The Multi-wavelength Extinction Law and its Variation in the Coalsack Molecular Cloud Based on the Gaia, APASS, SMSS, 2MASS, GLIMPSE, and WISE Surveys

Abstract: Accurate interpretation of observations relies on the interstellar dust extinction law, which also serves as a powerful diagnostic for probing dust properties. In this study, we investigate the multi-wavelength extinction law of the quiescent, starless molecular cloud Coalsack and explore its potential variation across different interstellar environments: the surrounding region, the nearby high Galactic latitude region, the inner dense region, and the inner diffuse region. Using a sample of 368,524 dwarf stars selected from Gaia DR3 as tracers, we establish the effective temperature Teff-intrinsic color relations to derive the intrinsic color indices and optical-mid-infrared (MIR) color excess (CE) for 20 bands. Linear fits to the CE-CE diagrams provide color excess ratios (CERs), which are subsequently converted into relative extinction. The resulting extinction curves for different environments exhibit steep slopes in the near-infrared (NIR) and flat profiles in the MIR. In the optical-NIR range, the Coalsack extinction law is consistent with R_V = 3.1 while in the MIR it follows R_V= 5.5 similar to the results of active star-forming clouds. At an angular resolution of 1.3', our extinction map reveals fine cloud structures. No correlation is found between R_V and E(B-V) for E(B-V) > 0.3 mag, implying a uniform optical extinction law in the Coalsack cloud. The derived average R_V value is 3.24.