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    The community of astronomical strawmen says that \({R(V)}\) should correlate with ISM density – dust grows and/or agglomerates in dense structures. We can look for this correlation in the intersection of the Valencic+ (year) and Jenkins (2009) samples. Valencic+ provides extinction information, including \({R(V)}\), and Jenkins provides ISM density and dust-to-gas ratio information along the same lines of sight. However, while there is a clear correlation between density and the dust-to-gas ratio (Figure \ref{fig:nH_F}), there does not appear to be a correlation between density and \({R(V)}\) (Figure \ref{fig:lognH_RV}).

    By looking at Eddie’s map of \({R(V)}\) over a large area, we can generate the hypothesis that there’s not a clear density-\({R(V)}\) correlation because much of the \({R(V)}\) variation in Eddie’s map happens on much larger spatial scales than the angular size of a dense ISM structure. There could be a density-\({R(V)}\) relationship on top of this large-scale variation, but there isn’t a clear \({E(B-V)}\) vs. \({R(V)}\) correlation because the large-scale variation has a higher magnitude.

    So, if we want to look for an \({E(B-V)}\) vs. \({R(V)}\) correlation, we need to filter out the large scale structure. One way to do this is to look at differences in \({E(B-V)}\) vs. differences in \({R(V)}\) between pairs of sightlines as a function of the sightlines’ separations.

    \label{fig:nH_F} The mean dust-to-gas ratio along a sightline (y-axis) as encoded by the \(F*\) parameter from Jenkins (2009) vs. the mean volume density of atomic and molecular hydrogen along the same sightline. \(F*=0\) and \(F*=1\) correspond to dust-to-gas mass ratios of around 1/250 and 1/100, respectively. This is a recreation of Figure 16 from Jenkins (2009).

    \label{fig:lognH_RV} \({R(V)}\) from Valencic+ (y-axis) vs. log of the mean density along the same sightline from Jenkins 2009 (x-axis). While the dust-to-gas ratio is clearly directly correlated with volume density (see previous figure), the dust properties traced by \(R(V)\) apparently are not.