Measuring the Slope of the Dust Extinction Law and the Power Spectrum of Dust Clouds Using Differentially Reddened Globular Clusters

Abstract

We present three methods for measuring the slope of the Galactic dust extinction law, RV, and a method for measuring the fine-scale structure of dust clouds in the direction of differentially reddened globular clusters. We apply these techniques to BVI photometry of stars in the low-latitude Galactic globular cluster NGC 4833, which displays spatially variable extinction/reddening about a mean AV ≈ 1. An extensive suite of Monte Carlo simulations is used to characterize the efficacy of the methods. The essence of the first two methods is to determine, for an assumed value of RV, the relative visual extinction δAV of each cluster horizontal-branch (HB) star with respect to an empirical HB locus; the locus is derived from the color-magnitude diagram (CMD) of a subset of stars in a small region near the cluster center for which differential extinction/reddening are relatively small. A star-by-star comparison of δAV from the (B - V, V) CMD with that from the (V - I, V) CMD is used to find the optimal RV. In the third method RV is determined by minimizing the scatter in the HB in the (B - V, V) CMD after correcting the photometry for extinction and reddening using the dust maps of Schlegel, Finkbeiner, & Davis. The weighted average of the results from the three methods gives RV = 3.0 ± 0.4 for the dust along the line of sight to NGC 4833. The fine-scale structure of the dust is quantified via the difference, (ΔAV)ij ≡ (δAV)i - (δAV)j, between pairs of cluster HB stars (i, j) as a function of their angular separation rij. The variance (mean square scatter) of (ΔAV)ij is found to have a power-law dependence on angular scale: var(r) ∝ rβ, with β = +0.9 ± 0.1. This translates into an angular power spectrum P(κ) ∝ κα, with the index α = -1.9 ± 0.1 for r ~ 1'–5', where κ ≡ 1/r. The dust angular power spectrum on small scales (from optical data) matches smoothly onto the larger scale power spectrum derived from Schlegel et al.'s far-infrared map of the dust thermal emission.