Exploring the diffuse interstellar bands with the Sloan Digital Sky Survey

We use star, galaxy and quasar spectra taken by the Sloan Digital Sky Survey to map out the distribution of diffuse interstellar bands (DIBs) induced by the Milky Way. After carefully removing the intrinsic spectral energy distribution of each source, we show that by stacking thousands of spectra, it is possible to measure statistical flux fluctuations at the 10^-3 level, detect more than 20 DIBs and measure their strength as a function of position on the sky. We create a map of DIB absorption covering about 5000 deg² and measure correlations with various tracers of the interstellar medium: atomic and molecular hydrogen, dust and polycyclic aromatic hydrocarbons (PAHs). After recovering known correlations, we show that each DIB has a different dependence on atomic and molecular hydrogen: while they are all positively correlated with N_{H I}, they exhibit a range of behaviours with N_{H_2} showing positive, negative or no correlation. We show that a simple parametrization involving only N_{H I} and N_{H_2} applied to all the DIBs is sufficient to reproduce a large collection of observational results reported in the literature: it allows us to naturally describe the relations between DIB strength and dust reddening (including the so-called skin effect), the related scatter, DIB pair-wise correlations and families, the affinity for σ/ζ-type environments and other correlations related to molecules. Our approach allows us to characterize DIB dependencies in a simple manner and provides us with a metric to characterize the similarity between different DIBs.