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

We present 3 methods for measuring the Galactic dust extinction law slope R_V and a method for quantifying fine structure in dust clouds in the direction of differentially-reddened globular clusters. We apply these methods to the low- latitude globular cluster NGC4833 which displays variable extinction/reddening about a mean <A_V> ~ 1. A set of Monte Carlo simulations is used to characterize the efficacy of the methods. The essence of the first 2 methods is to determine, for an assumed value of R_V, the relative visual extinction delta(A_V) of each cluster horizontal branch (HB) star with respect to an empirical HB locus; the locus is derived from the CMD of a subset of stars near the cluster center in which differential reddening is small. A star-by-star comparison of delta(A_V) from the (B-V,V) CMD with that from the (V-I,V) CMD is used to find the optimal R_V. In the third method, R_V 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 Schlegel et al. (1998) dust maps. The weighted average of the results from 3 methods gives R_V = 3.0 +/- 0.4 for the dust towards NGC4833. The dust fine structure is quantified via the difference, Delta(A_V)_ij = [delta(A_V)]_i - [delta(A_V)]_j, between pairs of cluster HB stars (i,j) as a function of their angular separation r_ij. The variance of Delta(A_V)_ij is found to have a power- law dependence on angular scale: var(r) \propto r^(+0.9 +/- 0.1). This translates into an angular power spectrum P(kappa) \propto kappa^(-1.9 +/- 0.1) for r ~ 1' - 5', where kappa = 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.