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The X-ray emissivity (i.e., luminosity per unit stellar mass) of globularclusters are an important indicator of their dynamical evolution history. Basedon deep archival \textit{Chandra} observations, we report a stacking analysisof 44 globular clusters (GCs) with 0.5-8 keV luminosities $L_{\rm X} \lesssim10^{35} {\rm~erg~s^{-1}}$ in the M\,31 bulge, which are supposed to bedominated by cataclysmic variables (CVs) and coronally active binaries (ABs).We obtain a significant detection at $5\sigma$ level in 0.5-8 keV band. Theaverage X-ray luminosity per GC and the average X-ray emissivity are determinedto be $5.3 \pm 1.6\times10^{33}\rm~erg~s^{-1}$ and$13.2\pm4.3\times10^{27}\rm~erg~{\rm s^{-1}~M^{-1}_{\odot}}$, respectively.Both of these values are consistent with those of MW GCs. What's more, themeasured emissivity of M31 GCs is also consistent with that of the MW fieldstars. Massive GCs have X-ray luminosities which are marginally higher withless massive ones. Massive GCs also show a lower emissivity ($4.5\pm2.4\times10^{27}{\rm~erg~s^{-1}~M^{-1}_{\odot}}$) than less massive ones($15.0\pm 7.8\times10^{27}{\rm~erg~s^{-1}~M^{-1}_{\odot}}$), which isconsistent with the scenario that the (progenitors of) CVs and ABs were moreefficiently destructed via stellar encounters in the more massive GCs. Nodependence of the X-ray emissivity on GC color or on the projectedgalactocentric distance of GCs were found.

A Chandra Study of The Stellar X-ray Emissivity of Globular Clusters in M\,31 Bulge