From a deep multi-epoch Chandra observation of the elliptical galaxy NGC 3379 we report the spectral properties of eight luminous LMXBs (LX>1.2E38 erg/s). We also present a set of spectral simulations, produced to aid the interpretation of low-count single-component spectral modeling. These simulations demonstrate that it is possible to infer the spectral states of X-ray binaries from these simple models and thereby constrain the properties of the source. Of the eight LMXBs studied, three reside within globular clusters, and one is a confirmed field source. Due to the nature of the luminosity cut all sources are either neutron star binaries emitting at or above the Eddington luminosity or black hole binaries. The spectra from these sources are well described by single-component models, with parameters consistent with Galactic LMXB observations, where hard-state sources have a range in photon index of 1.5-1.9 and thermally dominated sources have inner disc temperatures between ~0.7-1.55 keV. The large variability observed in the brightest globular cluster source (LX>4E38 erg/s) suggests the presence of a black hole binary. At its most luminous this source is observed in a thermally dominated state with kT=1.5 keV, consistent with a black hole mass of ~4 Msol. This observation provides further evidence that globular clusters are able to retain such massive binaries. We also observed a source transitioning from a bright state (LX~1E39 erg/s), with prominent thermal and non-thermal components, to a less luminous hard state (LX=3.8E38 erg/s, Gamma=1.85). In its high flux emission this source exhibits a cool-disc component of ~0.14 keV, similar to spectra observed in some ultraluminous X-ray sources. Such a similarity indicates a possible link between `normal stellar mass black holes in a high accretion state and ULXs.
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