Probing the Missing Link between the Diffuse Interstellar Bands and the Total-to-Selective Extinction Ratio $R_V$ $-$ I. Extinction versus Reddening

The carriers of the still (mostly) unidentified diffuse interstellar bands (DIBs) have been a long-standing mystery ever since their first discovery exactly 100 years ago. In recent years, the ubiquitous detection of a large number of DIBs in a wide range of Galactic and extragalactic environments has led to renewed interest in connecting the occurrence and properties of DIBs to the physical and chemical conditions of the interstellar clouds, with particular attention paid to whether the DIB strength is related to the shape of the interstellar extinction curve. To shed light on the nature and origin of the DIB carriers, we investigate the relation between the DIB strength and $R_V$, the total-to-selective extinction ratio, which characterizes how the extinction varies with wavelength (i.e., the shape of the extinction curve). We find that the DIB strength and $R_V$ are not related if we represent the strength of a DIB by its reddening-normalized equivalent width (EW), in contrast to the earlier finding of an anticorrelation in which the DIB strength is measured by the extinction-normalized EW. This raises a fundamental question about the appropriate normalization for the DIB EW.


INTRODUCTION
The enigmatic "diffuse interstellar bands" (DIBs) are a set of over 600 non-stellar absorption features observed in starlight crossing interstellar clouds, spanning the wavelength range of the near ultraviolet (UV) at λ > ∼ 4000Å to the near infrared (IR) at λ < ∼ 1.8 µm (e.g., see Sarre 2006). It is frustrating that, except five DIBs were recently identified as due to C + 60 , 1 the vast majority of DIBs have not yet been firmly identified, ⋆ E-mail: lia@missouri.edu † E-mail: fyxiang@xtu.edu.cn 1 Campbell et al. (20151 Campbell et al. ( , 2016 and Walker et al. (2015) measured the gas-phase spectrum of C + 60 at ultra-low temperatures and found that the spectral characteristics of gas-phase C + 60 are in agreement with five DIBs at 9348.4, 9365.2, 9427.8, 9577.0, and 9632.1Å (Cordiner et al. 2019), supporting the earlier assignment of the 9577 and 9632Å DIBs to C + 60 ) which was based on the absorption spectrum recorded in a neon matrix (Fulara et al. 1993). Omont (2016) further proposed that fullerenes of various sizes with endohedral or exohedral inclusions and heterofullerenes could be viable DIB carrier candidates.
despite an extensive observational, experimental, theoretical and computational exploration of an entire century -it has been exactly 100 years since the first serendipitous detection of two DIBs (at 5780 and 5797Å) by Mary Lea Heger, then a graduate student at Lick Observatory (see Heger 1922), although their interstellar origin was not firmly established until 15 years later by Merrill (1934).
Motivated by the ubiquitous detection of DIBs in various Galactic and extragalactic environments, in recent years much effort has been devoted to exploring whether and how the presence, strengths, and spectral profiles of DIBs are affected by the physical and chemical conditions of the interstellar environments (e.g., see Ruiterkamp et al. 2005, Cox & Spaans 2006, Vos et al. 2011, Xiang et al. 2011, Kos & Zwitter 2013, Clayton 2014, Sonnentrucker 2014). There is a rich literature on DIB profiles and their variations in different lines of sight. A number of the DIBs (including those at 5780, 5797, and 6284Å) seen toward stars in the Orion Trapezium region are both broadened and shifted to the red (Porceddu et al. 1992). Blueshifted DIBs (e.g., those at 5797 and 6614Å) which are broader than usual and whose red wings are more prominent than usual are seen toward the runaway star HD 34078 (Galazutdinov et al. 2006) which is currently interacting with a diffuse molecular cloud (Boissé et al. 2009). Anomalously broad DIBs at 5780, 5797, 6196, and 6614Å with remarkable extended tails toward red are found in absorption along the line of sight to Herschel 36, an O star multiple system illuminating the bright Hourglass nebula of the H ii region Messier 8 (Dahlstrom et al. 2013. In addition to the environmental variations of the DIB spectral profiles, the strength of a DIB, as measured by its equivalent width (EW), is also known to vary significantly from sightline to sightline. This variation appears to depend on the local environmental conditions (see Cami & Cox 2014 and references therein). 2 It has long been known that the DIB strength correlates with the interstellar reddening E(B − V ) caused by solid dust particles 3 -as a matter of fact, this correlation was one of the principal arguments supporting an interstellar origin of DIBs (Merrill 1934). Although the correlation between the DIB strength and the interstellar reddening does not necessarily mean that the interstellar reddening and DIBs share a common carrierit may merely reflect the fact that the DIB carriers are well mixed with dust and gas in interstellar clouds so that both the amount of DIB carriers and the quantity of interstellar dust grains are linearly proportional to the amount of interstellar gas along the line of sight. Nevertheless, the DIB carriers and interstellar dust grains could be physically related, e.g., the latter could protect the former from photodestruction by shielding the former from the UV starlight.
In this context, it would be of great value to explore how the DIB strength varies with RV ≡ AV /E(B − V ), the total-to-selective extinction ratio, which characterizes the steepness of the UV extinction: for lines of sight with a smaller RV , the UV extinction often increases more steeply with λ −1 , the inverse wavelength (e.g., see Figures 4,6 of Cardelli, Clayton & Mathis 1989, hereafter CCM). On a per unit AV basis, a smaller RV implies a more severe attenuation of the UV radiation and thus a more effective protection of the DIB carriers. While this scenario is complicated by the fact that those lines of sight with a smaller RV often subject to a smaller amount of visual extinction (AV ), observationally, this has been demonstrated in the σ Sco cloud toward HD 147165 (for which RV ≈ 4.25, Lewis et al. 2005) and the ζ Oph cloud toward HD 149757 (for which RV ≈ 3.08, Fitzpatrick & Massa 2007). While the interstellar reddening Oph] is similar for these two clouds, the 5780Å DIB of σ Sco is substantially stronger than that of ζ Oph. However, it is worth noting that the strengths of the 5797Å DIB of these very same two clouds are nearly identical (Kre lowski & Westerlund 1988). The effects of the UV starlight on the DIB strength has also been observationally studied by Cami et al. (1997) and Sonnentrucker et al. (1997) for a larger number of DIBs and a larger sample of sightlines.
To shed light on the physical and chemical nature of the still unidentified DIB carriers, we have initiated a program to explore the possible relations between the DIB strengths and the various interstellar parameters (e.g., extinction, UV radiation, and gas densities). In this work, we quantitatively examine how DIBs vary with RV , first for the sightlines toward the H ii region in M17 and then for a larger sample ( §2). It is found that the DIB strength, measured as EW/E(B − V ), the EW of a DIB normalized by reddening, is not correlated with RV . This is in contrast to the earlier finding of an anticorrelation made by Ramírez-Tannus et al. (2018) who normalized the DIB EW by AV . The results are discussed in §3 and summarized in §4.

IS THE DIB STRENGTH RELATED TO RV ?
Following Ramírez-Tannus et al. (2018), we first consider the prominent DIBs seen in M17, a giant H ii region. Located in the Carina-Sagittarius spiral arm of the Galaxy at a distance of ∼ 1.98 kpc, M17 is one of the brightest and beststudied giant H ii region (Hoffmeister et al. 2008, Povich et al. 2009, Ramírez-Tannus et al. 2017. M17 is selected for this study because the sightlines toward M17 exhibit a significant spread in both extinction (AV ∼ 3-15 mag) and RV (∼ 2.8-5.5). Hanson et al. (1997) investigated the behavior of the DIBs along the sightlines toward M17, over such a wide extinction range. They found that the DIBs show little change in spectral shape. Ramírez-Tannus et al. (2018) obtained the 300-2500 nm spectra of 11 pre-main sequence OB stars with the X-shooter Spectrograph mounted on the ESO Very Large Telescope (VLT). They determined the reddening, visual extinction, and RV for the lines of sight toward these stars. They also measured the EWs of 14 prominent DIBs for most of these sightlines. As tabulated in Table 1, we adopt the reddening E(B − V ), RV , and DIB EW data of Ramírez-Tannus et al. (2018) and examine the correlation between the DIB EW and R −1 V in M17. For different lines of sight crossing different amounts of interstellar matter, the DIB EW is expected to correlate with E(B −V ). 4 Therefore, to cancel out the common correlation between the DIB EW and E(B − V ) among the various lines of sight, we normalize the DIB EWs by E(B − V ). We perform a correlation analysis between the reddening-normalized EWs of 14 DIBs, EW/E(B − V ), and R −1 V for the lines of sight toward M17. As shown in Figure 1, for all 14 DIBs at 4430, 5780, 5797, 6196, 6284, 6379, 6614, 7224, 8620, 9577, 9632, 11797, 13176, and 15268Å, the Pearson correlation coefficient r never exceeds 0.50, indicating that EW/E(B − V ) and R −1 V are not correlated. 5 This is also supported by the Kendall's τ test (see Figure 1).
We have also performed the Pearson correlation analysis and the Kendall's τ test for six of these 14 DIBs for a large sample of 97 sightlines of which both EWs and RV have been compiled from the literature by Xiang et al. (2017). As illustrated in Figure 2, no correlation is found between EW/E(B − V ) and R −1 V .

DISCUSSION
Ramírez-Tannus et al. (2018) investigated the correlation between EW/AV , the extinction-normalized DIB EWs, and R −1 V for the 14 prominent DIBs seen in M17. As reproduced here in Figure 3, it is apparent that, with the Pearson correlation coefficient r exceeding 0.80 for five of the 14 DIBs and exceeding 0.60 for 10 of the 14 DIBs, EW/AV appears to correlate with R −1 V for the vast majority of the DIBs seen in M17. This is in stark contrast to our finding that there seems to be no correlation between EW/E(B − V ) and R −1 V (see §2).
The major difference between our approach and that of Ramírez-Tannus et al. (2018) lies in the normalization: while we normalize the DIB EW by reddening E(B − V), Ramírez-Tannus et al. (2018) took the visual extinction AV as the normalization. We argue that the anticorrelation between EW/AV and R −1 V may be related to the fact that, for the M17 sample of Ramírez-Tannus et al. (2018), AV and RV are themselves correlated. As shown in Figure 3(o), with a Pearson correlation coefficient of r ≈ −0.84 and a Kendall correlation coefficient of τ ≈ −0.79 and a corresponding probability p ≈ 0.0065 of a chance correlation, an anticorrelation between AV and R −1 V is apparent. 6 Therefore, even 4 In the ISM, dust and gas are well mixed as indicated by the relatively constant gas-to-extinction ratio, N H /E(B − V ) ≈ 5.8 × 10 21 H cm −2 mag −1 (Bohlin et al. 1978). Therefore, any two interstellar quantities that depend on either the amount of dust or the amount of gas in the line of sight will tend to, to some extent, correlate with each other. To explore the correlation between the DIB strength and the extinction parameters, the common dependence on the reddening E(B − V ) has to be cancelled out (e.g., see Witt et al. 1983, Xiang et al. 2011 Although somewhat arbitrary, we suggest that, for two variables to be considered to be (even weakly) correlated, the Pearson correlation coefficient (r) should at least exceed 0.5 (e.g., see https://explorable.com/statistical-correlation). if DIBs do not correlate with RV at all, the intrinsic anticorrelation between AV and R −1 V would lead to EW/AV to correlate with R −1 V . On the other hand, as demonstrated in Figure 1 V . This raises a fundamental question: when one explores the possible relations between DIBs and other interstellar parameters or among different DIBs, what is a more appropriate normalization, AV or E(B − V)? At a first glance, AV appears to be a better normalization since AV is a direct tracer of the dust column density. However, E(B − V) is a better discriminator of dust size and therefore of RV (e.g., see Figures 22.7, 22.8 of Draine 2011) in the sense that larger grains intend to be "grayer" and have larger RV . When correlating the DIB EW with RV , it thus seems more appropriate to normalize the DIB EW with E(B − V) than AV . In this way, any intrinsic relation between E(B − V ) and RV would have been cancelled out. Also, it is well known and can be easily verified with the DIB EW data available in the public domain 7 that the DIB strengths for most of the strong DIBs (e.g., those at 4430, 5780, 5797, 6284, 6613Å) are more strongly correlated with E(B − V ) than with AV . This appears to support E(B − V) as a more favorable normalization than AV . On the other hand, this could also be considered as evidence for supporting that DIBs actually physically anticorrelate with RV , at least through the socalled "skin" or "edge" effect (Snow & Cohen 1974), i.e., in dense molecular clouds characterized by larger-than-average RV values, DIBs are weak or even completely absent at the cloud cores but grow in strength toward the cloud edges. This is possibly caused by the accretion of the DIB carriers onto the surfaces of large dust grains under conditions which favor dust growth in dense molecular clouds. As a result, DIB carriers are relatively under-abundant and thus many DIBs exhibit smaller strengths in these environments, i.e., places where dust with larger values of RV typically resides. 8 We argue that neither AV nor E(B − V) is an accurate tracer of the dust column density since both quantities involve the properties (e.g., size, composition) of the dust along the line of sight which exhibit regional variations. We suggest the hydrogen column density (NH) is a more appropriate normalization than AV and E(B − V) since NH directly measures the amount of interstellar material along a given sightline, while both AV and E(B − V) are actually only used as proxies for NH. Unfortunately, in the literature there is no NH information for the M17 sightlines of interest This explains why the Pearson correlation coefficient r between A V and R −1 V is not −1 which should have been the case if R V was derived directly from A V /E(B − V ). 7 See, e.g., the University of Chicago DIB database at http://dib.uchicago.edu/public/index.html. 8 Indeed, Hansen et al. (1997) have already noted that the DIBs observed in the direction of M17, over the extinction range of A V = 3-10 mag, does not show any significant increase in strength. They suggested that either the DIB features are already saturated at a small value of A V , or that the interstellar material local to M17, where the increased extinction is being traced, does not contain DIB carriers.
here. This prevents us from a quantitative analysis of the relation between EW/NH and RV −1 .

SUMMARY
We have examined the relation between the DIB strength and RV which characterizes how the extinction varies with wavelength, first for 14 DIBs in eight lines of sight toward young OB stars in the giant H ii region M17 and then for six of these 14 DIBs in a large sample of 97 lines of sight compiled from the literature. It is found that the DIB strength, measured as the reddening-normalized DIB EW, is not correlated with RV , in contrast to the earlier finding of an anticorrelation between the extinction-normalized DIB EW and RV . We argue that, when comparing the DIB EW with RV , neither AV nor E(B − V) is an ideal normalization since AV is usually intrinsically higher for regions with larger RV (i.e., AV ∝ RV ) while E(B − V) preferably probes the surface layers of dense molecular cloud cores. We suggest that the really appropriate normalisation for the DIB EW, on physical grounds, would be NH, the hydrogen column density.