We present a systematic study of the diffuse hot gas around early-type galaxies (ETGs) residing in the Virgo cluster, based on archival {it Chandra} observations. Our representative sample consists of 79 galaxies with low-to-intermediate stellar masses ($M_* approx 10^{9-11}rm~M_odot$), a mass range that has not been extensively explored with X-ray observations thus far. We detect diffuse X-ray emission in only eight galaxies and find that in five cases a substantial fraction of the detected emission can be unambiguously attributed to truly diffuse hot gas, based on their spatial distribution and spectral properties. For the individually non-detected galaxies, we constrain their average X-ray emission by performing a stacking analysis, finding a specific X-ray luminosity of $L_{rm X}/M_* sim 10^{28}{rm~erg~s^{-1}~M_{odot}^{-1}}$, which is consistent with unresolved stellar populations. The apparent paucity of truly diffuse hot gas in these low- and intermediate-mass ETGs may be the result of efficient ram pressure stripping by the hot intra-cluster medium. However, we also find no significant diffuse hot gas in a comparison sample of 57 field ETGs of similar stellar masses, for which archival {it Chandra} observations with similar sensitivity are available. This points to the alternative possibility that galactic winds evacuate the hot gas from the inner region of low- and intermediate-mass ETGs, regardless of the galactic environment. Nevertheless, we do find strong morphological evidence for on-going ram pressure stripping in two galaxies (NGC 4417 and NGC 4459). A better understanding of the roles of ram pressure stripping and galactic winds in regulating the hot gas content of ETGs, invites sensitive X-ray observations for a large galaxy sample.
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