  We investigate X-ray binary (XRB) luminosity function (XLF) scaling relations
for Chandra detected populations of low-mass XRBs (LMXBs) within the footprints
of 24 early-type galaxies. Our sample includes Chandra and HST observed
galaxies at D < 25 Mpc that have estimates of the globular cluster (GC)
specific frequency (SN) reported in the literature. As such, we are able to
directly classify X-ray-detected sources as being either coincident with
unrelated background/foreground objects, GCs, or sources that are within the
fields of the galaxy targets. We model the GC and field LMXB population XLFs
for all galaxies separately, and then construct global models characterizing
how the LMXB XLFs vary with galaxy stellar mass and SN. We find that our field
LMXB XLF models require a component that scales with SN, and has a shape
consistent with that found for the GC LMXB XLF. We take this to indicate that
GCs are "seeding" the galactic field LMXB population, through the ejection of
GC-LMXBs and/or the diffusion of the GCs in the galactic fields themselves.
However, we also find that an important LMXB XLF component is required for all
galaxies that scales with stellar mass, implying that a substantial population
of LMXBs are formed "in situ," which dominates the LMXB population emission for
galaxies with SN < 2. For the first time, we provide a framework quantifying
how directly-associated GC LMXBs, GC-seeded LMXBs, and in-situ LMXBs contribute
to LMXB XLFs in the broader early-type galaxy population.
