Revisiting Eridani with NEID: Identifying New Activity-sensitive Lines in a Young K Dwarf Star

Our analysis begins with a set of observations of a star (in this case, Eri) and any line list or set of line lists. We use Level 2 data files reduced by the NEID DRP Version 1.1.2, which are multiextension astropy Flexible Image Transport System (FITS) files that contain the spectroscopic data (SCIFLUX) for each observation as well as various metadata, calibration information, blaze functions for each spectral order, measured RVs, and activity indicators. The median extracted signal-to-noise ratio (S/N) for our Eri observations is 463, so for this analysis, we first filter our observations for S/N of >300 to exclude three low-S/N observations. While processing our data, we also noticed a trend in the NEID Eri data in which certain observations with high photon counts seemed to near the saturation threshold of NEID and became "flattened," similar to what one would expect in a nonlinear response of the CCD, thus depressing the spectra and consequently affecting the shape of the spectral lines in those regions. We manually removed the observations affected by this phenomenon for this analysis. Then, before performing line-by-line analysis, we Doppler shift each spectrum to the rest frame of the star using the NEID DRP-derived radial velocity (CCFRVMOD) and barycentric velocity (SSBRVORD where ORD is the corresponding NEID echelle order number) to ensure consistency in our automated analysis. We convert this combined velocity to a wavelength shift and subtract this from the wavelength axis (SCIWAVE) of each spectrum. Then, we divide the spectra by the blaze function of each order (SCIBLAZE). After correcting for the blaze function, we normalize the spectra by fitting a segmented polynomial over sections of the spectra to estimate the continuum and dividing the spectra by this estimate. The resulting blaze-corrected, continuum-normalized, and shifted spectra are the inputs to our partially automated line-by-line analysis. Throughout this paper, all wavelengths reported are wavelengths in a vacuum and in the stellar rest frame.

To identify our initial candidates for activity-sensitive lines, we investigated 37 NEID observations for Eri spanning a range of 6 months from 2021 September to 2022 February, since it is a young and active star whose spectra had shown previous sensitivity to activity in W18. After applying the data processing detailed above, we were left with 32 high-S/N observations of Eri for our analysis. We used four different line lists to perform our analysis: a list of known, nonmagnetically sensitive solar lines ¹⁴ from Altrock et al. (1975; henceforth referred to as "Altrock et al."), the ESPRESSO K2 mask, a line list created by compiling several ESPRESSO masks for different star types (M2, K2, K6, G2, G8, G9, and F9) and removing duplicates (lines that are within 0.2 Å of each other, a window that is defined in Section 2.3) between masks, and an empirical line list created by our own line-finding algorithm applied to NEID solar spectra. We also used a line list generated by the Vienna Atomic Line Database 3 (VALD3, henceforth referred to as "VALD"; Pakhomov et al. 2019) using the stellar parameters of Eri from Drake & Smith (1993) and a line detection threshold of 0.1 to explore various features and atomic properties of our lines. We used this VALD line list and the nonmagnetically sensitive lines to calculate an expected noise floor for uncorrelated lines (see Section 2.2). The other three lists were combined into one line list in an effort to build as complete as possible of a list of all lines in the spectra: the ESPRESSO K2 mask served as a reference for Eri, the combined ESPRESSO mask list allowed us to probe for any lines that the K2 mask alone might have missed in the NEID Eri spectra, and finally, the empirical line list allowed us to probe the wavelength region beyond 7880 Å (the reddest wavelength detected by ESPRESSO) that is available to us with NEID spectra. We also separately investigated the list of activity-sensitive lines published by W18 (henceforth referred to as the "Wise line list") to verify their results.

Noisy, highly variable lines should evince significantly higher values than the noise floor. We investigate two metrics for the definition of "quiet" lines to calculate an expected noise floor for uncorrelated lines: (1) known, nonmagnetically sensitive solar lines from Altrock et al., and (2) low excitation energy lines from VALD.

We first calculated correlation matrices for each line, then computed an error-weighted mean of each individual correlation across all matrices to generate a "master" noise floor correlation matrix. Thus, these correlation coefficients are the values that we expect, on average, non-activity-sensitive lines to exhibit for each parameter activity index combination, purely from noise, and act as reference thresholds for values we expect to indicate significant correlation. We computed these noise floors using the absolute values of both Pearson's correlation coefficient (ρ) and Kendall's τ coefficient (τ). While we calculated the noise floor for all measured activity indices, we ultimately chose to investigate only the relationship between each line parameter and S-index (see Section 3.2). We therefore display the noise floors for correlation with RV and S-index only, including the errors on each correlation coefficient, in Table 1.

To cross-check metrics of quietness, we compared the lowest variability lines in our empirical sample (see Section 2.3), the magnetically quiet lines from Altrock et al., and the lowest excitation energy lines in VALD. We find that (a) only four out of 13 of Altrock et al.'s quiet lines had VALD excitation energies that were lower than the mean, (b) only one of our 50 empirically lowest variability lines overlapped with Altrock et al.'s list, (c) Altrock et al.'s sample has no overlap with the 50 lowest excitation energies from VALD, and (d) our 50 empirically lowest variability lines has no overlap with the 50 lowest excitation energies from VALD.

The results of these analyses suggest that Altrock et al.'s quiet lines are not the same lines that we found to have the lowest variability in observed line parameters and/or excitation energies from VALD. While noise floors computed from the Altrock et al. sample and VALD are different, we include both thresholds in Table 1 for completeness.

For each line in the compiled line list, our code retrieves all observations, performs the normalization and shifting mentioned in Section 2.1, extracts the RV and all measured activity indices ¹⁵ (Ca ii H & K/S-index, He i D3 line, Na i D1/D lines, Hα, Ca i, Ca ii infrared triplet, Na I near-infrared doublet, and Paschen delta) for each observation, then finds the line in the spectrum and fits and measures the centroid, depth, FWHM, and integrated flux across the line. We fit each line with a Gaussian function using scipy.curve_fit within an initial window of ±0.2 Å around the line center. In order to ensure that the Gaussian function is accurately fitting the line, if the centroid of the initial fit is not within 0.01 Å of the line center, we gradually narrow the window until it is. We discard lines for which the centroid of the fit never reaches within 0.01 Å of the line center at any window within ±0.2 Å, as we are searching for well-defined lines that can be identified and used as references in other observations. We measure the integrated flux by defining a uniform ± 3 km s⁻¹ window around each line center, interpolating the flux over that window, and summing the interpolation. Figure 1 shows an example line and how each parameter is measured. Note that the window over which we calculate integrated flux does not encompass the full line. Our tests showed that using a window of ±3 km s⁻¹ to calculate integrated flux captures enough variability in the flux to be sensitive to shape changes without sacrificing sensitivity by including parts of the wings of each line; i.e., wider windows were less sensitive to our activity indicators. The exception to this were lines that exhibited sensitivity to activity in FWHM and integrated flux only, but not depth (see Section 3). This is most likely due to the fact that integrated flux variability in those lines is driven by FWHM variation, in which case a wider window is more sensitive to that variation. However, in this case, using the window of ±3 km s⁻¹ acts as a filter in which only lines that exhibit FWHM variation strong enough to affect the narrower window are detected as candidates for activity-correlated lines.

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After fitting for and extracting all line features, we save these features along with the measured RV, activity indices, and errors on all parameters into an xarray DataArray object ("cube"). The resulting cube holds the following parameters and corresponding errors: centroid, depth, FWHM, integrated flux, RV, and all measured activity indices for each line and observation. This cube is available on GitHub ¹⁶ with a copy deposited in Zenodo. ¹⁷

The data can then be explored by retrieving any desired line feature or activity index for any line and observation by indexing the cube. The next step in our analysis involves iterating through the cube and correlating each feature with each activity index. However, some of the measured activity indices extracted from the observations were calculated multiple times using different procedures. Before performing the correlations, we combine each of these repeated activity indices into one using an error-weighted mean.

For each line in the cube, we compute a correlation matrix of each line feature (centroid, depth, FWHM, and integrated flux) with the measured RV and combined activity indices (including RV, nine indices in total) for a total of 36 separate correlation coefficients. We calculate these matrices using the absolute values of both ρ and τ. We compute errors on each of these correlation coefficients by calculating the same correlation coefficient within the error bounds of each parameter being correlated (e.g., depth and S-index) and taking the standard deviation of the resulting distribution. We then determine thresholds for correlation in both ρ and τ (this process is detailed in Section 3) and use these to filter through these correlation matrices for lines that we find to be correlated in various parameters.

After our initial filter for activity-sensitive lines, we manually cleaned each list for outliers and telluric-contaminated lines. First, we pruned lines from each line list that either exhibited clear outliers in the plots of their features correlated with the S-index (such that the slope of the correlation was significantly skewed) or where the lines themselves visually exhibited two or more peaks within in the fitting window or were extremely noisy (such that the Gaussian fit did not accurately fit and measure the line's parameters). Examples of the visual criteria we used to prune our line lists are shown in Figure 2. This pruning serves as a vetting of the lines we analyze for only lines that are well defined over time.

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Telluric absorption features caused by Earth's atmosphere tend to vary both in position and strength relative to stellar features. To ensure that our selection of activity-sensitive lines is not affected by these variations, we compared the integrated fluxes of each line to the integrated flux computed across the same window on the telluric model included in the NEID FITS files (TELLURIC). In the current NEID DRP, the telluric model is not normalized to 1, so we first renormalize the telluric model. We then computed an additional "baseline" model: a horizontal line at the maximum value of the telluric model (1 after normalization). Then, for each line, we calculated the absolute value of the difference between the baseline and the actual integrated flux of the line, as well as the absolute value of the difference between the baseline and the integrated flux over the telluric model in the same window. These values represent the deviation from the baseline of the actual observed spectrum and the deviation from the baseline of the telluric model. By dividing the telluric deviation by the observed spectrum deviation, we obtained a 0" percentage of telluric contamination" for each line. We then used a threshold of 1% to filter for telluric-contaminated lines and removed these lines from our line lists.

The first step in our analysis was to investigate and verify the Wise line list to both check our methods against previously studied lines and verify the lines published by W18. These 42 lines were found by W18 to have line core fluxes (the flux at the absolute minimum of the line) that correlated with the S-index (∣τ∣ ≥ 0.5) and were periodic at α Cen B's rotation period, suggesting that these lines trace activity similarly to known activity indices. W18 also investigated the "half-depth range" and "center of mass," which are defined similarly to FWHM and line centroid, and also reported lines whose correlations between half-depth range and S-index were ≥ 0.5, even if their correlations between line core flux and S-index were not. These additional lines still seemed to probe photospheric effects on the spectra, if not as strongly. While these lines did not meet the 0.5 threshold of correlation between line core flux and S-index, all of them did exhibit correlations of at least 0.4. Accordingly, we adopted a threshold of ∣τ∣ = 0.4 to determine whether a line was correlated or not in our parameters. We employ τ as one of our measures of correlation for similar reasons as W18: it probes both the covariance of our parameters with the S-index and the intrinsic measurement noise and additionally allows a direct comparison between our measurements and the results from W18. For robustness, we also employ Pearson's correlation coefficient ρ, a commonly used standard for measuring linear correlation between two variables, as a second metric. Pearson's correlation coefficient is more sensitive to outliers but incorporates the magnitudes of the variables themselves, which makes it a strong indicator of linear correlation between continuous variables, while Kendall's τ coefficient is a rank coefficient but is less susceptible to outliers as a result. We used a correlation threshold of ∣ρ∣=0.5 since tests showed that most lines that exhibited ∣τ∣ ≥ 0.4 also exhibited ∣ρ∣ ≥ 0.5, and vice versa, but some did not. Therefore, filtering for lines that meet both thresholds adds an additional layer of confidence in the lines' correlations.

These thresholds were chosen based on these previous results and used to verify the activity-sensitive lines published by W18, but they are also >3σ, where σ is the error on the noise floor correlations, above the respective ∣ρ∣ and ∣τ∣ noise floor values for correlations between each of our line features (depth, FWHM, and integrated flux) and S-index; see Table 1. We therefore chose to employ these same thresholds for our independent line analysis. While we found that some of the noise floor values for correlations with other activity indices (e.g., for correlation between FWHM and Hα) were ≥ 0.4 or ≥ 0.5, respectively, we eventually chose to focus only on correlations between line parameters and S-index, a decision that is detailed in Section 3.2. With that in mind, we expected our analysis of NEID Eri spectra to show ∣τ∣ ≥ 0.4 and ∣ρ∣ ≥ 0.5 for correlations between depth (analogous to line core flux) and S-index for all lines in the Wise line list.

The results of our analysis of the Wise line list using our partially automated analysis and NEID Eri spectra are shown in Figure 3. For each individual line, we did not expect our calculated values of ∣τ∣ for correlation between depth and S-index to necessarily match the values found by W18, since we are looking at a different time period of Eri data in which activity levels were slightly lower: W18 observed an S-index range of 0.388–0.469 in their archival HARPS data, while our data spanned an S-index range of 0.363–0.394. This small difference might arise from the details of our measurement method or due to true subtle variations from long-term magnetic cycles on the star. However, we did see that for most lines in the Wise line list, our calculated ∣τ∣ values for correlation between depth and S-index were ≥ 0.4 except for five lines: 5108.87 Å (Fe i), 6254.29 Å (Fe i), 6395.38 Å (Fe i), 6432.63 Å (Fe i), and 5421.86 Å (Mn i). These five lines also did not exhibit ∣ρ∣ values ≥ 0.5, as well as one additional line, 5708.58 Å (V I), that had ∣τ∣ > 0.4 but ∣ρ∣ < 0.5. Overall, we found that 37 of the 42 lines published by W18 met the criterion of having a value of ∣τ∣ for correlation between depth and S-index ≥ 0.4 (both our threshold for correlation with ∣τ∣ and the threshold used in W18), while 36 of the 42 lines met both of our criteria (∣τ∣ ≥ 0.4 and ∣ρ∣ ≥ 0.5) for correlation between depth and S-index.

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In addition, we include histograms of the ∣τ∣ and ∣ρ∣ values we calculated for the correlations between depth and S-index for the Wise line list in Figure 3. The ∣ρ∣ values are consistently higher than the ∣τ∣ values for the same correlation in the same line, which supports our choice to use a lower correlation threshold for ∣τ∣ (≥ 0.4) than ∣ρ∣ (≥ 0.5).

To independently identify our new list(s) of activity-sensitive lines, we first combined all three lists described in Section 2 (the ESPRESSO K2 mask, the combined ESPRESSO mask list, and the empirical line list created from NEID spectra) and removed duplicates to produce a single "master" list of lines containing ∼11,500 lines total. We then performed our line-by-line analysis on this master list and using our set of 32 NEID observations of Eri. This resulted in a data cube holding all parameters and measured activity indices for each of our ∼11,500 lines and 32 observations. Using this cube, we then computed the corresponding correlation matrices for each line.

We then filter these correlation matrices for the thresholds that we determined to indicate significant correlation (∣τ∣ ≥ 0.4 and ∣ρ∣ ≥ 0.5). We expect stellar activity to be more likely to cause shape changes in the lines rather than translational shifts. While stellar activity can sometimes cause shape changes that masquerade as translational shifts in the line centroid depending on the method used to measure the centroid, correlating only shape changes with stellar activity avoids the possibility of misinterpreting fits skewed by shape changes for real translational shifts. Moreover, we know that real planetary signals should cause translational shifts but not shape changes. Therefore, we focus on the correlations between depth, FWHM, and integrated flux with activity indices to identify our activity-sensitive lines. We began by filtering only for correlations between depth, FWHM, and integrated flux with the S-index, since the S-index is a widely known and used activity indicator. We filtered the correlation matrices for lines that had ∣τ∣ ≥ 0.4 and ∣ρ∣ ≥ 0.5 for correlations between any of these three parameters with the S-index. This yielded three lists of correlated lines: one that exhibited ∣τ∣ ≥ 0.4 and ∣ρ∣ ≥ 0.5 for correlation between depth and S-index, one that exhibited ∣τ∣ ≥ 0.4 and ∣ρ∣ ≥ 0.5 for correlation between FWHM and S-index, and one that exhibited ∣τ∣ ≥ 0.4 and ∣ρ∣ ≥ 0.5 for correlation between integrated flux and S-index.

We also tried filtering for correlations between each line feature and our other activity indices. While we did find that some lines showed significant correlations between line features and other activity indices (such as Hα), we found that these lines generally did not overlap with the lines whose line features were correlated with the S-index. This could be due to several factors: the lines that we filtered for (well-defined lines that could be fit within a window of ±0.2 Å) could be affected mostly by the particular chromospheric and photospheric changes reflected in the S-index in Eri. Alternatively, the line features that we selected (depth, FWHM, and integrated flux) themselves could be more sensitive to S-index than other activity indices. Since different activity indicators trace different sources of stellar activity, we chose to focus on the lines that we found to be correlated with the S-index for the scope of this paper, as S-index is the most widely known and used activity indicator in stellar activity studies (Wilson 1968; Vaughan et al. 1978) and serves as a useful reference point for probing spectral sensitivity to stellar activity. We encourage future studies to explore lines sensitive to stellar activity through other indices.

After compiling our three lists of lines correlated with the S-index separately in depth, FWHM, or integrated flux, we then cross referenced each of these three lists with the others, as well as all three with each other, to produce four additional lists: lines that exhibited correlation with the S-index in both depth and FWHM, depth and integrated flux, and FWHM and integrated flux, and lines that exhibited correlation with the S-index in all three parameters. Then we removed duplicates from each list, such that our final seven lists are exclusive and do not overlap with each other. Finally, we manually pruned outliers and telluric-contaminated lines from the lists, as detailed in Section 2.4.

This resulted in seven exclusive line lists: lines correlated with the S-index in all three parameters (depth, FWHM, and integrated flux), lines correlated with the S-index in depth and FWHM only, lines correlated with the S-index in depth and integrated flux only, lines correlated with the S-index in FWHM and integrated flux only, and lines correlated with the S-index in depth, FWHM, or integrated flux only. These lists had 9, 55, 79, 6, 167, 131, and 44 lines respectively. Although the number of activity-sensitive lines we identified (even just in depth only) is significantly higher than the 42 lines identified by W18, we note that we investigated a list of ∼11,500 lines while W18 looked at ∼1500 lines, a difference of nearly an order of magnitude. Figure 4 displays the number of lines in each list and how they overlap. Figure 5 shows the range of each line list over NEID's wavelength range; note that the line lists are fairly evenly distributed below ∼6500 Å. While we found a couple of correlated lines in the redder half of NEID's wavelength range, there is a gap between ∼6500 and 9000 Å. This may be due to physical effects that make lines in that range less sensitive to chromospheric variation in the features that we chose, the presence of large telluric water and oxygen absorption bands in this region, biases in the empirical line list that we used, or the sparsity of the empirical line list we used. We present our final seven line lists in Tables 2–8 in the Appendix; the tables contain the full lists for those with fewer than 10 lines and only the first five lines for the others. The remainder of those lists are included in machine-readable tables.

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While all seven of our lists contain lines that are correlated with the S-index in some feature and therefore show some sensitivity to stellar activity, each of these individual lists further probes the activity sensitivity of the lines in unique ways and provides additional insight into the mechanisms of how those lines are affected by and trace stellar activity. Here, we offer an initial probe into what those mechanisms may be; we note that we are not aiming to provide a complete theoretical explanation of the physical behaviors of these lines but rather discuss some possible explanations and directions for further research.

In order to investigate on what timescale our correlations may be acting, we generated periodograms of the measured RVs and S-indices for each observation used in our analysis. We used astropy.timeseries.LombScargle (VanderPlas et al. 2012 Astropy Collaboration et al. 2013; VanderPlas & Ivezic 2015; Astropy Collaboration et al. 2018, 2022) to generate these periodograms, shown in Figure 6 along with their time series. Both periodograms exhibit a peak at ∼11 days, the rotational period of Eri (Howard & Fulton 2016; Mawet et al. 2019). This suggests that the correlations that we see in this paper are tracing stellar activity modulated by the rotational period of the star.

We consider our list of lines that are correlated with the S-index in all three parameters (depth, FWHM, and integrated flux) to be the strongest candidates for activity-sensitive lines. While the other six line lists probe activity sensitivity in unique ways, this line list shows strong correlations in all three of the features we investigated. These lines exhibit variations in depth and FWHM that trace activity and are not only significant enough to independently show correlation with the S-index but also significant enough to concurrently affect integrated flux. Therefore, these lines exhibit shape changes that appear to be the most sensitive to S-index. Notably, when these lines are traced back to their source line list, all are present in multiple ESPRESSO masks for different stellar types. Since we have found these lines to be particularly sensitive to stellar activity, we recommend that these lines be removed from masks used to calculate RVs. Since these lines exhibit concurrent FWHM and integrated flux variation, it is also possible that some of these lines may be "invisibly" blended (i.e., blended lines whose component lines overlap so much they appear to be a single line), and the supposed FWHM variation is actually driven by depth variations in the "invisible" neighboring line. The question of whether any of our lines are blended is investigated in Section 3.4. These FWHM variations could also be due to Zeeman splitting driven by changes in the star's magnetic field strength or asymmetries in the line profile caused by granulation (Gray 2005). The possibility of Zeeman splitting in our lines sensitive to activity in FWHM is further explored in Section 3.4.

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Notably, four out of these nine lines were not previously identified by W18 to be activity sensitive; they represent new, independently identified lines that are sensitive to activity in all three of our measured line parameters. Figure 7 shows plots of the correlations between line depth, FWHM, integrated flux, and S-index for these four lines. The other five out of these nine lines are in the list of activity-sensitive lines published by W18, providing a secondary confirmation and strong evidence that these five lines are sensitive to stellar activity. Figure 8 displays plots showing the correlations between each of the three line features and the S-index for these five lines.

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The lines that are correlated with the S-index in both depth and FWHM, but not integrated flux, are most likely lines whose depths and FWHMs both vary in tandem with activity in such a way that the integrated flux over the uniform window does not vary significantly. Another explanation is that the window over which we calculated integrated flux is wide enough such that the absolute variations in depth and FWHM are too small to translate into flux variations, although since we use a narrow window that generally captures only the core of each line (see Figure 1), this would be most probable only in lines that are particularly narrow such that most of the line is encompassed by the integrated flux window. Since these lines exhibit FWHM variation, this behavior may also be driven by Zeeman splitting or granulation. The concurrent depth variation may be further evidence that these lines are particularly sensitive to granulation in the photosphere, which we would expect to cause spectral lines to be both shallower and broader (Gray 2005). Another feature of this line list is the fact that both the FWHMs and depths of these lines vary with activity, helping to check against the possibility that these lines are tracing some artifact of our continuum normalization scheme in depth variation rather than stellar activity, since the FWHM of the line is less affected by continuum normalization.

The lines correlated with the S-index in both depth and integrated flux, but not FWHM, are most likely lines in which the variations in integrated flux are driven by variations in depth. The absolute variations of these line depths are large enough to affect the integrated flux as well, which manifests in correlations with the S-index in both parameters. The list of lines correlated with the S-index in both FWHM and integrated flux, but not depth, exhibits similar behavior; since integrated flux is partially tied to FWHM as well, these lines have widths that vary significantly enough with activity to affect the integrated flux. As noted in Section 2.3, because of the narrowness of the window we used to calculate integrated flux, these lines are also further filtered for FWHM variations that are particularly significant enough to affect the core/narrow window. Since these lines do not have depths that also vary similarly with activity, the physical processes that drive variations in the line shape caused by stellar activity in these lines affect mostly width and not depth. As with the other lines that exhibit FWHM variation, some possible physical explanations for this are Zeeman splitting or granulation.

For each of the three lists of lines correlated with the S-index in only one feature, the variability in that feature does not affect the other features significantly enough to be correlated in that feature as well. For example, the lines correlated in depth may only exhibit absolute depth variation that is too small to affect the integrated flux over that line but still vary enough to exhibit correlation with the S-index. Note that these lines are also the most sensitive to the effects of continuum normalization. This is an important distinction from other lines that show a correlation in depth and another feature, where the absolute depth variation is most likely either driving variation in the other parameter (i.e., integrated flux) or at least varying in tandem with it (i.e., FWHM). Similar distinctions apply to the lists of lines correlated in FWHM only and integrated flux only. For the lines correlated in FWHM only, these lines may also exhibit absolute FWHM variation that is too small to affect integrated flux but still varies enough to correlate with activity. As noted earlier, this behavior could be caused by Zeeman splitting or granulation. The lines correlated in integrated flux only, but not FWHM or depth, may exhibit variations in depth and FWHM that are not significant enough to show correlation with the S-index but exert a combined effect on integrated flux that is significant enough to show a correlation.

As a first step in investigating the physical processes behind the behavior of our lines, we used the line list generated from VALD using the stellar parameters of Eri from Drake & Smith (1993) and a line detection threshold of 0.1 to determine the species of our lines, investigate if the activity sensitivity of our lines is correlated with Landé factor, explore the possibility of detecting Zeeman line splitting on our data set, and investigate whether or not any lines in our line lists are blends. The species of each line and the atomic transition with which it is associated are listed in Tables 2–8 in the Appendix.

We explored the relationships between the estimated Landé factor from our VALD query and all ∣τ∣ and ∣ρ∣ values for each line across all of our activity-sensitive lines. These relationships measure the dependence of the strength of the line's sensitivity to activity on the line's Landé factor, and we calculate ∣τ∣ and ∣ρ∣ values to quantify each relationship. Similar to Wise et al. (2022), we found no correlation coefficient >0.2 between Landé factor and any ∣τ∣ or ∣ρ∣. This suggests that the strength of a line's sensitivity to activity is not solely dependent on its Landé factor.

We also used VALD to explore the possibility of empirically detecting Zeeman line splitting in our data set, which would enable a physically motivated identification of active lines. To do this, we scrutinized the highest FWHM lines in our data cube, since that is how evidence of line splitting would be captured in automated routines fitting single Gaussians. These lines are typically rejected under suspicion of being blends. However, correlating (1) all the lines and (2) only the 50 lines with the widest FWHMs from our line lists with VALD atomic properties yielded no significant (∣ρ∣ > 0.5, per our threshold) correlation with any properties. Our conclusion, consistent with extant literature, is that the Zeeman signature is difficult to directly measure on individual lines, at these resolutions, on the unpolarized disk-integrated profile of a solar-type star (Semel et al. 2009).

We then investigated our lines for blends. We considered a line to be "invisibly blended" if we found one or more VALD lines within the same ±3 km s⁻¹ window of the line center that we used to calculate integrated flux, a method similar to the one employed by Cretignier et al. (2020) which used a depth contamination threshold to detect blended spectral lines. In order to be self-consistent, we search for contaminants specifically within the same window across which we measured the integrated flux since we expect correlated effects to be contained in that region. The results of this analysis are listed in the tables of our line lists in the Appendix. Notably, we found that none of the lines correlated with the S-index in FWHM and integrated flux only are "invisible" blends, suggesting that the FWHM variation in these lines is driven by true width variation, but several of our other lines correlated with the S-index in other parameters did exhibit one or more VALD lines within ±3 km s⁻¹ of their line centers, including two out of our nine lines correlated with the S-index in all three parameters. Figure 9 plots these two lines along with the VALD wavelengths and depths of the lines with which they are blended. This provides further evidence that the aforementioned lines should not be used for RV measurement.

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As an initial test of how the removal of the lines we identified to be the most sensitive to activity affects measured RVs, we computed the RVs of our NEID Eri observations using three separate masks: (1) the combined ESPRESSO mask that we used in our data cube, (2) just the G2 ESPRESSO mask, and (3) just the K2 ESPRESSO mask. For each mask, we also created a corresponding mask with our most activity-sensitive lines removed. Comparing the RVs measured using the full masks versus the masks with the lines removed resulted in improvements of 2–3 cm s⁻¹. While the improvement is small in this data set, this result further cautions against the use of these lines to measure RVs.