Extinction law in the range 0.4-4.8 $μ$m and the 8620 $Å$ DIB towards the stellar cluster Westerlund 1

Abstract: The young stellar cluster Westerlund 1 (Wd 1: $l$=339.6$^\circ$, b=$-$0.4$^\circ$) is one of the most massive in the local Universe, but accurate parameters are pending on better determination of its extinction and distance. Based on our photometry and data collected from other sources, we have derived a reddening law for the cluster line-of-sight representative of the Galactic Plane (-5$^\circ<$b$<$+5$^\circ$) in the window 0.4-4.8 $\mu$m: The power law exponent $\alpha$=2.13$\pm$0.08 is much steeper than those published a decade ago (1.6-1.8) and our index $R_V$=2.50$\pm$0.04 also differs from them, but in very good agreement with recent works based on deep surveys in the inner Galaxy. As a consequence, the total extinction $A_{Ks}$=0.74$ \pm $0.08 ($A_V$=11.40$ \pm$ 2.40) is substantially smaller than previous results(0.91-1.13), part of which ($A_{Ks}$=0.63 or $A_V$=9.66) is from the ISM. The extinction in front of the cluster spans a range of $\Delta A_V\sim$8.7\,mag with a gradient increasing from SW to NE across the cluster face, following the same general trend of warm dust distribution. The map of the $J-Ks$ colour index also shows a trend of reddening in this direction. We measured the equivalent width of the diffuse interstellar band at 8620 $\AA$ (the "GAIA DIB") for Wd 1 cluster members and derived the relation $A_{Ks}$=0.612 $EW$ $-$ 0.191 $EW^2$. This extends the Munari et al. (2008) relation, valid for $E_{B-V}$ $<$ 1, to the non-linear regime ($A_V$ $>$ 4).