The Apache Point Observatory Catalog of Optical Diffuse Interstellar Bands

To distinguish DIBs from stellar lines is crucial for all DIB studies. However, even if identified, the stellar lines still hinder the detection of DIBs at adjacent wavelengths. To minimize the impact from stellar lines, repetition in the spectral types of the program stars is (to the maximum degree) avoided in our data sample. Our program stars consist of 6 O-type stars, 14 B-type stars, and 5 A-type stars and include stars known to be main-sequence stars, giants, and supergiants. Twelve out of the 25 program stars show up as spectroscopic binaries in spectra from our limited epochs of observations.¹² For these targets, the Doppler motions also help in identifying the interstellar lines from the stellar lines when examining their spectra. The variety of spectral types reduces the chance of a DIB being repeatedly blocked by the same stellar line, or of a false identification being triggered by misidentified stellar lines.

For a DIB of a given width, the equivalent width (EW) detection limit depends on the S/N of the spectrum. We took the spectrum with the highest S/N from our archive, when multiple choices of stars with similar spectral types, E_B−V, and the ISM conditions along the sight lines are available. The S/N is mainly set by the magnitudes of our stars on the night of observation, the optical efficiency of the telescope and instrument system, and the weather conditions during observations. The average S/N for the final, accumulated spectra of the 25 program stars near 6400 Å is 1750, and the median value is 1300. These values are higher than the typical S/N of ∼1000 in our larger database.

The distances of the program stars affect the volume of space sampled for DIBs. Distances accurate to better than 20% are available from Gaia for 18 of our stars (Gaia Collaboration et al. 2018). Six additional stars have photometric distances (Neckel et al. 1980). For these 24 stars, the average distance is 1000 pc and the median distance is 600 pc. The nearest star is HD 147084 (omi Sco) at 126 pc, and the most distant is HD 190603 at 3948 pc. The only star we could not find a reliable distance for is BD +31°640. The program stars are mostly distributed in the plane of the Milky Way, with a few of the closer stars as far as 20° off the plane. A few of the program stars are in tight groups with possible or confirmed regional differences: Scorpius (3 stars), Cygnus (3 stars), and Perseus (IC 348, five stars; Sonnentrucker et al. 1999).

The reddening is one of our prime considerations during the selection of the program stars. The sight line must be sufficiently reddened to promote the detections of DIBs, especially for the weaker ones. Heavily reddened sight lines are also more likely to contain clouds of different types where new DIBs might be found (Bailey et al. 2015). The reddening of the program sight lines in this work ranges from 0.31 mag (HD 23180/omi Per and HD 175156) to 3.31 mag (VI Cyg 12/Cyg OB2 12); the average and median values are, respectively, 1.02 and 0.67 mag. These reddenings are comparable to the two atlas sight lines used in Hobbs et al. (2008, 2009; E_B−V = 1.11 and 1.27 mag, respectively, which are included and remeasured in this work). There are a few sight lines with E_B−V less than 0.5 mag, which is a necessary compromise to other considerations related to the ultimate comprehensiveness of the catalog, as described below.

The sample includes 17 stars for which the UV extinction curves have been published using the techniques of Fitzpatrick & Massa (1990, 2007). Four of these sight lines (HD 23180, HD 23512, HD 24534, and HD 28482) have unusually steep far-UV rises along with broad 2175 Å bumps. Another two stars (HD 175156 and HD 204827) have steep far-UV rises but with weak bumps of normal width, while HD 147889 has steep far-UV extinction and normal bump. Four sight lines have shallow far-UV extinction combined with weak 2175 Å bumps (HD 37061, HD 37093, HD 148579, and HD 190603). The remaining six sight lines (HD 24912, HD 166734, HD 168625, HD 183143, HD 206267, and HD 281159) have normal far-UV extinction.

Plenty of previous studies have shown that, besides the reddening, other environmental conditions along the sight line also affect the strengths and profiles of some DIBs. Such examples include the lambda-shaped behavior of W(DIBs)/E_B−V when plotted against the fraction of molecular hydrogen¹³ (f_H2; Fan et al. 2017 and references within), the effect of radiative pumping as seen toward Herschel 36 (Oka et al. 2013), and the various indications found in Galazutdinov et al. (2015). The f_H2 value can be used as a general indicator of the average ISM along the sight line (see the discussions in Fan et al. 2017). For the 25 program sight lines of this work, it has a range from 0.02 (HD 37061) to >0.78 (Cernis 52), and its average and median values are 0.43 and 0.44, respectively.

The low abundances of certain atomic and molecular species and anomalously weak DIBs are often attributed to the presence of strong radiation fields (e.g., Savage et al. 1977; Herbig 1993; Welty & Hobbs 2001) because these species are either ionized or dissociated via photon processes. On the other hand, when dense cloud components are involved in the sight line, the strengths of some DIBs are also found to be depressed (e.g., Wampler 1966; Adamson et al. 1991; Fan et al. 2017 and references therein). Such behavior might be related to the competition between radiation field and shielding effect from the ISM cloud, and subsequent ionization via photon processes (see, e.g., Jenniskens & Desert 1994; Sonnentrucker et al. 1997), although other mechanisms such as depletion and hydrogenation/de-hydrogenation may be involved as well (Vuong & Foing 2000).

If the destruction of DIB carriers is governed by photon processes, their fragments might be found in sight lines containing intense radiation fields where photon dissociation takes place efficiently. Meanwhile, the precursors of DIB carriers might be found in dense cloud components. Additional DIB-like features may be found in both cases, and it would be interesting to see whether such features lie in the optical region as new DIBs (Cami et al. 1997), or if certain groups of DIBs show up uniquely under certain sets of interstellar conditions as was seen for the C₂ DIBs (Thorburn et al. 2003; Elyajouri et al. 2018).

The mean intensity of the interstellar radiation field (ISRF) at 1300 Å at the midpoint of each of our sight lines was calculated based on a new evaluation by A. Witt & E. Polster (2019, private communication). The calculation uses Gaia parallaxes (Gaia Collaboration et al. 2018) of the background stars and places them in the integrated field. For the 25 program sight lines, the mean ISRF at 1300 Å averages 3.7 × 10⁻⁶ erg cm⁻² s^-1 Å^-1, and the median value is 1.5 × 10⁻⁶ erg cm⁻² s^-1 Å^-1. Five of the program stars (HD 23512, HD 37903, HD 147084, HD 147889, and HD 148579) stand out as having the highest radiation fields, with an average value of 13 × 10⁻⁶ erg cm⁻² s^-1 Å⁻¹, whereas the average value for the remaining 20 stars is 1.3 × 10⁻⁶ erg cm⁻² s^-1 Å⁻¹. These numbers are meant to be indicative of sight lines that could be subject to strong ISRF, rather than for direct usage since the distance of the interstellar cloud(s) is not considered. But their variety here does indicate the variation of ISRF along our program sight lines, which is the point of the discussion here.

The order-of-magnitude range exhibited by the W(5780)/W(5797) ratio in different sight lines, known as the sigma–zeta effect (named after the early examples σ Sco and ζ Oph; Sneden et al. 1991; Krełowski et al. 1992), is often associated with the strength of the local UV radiation field. In this picture, the carrier of the 5797 DIB is more easily destroyed by UV radiation than the carrier of the 5780 DIB, so that small W(5780)/W(5797) ratios (below ∼2.0) are found for sight lines with weaker UV fields, while sight lines with stronger UV fields have larger ratios (up to ∼10; e.g., Vos et al. 2011; Fan et al. 2017). In our data sample, the W(5780)/W(5797) ratio ranges between 1.1 and 8.9, with a median value of 3.1. Both the overall range and the typical value for these 25 sight lines thus are similar to those seen in the larger data sample of more than 180 sight lines used in Fan et al. (2017),¹⁴ as well as those found in other studies of DIBs in the Galactic ISM—suggesting that these 25 sight lines sample a range in UV field strength.

While we know little in detail about how the UV ISRF affects the DIBs, we do know how it affects some identified molecules. It is thus important to find robust patterns or correlations between those known molecules and DIBs, to better connect the DIBs to known physical quantities, such as the radiation field or the volume density of hydrogen (e.g., the C₂ DIBs and the C₂ molecules; see Thorburn et al. 2003). Our sample is heavily selected toward sight lines with detections of diatomic (CN, CH) or triatomic molecules (${{\rm{C}}}_{3},{{{\rm{H}}}_{3}}^{+}$). Randomly chosen sight lines would largely miss these regions, but those with the highest column densities where DIBs might be easiest to detect, as well as those involving concentrations (highest volume densities) where different kinds of DIBs may be found, are prime targets of this survey. An extensive data collection is maintained by one of us (D.E.W.). These data are obtained from measurement of archival spectra and searches of the literature. Detection of or sensitive limits for CH⁺, CH, C₂, and CN in common are available for 21 stars, as well as two more stars missing only the measurement of C₂. Of these stars, half have sensitive detections of ${{{\rm{H}}}_{3}}^{+}$ and/or C₃. In addition, nine stars in our sample have sensitive detections or limits of CO and six have measurements of OH. Among the 21 sight lines noted above, the column density varies over a factor of 29 for C₂, 50 for CH, 93 for CH⁺, and 251 for CN. The range of variation is much less for ${{{\rm{H}}}_{3}}^{+}$ and OH, but much higher for CO, though there are fewer measurements in all three cases for observational reasons. The ratios of N(CH⁺)/N(CH) and N(CN)/N(CH) both spread over a factor of ∼35 and suggest great variety of the ISM environments found along the program sight lines of this work (Federman et al. 1994; Godard et al. 2014).

Each of the molecules exists under different optimal conditions, which can in principle be discerned by intercomparing observations. For instance, ${{{\rm{H}}}_{3}}^{+}$ is sensitive to the low-energy cosmic-ray flux (Indriolo et al. 2007), CN is thought to exist under high-density conditions (Federman et al. 1994), and CH⁺, while of uncertain environmental factors, evidently forms via nonequilibrium processes (Godard et al. 2012).

Assuming that the denser cloud conditions in the ISM under which these molecules exist may have different morphologies (sheets, filaments, approximate spheres, etc.), the conditions from the outside to the inside of an identifiable region are presumably continuous and give rise to different molecules in different zones from lower to higher densities (Pan et al. 2005; Kos 2017). These different zones may have dimensions of astronomical units to parsecs, and each star probes all the density zones that happen to be present on a given sight line. The zones may be typically similar from one cloud situation to another, and the molecules that exist, regardless of the physical mechanism at play (history, formation, or destruction), presumably have repeatable patterns from one case to another. This is true provided that the various typical zones are present, whereas HD 62542 is an example where the typical "zone" distribution has been altered (Cardelli et al. 1990; Snow et al. 2002; D. E. Welty et al. 2019, in preparation).

Similarly to known molecules, some of the DIB carriers may have related and repeatable patterns as for the C₂ DIBs and the C₂ molecules (Thorburn et al. 2003), and probing the many different zones indicated for diatomic or triatomic molecules may show up with different DIB carriers (Welty et al. 2014; Fan et al. 2017). The wide range of molecular ratios indicated above over our particular sample of 25 stars provides a high probability that if related DIB carriers are present on these sight lines, they could show up, providing only that they are above our detection threshold. It has been suggested that the strongest DIBs may, similarly, show a consistent spatial ordering in different clouds (Fan et al. 2017 and references within). Our sample may therefore include related zones of both DIBs and simple molecules and provide a fairly complete survey of such regions to promote the completeness of the DIB catalog.

Some of the targets in this study were selected owing to their known unusual ISM conditions, as follows.

HD 37061 (NU Ori) is in the H ii region M43, close to the Trapezium stars in the Orion region. The interstellar material is exposed to an intense radiation field from nearby early-type stars. This leads to a very small molecular fraction of hydrogen (f_H2 = 0.02). Many of the strong and well-known DIBs are greatly weakened (compared to E_B−V) or even absent in the sight line, such as DIBs λλ5780.6, 5797.1, 6196.0, and 6613.6 (Fan et al. 2017).

The sight line of HD 24534 (X Per) stands opposite to HD 37061 in terms of the radiation field and shielding of H₂. The high molecular abundances (Mason et al. 1976; Lien 1984a, 1984b, 1984c; Federman & Lambert 1988) give the sight line a rich interstellar molecular spectrum and a large value for f_H2 of 0.76, the second largest in our data sample (Table 1). The strength ratio W(5780)/W(5797) is 1.2 in this sight line, which is one of the smallest ratios ever observed. The UV spectra available for this sight line have yielded measurements of total hydrogen density and the excitation temperatures of CO, C₂, and H₂ molecules (Sonnentrucker et al. 2007).

The W(5780)/W(5797) ratio generally decreases with increasing f_H2, but the sight line of HD 37903 is an extreme outlier in this regard, with a W(5780)/W(5797) ratio of 8.2 at f_H2 = 0.55 (Fan et al. 2017, Figure 5). This B1.5V star is embedded in the front part of the molecular cloud LDN 1630 (Witt et al. 1984). Vibrationally excited H₂ lines have been observed in this sight line (Meyer et al. 2001). However, the radiation input from this early B-type star is not as harsh as that to which the gas around the nearby stars in the Orion Nebula is exposed. This sight line is thus characterized by the unusual combination of an intense radiation field and a fairly high f_H2.

The young stars VI Cyg 5 and VI Cyg 12 belong to a massive OB association containing some 2600 stars (Knödlseder 2000). It is behind the Great Cygnus Rift (Hanson 2003; Guarcello et al. 2012), and the dust in the dark lane results in very large extinction (E_B−V = 1.99 mag for VI Cyg 5 and 3.31 mag for VI Cyg 12). The high column densities of the ISM species and large reddenings along these long sight lines make them perfect targets for detecting weak DIBs from dusty material (Chlewicki et al. 1986). The extinction along the sight lines is similar to typical interstellar material in the diffuse field (Whittet 2015), but the detections of various small molecules, such as C₂, CN, and CO, strongly favor the presence of dense cloud components. Mapping of the emissions from the CO molecules suggests that the molecular gas might have a clumpy distribution in this region (Scappini et al. 2002; Schneider et al. 2006). Thus, there can be complex density structures (Hamano et al. 2016).

The polycyclic aromatic hydrocarbon (PAH) molecules have been thought by some investigators to be promising candidates for DIB carriers (e.g., Gredel et al. 2011), although no matches between the DIBs and PAH absorptions have been found. The simplest PAH molecule, the naphthalene cation (${{\rm{C}}}_{8}{{{\rm{H}}}_{10}}^{+}$), was reported to be detected in the sight line of Cernis 52 (Iglesias-Groth et al. 2008; González et al. 2009), though Searles et al. (2011) and Galazutdinov et al. (2011) showed that the naphthalene lines, if present at the known lab wavelengths, would have too broad and shallow profiles and be hard to detect with echelle spectra with confidence (Hobbs et al. 2008; Sonnentrucker et al. 2018). This issue deserves further study with much better spectra than currently available. A microwave emitting cloud is at a similar distance as this star in the sight line (Cernis 1993). These anomalous microwave emissions (Watson et al. 2005) can be caused by an enhanced presence of small spinning dust grains in the diffuse ISM (Draine & Lazarian 1998) and were suggested by Bernstein et al. (2015) to be associated with DIBs.

Our particular selection of 25 stars thus provides a set of search regions for DIBs that might exist in the ISM, sampling a range of external effects such as varying UV and IR radiation field, properties of interstellar grains, cosmic radiation, stellar outflows, etc. It is to obtain the wide sample of different cloud morphologies and external conditions that we chose this sample and sought to obtain the highest S/N possible.

While this section points out the strengths of our selection of stars in probing a variety of unusual environmental conditions for a DIB search, the sample is nonetheless too limited to satisfy the need to explore all the places where DIBs might appear and also to satisfy the requirement that each DIB feature be detected in at least five sight lines (see Section 5). Some possible additional sites where new DIBs might occur are included in our survey by default. For instance, there are many more clouds without molecules than with molecules, and both are probed by the lines of sight we have emphasized. Likewise, stellar outflows from hot stars and the gas in H ii regions are covered. Meanwhile, comets and circumstellar disks are beyond the scope of this search, as are objects in the high halo of the Galaxy, where the 21 cm high-velocity clouds are found (Wakker & van Woerden 1997; Wakker et al. 2007). These are just three examples of specific easily identified additional locations that should be explored and could shed new light on the origin of the DIBs.

A comparison between the DIBs detected in the two atlas sight lines of HD 183143 and HD 204827 was performed in 2010 by L.M.H. to combine the results. This led to the unpublished Atlas Catalog used as the starting point for our extended DIB survey. This atlas is presented as Column (5) (wavelength) and Column (8) (FWHM) of Table 2. A key step in building this preliminary merged atlas was to identify the common DIBs in the two atlas stars, based primarily on agreement in the central wavelengths.

To begin the new evaluating of each DIB with respect to the expanded list of observed stars, we considered DIBs in the Atlas Catalog whose central wavelengths agreed to within 0.5 Å and whose FWHM agreed to within 50% as referring to the same DIB. Cases of larger differences in wavelength and/or FWHM were examined to see whether they might be due to previously unrecognized blends toward one or both of the atlas stars. As will be discussed in Section 6, such differences are larger than those that might be related to the differences in the interstellar component structure observed in higher-resolution spectra of those two stars, and they can be evaluated by examining the spectra of the other 23 program stars of this work. The most repeatable solution, regarding whether or not to subdivide the absorption profile and how, was deduced and served as the proposed update (see examples below). After that, measurements of the subject feature were made using the semiautomated program arcexam (see Section 4.3) following both the original Atlas Catalog and the proposed tentative update for the APO Catalog of DIBs. Finally, the proposed update was accepted if it provided more consistent measurements and results than the comparison from the two results of the original atlas stars (where the measurements were originally made by hand). We emphasize again that by "being consistent" we refer to a set of measuring techniques (continuum placement and boundary setting) that can be applied to most of the selected spectra. The separation point for possible blended DIBs is not fixed to a particular wavelength, but to a specific feature within the spectrum, such as the inflection point consistent with the independently set continuum level in the region.

Among the updates suggested for the Atlas Catalog of Hobbs et al. (2008, 2009), we found the most common cases to be DIBs with similar wavelengths but quite different FWHM in the atlas stars. Keeping in mind that we do not know the intrinsic profile of any given DIB or the extent to which that profile can vary in different environments, the solution is usually to split the broader DIB into multiple narrower features, each of which has similar profiles in the multiple program spectra being examined for in this work. This is similar to the approach used by Porceddu et al. (1991), who concluded that DIB λ6203.6 was a combination of two separate DIBs. One such example in this work is the DIB at 4501.8 Å. Its FWHMs are reported to be 3.01 and 2.05 Å in HD 183143 and HD 204827, respectively, in the Atlas Catalog (Column (8), index lines 6 and 7 of Table 2). This DIB has a broader profile in HD 183143 than in HD 204827, because of the structure centered at ∼4504.5 Å beside the dominating absorption (top and second spectra of the left panel of Figure 1). A similar structure is in fact seen in the spectrum of HD 204827, but it could be due to the stellar contamination (Hobbs et al. 2008). However, by plotting the same wavelength region in more spectra, we found the same structure in other sight lines whose comparison stars suggest no stellar contamination. An inflection point can be found around 4503.4 Å and can be very close to the continuum level in some cases (e.g., HD 43384, third spectrum in the same panel). Our evaluation of this region thus indicated that splitting this broad feature into two separate DIBs at 4501.5 and 4504.5 Å would be more appropriate. The (average) FWHMs of the two DIBs are 2.53 and 0.83 Å, respectively (Columns (1) and (5), index numbers 6 and 7 of Table 2). This correction could not have been made with evaluation of a single spectrum for this DIB, even if it has a very high S/N.

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Another example involves the two DIBs between 7482 and 7485 Å (Figure 1, right panel). Two narrow DIBs, centered at 7482.9 and 7484.2 Å and with FWHM = 0.61 and 0.55 Å (respectively), were reported for HD 204827. On the other hand, a single, much broader DIB (FWHM = 2.23 Å) was identified at 7483.3 Å toward HD 183143. In the Atlas Catalog, the DIBs at 7482.9 (from HD 204827) and 7483.3 Å (from HD 183143) were considered as a common DIB, despite their very different widths (Columns (4) and (7), index lines 521 and 522 of Table 2). By checking the expanded spectral sample of this work, we found two narrow features with similar central wavelengths and FWHMs to those observed toward HD 204827 in most of the program sight lines. An inflection point is usually found around 7483.5 Å and is also seen in the spectrum of HD 183143, but it did not reach the local continuum level. In Hobbs et al. (2008, 2009), DIBs that appeared to have structure were considered as one DIB if the high point in the feature did not reach the continuum. This convention led to the identification of one broader DIB instead of two narrower ones in HD 183143 for the Atlas Catalog. We concluded that two narrow DIBs at 7482.9 and 7484.2 Å (as identified in HD 204827) are present in this region, and they are found in both atlas stars.

Sometimes, it can be very hard to properly separate an absorption complex without referring to spectra of multiple sight lines. The weaker of two blended DIBs can be easily taken as a substructure or wing of the stronger DIB, especially in highly reddened sight lines, and vice versa. The genuine separation point can also be blurred owing to severe blending, or be hidden in the noise fluctuation or continuum placement uncertainties. For weak DIBs, it is almost impossible to distinguish a real inflection point between two features from noise based on a single spectrum.

On the other hand, the use of multiple program spectra allows us to check the repeatability of profiles of the DIB. If an inflection point is always found at a relatively fixed wavelength in multiple program sight lines, we can then tell that it is real rather than random. This is crucial for resolving the possible structures within a "single DIB" and finding the inflection point to divide them. But we may not be able to confirm whether the structures are blends of DIBs from different carriers, or from multiple transitions of a single carrier (see Figure 1 for examples; note that these structures identified in our spectra are different from the substructures observed in, e.g., DIB λ5797.2 in ultra–high-resolution spectra; Sarre et al. 1995). Such a problem may be settled by the use of spectra of higher resolution and testing the correlations between these structures, or ultimately after specific carriers are assigned to a particular absorption feature. Despite the adjustments made in this work, observations at higher resolution or the use of new techniques may lead to slightly different definitions of these DIBs.

We searched for new DIBs in the selected sight lines following the classical routine (see, e.g., Galazutdinov et al. 2000; Tuairisg et al. 2000; Weselak et al. 2000; Hobbs et al. 2008, 2009). Each program spectrum is examined by eye in a 50 Å wide window using the plotting function of our online database,¹⁵ along with its comparison star, which has similar spectral type, small projected rotational velocity (v sin i), and minimal reddening (Table 1). The spectrum of the comparison star is used as a reference for the stellar lines that could be present in the program star spectrum. The spectrum of a telluric reference star, 10 Lac, from which telluric lines have not been removed (labeled as 10 Lac-tel in our database) is also displayed to provide guidance for locations with possible telluric residuals. Known DIBs are marked with vertical bars at the central wavelengths, and the spectra of HD 183143 and HD 204827 are used for DIB profile reference. If observations on multiple nights were available, these spectra (of each separate night) are displayed along with the sum of all available spectra of the program star.

The primary requirement of the DIB candidates is that the feature should have relatively fixed central wavelength, FWHM, and profiles in all nightly spectra, as well as the co-added final spectrum. For each of the sight lines thus visually examined, the estimated central wavelength and FWHM of all new DIB candidates are recorded in a temporary list.

The possible new DIBs were then cross-matched within all the program sight lines. A semifinal list of new DIB candidates was then compiled for the candidates detected in multiple program sight lines with similar central wavelengths and profiles. Additional new DIB candidates came from the "possible DIBs" in HD 183143 listed in Table 3 of Hobbs et al. (2009). There has been no report that HD 183143 is a binary system (Chentsov 2004; Hobbs et al. 2009), and multiple searches for signs of a binary system were carried out by D.G.Y. in 2014 without success. These "possible DIBs" had about the same width as the rotational widths of stellar lines of HD 183143 and could not be unambiguously confirmed using spectra of HD 183143 alone.

Measurements of the possible new DIBs in this semifinal list were then made with arcexam (see the next section) for all program sight lines. For the final confirmation, we require repeated detections of the new DIB candidates in at least five sight lines (20% threshold) and that their strengths (represented by EW) be positively related to the reddening. Details of these tests are given in Section 5.

All measurements in this work were made using arcexam, a semiautomated routine written by D.E.W. The display of the spectra in arcexam is similar to that of the plotting function of our online database. For each of the measurements, a small section of the program spectrum around the DIB was displayed along with spectral segments from the atlas stars (HD 183143 and HD 204827) and 10 Lac-tel. These spectra were used to provide reference regarding the expected DIB profiles and to identify possible residuals from imperfect telluric line corrections. The spectrum of the comparison star (Table 1) is displayed to identify possible blends from stellar absorptions. A DIB would be deemed unmeasurable and rejected from the measurement if a strong stellar contamination was discerned. Otherwise, if the possible stellar contamination is minor compared to the DIB, we carried out the measurement and marked the measurement with an "s" flag. Such measurements were excluded from the analysis described in the following sections.

An initial automatic fit to the local continuum is provided at the beginning of the measuring process of each DIB. The user can make manual adjustments if the automatic fit is not acceptable (e.g., when points in stellar lines or telluric residuals were used for continuum placement and the outcome continuum contains too much curvature). Then, the extent of the absorption is determined based on the continuum, and again the user can choose to accept or change end points of the DIB absorption vis-à-vis the continuum (D. E. Welty et al. 2019, in preparation).

We assume no specific profile for any of the DIBs being measured, and we use the direct integration under the continuum within the end points as the EW of the DIB. The uncertainty in the EW is then calculated based on the width of the DIB and the fluctuations in the local continuum region on both sides of the DIB integration window (Jenkins et al. 1973; Savage & Sembach 1991), and a 3σ criterion is adopted for DIB detection. If a DIB is detected, arcexam calculates its FWHM¹⁶ and central wavelength, as well as three additional factors labeled as xm2, xm3, and xm4. The three xm-factors are apparent-optical-depth-weighted moments of the profile and are related to the width, skewness, and kurtosis¹⁷ of the absorption profile, respectively. The final measurements for each star were incorporated into a visual presentation of the spectra of all the stars, as described in the Appendix.

For the more general DIB survey project, we have now measured and examined about 250 selected DIBs toward about 180 stars from our current database of about 450 stellar spectra (Thorburn et al. 2003; Friedman et al. 2011; D. E. Welty et al 2019, in preparation). In this process, we visually examine wavelength regions from 5 to 10 times the widths of the DIBs measured for the presence of contaminating stellar lines, contaminating telluric lines, and any other DIB-like features. The measurements are evaluated independently and quantitatively, by intercomparison of the behavior of each DIB in large numbers of stars and by intercomparison of repeated measurements by different measurers (D. G. York et al. 2019, in preparation). For the purpose of this paper, the error of EW can be regarded as at a 5σ level of 6 mÅ for most lines narrower than 1 Å, increasing linearly with line width up to 6 Å, and is uncertain in different ways for broader lines, due to our use of echelle spectra (see also Section 5.2). The smallest 1σ errors for the narrowest lines are typically several tenths of a mÅ. More details of the measuring techniques will be included in upcoming papers (D. E. Welty et al. 2019, in preparation; D. G. York et al. 2019, in preparation).

The efficiency of detection in this work is constrained by different effects and mechanisms. At short wavelength, the poor detection limits are primarily due to the presence of many stellar lines, which is clearest at λ < ∼4500 Å for early B stars and at λ < ∼5000 Å for A stars and becomes progressively more severe for cooler stars. The threshold for DIB detection is also raised by increasing extinction and by decreasing instrumental sensitivity toward shorter wavelengths.

On the other hand, toward the red part of the spectrum (λ > ∼7000 Å), the telluric bands become the major obstacle to DIB detection. The telluric lines are carefully corrected, and we visually compare the residuals as they appear in our co-added and telluric-corrected spectra of the program star with the uncorrected telluric reference spectrum (10 Lac-tel; see Section 4.3). The telluric residuals from slight miscorrections can still contaminate the spectrum in some cases by affecting the placement of the continuum, which in turn contributes significantly to the uncertainties of DIB EWs. At even longer wavelengths (λ > ∼8000 Å), usually beyond the wavelength limits of the APO Catalog of DIBs region, the flat-fielding (and thus the continuum determination) is compromised by the appearance of interference fringes from the CCD detector.

Aiming for a self-consistent catalog, we investigate the repeatability of the central wavelength and width of a given DIB in all sight lines as a measurement of the reality of a given DIB. Note that we have some acceptance for variations in the wavelength, width, and end points for a given DIB, rather than forcing these parameters to a very specific value in different sight lines. This is to account for possible physical effects within a given region caused by local conditions (e.g., Dahlstrom et al. 2013). The detection percentage of an individual DIB is defined as the number of detections of this DIB in our program sight lines, divided by 25, which is the total number of program sight lines selected in this work. The histogram of the detection percentages of DIBs in the Atlas Catalog (the aggregate of the results from Hobbs et al. 2008, 2009) is presented as light-gray bars in Figure 2. We have excluded DIBs that do not agree in wavelength and/or width in the two atlas stars, and the remaining 504 DIBs were used in this analysis. The histogram for DIBs in the new APO Catalog of DIBs is presented as diagonal bars in the same figure.

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The detection percentages for the 504 DIBs from the Atlas Catalog being tested range between 4% and 100%, with the median value of 52% (note that the detection in each of the 25 program sight lines contributes 4% to the detection percentage). However, the variation of the number of points among the bins is rather smooth, and no obvious edge or cutoff can be found in the histogram (gray bars in Figure 2). Many of the DIBs with very low detection rates are seen primarily toward the most reddened stars. We set a minimum number of detections for a DIB to be considered real for the APO Catalog of DIBs at 20%, which would omit ∼5% of the DIBs being studied (see the accumulated curve in Figure 2 with the inverted ordinate at the right side of the figure). The requirement of a minimum number of detections across the 25 stars in the APO Catalog of DIBs is meant to strengthen our confidence that extraneous detections are not included as official DIBs. Although this criterion is somewhat arbitrary, DIBs with only a handful of detections would result in even fewer clean measurements (measurements without contaminations from any sources).

As an example of the type of errors that necessitate a cutoff for the number of stars in which a DIB is detected, consider that "perfect" spectral comparison stars with low reddening and low v sin i are hard to find. Abundance differences between stars may produce cases in which a stellar line appears in the program star but not in its comparison star. In a classical routine the most straightforward conclusion may be that this feature is not, after all, stellar. This choice would then produce a false DIB. Such an error would be recognized when this "false DIB" is not detected in other program stars of different spectral types in this study. Thus, confirmation of each real DIB is essential.

We examined the DIBs with insufficient detections in our more extended database containing measurements of 232 spectra by the date of this work. The number of detections of these DIBs ranges between 5 and 34, corresponding to the detection percentages between 2.2% and 14.7%. These detection percentages are similar to what are reported in this work. Hence, it is possible that some of the features with relatively low detection percentages are genuine but rare DIBs, while the features with very limited detections in the more extended data sample are most likely not real. But for the reason of being consistent within this work, we still consider these DIBs "unconfirmed."

The correlation between the EW of each DIB and the E_B−V of the sight line is also tested. For each of the DIBs being considered, we use all clean measurements made in the 25 program spectra and normalize these measurements by the largest EW we obtained for this DIB. These normalized EWs are fitted to a linear regression with the reddening of the sight lines by the least-squares method considering both the uncertainties in the EWs of the DIBs and those in the E_B−V values. A general growing trend is expected in the comparison, as specified by the interstellar origin of the DIBs. The DIBs being examined showing negative or close-to-zero slopes are considered "unconfirmed." The intercepts of the best-fit lines for DIBs with positive slopes are typically smaller than 0.3, an after-the-fact criterion; there is no requirement regarding how good the correlation is (e.g., as given by the linear correlation coefficient r). In total, 20 DIBs have unsatisfying correlations with E_B−V, many of which have very limited points (typically <5 points). We found no robust negative slopes for any DIB when compared to the reddening (Baron et al. 2015).

The 559 DIBs that satisfy the two criteria (of a minimum detection percentage in the 25 stars, and showing a generally growing trend with E_B−V) are listed in Table 2, which served as our "Apache Point Observatory Catalog of Optical Diffuse Interstellar Bands" (APO Catalog of DIBs). As we are using spectra from multiple sight lines, average values over the detections from the 25 stars are used as the final results for the central wavelengths (Column (2)), FWHMs (Column (6)), and the xm2 factors (Column (9); see Section 4.3). Their corresponding uncertainties are represented by the standard deviation (SD) values, as listed in Columns (3), (4), (7), and (10), where the SD of wavelength is given in the units of Å as well as km s⁻¹. We also report the average normalized EWs (by E_B−V) of each DIB as their typical strength in Column (11). To ensure the quality of the values reported in the APO Catalog of DIBs, we restricted ourselves to only the clean measurements free from any apparent contaminations by stellar lines or telluric lines. The central wavelengths and FWHMs reported in Hobbs et al. (2008, 2009; essentially the Atlas Catalog) are listed in Columns (5) and (8), respectively, for comparison. The numbers of detections, limits (measured but not detected), and rejections (not measured for various reasons) are listed in Column (12). These numbers lead to the two detection percentages reported in Column (13), where the "all detection percentage" is the number of detections divided by 25 (the total number of program sight lines), and the "measured detection percentage" is the number of detections divided by the sum of detections and limits (the measurable portions of the 25 program spectra). The main entries of the new APO Catalog of DIBs are Columns (2), (6), and (9) of Table 2.

However, both the necessary number of confirming detections for a given DIB and the "apparent" growing trend for its EW with reddening are somewhat arbitrary. We therefore list in Table 3 of this work the wavelengths and FWHMs of the features that failed either of the two tests, on the detection percentage and E_B−V correlation. These values are taken from the Atlas Catalog, in case they are later found to be just very rare DIBs. However, it is interesting to note that none of these features are considered "common DIBs" in the Atlas Catalog (see Columns (2) and (3) of Table 3, which indicate the detections of all of these DIBs in only one of the atlas stars). Table 3 also lists the particular criterion a given DIB failed. The broad DIBs listed as possible in Sonnentrucker et al. (2018, hereafter S18) are also given in Table 3 since further confirmation is needed for these DIBs.

The efficiency of the detection of DIBs is subject to various observation factors (Section 4.4). In Figure 3, we summarize the number of DIBs detected in 200 Å wide wavelength windows between 4000 and 9000 Å. The wavelength regions where telluric regions are corrected are noted as diagonal areas in the figure. It is not surprising to find that the most sensitive wavelength region for DIB detections is between approximately 5500 and 7000 Å. The sharp decreases in the number of DIBs at λ > 7500 Å and λ < 5000 Å are partly due to the presence of telluric bands and more stellar lines, and our list could be incomplete in these regions, especially for weak DIBs. But with the high S/N of our spectra, the dearth of DIBs in those regions could also be real. Observations toward fast-rotating (very large v sin i value) early-type stars may help to ease the obstacles from stellar lines, especially for λ < ∼5000 Å, and additional DIBs may still be found with the use of spectra with even higher S/N, observations from space that avoid strong telluric lines (like the A-band), studies such as this one with larger spectral samples, or confirmation of some of the possible candidates listed in Table 3 of this work.

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The identification of broad DIBs has always been a difficult task owing to the placement of continuum and unresolved blends with stellar lines and other DIBs. For a given EW, the DIB profile becomes shallower with increasing width. When the central depth of the profile is too small, the profile is very likely to be hidden in the fluctuations due to noise and difficult to distinguish from the continuum. The use of medium- to high-resolution echelle spectra also contributes to difficulties for the broad DIBs. Spectra extracted from each order suffer a curvature owing to the blaze function of the spectrograph. This leads to the uncertainties in the global continuum, especially when a DIB straddles the joining point between adjacent orders. A threshold of ∼6 Å was adopted by Hobbs et al. (2008, 2009) as the limit for the FWHM for which the continuum can be accurately determined in the ARCES spectra. The spectra used in this paper were taken from the same data collection.

While more narrow DIBs could in principle be discerned in the echelle spectra as used in this work, the detections of broad DIBs are uncertain given the difficulties listed above. Thus, we refer to the broad DIB catalog of Sonnentrucker et al. (2018, S18). This catalog is based on a specially designed homogeneous survey of broad DIBs using R ∼ 500 spectra and contains nine confirmed cases and 11 possible candidates with FWHM > 6 Å.

While examining the 25 program stars of this work, we detected six of the nine confirmed broad DIBs from S18. All of these nine confirmed broad DIBs are included in Table 2, regardless of their numbers of detections in our data sample. We also detected two broad DIBs listed as "possible" in S18, and these are included in Table 2. Thus, 11 DIBs in Table 2 of this paper come uniquely from S18 (two possible broad DIBs plus all the nine confirmed broad DIBs in S18), eight of which are independent detections in this work. The rest of the possible broad DIBs in S18 are summarized in Table 3 of the current paper as possible DIB candidates for completeness.

However, despite the identification of the broad DIBs, their true continua are hard to determine in our spectra. The measured EWs and other parameters (central wavelengths, FWHM, and the xm2 factors) for the broad DIBs are thus subject to larger uncertainties as illustrated in Columns (3), (4), (7), and (10) of Table 2. Such systematic errors have already been suggested by Hobbs et al. (2008, 2009). With more stars in the data sample, we will show in Section 6 that the uncertainty of the DIB central wavelength does indeed increase with the width of its profile.

5.3.1. Atlas Catalog by Hobbs et al.

5.3.2. Other Works

As noted in Section 1, Hobbs et al. (2008, 2009) found a rather different mix of DIBs in the two atlas stars: 165 DIBs uniquely found in HD 183143, 131 DIBs uniquely found in HD 204827, and 249 DIBs common to both. One of the prime motivations for this paper was to see whether additional diversity in the DIB population would be revealed when more stars were investigated.

However, the apparent diversity of the DIB population in the atlas sight lines is less strong than it first appeared in the Atlas Catalog. Among the 559 DIBs, we found 416 detected in both of the atlas sight lines at the 3σ level. There are 56 DIBs uniquely detected toward HD 183143, 75 toward HD 204827, and 12 not detected in either of the two sight lines. The sets of the DIBs detected in the two atlas sight lines are very similar, despite the very noticeable differences in ISM conditions found along them (Hobbs et al. 2008, 2009, and references within). The increase in the fraction of the common DIBs of the two atlas stars might be a combination of the following factors:

• (1)  
  Some DIBs previously considered to be unique to one atlas star appear to be weakly present in the other as well, and some of the possible DIBs found in HD 183143 (Table 3 of Hobbs et al. 2009) were confirmed in HD 204827.
• (2)  
  The adjustment effort of this work unified some previously unique DIBs in the Atlas Catalog. And some common DIBs were divided into multiple DIBs during the same process, resulting in an increase in the number of common DIBs.
• (3)  
  This work failed to confirm 34 unique DIBs from the Atlas Catalog (Table 3). They were not included in the APO Catalog of DIBs, which reduces the difference in the kinds of DIBs detected in the two atlas stars.
• (4)  
  The contribution from the new DIBs found in this work.

Hence, the diversity of DIB populations is related to the DIB catalog being used and may be a matter of relative strength rather than of presence or absence. The large databases now being constructed (e.g., the EDIBLES survey; Cox et al. 2017) and correlations between the DIBs and independently determined physical conditions will shed light on these matters in the future.

6.1.1. Detection Percentages of Individual DIBs

6.1.2. Detection Percentages of Individual Sight Lines

The detection percentage for an individual sight line is defined as the number of DIBs detected in the sight line divided by 559, the number of DIBs listed in the APO Catalog of DIBs. This rate does not account for cases where a DIB was contaminated by telluric or stellar lines (emission or absorption). The Column "Det. Pct.—All" in Table 1 lists the detection percentages for each of the 25 sight lines. In Figure 4, this detection percentage is compared to three quantities that might affect the detectability of the DIBs: the reddening E_B−V as an estimate of the total amount of interstellar material along the sight line, the spectral type of the program star, and the molecular fraction of hydrogen f_H2 representing the overall ISM conditions along the sight line (e.g., Weselak et al. 2004; Vos et al. 2011; Welty 2014).

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It is not surprising that the detection percentage generally increases with the reddening (Figure 4, top panel). For spectra of a given S/N, the weaker DIBs should be more readily detectable in sight lines containing more interstellar material. The steady growth in the detection percentage with increasing reddening can be represented by a linear relationship for the sight lines with E_B−V < ∼2 mag. A slope of 33.1% per magnitude would be obtained for this linear correlation from the top panel of Figure 4. Some of the scatter in this relationship can be ascribed to possible secondary dependences on the spectral type of the background star and/or the molecular fraction f_H2 (see discussion below). For higher reddening, this trend starts to flatten owing to the hard limit of 100% in the detection percentage, so that the detection percentage for the sight line toward VI Cyg 12 (E_B−V = 3.31 mag, the most heavily reddened in our data sample) is similar to that for sight lines with E_B−V ∼ 2 mag. Some DIBs were not detected in those most reddened sight lines, however, due to stellar contamination and/or low S/N at the shorter wavelengths (the latter also a consequence of the significant reddening).

A decreasing trend between the detection percentage of DIBs and the spectral type of the program star can be expected, as a result of the increased density of stellar lines in the spectra of cooler stars. However, this decreasing trend can only be loosely identified in our data (Figure 4, middle panel), as the effects associated with the reddening appear to be stronger. To account for the clear trend between detection percentage and the reddening, we examine the residuals of the detection percentages from the best-fit line described above to look for possible secondary trends. The residuals are then plotted against the spectral type of the program star in Figure 5 (top panel), and the decreasing trend becomes more condensed and easier to identify. While the increased blending with stellar lines in cooler stars appears to have a smaller effect on the detection percentages than the reddening, it is one of the key reasons that most DIB studies have been focused on early-type stars.

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A lambda-shaped behavior is found for the EWs of some well-studied non-C₂ DIBs when compared to the f_H2 value of the sight line (Fan et al. 2017). Their EWs, whether normalized or not by E_B−V, first increase and then decrease with f_H2, with a peak at f_H2 ∼ 0.3. The normalization of the EW reduces the dispersion among the individual sight lines at similar f_H2, which could be due to differences in distance and reddening. But this lambda-shaped behavior is not observed among the C₂ DIBs. These DIBs seem to be stronger in sight lines of higher f_H2, where the C₂ molecules are preferentially detected (Thorburn et al. 2003).

This lambda-shaped behavior is also observed in the direct comparison between the detection percentage and the f_H2 value of the sight line (Figure 4, bottom panel), especially for the decreasing part at larger f_H2, where more of the data points in our small sample are located. The DIB population is dominated by weak features (Figure 2) whose detectabilities are closely related to their strengths. As only a small percentage of the DIBs are C₂ DIBs, the lambda-shaped behavior might characterize the majority of the DIBs. They would be more easily detected when their strength is near the peak value at f_H2 ∼ 0.3, resulting in the lambda-shaped trend observed between the detection percentage and the f_H2 value of the sight line. Note that the above analysis is similar to the direct comparison between f_H2 and the unnormalized EWs of DIBs, without considering the reddening or the spectral type of the background star. Their effects can be clearly seen in some of the outliers in the plot, e.g., HD 204827 at f_H2 = 0.67 and detection percentage of 87.8%. The high detection percentage, compared to other sight lines with similar f_H2 values, could be due to the large reddening and hot background star of this sight line.

To better study the dependence of detection percentage on f_H2, a modified detection percentage is used, which is the number of detected DIBs divided by the total attempts of measurements for the sight line. For example, among the 559 DIBs listed in our APO Catalog, 351 were detected in HD 20041, and 93 were not measured for various reasons. The total attempts of measurements would thus be 559 − 63 = 496, and the corresponding detection percentage is 351/496 = 75.6%. This modification is an attempt to account for the effect from stellar contamination, as the rejected cases are not considered, and the result is given in the Column "Det. Pct—Mea." of Table 1. To address the dependence on E_B−V, these modified detection percentages are then compared to the reddening of the sight lines, and their residuals from the best-fit line are obtained. These residuals are plotted against f_H2 in Figure 5 (bottom panel).

The modified detection percentages reduce the cosmic scatter among sight lines with similar f_H2 values, just as in the comparison between f_H2 and EWs (Fan et al. 2017), as seen more clearly for the declining trend at f_H2 > 0.3. On the other hand, we only have three sight lines with f_H2 < 0.3, and the result may be less well determined for the rising part of the lambda-shaped behavior. To conclude, a larger data sample is needed to study how the detection percentages vary with the f_H2 of a sight line. We would also like to note that sight lines with similar detection percentage may not contain the same kinds or classes of DIBs. There could be hidden patterns regarding the presence of DIBs at different f_H2 levels, but exploring these patterns is beyond the scope of this work.

Two parameters reported in Table 2 are related to the width of the DIB profile: the FWHM and the xm2 factor, which is the apparent-optical-depth-weighted second moment of the DIB profile (Section 4.3). While the FWHM is often used to characterize the widths of features in spectral studies, it often reflects an assumed or fitted line profile (usually Gaussian or Lorenztian). As we made our EW measurements via direct integration, our FWHMs were not obtained by fitting the profiles, but were calculated as the wavelength difference of the two points located at half of the measured maximum depth (Hobbs et al. 2008, 2009). This "full width at half-maxima" is based solely on three points within the DIB profile (the two half-maximum points and the deepest point in the middle of the profile) and is subject severely to the noise fluctuations of these points. On the other hand, the xm2 factor is based on all the points between the integral limits, reducing the effects of the noise.

In Figure 6 (top panel), we compare FWHM to the xm2 factor (both converted to the units of Å) for all the DIBs reported in Table 2. The only obvious outlier is for the DIB at 5779.6 Å (5778.0 Å in Hobbs et al. 2008, 2009), which is the measurement over the whole 5780 Å region. This DIB feature has a complex profile, consisting of a relatively narrow and deep central absorption (the DIB λ5780.6) plus a shallow but extended feature that appears to be due to multiple blended components (Hobbs et al. 2008, 2009; Dahlstrom et al. 2013; Sonnentrucker et al. 2018 and references therein). While xm2 took both the narrow peak and broad base into consideration, the FWHM focused only on the central absorption of this feature, thus leading to a small FWHM at large xm2 value. Other than that, a linear trend is well established, with an intercept near 0.0 and a slope of 0.38. This slope is close to the expected ratio of 0.42 between the xm2 factor and the FWHM for a Gaussian profile. The difference is likely due to the fact that the DIB profiles are not Gaussian and due to the optical depth weighting used in calculating the xm2 factor.

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The main advantage of the xm2 factor should be the improved accuracy, as the use of more points in the spectrum helps to average out (to some degree) the noise fluctuations. We compare the relative uncertainties (the standard deviation error divided by the average value) of the xm2 factor and of the FWHM (Figure 6 bottom panel), and it is clear that the xm2 factor tends to have smaller relative uncertainties. For the measurements made in this work, the xm2 factor may thus be a more accurate descriptor of the width of the DIB profile. The average value of the xm2 factor and its uncertainty for each of the DIBs are listed in Table 2, and we will use this parameter for the width of the profile of each DIB in the following discussion.

For all the program spectra in this work, including the two atlas stars HD 183143 and HD 204827 (Hobbs et al. 2008, 2009), the wavelength scale is set to the interstellar frame. This is achieved by setting the apparently strongest component (in our ARCES spectra) of the interstellar K i line at 7698.9645 Å (Morton 2003) to zero velocity. Slight differences in the central wavelengths (typically several tenths of an angstrom) are found for the common DIBs toward the two atlas stars (except for the DIBs where adjustments were made; see Section 3.1). Such differences are also observed among the 25 sight lines in our data sample. For the 559 DIBs reported in Table 2, the average and median values for the standard deviations of the central wavelengths are 7.5 and 5.8 km s⁻¹, respectively. The histogram is presented in Figure 7 (top left panel).

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The various atomic and molecular species in the ISM often exhibit complex velocity structure when observed at high spectral resolution (e.g., Welty et al. 1994, 1996; Welty & Hobbs 2001; Crane et al. 1995). Spectra of the two atlas stars obtained at resolutions of 175,000–200,000 indicate that the K i λ7698 absorption toward HD 204827 is due to at least eight components over a velocity range of ∼15 km s⁻¹, dominated by two strong components separated by about 3 km s⁻¹ (Pan et al. 2005), and that the K i absorption toward HD 183143 is due to at least 10 components over a velocity range of ∼24 km s⁻¹, dominated by two groups of components separated by ∼15 km s⁻¹ (McCall et al. 2002). Our lower-resolution ARCES spectra exhibit a single, fairly symmetric K i "component" toward HD 204827, but two "components"—of similar depth, separated by 15 km s⁻¹—toward HD 183143 (Hobbs et al. 2008, 2009). The measured wavelength of a given DIB will depend on its relative amounts in each component in which it exists. Such quantities, in general, cannot be determined at our resolution, but the overall effects may be observed. By comparing the measurements reported in Hobbs et al. (2008, 2009), D. G. York et al. (2019, in preparation) found a systematic offset in the central wavelengths that appears to be related to the radial velocities of the K i components in the two sight lines. Considering the large velocity dispersion of the major components in the sight line of HD 183143, the central wavelengths measured in this sight line alone may not provide very precise references for the other sight line. This is another reason for us to report the average wavelength of each DIB in Table 2.

Other than HD 183143, seven of the program stars, HD 20041, HD 43384, HD 166734, HD 168625, HD 190603, HD 194279, and HD 223385, show significant velocity structure in the profiles of K i and Na i absorptions in high-resolution spectra (provided by G. Galazutdinov, the referee of this work). They also have more than one velocity component in our ARCES spectra. Based on the concern of the referee, we redid the calculation of the mean wavelength, FWHM, and the xm2 factor after omitting all eight of these stars, but no significant differences were found in comparing the results of the two samples. As a further check, we compared the central wavelengths and FWHMs of the common DIBs between our APO Catalog of DIBs and the Bondar (2012) atlas, which focused on sight lines lacking evident Doppler splitting in the interstellar K i line in R ∼ 100,000 spectra. The average and median differences of the central wavelengths (APO—Bondar) are both 0.01 Å, and the standard deviation of the difference is 0.11 Å. As for the FWHM ratios (APO/Bondar), the average and median values are 1.15 and 1.09, respectively, with the standard deviation being 0.47. Thus, to use sight lines containing multiple velocity components appears not to have significantly compromised the accuracy of wavelengths. While these components may be reflected in the profiles of some narrow DIBs such as λ6196.0, their effects, in general, are secondary compared to the uncertainty in the measurements (see discussions below).

For comparison purposes, we measured six absorption lines from known ISM species¹⁸ in the program spectra. The standard deviations of their central wavelengths range from 2.5 to 4.8 km s⁻¹, and we take 3.5 km s⁻¹ as the typical value (median value, represented by the dashed line in Figure 6, top left panel), which is about half of the typical DIB value. Thus, the Doppler shift from ISM clouds can only explain part of the uncertainties in DIB wavelengths.

In Figure 7 (the top right and the two bottom panels), three parameters related to the DIB profiles were compared to the fluctuations in their central wavelengths: the xm2 parameter representing the width of the profile, the average normalized EW representing the typical strength of the DIB (Column (10) of Table 2), and an approximate central depth (CD) based on the average normalized EW and the xm2 factor of each DIB. Assuming Gaussian profiles for each DIB, and with the linear relationship between FWHM and the xm2 factor acquired in Section 6.2, we have

$$\begin{eqnarray*}\begin{array}{rcl}\mathrm{EW} & = & \sqrt{2\pi }\ast \mathrm{CD}\ast \mathrm{FWHM}/2.355\\ & = & \sqrt{2\pi }\ast \mathrm{CD}\ast \mathrm{xm}2/(2.355\ast 0.38)\\ \mathrm{CD} & = & 0.36\ast \mathrm{EW}/\mathrm{xm}2.\end{array}\end{eqnarray*}$$

Note that this assumption is not true for our measurements of DIBs (Section 4.3), and this approximate central depth could be different from the real central depths observed in the spectra.

There is a roughly square-root relationship between the xm2 factor and the standard deviation of the central wavelength (Figure 7, top right panel). The central wavelength used here is the weighted average within the integral limits (see Section 4.3) and is thus a weighted sum of N terms (where N is the number of points, proportional to the profile width). The variance of the central wavelength would also be roughly proportional to the number of points, and the corresponding standard deviation will go roughly as the square root of the profile width. The difficulties in determining the accurate central wavelengths for broad DIBs have been noted in Hobbs et al. (2008, 2009). This can be extended to the region of relatively narrow DIBs, which is clearly demonstrated here with more data from multiple sight lines.

On the other hand, the dependences on the EW and the surrogate central depth are not clear, as no obvious trend can be found in either of the bottom panels of Figure 7. For the normalized EW comparison, there is considerable scatter. All of the extreme outliers (labeled) are relatively broad features (Table 2), with xm2 larger than 2.5 Å or FWHM larger than 6 Å. This is also the width limit adopted in Hobbs et al. (2008, 2009) for denoting broad DIBs, and the threshold suggested by Sonnentrucker et al. (2018) beyond which the DIBs are too broad to be studied in echelle spectra. The large fluctuations in their wavelengths are likely due to their width rather than their strength. As for the central depth comparison, we found that DIBs with large fluctuations usually have small central depth, but the scatter of points in this region is very large. These outliers are for the broadest DIBs with medium strength, rather than strong DIBs with average width (Table 2).

Thus, we conclude that the fluctuations in the measured DIB central wavelength among different sight lines are mostly related to measurement uncertainties that depend on the width of the DIB profile; cloud multiplicity can also play a role in some cases. However, we would also like to note that this conclusion is based on the analysis of the 559 DIBs reported in Table 2. Many of these DIBs are weak features with less well-defined continuum than the stronger features. Use of the central wavelengths of DIBs to trace the velocity components in the ISM may become more feasible if the errors obtained for a larger sample of stars are more thoroughly explored. Such a study is underway for several DIBs seen toward several hundred stars (D. G. York et al. 2019, in preparation).