Probing the Missing Link between the Diffuse Interstellar Bands and the Total-to-Selective Extinction Ratio $R_V$ $-$ I. Extinction versus Reddening
Kaijun Li Aigen Li F. Y. Xiang


























































 

 

 







































    The Missing Link between DIBs and R_V]
        
        
        
        
        Probing the Missing Link 
        between the Diffuse Interstellar Bands and
        the Total-to-Selective Extinction Ratio R_V– I. Extinction versus Reddening
        Li, Li & Xiang]
                    Kaijun Li^1,2, 
                     Aigen Li^2E-mail: lia@missouri.edu, and
                     F.Y. Xiang^1,2E-mail: fyxiang@xtu.edu.cn
        ^1 Department of Physics, Xiangtan University, 
                          411105 Xiangtan, Hunan Province, China
        ^2 Department of Physics and Astronomy,
                          University of Missouri,
                          Columbia, MO 65211, USA
        firstpage–lastpage2019[
            [
            Received date  / Accepted date 
        ===================================
        
        
        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. We argue that
        the hydrogen column density is 
        a more appropriate normalization
        than extinction and reddening. 
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        ISM: dust, extinction — ISM: lines and bands
                   — ISM: molecules
        
        
        § 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 4000 
        to the near infrared (IR) 
        at λ 1.8	
        (e.g., see Sarre 2006).
        It is frustrating that, 
        except five DIBs were recently
        identified as due to C_60^+,[
           Campbell et al. (2015, 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 9632.1
           (Cordiner et al. 2019),
           supporting the earlier assignment of 
           the 9577 and 9632 DIBs 
           to C_60^+ (Foing & Ehrenfreund 1994) 
           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.
           ]
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        the vast majority of DIBs
        have not yet been firmly identified,
        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 5797) 
        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).
        
        
        Nevertheless, in recent years much progress 
        has been made in detecting a large number of DIBs
        in a wide variety of Galactic interstellar environments,
        ranging from sightlines toward diffuse clouds,
        translucent clouds, molecular clouds,
        bright reflection nebulae, 
        giant H  ii regions,
        massive star forming regions,
        massive young stellar clusters,
        and the Galactic center
        (see Snow & McCall 2006,
        Hobbs et al. 2008, 2009, 
        Cox 2011, Cami & Cox 2014, 
        Krełowski 2018,
        Sonnentrucker et al. 2018).
        The detection of DIBs in extragalactic
        environments has also been reported
        (see Cordiner 2014),
        ranging from the Local Group galaxies
        including the Large and Small Magellanic Clouds 
        (Ehrenfreund et al. 2002; Cox et al. 2006, 2007;
        Welty et al. 2006; van Loon et al. 2013), 
        M31 (Cordiner et al. 2008b, 2011),
        M33 (Cordiner et al. 2008a),
        M 82 (Welty et al. 2014),
        and the Antennae galaxies 
        (Monreal-Ibero et al. 2018),
        to more distant starburst galaxies 
        (Heckman & Lehnert 2000),
        host galaxies of Type Ia supernovae 
        (Sollerman et al. 2005, Cox & Patat 2008,
        Phillips et al. 2013),
        interacting spiral galaxies (Monreal-Ibero et al. 2015),
        intervening absorption systems toward quasars 
        (Ellison et al. 2008) and damped Lyα absorbers 
        at cosmological distances (DLAs; Junkkarinen et al. 2004, 
        York et al. 2006, Lawton et al. 2008).
        
        
        
        
        
        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 et al. 2006, 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 6284) 
        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 6614) 
        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 6614 
        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, York et al. 2014).
        
        
        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).[
          For example, DIBs were observed to be weaker 
          by factors of 2 or more on a per unit reddening
          basis in photon-dominated regions 
          (PDR; see Jenniskens et al. 1994). 
          ]
        It has long been known that the DIB strength 
        correlates with the interstellar reddening
        E(B-V) caused by solid dust particles[
           Also known as the “color excess”,
           the interstellar reddening is defined 
           as the extinction difference between
           two wavebands, e.g., E(B-V) = A_B-A_V
           is the difference between the B-band
           extinction (A_B) at λ≈4400
           and that of the V-band  (A_V) 
           at λ≈5500.
           ]
        — 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 carrier — it 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 R_V≡ A_V/E(B-V),
        the total-to-selective extinction ratio, 
        which characterizes the steepness of
        the UV extinction: for lines of sight with
        a smaller R_V, 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 A_V basis,
        a smaller R_V 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 R_V often subject to 
        a smaller amount of visual extinction
        (A_V), observationally, this has been 
        demonstrated in the σ Sco cloud 
        toward HD 147165 
        (for which R_V≈4.25, Lewis et al. 2005) 
        and the ζ Oph cloud toward HD 149757 
        (for which R_V≈3.08, Fitzpatrick & Massa 2007).
        While the interstellar reddening 
        [E(B-V)≈0.34 for σ Sco
        and E(B-V)≈0.32 for ζ Oph]
        is similar for these two clouds,
        the 5780 DIB of σ Sco
        is substantially stronger than that of ζ Oph.
        However, it is worth noting that the strengths of 
        the 5797 DIB of these very same 
        two clouds are nearly identical
        (Krełowski & 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 R_V, first for the sightlines 
        toward the H  ii region in M17 
        and then for a larger sample 
        (<ref>).
        It is found that the DIB strength, 
        measured as , 
        the EW of a DIB normalized by reddening, 
        is not correlated with R_V.
        This is in contrast to the earlier finding 
        of an anticorrelation 
        made by Ramírez-Tannus et al. (2018)
        who normalized the DIB EW by A_V.
        The results are discussed in <ref>
        and summarized in <ref>.
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        § IS THE DIB STRENGTH RELATED TO R_V?
        
        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, M17 is one of 
        the brightest and best-studied 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 (A_V ∼ 3–15)
        and R_V (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 R_V 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 <ref>,
        we adopt the reddening E(B-V), R_V, 
        and DIB EW data of Ramírez-Tannus et al. (2018) 
        and examine the correlation between the DIB EW
        and R_V^-1 in M17.
        For different lines of sight crossing different
        amounts of interstellar matter, the DIB EW
        is expected to correlate with E(B-V).[
          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^-2^-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).
          ]
        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, , and R_V^-1
        for the lines of sight toward M17.
        As shown in Figure <ref>, 
        for all 14 DIBs at 4430, 5780, 5797, 6196,
        6284, 6379, 6614, 7224, 8620, 9577, 
        9632, 11797, 13176, and 15268,
        the Pearson correlation coefficient r 
        never exceeds 0.50, 
        indicating that  and R_V^-1
        are not correlated.[
           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).
           ]
        This is also supported by the Kendall's τ test
        (see Figure <ref>). 
        
        
        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 R_V 
        have been compiled from the literature 
        by Xiang et al. (2017).
        As illustrated in Figure <ref>,
        no correlation is found between
         and R_V^-1.
        
        
        
        § DISCUSSION
        
        
        
        
        
        
        
        
        Ramírez-Tannus et al. (2018) investigated the correlation
        between , the extinction-normalized DIB EWs,
        and R_V^-1 for the 14 prominent DIBs seen in M17. 
        As reproduced here in Figure <ref>, 
        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, 
         appears to correlate with R_V^-1
        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 
         and R_V^-1 (see <ref>).
        
        
        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 ,  
        Ramírez-Tannus et al. (2018) took the visual
        extinction  as the normalization.
        We argue that the anticorrelation 
        between  and R_V^-1 
        may be related to the fact that,
        for the M17 sample of Ramírez-Tannus et al. (2018), 
        A_V and R_V are themselves correlated.
        
        As shown in Figure <ref>(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 A_V
        and R_V^-1 is apparent.[
           Ramírez-Tannus et al. (2018) determined 
           A_V and E(B-V) by comparing the observed 
           magnitudes of the target stars to the intrinsic 
           ones of the same spectral type, i.e., A_V= V-V_0,
           and E(B-V) = (B-V)-(B-V)_0.
           They derived R_V using the relation reported
           in Fitzpatrick & Massa (2007):
           R_V ≈ -0.26 + 1.19 (A_V-A_K)/(A_B-A_V),
           where A_K is the K-band extinction.
           This explains why the Pearson correlation coefficient
           r between A_V and R_V^-1 is not -1
           which should have been the case if R_V was derived
           directly from A_V/E(B-V).
           ]
        Therefore, even if DIBs do not correlate with R_V at all, 
        the intrinsic anticorrelation between A_V and R_V^-1
        would lead to  to correlate with R_V^-1.
        On the other hand, as demonstrated 
        in Figure <ref>(o), E(B-V) is
        not related to R_V^-1.
        
        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,  or ?
        
        
        
        
        
        
        At a first glance,  appears to be a better
        normalization since  is a direct tracer of 
        the dust column density.
        However,  is a better discriminator 
        of dust size and therefore of 
        (e.g., see Figures 22.7, 22.8 of Draine 2011)
        in the sense that larger grains intend 
        to be “grayer” and have larger R_V.
        
        
        When correlating the DIB EW with ,
        it thus seems more appropriate to normalize
        the DIB EW with  than .
        In this way, any intrinsic relation 
        between E(B-V) and R_V 
        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[
           See, e.g., the University of Chicago DIB database at
            http://dib.uchicago.edu/public/index.html.
           ]
        that the DIB strengths for most of the strong DIBs 
        (e.g., those at 4430, 5780, 5797, 6284, 6613)
        are more strongly correlated with E(B-V) than with A_V. 
        This appears to support  as a more favorable
        normalization than .
        On the other hand, this could also be considered
        as evidence for supporting that DIBs actually 
        physically anticorrelate with ,
        at least through the so-called 
        “skin” or “edge” effect (Snow & Cohen 1974),
        i.e., in dense molecular clouds characterized by 
        larger-than-average R_V 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 R_V typically resides.[
          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, 
          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. 
          ]
        
        
        We argue that neither  nor  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 () is 
        a more appropriate normalization
        than  and  since  directly measures
        the amount of interstellar material along a given sightline,
        while both  and  are actually only used
        as proxies for .
        Unfortunately, in the literature there is no  information 
        for the M17 sightlines of interest here. 
        This prevents us from a quantitative analysis 
        of the relation between  and ^-1.
        
        
        
        
        
        § SUMMARY
        
        
        
        
        
        
        
        We have examined the relation 
        between the DIB strength and R_V
        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 R_V, in contrast to the earlier finding of 
        an anticorrelation between the extinction-normalized 
        DIB EW and R_V.
        
        We argue that, when comparing the DIB EW 
        with , neither  nor  is an ideal 
        normalization since  is usually intrinsically 
        higher for regions with larger  
        (i.e., ∝)
        while  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 , the hydrogen column density. 
        
        
        
        
        § ACKNOWLEDGEMENTS
        
        We thank the anonymous referee
        for his/her very helpful comments and
        suggestions which have considerably 
        improved the presentation of this work.
        KJL and FYX are supported in part by 
        the Joint Research Funds in Astronomy
        (U1731106, U1731107 and U1531108) 
        under cooperative agreement between 
        the National Natural Science Foundation of China 
        and Chinese Academy of Sciences.
        AL is supported in part by NSF AST-1816411.
        
        
        
        
        
        
        
        
        
        
        
        
        
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