decomposition is performed, the velocities of the secondary components are much higher (Raju, Chandrasekhar, and Ashok, 2011).

Figure 3
figure 3

Normalized histograms of (a) the Doppler velocity, (b) the centroid, and (c) the asymmetry.

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The normalized histogram of the half-width is shown in Figure 4. The half-width falls in the range 0.7 – 1.3 Å and the peak at 0.96 Å. This would correspond to a temperature of 3.5 MK. Considering the nonthermal broadening that could add to the line width and the line formation temperature of 2 MK, we find that the nonthermal velocity is close to 22 km/s (Raju, Chandrasekhar, and Ashok, 2011) from the following relation:

$$\begin{aligned} \frac{2kT_{0}}{M} =& \frac{2kT_{\mathrm{D}}}{M} + v_{\mathrm{t}}^{2}, \end{aligned}$$

where \(k\) is the Boltzmann constant, \(T_{0}\) is the observed line-width temperature, \(M\) is the mass of the emitting ion, \(T_{\mathrm{D}}\) is the Doppler temperature of the line width, and \(v_{\mathrm{t}}\) is the nonthermal velocity characterizing microturbulence.

Figure 4
figure 4

Normalized histogram of the half-width of the line profiles.

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Furthermore, we studied the variation in half-width and Doppler velocity of the line profiles with respect to their heights from the solar center. In Figure 5a, we plot the half-width against the coronal height. We have tried linear, quadratic, and cubic polynomial fits, and a detailed statistical analysis was performed. The details are given in Table 3. The different columns in the table give the values of the correlation coefficient (\(R\)), the coefficient of the determination (\(R^{2}\)), and the standard error in the fittings. The table shows that the best fit is obtained from the cubic polynomial fit, where the value of \(R=0.21\) and \(R^{2}=4.4\%\). The best-fit polynomial and the standard error are plotted in the figure. The total variation is comparable to the standard error in the fitting, and the trend is therefore insignificant.

Figure 5
figure 5

(a) Variation in half-width and (b) Doppler velocity with height above the limb. The solid line shows the best-fit polynomial. The error bar indicates the standard error in the fittings.

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Table 3 Values of \(R\), \(R^{2}\), and standard errors for the plots in Figures 5 and 6 for linear, quadratic, and cubic fittings.
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This result is different from what is observed in Mierla et al. (2008), who stated that the width remains almost constant or increases up to a height of \(1.3~\text{R}_{\odot}\). It is also different from what was described in Prasad, Singh, and Banerjee (2013) and Beck et al. (2016), who reported a decrease in line widths with height of the line profiles.

Figure 5b shows the variation in Doppler velocity of the line profiles with coronal height. Table 3 shows that the coefficients \(R\) and \(R^{2}\) do not show much improvement from quadratic to cubic fits. A quadratic fit was therefore considered for this plot. Here the total variation is less than the standard error and hence insignificant.

We further studied the variation in half-width of the line profiles with Doppler velocity and centroid, which are shown in Figure 6a and b. From Table 3, it is evident that the quadratic fit is better than the linear fit, where the coefficients show a marked improvement. There is no marked improvement in the cubic fit. The total variation is almost twice the standard error, and these fits were therefore retained. The correlation coefficients are 0.23 and 0.21 for velocity and centroid, respectively, which means a mild correlation. The \(R^{2}\) values, which give the percentage of this variation, are about 5%. This implies that the relationship between half-width and Doppler velocity or centroid is weak. A variation like this was observed in Bryans, Young, and Doschek (2010) for Active Region AR 10978. Raju, Chandrasekhar, and Ashok (2011) examined the relationship between half-width and Doppler velocity from two cases with a limited number of samples and a positive angle coverage of \(20^{\circ}\). They reported a weak correlation in one case and a lack of correlation in the other. It may therefore be concluded that the weak correlation found between the half-width and Doppler velocity or centroid could be real. Peter (2010) reported that the positive correlation between these quantities suggests a flow associated with a heating process.

Figure 6
figure 6

(a) Variation in Doppler velocity, (b) centroid, and (c) asymmetry of the line profiles with half-width. The solid line shows the best-fit polynomial. The error bar indicates the standard error in the fittings.

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The variation in half-width with respect to the asymmetry of the line profiles is given in Figure 6c. Here the quadratic or cubic fit do not improve the linear fit. The coefficients \(R\), \(R^{2}\), and standard error remain almost constant in all the three cases. The linear trend is comparable to the standard error and is not significant. This is found to be very different when compared to the variation in Doppler velocity and centroid with half-width.

4 Conclusion

We studied various characteristics of the inner solar corona by analyzing the line profiles obtained from the analysis of Fabry–Perot interferograms. We found that a majority of these line profiles comprise multiple components, with a higher contribution from blueshifts (59%). This is followed by single-component profiles, which contribute 34%. Redshifts contribute very little, just 7%. This result, although found to be in agreement with related works reported earlier, shows a very high percentage of blueshifts. Line profiles showing the greatest asymmetry were found to be blueshifted, and they constitute close to 7.5% of the observed line profiles. The multiple component profiles with blueshifts were found to have a maximum Doppler velocity of \(-18~\mbox{km}\,\mbox{s}^{-1}\), and the redshifted multiple components were found to have a maximum Doppler velocity of \(11~\mbox{km}\,\mbox{s}^{-1}\). These values specify the Doppler velocity of the composite profile, and the actual values of the Doppler velocity of the components could be much higher. The excess blueshifts could be related to type-II spicules or to the nascent solar wind flow. Furthermore, the variation in half-width and Doppler velocity with respect to the coronal height are found to be insignificant. The variation in half-width with respect to the Doppler velocity or centroid shows a parabolic trend with a weak correlation. The positive correlation is important because it suggests a flow that is associated with a heating process. The trend between half-width and asymmetry is inconclusive, which is not understood. These results need to be examined further to understand the problems in coronal physics.