A multi-diagnostic spectral analysis of penumbral microjets

In order to facilitate a holistic overview of individual PMJs using all major first-order diagnostics and their temporal evolution, we created two sets of videos for each dataset that show individual PMJs. Two videos show each PMJ in both datasets at their peak brightness, while the second set shows all PMJs through time for both datasets.

The videos showing all PMJs at only peak brightness for dataset A and B are available in Video 1 and Video 2, respectively. The videos detailing the temporal evolution of PMJs in dataset A and B are available in Video 3 and Video 4, respectively.

A more detailed description of these videos and their layout is given in Appendix B. We strongly encourage readers to view at least videos 1 and 2 for an overview of all PMJs. Videos 3 and 4 are useful in order to gain an overview of the temporal evolution of specific PMJs. We also particularly suggest inspecting the example PMJs mentioned in the text.

PMJs in our observations adhere to the same type of morphology as when previously studied in a variety of works, and they present as elongated brightenings that appear and disappear on time scales of minutes or less than a minute. This overall appearance also holds true when PMJs are viewed in multiple wavelength channels simultaneously. As mentioned, PMJs often display a rainbow-like signature in composite-channel RGB images, which was used as another aid both in discovering and identifying PMJs, but it was not used as a strict criterion in order to make a positive identification. Figures 4 and 5 display all of the studied PMJs in composite RGB images for datasets A and B, respectively. Many PMJs exhibit a rainbow signature with a connected red-to-green-to-blue elongated structure that reaffirms the observation that PMJs typically exhibit a signal in channels associated with temperatures that correspond to the chromosphere and up to the TR, suggesting that PMJs range through such temperatures.

PMJs do not always exhibit a clear rainbow pattern. In some instances, this is due to the PMJ in question, which simply does not exhibit a signal in the relevant channel. Positing that a PMJ originates in the chromosphere (the validity of which is discussed in Sect. 5), less energetic ones may not reach the relevant temperature (or height) to which the channel corresponds. In other cases, it is due to a failure in capturing the relevant signal. Another source for absent rainbow patterns may result from the automated mixing in the RGB image resulting from the three diagnostic images, which may not always yield favourable visual results. Lastly, in several images, the shadow of the IRIS spectrograph slit is also evident, usually as a purplish line in the images, and it may obscure possible rainbow patterns. Despite a number of PMJs that do not exhibit a rainbow pattern, a majority of the detected PMJs can reasonably be said to display such a pattern for both our dates of observations.

We measured a lower bound on PMJs lengths that are based on two sets of sampling positions. The first is the sampling position of Ca ii 8542 Å and the second is the sampling position of the Si iv lines. The inferred lengths are the straight-line distances between these two sampling positions for any given PMJ. These sampling positions are located at the nominal peak-intensity pixels at the nominal peak-intensity time. As such, the sampling positions do not measure the maximum extents of our PMJs, as there is often still some appreciable signal away from the given peak-intensity pixel. However, Si iv line core intensities typically dropped dramatically with increased pixel distance from the peak-intensity pixel. Ultimately, the presented lengths must therefore be considered a lower bound on projected PMJ lengths when measured from the chromosphere to the TR. See both the overview in Figures 2 and 3 and the PMJ RGB-images in Figs. 4 and 5 for reference.

The mean lower-bound lengths with associated standard deviations for our studied PMJs were found to be $(2204\pm 195.0)$ km and $(1940\pm 138.2)$ km for datasets A and B, respectively.

Multi-channel PMJ width estimates necessitate measurements in IRIS SJI 2796 images since PMJs usually display their midsection in this channel. However, widths of most PMJs fell close to the pixel resolution of the Mg ii SJI images, typically of the order of 1-3 pixels, meaning potential width distributions would be of dubious value at best. We thus constrain ourselves to the observation that our PMJs have typical widths of 243 km - 729 km, corresponding to the widths of 1 - 3 pixels in the Mg ii SJI images.

Figures 6 and 7 show spectral profiles for all of our studied PMJs. The average event profiles and average profiles for the penumbra and the entire FOV for each date observation for all given lines are also shown. We note that H $\alpha$ line profiles for PMJ dark features are presented separately in Sect. 4.8.

PMJs may exhibit signals in all of the lines. However, the studied PMJs display enhancement more readily in some of the lines than in others.

The figures highlight that there is a large spread in the profiles for all channels, but for both datasets it is evident that PMJs often display strong signals in the Ca ii 8542 Å and the Mg ii h and k lines compared to the penumbral average, while enhancement in other lines is somewhat less common, especially the Mg ii triplet lines. We note that C ii 1334 Å & 1335 Å typically exhibit double peaks when in emission, but also some single peaks. When in emission, the Si iv 1394 Å & 1403 Å lines always present as single peaked and near-Gaussian.

There exists one example of a PMJ exhibiting enhancement in the O iv 1401 Å line in dataset B (see Fig. 7). This event also corresponds to the strongest event in terms of intensity for the Si iv  lines, and with very defined profiles with strong intensities for the other lines (but with no emission in the Mg ii triplet). This may indicate that the specific PMJ event may be heated to temperatures far beyond earlier observed examples. This specific PMJ is presented in Sect. 4.7, albeit briefly, as a single event should not be overanalysed nor overemphasised.

Table 1 summarises the number of PMJs that exhibit clear signals in the various channels studied. A clear signal means that a given line profile shows an enhancement when compared to nearby pixels in space and time, and it is thus based not only on a comparison to the penumbral average for a given line since profile intensities can vary substantially with regards to position throughout the sunspot. This investigation was performed visually to give an estimate of the PMJ signal frequency in the different channels.

The line core shifts of the Mg ii h & k lines, $\Delta\text{v}_{\text{k3}}$ and $\Delta\text{v}_{\text{h3}}$, both strongly correlate with the line of sight velocity at the formation height of the $\text{h}_{\text{3}}$ and $\text{k}_{\text{3}}$ features at optical depth unity. The correlation coeffiecient was shown to be close to unity in Leenaarts et al. (2013b), and these shifts therefore hold great immediate diagnostic value and constitute the most reliable of the Mg ii diagnostics, probing either PMJs or the atmospheric conditions in their immediate surroundings. The height of optical depth unity for both $\text{h}_{\text{3}}$ and $\text{k}_{\text{3}}$ is close to that of the very upper chromosphere, and the Doppler-velocity offsets of the $\text{h}_{\text{3}}$ and $\text{k}_{\text{3}}$ features can therefore be taken as diagnostic proxies for the line of sight velocities at this height. Table 3 gives the Doppler-velocity offsets of the $\text{h}_{\text{3}}$ and $\text{k}_{\text{3}}$ features for our sample positions in the Mg ii h & k lines for our detected PMJs for both our sets of observations. The measured values are consistent across all four given values, and they are all close to zero with an absolute value range $\leq 0.97$ km s^-1.

We define the peak separations of the Mg ii h & k line as the absolute sum of the Doppler shifts of the two peaks in each Mg ii line, $\lvert\Delta\text{v}_{\text{x2v}}\rvert+\lvert\Delta\text{v}_{\text{x2r}}\rvert$ (where ‘x’ may be k or h). Leenaarts et al. (2013b) and Pereira et al. (2013) show that this quantity correlates with the difference between the maximum and minimum of the atmospheric line of sight velocity between the mid-chromospheric formation heights of the peaks and heights above. The relation is less reliable than the previous diagnostics, with an average correlation coefficient of 0.57, which was inferred for the two lines. Further, it was shown that a temperature maximum in the lower chromosphere can also cause wider peak separations, which means that a discussion regarding this diagnostic must be more nuanced, especially given that PMJs are energetic events that are hypothesised to form in the chromosphere. Table 3 gives the peak separations for the h & k line of our Mg ii sample positions of our detected PMJs for both dates of observations.

All values for the peak separations for both dates are rather consistent, with values slightly higher for the k line than for the h line for both dates of observations, and the separations are overall higher for the observations of dataset B. Overall, the peak separation values are of the order of $\approx 30$ km s^-1. This may indicate a maximum velocity difference between the mid-chromosphere and above in this range, assuming there is no temperature maximum in the lower chromosphere. This assumption, however, is challenged in Sect. 5 due to other diagnostics indicating that there may indeed exist such a temperature maximum.

Leenaarts et al. (2013b) and Pereira et al. (2013) show that the average Doppler shifts of the Mg ii $\text{h}_{2}$ and $\text{k}_{2}$ peaks correlate with the line of sight velocity at the optical depth $\tau=1$ height for the peaks in each line. Further, the $\text{h}_{2}$ and $\text{k}_{2}$ peaks are shown to form in the mid-chromosphere, about 1 Mm below their line cores ($\text{h}_{\text{3}}$ and $\text{k}_{\text{3}}$). The average Doppler shifts of the peaks thus correlate to the line of sight velocity at this height. The average of the correlation coefficients between average peak Doppler shifts for the two lines and the line of sight velocity at their formation heights is $0.66$, and thus this diagnostic is somewhat less reliable than the one for the line core Doppler shifts, but it still provides a strong correlation.

From Table 3 we see that the averaged peak Doppler shifts are all close to zero km s^-1 in magnitude; the majority of which are negative, indicating an upflow. With standard errors included, we find the very small upper absolute value of $\leq 0.49$ km s^-1 for the average peak Doppler shifts across all PMJs. Overall, negative values may indicate a possible subtle upflow in the lower chromosphere, though in which case it is close to zero in value.

The line cores of the C ii 1334 Å and 1335 Å are formed approximately just below the TR (Rathore et al. 2015a), and the line core offsets of the two lines thus offer a diagnostic to approximate the line of sight velocity at this height. In Rathore et al. (2015a), it is shown that for the C ii 1334 Å and 1335 Å lines, there is a good correlation between the offsets in their line cores to the vertical velocity at line core formation heights, with correlation coefficients of 0.69 and 0.63, respectively.

From Table 4, we see that values for the C ii 1334 Å and 1335 Å line core shifts are consistent across the dates of observations, both having the same sign for each line and being on the same order of magnitude. The 1334 Å line has a negative line core offset for both dates, with a maximum absolute value of $\leq 2.81$ km s^-1 when considering standard errors. The 1335 Å line has a positive sign for both mean values for the two dates of observations, with a maximum absolute value of $\leq 6.94$ km s^-1 when considering standard errors.

The line core offsets with conflicting signs for the two lines indicate a low overall line of sight velocity close to the TR that is less than 7 km s^-1 in absolute value. Even though both C ii lines form close to the TR, the stronger 1335 Å forms slightly higher than the 1334 Å line. Thus, in principle, the difference in sign for the core offsets may indicate a small difference in the line of sight velocity at these slightly different heights.

The integrated intensity ratio of the C ii 1334 Å and 1335 Å lines can be used as a measure to determine whether it is formed under optically thick or possibly under optically thin conditions. The line intensity ratio is also correlated to the number of peaks present in the given profile, and the number of peaks gives insight into the type of source function that produces their line profiles. We follow the definition of the integrated line ratio of the C ii 1334 Å and 1334 Å lines in Rathore & Carlsson (2015), such that we define the intensity ratio as $\text{R}_{\text{I}}=\frac{\text{I}_{\text{1335}}}{\text{I}_{\text{1334}}}$. Here, the intensities $\text{I}_{\text{1334}}$ and $\text{I}_{\text{1335}}$ are the intensities of the two lines integrated over the region of $\pm 20$ km s^-1 around the nominal line core for each given line. It was shown that this ratio can, in principle, take any value in the case of optically thick line formation, but it has the value $\text{R}_{\text{I}}=1.8$ for the case of optically thin line formation. This means that $\text{R}_{\text{I}}=1.8$ is compatible with optically thin line formation, but this does not prove it, whilst any other value indicates optically thick line formation. Furthermore, it was shown in modelling that the value of $\text{R}_{\text{I}}$ is typically lower for double peak profiles, with values around $1.4$, whilst single peak profiles have typical values around $1.7$ (Rathore et al. 2015a).

Table 4 gives the values of the integrated line-pair ratio for the two dates of observations in column five together with its associated standard error. The values are consistent and overlap, given their standard error and give a range of ($1.12$ – $1.28$). The values thus indicate optically thick line formation. The values are also closer to the mean value of $\text{R}_{\text{I}}=1.4$ expected for double peak profiles than the one for single peak profiles. This is congruent with the fact that we find a majority of double peak profiles when there is enhancement in either of the lines. The number of single and double peak profiles are given in Table 4. For all but the case of the C ii 1334 Å line for dataset A, we find a greater number of double peaks than single peaks when there is any clear enhancement in the given line.

Single peak profiles in both the C ii 1334 Å and 1335 Å lines are formed when the source function of the given line increases monotonically up to the height where the line core has optical depth unity. Double peak profiles are formed when there is a local maximum in the source function deeper down in the atmosphere, and if the source function above this local maximum decreases in value with increasing height until optical depth unity for the line core is reached. The C ii 1335 Å line overall tends to have a higher number of double peaks than its counterpart, since its line core forms overall a little higher than that of the C ii 1334 Å line, and thus there is a greater likelihood that the 1335 Å line core forms at a greater height than a potential local maximum in its source function compared to the 1334 Å line (Rathore & Carlsson 2015; Rathore et al. 2015a, b). We see the latter effect exemplified in Table 4, as there is a greater prevalence of double peaks in the 1335 Å line than for the 1334 Å line for both dates of observation. Further, as we have a greater number of double peaks than single peaks overall, we can reasonably conclude for a majority of cases in which there is an enhancement in the C ii line pair that there is a local maximum in the source function below the formation height of the line cores of the two lines.

We measured the line widths of C ii 1334 Å and 1335 Å  where the line width for each given line was defined as $\text{w}_{\text{FWHM}}=2\sqrt{2\ln 2}\sigma$, where $\sigma$ is the standard deviation of a Gaussian, and thus $\text{W}_{\text{FWHM}}$ is the full width at half maximum of the same Gaussian. This follows the approach outlined in Rathore & Carlsson (2015), where it is shown through the use of synthetic profiles and a model atmosphere that the use of Gaussian fits of C ii 1334 Å and 1335 Å line profiles yield useful estimates for $\text{w}_{\text{FWHM}}$ using the Gaussian standard deviations, even in the case that the two lines are formed under optically thick conditions and when they exhibit double peaks. The measured $\text{w}_{\text{FWHM}}$ line widths for C ii 1334 Å and 1335 Å for datasets A and B are given in Table 4, together with their standard errors.

The line widths of the C ii 1334 Å and 1335 Å lines were shown to be correlated to the non-thermal velocity at the heights at which the cores of the two respective lines are formed in Rathore et al. (2015a). The line width is also determined by the thermal velocity, but the line width was further shown to be predominately determined by the non-thermal velocity for line widths greater than $6$ km s^-1. Profiles with widths smaller than $6$ km s^-1 were shown to have dominant optically thin components. In Sect. 4.5.2, we show that for the case of our observed PMJs, the line ratios, $\text{R}_{\text{I}}$, imply optically thick line formation. For both dates of our observations and for those PMJ profiles in the C ii lines that exhibit emission, the line widths exhibit values greater than $6$ km s^-1. As such, our measured line widths can be used as a diagnostic to probe the non-thermal velocity at the formation heights of the C ii line pair.

To estimate the non-thermal line widths, we used the relation

Here, $\text{w}_{\text{nth}}$ is the estimate of the non-thermal line width for any given observed value of $\text{w}_{\text{FWHM}}$ (given in Table 4), $\text{w}_{\text{th}}$ is the thermal line width, and $\text{w}_{\text{I}}$ is the instrumental line width of IRIS in the far ultraviolet (FUV) bandwidth. The instrumental width of IRIS in the FUV is $\text{w}_{\text{I}}=12.8$ mÅ (De Pontieu et al. 2014), or $\text{w}_{\text{I}}=5.84$ km s^-1 for both C ii 1334 Å and 1335 Å.

In order to calculate estimates for $\text{w}_{\text{nth}}$, we first computed a fitting theoretical estimate for $\text{w}_{\text{th}}$, for which we used the expression

Here, $k_{B}$ is the Boltzmann constant, $T_{\text{ion}}$ is the temperature of the C ii ion, and $m_{\text{ion}}$ its mass.

In Rathore et al. (2015a, b) it was found that the C ii lines are formed mainly in the optically thick regime, as we observe, and with a mean formation temperature of $10$ kK. More specifically, in Rathore et al. (2015a) it was found that when the source function for the C ii lines has a peak in the low atmosphere, this leads to steep emission flanks and a double peak intensity profile. They show an example of this (their Fig. 17) for which the temperature in the line forming region is $9.6$ kK. Since we see a majority of double peak profiles and as other results already indicate that PMJs are due to heating events in the lower atmosphere, a temperature of $T_{\text{ion}}=10$ kK is thus a reasonable estimate for our purposes, and we find a corresponding thermal line width for the C ii ion of $\text{w}_{\text{th}}=6.19$ km s^-1.

Finally, we thus find mean non-thermal line width values of $\text{w}_{\text{nth, 1334, A}}=30.2$ km s^-1 and $\text{w}_{\text{nth, 1334, B}}=42.3$ km s^-1 for the 1334 Å line for datasets A and B, respectively, and $\text{w}_{\text{nth, 1335, A}}=40.8$ km s^-1 and $\text{w}_{\text{nth, 1335, B}}=50.7$ km s^-1 for the 1335 Å line for datasets A and B, respectively. We refrain from providing uncertainty values for these non-thermal line widths, as the assumed formation temperature of $T_{\text{ion}}$ alone would render these dubious at best. As we can see, we find a range of values for the two lines and datasets of $\text{w}_{\text{nth}}\approx(30,51)$ km s^-1. The non-thermal line widths are also affected by opacity broadening, which most likely skews them to higher values as typical opacity broadening values are of the order of 1.2-4 (Rathore et al. 2015a) due to optically thick line formation and the double peak profiles that are broader than single peak profiles. Thus, our inferred non-thermal line width ranges serve as upper limits for non-thermal velocities in the formation region of the C ii line pair at the upper chromosphere or just below the TR.

The line core offsets of the Si iv 1339 Å and 1403 Å are proxies for the line of sight velocity at the TR formation height of their cores. We ascertained the line core offsets of both lines by fitting PMJ Si iv line profiles with a Gaussian profile and using its centre as an estimate. The means of these measured line core offsets for the Si iv line pair with their standard errors and sample sizes are given in Table 5 for both datasets.

The sampling sizes for both dates and both lines are indicative of the number of profiles in each line for which a Gaussian profile could be fitted with a Gaussian $\chi^{2}$ goodness-of-fit value (using the IDL ‘gaussfit’ function) that proved suitable to select those profiles with large enough intensity enhancements and with profiles that are well-shaped enough to extract meaningful line core offsets. For peak-brightness times, these profiles were then verified by eye. These sample sizes therefore also present the number of profiles in each case that correspond to events with visible enhancement in the given Si iv line for the given date.

From Table 5 we see that the mean line core offsets for both dates and both lines are consistently of positive values, and they are close to zero. They have a maximum absolute value of $\leq 3.20$ km s^-1, taking standard errors into consideration. As such, we find that the line of sight velocity at the site of PMJ signals in the Si iv line pair at the shared approximate height of line core formation for the two lines is likely no more than a few km s^-1 and may be close to zero given our standard errors.

Our Si iv line pair profiles exhibit single peaks and are clearly Gaussian in shape for those cases in which we observe any appreciable intensity enhancement. The line core intensity ratios of the Si iv 1394 Å and 1403 Å lines can be utilised to estimate whether the lines form under optically thick or thin conditions. We calculated the peak intensity ratios of the Si iv 1394 Å and 1403 Å lines, which are defined such that the ratio is given by $\text{R}_{\text{core}}=\frac{\text{I}_{\text{1394}}}{\text{I}_{\text{1403}}}$. Here, $\text{I}_{\text{1394}}$ and $\text{I}_{\text{1403}}$ are the instrument-count intensities at the position of the line core of the given line.

Under optically thin conditions, the line core intensity ratio for the line pair has a value of $\text{R}_{\text{core}}=2$, owing to the fact that the 1394 Å line has an oscillator strength that is twice that of the 1403 Å line. If the lines form under optically thin conditions, the 1394 Å should therefore also present twice the absolute intensity in the line core as that of the 1403 Å line. Nonetheless, line formation under optically thick conditions can also produce a line ratio of $\text{R}_{\text{core}}=2$, and thus this value does not guarantee optically thin formation, but a significantly lower value than this does thus preclude thin formation.

We find typical values for $\text{R}_{\text{core}}\approx 2$. The average intensity line core ratio of the two lines is close to two for both datasets, as shown in Table 5. The range of line core intensity ratios over both dates is $(1.85-2.09)$, taking standard errors into account. We can thus conclude that the Si iv 1394 Å and 1403 Å line PMJ profiles may form under optically thin conditions.

PMJs have mostly been studied in the Ca ii lines, and not so much in the H $\alpha$ line. Recently, however, Buehler et al. (2019) reported on PMJs that present with darkenings in H $\alpha$ images when studied by eye and are viewed in the inner line core, with accompanying H $\alpha$ line profiles exhibiting subtle decreases in intensity in the inner line core at sites adjacent to PMJs that are visible in concurrent Ca ii 8542 Å line observations. We investigated the appearance of PMJs in H $\alpha$ and Ca ii 8542 Å images together with their line profiles at selected locations. We confirm the appearance of dark features in the inner wings of the H $\alpha$ line associated with PMJs.

We also report the existence of dark features in the inner wings of the Ca ii 8542 Å line that strongly correlate spatially and temporally with those in the inner line wing of the H $\alpha$ line. Utilising CRISP images at line core offsets of $-400$ mÅ and $-350$ mÅ in the H $\alpha$ and Ca ii 8542 Å lines, respectively, we found elongated dark features that trace the direction of the surrounding penumbral fibril structures and that sit at the origin of PMJs, preceding and following PMJs in time. We selected sampling positions by eye, targeting dark features for the subset of PMJs for which we could positively identify them.

Figure 9 shows the temporal evolution of example PMJ A10. The PMJ is a very clear example of a PMJ that presents with typical brightening in the Ca ii 8542 Å line at an offset of $-350$ mÅ  but that also exhibits dark features in both the H $\alpha$ and Ca ii 8542 Å inner line wings, which both have their approximate footpoints at the site where the PMJ bright feature appears.

In the composite images, bright red indicates the presence of dark Ca ii 8542 Å $-350$ mÅ features and bright cyan indicates dark H $\alpha$ $-400$ mÅ features. Co-spatial dark features in the two channels appear white when they are combined in their respective composite images. The dark features both precede and follow the bright feature in the Ca ii 8542 Å line by over 2 minutes. In the case of the dark feature visible in the Ca ii 8542 Å line, it becomes rather obscured at peak enhancement of the Ca ii 8542 Å bright-feature, and thus it is less identifiable at this time, which probably made identification less likely in earlier observations and studies.

PMJ A10 is a particularly clear example of the behaviour described above. However, we find numerous PMJs in both datasets for which the same trend of near-cospatial dark features in the inner line wings of the H $\alpha$ and Ca ii 8542 Å lines, both of which seem to originate at the approximate point of the Ca ii 8542 Å bright feature, holds true. Typically the dark features also precede and follow the bright feature in time in the other cases. An additional example of this type is included in the Appendix in Fig. 15 for the PMJ B21.

We selected all PMJ events for which we could detect dark features in either or both of the inner line wings of the H $\alpha$ and Ca ii 8542 Å lines and determined their spectral profiles in these lines at the time of maximum brightness for the typical bright feature that is visible in the Ca ii 8542 Å line. For observations in the Ca ii 8542 Å line, we selected a number of clear sampling positions and dark features of $\text{N}_{\text{dark}}\left(\text{{Ca {ii}}, A}\right)=25$ (= 76%) and $\text{N}_{\text{dark}}\left(\text{{Ca {ii}}, B}\right)=31$ (= 70%) for datasets A and B, respectively. For the H $\alpha$ line we found a number of equivalent dark features of $\text{N}_{\text{dark}}\left(\text{\mbox{H\hskip 0.43057pt$\alpha$}, A}\right)=29$ (= 88%) and $\text{N}_{\text{dark}}\left(\text{\mbox{H\hskip 0.43057pt$\alpha$}, B}\right)=36$ (= 82%) for datasets A and B, respectively. The percentages are all in relation to the total number of PMJs detected for each dataset. We see that a significant majority of PMJs in both lines exhibit these dark features; there are fewer of them for observations in Ca ii 8542 Å. This is most likely both due to the Ca ii 8542 Å PMJ bright features obscuring some of the Ca ii 8542 Å dark features, as well as a general lower contrast in the Ca ii 8542 Å observations compared to those in the H $\alpha$ line. Figure 10 shows all individual Ca ii 8542 Å and H $\alpha$ PMJ profiles for these dark features, together with the PMJ mean profiles of these.

The average PMJ profiles in the H $\alpha$ line for both dates confirm a slight decrease in intensity in the inner line wings of the studied PMJs, which is consistent with the profiles presented in Buehler et al. (2019). The average Ca ii 8542 Å line profiles for our selected dark features show less distinct behaviour, and they have mean profiles that are overall slightly enhanced compared to the penumbral mean profile, even though the CRISP images at an offset of $-350$ mÅ clearly show features that are darker than their surroundings. The darkenings found in the images of the inner line wing of the H $\alpha$ line appear very similar to those as presented in Buehler et al. (2019). The spectral formation process of the dark features in the inner ling wings of both the Ca ii 8542 Å and H $\alpha$ lines has yet to be explained and warrants further investigation, possibly in the form of modelling.

Given that PMJs may be caused by reconnection events and the subsequent heating that takes place in the low chromosphere or photosphere, one may expect to find enhancement in the outer wings of the H $\alpha$ line as observed for Ellerman bombs (see for example Rutten et al. (2013)). So far however, we have not found evidence of any such enhancement in H $\alpha$ profiles for PMJs. This can be seen in Fig. 10 for the sampling positions of the inner wing of the H $\alpha$ line dark features. The lack of any consistent enhancement in the outer wings of H $\alpha$ compared to the penumbral and full FOV line profile average may warrant further investigation in the future, especially in light of evidence for heating at chromospheric or photospheric heights, such as enhancement in the Mg ii triplet blend. We conclude that dark structures that precede and follow the nominally bright PMJ events in time exist in both the inner line wing of the H $\alpha$ line as previously reported, but also in the inner line wing of the Ca ii 8542 Å line.

Figure 11 shows a selection of PMJs from dataset A that show clear dark features in the blue wing of the Ca ii 8542 Å line, the inner blue wing of the H $\alpha$ line, and that exhibit clear brightenings in IRIS Mg ii SJ images, together with an amalgamation RGB image that combines these three channels. The RGB image uses the intensity-inverted SST images for the Ca ii 8542 Å (red) and H $\alpha$ (blue) channels. As such, darkenings yield brighter colours for these two channels. The concurrent darkenings in the two channels that overlap with brightenings in the Mg ii SJ images thus tend towards bright (white) values. The figure illustrates a clear trend in which the brightening in the chromospheric Mg ii SJI images overlaps with the darkenings in the Ca ii 8542 Å and H $\alpha$ lines. We find that this trend is typical for both datasets of PMJs and may indicate that these darkenings map to the same chromospheric object as the brightening in the Mg ii channel. PMJs from dataset B that were selected following the same criteria as described above are shown in Fig. 16, which is included in the Appendix.

The different spectral diagnostics that we have used to study PMJs are sensitive to different broad regions in the solar atmosphere. In rough order of atmospheric height, from the photosphere and upwards, we can infer the following:

• •

  Emission in the Mg ii triplet wings provides evidence for heating at photospheric heights for a subset of PMJs.

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  Mg ii $\text{h}_{2}$ & $\text{k}_{2}$ average peak Doppler shifts yield estimates for the line of sight velocity in the lower chromosphere that are close to zero.

• •

  Mg ii $\text{h}_{2}$ & $\text{k}_{2}$ peak separations are measured to be of the order of 30 km s^-1. The interpretation of this enhanced separation as a difference in line of sight velocity between the mid- and more upper chromosphere has a high uncertainty. It is more likely a result of enhanced heating in the lower chromosphere.

• •

  C ii widths yield estimates for the non-thermal line widths and thus upper limits for the non-thermal velocity in the upper chromosphere or just below the TR of $\approx(30,51)$ km s^-1.

• •

  Mg ii $\text{h}_{3}$ & $\text{k}_{3}$ line core offset values yield estimates for the line of sight velocity in the upper cromosphere, with values close to zero.

• •

  C ii line-pair line core offset values yield estimates for the line of sight velocities in the upper chromosphere or TR heights, with absolute values $\leq 7$ km s^-1, ranging slightly below and above zero.

• •

  C ii line-pair ratio values imply optically thick line formation in the upper chromosphere for these lines.

• •

  The typical number of (double) peaks in the C ii line pair implies a peak in the source function of the lines below the upper chromosphere or TR for the majority of PMJs that show an appreciable signal in these lines.

• •

  Values for the Si iv line-pair line core offsets yield estimates for the line of sight velocity at the TR, with modest values of absolute values $\leq 3.2$ km s^-1.

• •

  The ratio of the Si iv line pair peak intensity ratios imply optically thin line formation in the TR for these lines.

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  One example of emission in the O iv 1401 Å line implies heating to TR or flare conditions in one instance.

PMJs exhibit dark features in the inner wings of the H $\alpha$ line, which was first shown in Buehler et al. (2019). We confirmed these H $\alpha$ line dark features, and further found that PMJs also exhibit dark features in the inner line wing of the Ca ii 8542 Å line, with a large degree of spatial overlap at the two wavelengths. In both channels, the elongated dark features are aligned with the direction of the typical PMJ brightening in the inner line core of the Ca ii 8542 Å line, originating at the head of the jet-like PMJ event.

At peak brightness, the Ca ii 8542 Å bright feature may obscure the dark feature to some degree. The dark features are observable on timescale of minutes before and after the bright PMJ event itself, and they are aligned with the fibril structure of the sunspot.

This provides evidence for the scenario in which PMJs are heating events that follow the already existing fibril structure. We also find that the PMJ darkenings in the inner wings of the H $\alpha$ and Ca ii 8542 Å lines are spatially well-aligned with the typical PMJ brightenings in the IRIS Mg ii SJI channel, indicating that these darkenings are chromospheric events.

By using Mg ii h & k PMJ spectral profiles along the length of IRIS raster-slit positions, we produced Dopplergrams and bisector plots in order to investigate potential twisting motions in PMJs. We only found a few events that exhibited a reversal of blue-to-red or red-to-blue enhancement in PMJ Mg ii h & k line profiles along IRIS raster slits, which is indicative of twisting motions. Only 5 (6%) out of the total 77 studied PMJs exhibited Dopplergram or bisector features that are clearly congruent with twisting motions. We found a further 7 (9%) and 21 (27%) PMJs that exhibited only red or blue enhancement, respectively, in the Mg ii h & k lines. We conclude that twisting motions in the PMJs in our datasets are rare and that they are not a universal property requisite for their formation at the scales we observe.

The temporal evolution of PMJ brightenings when studied across different spectral lines reveals that their onsets do not differ significantly on the timescale of our IRIS raster cadence of $\sim 40$ s. As such, we do not observe that PMJs present at a particular temperature or atmospheric layer corresponding to a specific wavelength before others. If PMJs consist of true mass motions, one would expect discrepancies between onset times between different channels. The limiting cadence of $\sim 40$ s for the IRIS raster channel is less than the upper limit of the time range of 10 s to 1 min differences in onset times between bright dots and associated PMJs reported in Samanta et al. (2017).