The Behavior of Selected Diffuse Interstellar Bands with Molecular Fraction in Diffuse Atomic and Molecular Clouds

We study the behavior of eight diffuse interstellar bands (DIBs) in different interstellar environments, as characterized by the fraction of hydrogen in molecular form [$f$(H$_2$)], with comparisons to the corresponding behavior of various known atomic and molecular species. The equivalent widths of the five "normal" DIBs ($\lambda\lambda$5780.5, 5797.1, 6196.0, 6283.8, and 6613.6), normalized to $E(B-V)$, show a "Lambda-shaped" behavior: they increase at low $f$(H$_2$), peak at $f$(H$_2$) ~ 0.3, and then decrease. The similarly normalized column densities of Ca, Ca$^+$, Ti$^+$, and CH$^+$ also decline for $f$(H$_2$) > 0.3. In contrast, the normalized column densities of Na, K, CH, CN, and CO increase monotonically with $f$(H$_2$), and the trends exhibited by the three C$_2$ DIBs ($\lambda\lambda$4726.8, 4963.9, and 4984.8) lie between those two general behaviors. These trends with $f$(H$_2$) are accompanied by cosmic scatter, the dispersion at any given $f$(H$_2$) being significantly larger than the individual errors of measurement. The Lambda-shaped trends suggest the balance between creation and destruction of the DIB carriers differs dramatically between diffuse atomic and diffuse molecular clouds; additional processes besides ionization and shielding are needed to explain those observed trends. Except for several special cases, the highest $W$(5780)/$W$(5797) ratios, characterizing the so-called "sigma-zeta effect", occur only at $f$(H$_2$) < 0.2. We propose a sequence of DIBs based on trends in their pair-wise strength ratios with increasing $f$(H$_2$). In order of increasing environmental density, we find the $\lambda$6283.8 and $\lambda$5780.5 DIBs, the $\lambda$6196.0 DIB, the $\lambda$6613.6 DIB, the $\lambda$5797.1 DIB, and the C$_2$ DIBs.