Spectroscopic Diagnostic of the Footpoints of the Cool loops

Active regions (ARs) are the areas with strong magnetic fields, and they encompass the curvilinear magnetic flux confining plasma (see Reale 2010, and references cited therein) referred to as coronal loops (e.g., Del Zanna, G. & Mason, H. E. 2003; Reale 2010). Coronal loops include hot core loops (Del Zanna 2008), warm loops (Del Zanna et al. 2011), and fan loops (Winebarger et al. 2013; Young et al. 2012; Warren & Brooks 2009). Here, it is worth mentioning that different types of coronal loops are well resolved and studied using observations taken by various instruments (e.g.,Ugarte-Urra et al. 2009; Reale 2010; Tripathi et al. 2012; Gupta & Nayak 2022). In addition to the coronal loops, ARs do have another type of loop structure which are visible at low temperature (i.e., transition region (TR)). They are referred to as cool loops or TR loops (e.g., Hansteen et al. 2014; Huang et al. 2015; Polito et al. 2016; Rao et al. 2019a, b).These cool loops are found to be well-structured and are dynamic structures of the TR. Hence, the diagnosis of the cool loops is extremely important to understand the TR and the link between the corona from the lower atmosphere in a better way. Unfortunately, cool loops are not examined in depth, so far, due to the lack of high-resolution observations. Due to the less availability of studies on cool loops our understanding about them is limited.
In several studies of cool loops, an off-limb loop was investigated using coronal diagnostic spectrometer observations (CDS; Harrison et al. 1995), and the Doppler velocity of around 50 km/s was found along the loop (Brekke et al. 1997). Similarly, Chae et al. 2000 had investigated an off-limb cool loop using observations from Solar Ultraviolet Measurements of Emitted Radiation (SUMER) instrument (Wilhelm et al. 1995) onboard Solar and Heliospheric Observatory (SoHO; Domingo et al. 1995). Furthermore, using SUMER observations, Doyle et al. (2006) have reported net redshifts of $\approx$20 km/s in footpoint of cool loops using N v 1238.82 Å.

The Interface Region Imaging Spectrograph (IRIS; De Pontieu et al. 2014) provides an opportunity to diagnose the cool loops in great detail as this instrument observes TR with unprecedented spatial and spectral resolution. Some research on cool loops has already been conducted utilising IRIS observations. Mostly, it is reported that the plasma flows up along the loop from one footpoint (i.e., blueshifted footpoint) and falls down towards another footpoint of the loop (i.e., redshifted footpoint) – siphon flows (i.e., driven by the pressure difference of the plasma at the footpoints of the loops having different magnetic field strengths) in the AR loops (Doyle et al. 2006; Bethge et al. 2012).

As a result, one footpoint of a cool loop can be red-shifted while the other is blue-shifted, or vice versa. Firstly, using the IRIS observations, Huang et al. (2015) showed the occurrence of siphon flow in cool loops, and they found significant variations in the blue-shifted (i.e., from -5 to -10 km/s) and red-shifted footpoints (i.e., 12 to 20 km/s) of the cool loops in Si iv line. Similar to Huang et al. (2015), using the same Si iv, Rao et al. (2019b) have also reported significant variations in the blueshifts (i.e., 5–10 km/s) as well as redshifts (i.e., 10– 15 km/s) in footpoints of the cool loops. Furthermore, these blue-shifted and red-shifted footpoints were investigated at different heights using different IRIS spectral lines (Rao et al. 2019b), and it was found that the blueshifts as well as redshifts at the footpoints of the loops increase from the photosphere to the transition region. Apart from the siphon flow of cool loops, the TR is dominated by redshifts, for instance, Brekke et al. (1997) have shown that TR of quiet-Sun (QS) has redshifts of 5 km/s. Similarly, some other works also report the dominance of redshifts in QS, coronal hole (CH), and TR of ARs (e.g., Peter & Judge 1999; Dadashi et al. 2011; Dadashi et al. 2012; Kayshap et al. 2015).

The cool loops are the integral feature of the solar TR, and most of the spectral profiles forming within the TR are non-Gaussian in nature. Using Solar Ultraviolet Measurements of Emitted Radiation (SUMER) onboard Solar and Heliospheric Observatory (SoHO) observations, it has been found that shown that several TR lines (e.g., C ii 1335 Å, C iii 977 Å, Si iv 1403 Å, and many more) are non-Gaussian, and the spectral lines are well characterized by double Gaussian for core and broad second components (e.g., Peter 1999, 2000, 2001, 2006). Further, using Extreme-ultraviolet Imaging Spectrometer (EIS)/Hinode observations, Peter (2010) has shown that not only the TR lines but also coronal spectral lines of the active region (AR) are non-Gaussian, i.e., the spectral lines can be well fitted with double Gaussian. Recently, with the help of the IRIS observations, the Si iv in the ARs shows excessive wing emission (i.e., non-Gaussian profile), and it can be well fitted with non-Maxwellian $\kappa$ distribution (Dudík et al. 2017). Apart from these various solar regions (e.g., network, inter-network, and ARs), the non-Gaussian profiles do exist in the network jets (Kayshap et al. 2021). Hence, in short, we can say that the nature of the spectral profiles in TR is important and may reveal important physical processes in the in-situ plasma.

There are different types of AR depending on the complexity, namely, unipolar, bipolar, and complex groups (for more details see Hale et al. 1919). The cool loops exist in all ARs irrespective of their type. However, the physical properties of cool loops may change depending on the complexity of ARs. Hence, the present work is an attempt to diagnose the footpoints of the cool loops in two different types of AR, i.e., $\beta$ and $\beta$-$\gamma$. We have found that the physical properties/behaviour of the footpoints of cool loops of $\beta$ type ARs are significantly different from that of $\beta$-$\gamma$ type ARs. The paper is organized as follows: Section 2 describes the observational details and data reductions. The results are described in Section 3 followed by a summary and conclusion in the last Section.

The Interface Region Imaging Spectrograph (IRIS) provides high-resolution spectroscopic observations of various regions of the solar atmosphere including AR. IRIS observes far-ultraviolet (FUV) and near-ultraviolet (NUV) parts of the solar spectrum (see De Pontieu et al. 2014). The FUV, as well as NUV spectra have several emission and absorption lines, and these lines are important to diagnose the different regions of the solar atmosphere. Si iv spectral lines (i.e., Si iv 1393.755 Å and Si iv 1402.77 Å) form in TR, and the cool loops are the main features of TR. We have utilized both Si iv lines to diagnose the foot points of the cool loops. In this work, we have utilized 10 different AR observations to diagnose the foot points of the cool loops.

In Figure 1, we have displayed IRIS/SJI 1400 Å intensity maps of AR11937 (first $\beta$ type; (panel a)) and AR11934 (first $\beta$-$\gamma$ type; panel c). The first $\beta$ type AR11937 (first observation of the table 1) and the first $\beta$-$\gamma$ type AR 11934 (sixth observation of the table 1) were observed on January 1^st, 2014 and December 27^th, 2013, respectively. The overplotted white boxes in panels (a) and (c) outline the region of interest (ROI) in both types of AR and ROI is filled with several cool loops.

Further, we have also displayed the Heliosesmic and Magnetic Imager (HMI) line-of-sight (LOS) magnetogram of AR11937 (panel b) and AR11934 (panel d). In both LOS magnetograms, the black region corresponds to negative polarity while the white region corresponds to positive polarity. Here, please note that the red rectangular boxes on these magnetograms display the same ROI as shown by white boxes in panels a & c. In case of AR11937 (i.e., panel b), we have drawn the polarity inversion line (PIL) by green dashed line that clearly distinguish the positive and negative polarity, and one PIL is sufficient to separate positive and negative polarity. The existence of only one PIL justifies that AR11937 has a simple bipolar nature, and it is categorized as $\beta$ type AR. On the contrary, at least, we need three different PILs (see three green dashed lines within the red box in panel d) to draw the boundary between positive and negative polarity in the magnetogram of AR11934. Hence, unlike the AR11937, the presence of three different PILs justify that this AR11934 has a complex configuration of the magnetic field. Therefore, AR11934 is a $\beta$-$\gamma$ type AR. Later, we checked the LOS magnetograms of all ARs, and we found that five out of 10 observations are $\beta$ type ARs while the rest five observations are of $\beta$–$\gamma$ type AR (see table 1). All the necessary details of all $\beta$ and $\beta$–$\gamma$ type ARs are tabulated in the table1. Further, please note that the information about the types of ARs are mentioned on the solar monitor website¹¹1www.SolarMonitor.org, and our classification is consistent with the information provided on the solar monitor website.

We have utilized uncalibrated (i.e., data numbers (DN/s)) as well as calibrated spectra (i.e., erg/cm²/s/sr) in the present work. We have used iris$\_$getwindata.pro routine with calib keyword to get calibrated spectra. It is to be noted that we have used the latest version (version - 009) of iris calibration to get the calibrated spectra. The same routine is used with the norm keyword (and without calib keyword) to get uncalibrated spectra. In the next step, Si iv 1402.77 Å line is fitted with the single Gaussian function to get the peak (or central) intensity, centroid, and Gaussian width (i.e., $\sigma$) at each location of ROI. It is also to be noted that Gaussian fit is applied on both uncalibrated and calibrated spectral profiles. Then, using peak intensity and Gaussian width, we have calculated the total intensity (i.e., the area under the curve) at each location of ROI. Again, it is to be noted that the total intensity is estimated in DN/s as well as erg/cm²/s/sr. Further, the Gaussian width is converted into full width at half maximum (FWHM) using FWHM = 2.3548$\times$Gaussian width, and the centroid is converted into the Doppler velocity with the help of the rest wavelength of Si iv line. Here, it should be noted that estimating the rest wavelength is crucial as it can directly affect the Doppler velocity. There are three different methods to calculate the rest wavelength, namely, limb method, chromospheric method, and lamp method (Peter & Judge 1999).

The present work utilizes the neutral/single ionized lines (i.e., cool lines) to estimate the rest wavelength of the Si iv line. Usually, the cool photospheric/chromospheric lines have low systematic Doppler shifts, and this low systematic Doppler shift is considered the least plasma flow that exists in the solar atmosphere. Therefore, cool photospheric/chromospheric lines are used in this method to calibrate the rest wavelength of any spectral line.

IRIS provides several cool lines that can be used in the rest wavelength estimation. And, we have utilized Fe ii and S i lines to calculate the rest wavelength. We have followed the same procedure as described in the IRIS Technical Note 20 available at IRIS/LMSAL website²²2https://iris.lmsal.com/search/. Finally, in table 2, we have tabulated all the necessary information related to the rest wavelength estimation, namely, used cool lines, observed centroid of cool lines, the difference between observed centroids and standard wavelength of cool lines (i.e., taken from CHIANTI database), and, the rest wavelength of Si iv. Using the estimated rest wavelength, the centroids are converted into the Doppler velocity.

The integrated (total) calibrated intensity(panel a), Doppler velocity (panel b), and FWHM maps (panel c) of ROI from the first $\beta$ AR are displayed in the top row of figure 2. Similarly, the bottom row displays total calibrated intensity (panel d), Doppler velocity (panel e), and FWHM maps (panel f) of the first $\beta$–$\gamma$ AR.

The present work is to statistically investigate the footpoints of cool loops using IRIS and HMI/SDO observations. IRIS has revealed that cool loops are an integral part of ARs (e.g., Huang et al. 2015; Rao et al. 2019a, b). In the present work, we have taken five $\beta$ type ARs and five $\beta$–$\gamma$ type ARs to diagnose the footpoint of cool loops. Further, a comparison is also performed between the properties of the footpoints of these cool loops in $\beta$ and $\beta$–$\gamma$ type ARs. Through the statistical approach, we have derived some important findings about the footpoints of cool loops, which are summarized below.

• •

  The mean calibrated and uncalibrated intensities from first $\beta$ AR are 98.92$\pm$50.40 erg/cm²/s/sr and 4.25$\pm$2.17 DN/s, respectively. The same intensities for first $\beta$–$\gamma$ AR are 884.59$\pm$3278.18 erg/cm²/s/sr and 38.45$\pm$142.48 DN/s.

• •

  Similarly, the mean calibrated and uncalibrated intensities from all five $\beta$ ARs are 92.38$\pm$58.47 erg/cm²/s/sr and 2.47$\pm$1.64 DN/s, respectively. The same intensities are 396.65$\pm$1533.52 erg/cm²/s/sr and 11.49$\pm$66.37 DN/s but for all five $\beta$–$\gamma$ ARs.

• •

  The mean Doppler velocity and FWHM of the footpoints of the cool loops in all five $\beta$ type ARs are 8.15$\pm$9.20 km/s, and 0.17$\pm$0.047 Å, respectively. The same parameters are 7.83$\pm$14.92 km/s and 0.24$\pm$0.13 Å but for all five $\beta$–$\gamma$ ARs.

• •

  The mean calibrated and uncalibrated intensities are 9 times stronger in the $\beta$–$\gamma$ AR in comparison to the $\beta$ AR if we consider both AR close in time, i.e., no instrumental degradation. The same intensity difference is reduced to 4 times if we consider all the ARs. These ARs are observed over 9 years, therefore, the reduction in the intensity difference is most probably due to the instrumental degradation.

• •

  There is no correlation between the central (peak) calibrated intensity and FWHM, and between the central calibrated intensity and Doppler velocity of the footpoints of the loops in $\beta$ as well as $\beta$-$\gamma$ type ARs. However, the Doppler velocity and FWHM of the cool loop footpoints in both types of ARs are weakly correlated.

• •

  The Si iv line ratios from the footpoints of cool loops in both types of ARs are significantly deviated from the theoretical intensity ratio of Si iv. Here, we find that the opacity is important for more than half of the footpoint locations.

• •

  If the line ratio drops below 1.90 then the intensity of the footpoints becomes stronger. The intensity is getting weaker when the ratio goes beyond 2.10. However, the Doppler velocity and FWHM increase for low (i.e., the ratio less than 1.90) as well as high ratio values (i.e. ratio greater than 2.10).

• •

  Lastly, we find that the footpoints of cool loops have more complex profiles in $\beta$-$\gamma$ type ARs (i.e., 27.70%) than that in $\beta$ type ARs (i.e., 1.06%). The complex profiles are almost 26 times higher in $\beta$-$\gamma$ type ARs than that in the $\beta$ type ARs.

This is the first-ever research that demonstrates the complexity of ARs affecting, directly, the mean attributes of the footpoints of the cool loops. We examined a total of 200 footpoints of the cool loops from both types of ARs, i.e., 120 footpoints in $\beta$ type ARs and 80 footpoints in $\beta$–$\gamma$ type ARs. Statistically, we have found significantly higher mean intensities of the loop footpoints in the complex $\beta$–$\gamma$ type ARs than that in $\beta$ type ARs. We know that any instrument including IRIS degrades with time. Hence, the intensities from $\beta$–$\gamma$ are significantly affected due to the instrumental degradation because most of $\beta$–$\gamma$ ARs are observed later than $\beta$ ARs. Hence, the intensity differences between the loop footpoints of $\beta$–$\gamma$ ARs and $\beta$ ARs (, i.e., loop footpoints in $\beta$–$\gamma$ ARs have 4 times higher intensity than the corresponding intensity in $\beta$ ARs) are underestimated.

The plasma flows within the footpoints of cool loops are almost similar in both types of AR. In this analysis, we have considered blueshifted and redshifted footpoints of cool loops, and it is found that the majority of the footpoints are redshifted. The mean redshifts of these footpoints are around 8.0 km/s in both types of AR. In general, solar TR of quiet-Sun, coronal hole, and ARs are red-shifted (Teriaca et al. 1999; Peter 1999; Peter & Judge 1999; Dadashi et al. 2011; Kayshap et al. 2015; Kayshap & Dwivedi 2017). In the present analysis, similar to previous works, we have also found that the footpoints of the cool loop in both ARs are redshifted. Please note that the Doppler velocity of ARs varies as per the location of the AR on the solar disk, i.e., center-to-limb variations (CLV) do exist in the Doppler velocity of ARs (e.g., Ghosh et al. 2019; Rajhans et al. 2023). The Doppler velocity is maximum at the disk center which decreases while moving toward the solar limb. The Doppler velocity near the disk center is around 7–9 km/s (Rajhans et al. 2023). In the present work, most of the ARs are close to the disk center (see the $\mu$ values in table 1), and the on-average Doppler velocity of footpoints of cool loops is $\approx$ 8.0 km/s. It (i.e., the mean value of Doppler velocity) is consistent with previously reported Doppler velocity of the footpoints of cool loops (e.g., Rao et al. 2019b, a) and ARs (Rajhans et al. 2023).

The footpoints of the cool loops exhibit large variations in the FWHM as shown by Rao et al. (2019b), i.e., 0.095–0.246 (first set of observations), 0.094–0.200 (second set of observations), and 0.125–0.182 (third set of observations). Earlier, Huang et al. (2015) also showed broad spectral profiles at the footpoints of cool loops. Recently, Srivastava et al. (2020) have found large FWHM (more than 0.25 Å) around the footpoint of the cool loops. The present work systematically estimates the FWHM in the footpoints of cool loops in both types of ARs. The spreads of FWHM are 0.10–0.40 Å and 0.10–0.70 Å in the footpoints of the cool loops in $\beta$ and $\beta$ $\gamma$ ARs, respectively, and the reported range is consistent with the previous findings (e.g., Rao et al. 2019a, b). Most importantly, the mean FWHM in the loop footpoints is higher in $\beta$–$\gamma$ ARs than $\beta$ ARs. In addition, the spread in FWHM is more than 2 times in the footpoint of the cool loops in $\beta$-$\gamma$ than $\beta$ type ARs. In conclusion, both aspects justify higher activity levels in the loop footpoints of $\beta$–$\gamma$ ARs than $\beta$ ARs.

The line with high oscillator strength is affected the most due to opacity, and therefore, we do observe the reduced ratio, i.e., less than 2.0. The magnetic reconnection triggers various dynamic events within the lower solar atmosphere, like explosive events, and small-scale brightening (e.g., Isobe et al. 2007; Peter et al. 2014; Gupta & Tripathi 2015; Kayshap & Dwivedi 2017). Such events can enhance the electron density along the line of sight (LOS), and as a result, a thick atmosphere will form. The reabsorption probability of Si iv 1393.78Å photon in the thick atmosphere is twice in comparison to that of Si iv 1402.77 Å. Hence, the intensity of Si iv 1393.78Å reduces more and more as electron density increases in the LOS, and as a result, the ratio reduces more and more. In the present study, 23% locations in $\beta$ ARs and 31% locations in $\beta$–$\gamma$ ARs have ratio values less than 1.90 (i.e., significantly less than 2), and we know that footpoints of the cool loops are much prone area to the dynamic events mentioned above (e.g., Huang et al. 2015; Huang et al. 2019; Rao et al. 2019a, b; Srivastava et al. 2020). In addition, we have seen complex spectral profiles in the footpoints of the cool loop which are most probably due to the occurrence of magnetic reconnection in the vicinity of footpoints. Hence, such events at the loop footpoints have enhanced the opacity, and it is reflected as the reduced ratio of Si iv lines. On the other hand, 29% locations in $\beta$ ARs and 24% locations in $\beta$–$\gamma$ ARs have an intensity ratio greater than 2.10, and the intensity ratio higher than 2 is due to the resonant scattering (e.g., Wood & Raymond (2000); Gontikakis & Vial (2018); Tripathi et al. (2020)). Hence, it may also be possible that the resonant scattering is happening in the vicinity of footpoints. While further studies based on the modelling of Si iv lines are required to know this issue in great detail.

The estimation of the chi-square value is necessary to know the level of complexity in the spectral profiles. The chi-square analysis establishes that $\beta$-$\gamma$ type ARs have more than 26 times more complex profiles than the complex profiles of $\beta$ type ARs. Hence, we can say that the footpoints of cool loops are much more complex in $\beta$-$\gamma$ type ARs than that in $\beta$ type ARs. In addition, we have also noticed complex profiles (i.e., non-Gaussian, broad, and multi-peak profiles) within the footpoints of cool loops of both ARs and similar observational findings are already reported (e.g., Huang et al. 2015; Rao et al. 2019b; Srivastava et al. 2020).

In conclusion, we find that the footpoints of the cool loop in $\beta$ $\gamma$ ARs are far more complex than that in $\beta$ type ARs, and the intensity $\&$ FWHM are higher in $\beta$–$\gamma$ ARs than those in $\beta$ type ARs. On the contrary, the Doppler velocities are the same in both ARs.

We gratefully acknowledge the reviewer (Dr. Jaroslav Dudík) for his constructive comments that substantially improved the manuscript. B. Suresh Babu and P. Kayshap express gratitude and acknowledgment to Dr. Georgios Chintzoglou (LMSAL)and Dr. Bart De Pontieu (LMSAL) for the valuable inputs during a discussion at Hinode-16/IRIS-13 meeting. Based on their suggestions, we modified the analysis, particularly for the Si iv ratio estimation. P. Jelínek acknowledges support from grant 21-16508J of the Grant Agency of the Czech Republic. 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 Centre. We also acknowledge the use of HMI/SDO.

The data underlying this article are available at https://iris.lmsal.com/data.html (NASA/IRISwebsite) and at https://iris.lmsal.com/search/(LMSAL search website). Note that IRIS data are publicly available with the observation ID OBS 3630088076, OBS 3620106076, OBS 3620108077, OBS 3840257196, OBS 3610108077, OBS 3860257446, OBS 3620110077, OBS 3620110077, OBS 3620108077, OBS 3610108077.