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The $\rho$ Oph molecular cloud is one of the best examples of spinning dustemission, first detected by the Cosmic Background Imager (CBI). Here we present4.5 arcmin observations with CBI 2 that confirm 31 GHz emission from $\rho$ OphW, the PDR exposed to B-type star HD 147889, and highlight the absence ofsignal from S1, the brightest IR nebula in the complex. In order to quantify anassociation with dust-related emission mechanisms, we calculated correlationsat different angular resolutions between the 31 GHz map and proxies for thecolumn density of IR emitters, dust radiance and optical depth templates. Wefound that the 31 GHz emission correlates best with the PAH column densitytracers, while the correlation with the dust radiance improves when consideringemission that is more extended (from the shorter baselines), suggesting thatthe angular resolution of the observations affects the correlation results. Aproxy for the spinning dust emissivity reveals large variations within thecomplex, with a dynamic range of 25 at 3$\sigma$ and a variation by a factor ofat least 23, at 3$\sigma$, between the peak in $\rho$ Oph W and the location ofS1, which means that environmental factors are responsible for boostingspinning dust emissivities locally.

Resolved observations at 31 GHz of spinning dust emissivity variations in $\rho$ Oph