A Chandra Study of The Stellar X-ray Emissivity of Globular Clusters in
  M\,31 Bulge
  The X-ray emissivity (i.e., luminosity per unit stellar mass) of globular
clusters are an important indicator of their dynamical evolution history. Based
on deep archival \textit{Chandra} observations, we report a stacking analysis
of 44 globular clusters (GCs) with 0.5-8 keV luminosities $L_{\rm X} \lesssim
10^{35} {\rm~erg~s^{-1}}$ in the M\,31 bulge, which are supposed to be
dominated by cataclysmic variables (CVs) and coronally active binaries (ABs).
We obtain a significant detection at $5\sigma$ level in 0.5-8 keV band. The
average X-ray luminosity per GC and the average X-ray emissivity are determined
to 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, the
measured emissivity of M31 GCs is also consistent with that of the MW field
stars. Massive GCs have X-ray luminosities which are marginally higher with
less massive ones. Massive GCs also show a lower emissivity ($4.5\pm
2.4\times10^{27}{\rm~erg~s^{-1}~M^{-1}_{\odot}}$) than less massive ones
($15.0\pm 7.8\times10^{27}{\rm~erg~s^{-1}~M^{-1}_{\odot}}$), which is
consistent with the scenario that the (progenitors of) CVs and ABs were more
efficiently destructed via stellar encounters in the more massive GCs. No
dependence of the X-ray emissivity on GC color or on the projected
galactocentric distance of GCs were found.
