For the first time, we have systematically explored the population of discrete X-ray sources in the outskirts of early-type galaxies. Based on a broad sample of 20 galaxies observed with Chandra we detected overdensity of X-ray sources in their outskirts. The overdensity appears as halos of resolved sources around the galaxies. These halos are broader than the stellar light, extending out to at least ~ 10 Re (Re is the effective radius). These halos are composed of sources fainter than ~5E38 erg/s, whereas the more luminous sources appear to follow the distribution of the stellar light, suggesting that the excess source population consists of neutron star binaries. Dividing the galaxy sample into four groups according to their stellar mass and specific frequency of globular clusters, we find that the extended halos are present in all groups except for the low-mass galaxies with low globular cluster content. We propose that the extended halos may be comprised of two independent components, low-mass X-ray binaries (LMXBs) located in globular clusters (GCs), which are known to have a wider distribution than the stellar light, and neutron star (NS) LMXBs kicked out of the main body of the parent galaxy by supernova explosions. The available deep optical and X-ray data of NGC 4365 support this conclusion. For this galaxy we identified 60.1+/-10.8 excess sources in the 4-10 Re region of which ~ 40% are located in GCs, whereas ~ 60% are field LMXBs. We interpret the latter as kicked NS LMXBs. We discuss the implications of these results for the natal kick distributions of black holes and neutron stars.
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