SIMBAD references

We present three methods for measuring the slope of the Galactic dust extinction law, R_V, 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 <A_V>~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 R_V, the relative visual extinction δA_Vof 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 δA_Vfrom 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_Vis 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 R_V=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, (ΔA_V)_ij≡(δA_V)_i-(δA_V)_j, between pairs of cluster HB stars (i, j) as a function of their angular separation r_ij. The variance (mean square scatter) of (ΔA_V)_ijis found to have a power-law dependence on angular scale: var(r)∝r^β, with β=+0.9±0.1. This translates into an angular power spectrum P(κ)∝κ^α, 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.