We present new Chandra constraints on the X-ray luminosity functions (XLFs) of X-ray binary (XRB) populations, and their scaling relations, for a sample of 38 nearby galaxies (D = 3.4-29 Mpc). Our galaxy sample is drawn primarily from the Spitzer infrared nearby galaxy survey (SINGS), and contains a wealth of Chandra (5.8 Ms total) and multiwavelength data, allowing for star-formation rates (SFRs) and stellar masses (M*) to be measured on subgalactic scales. We divided the 2478 X-ray detected sources into 21 subsamples in bins of specific-SFR (sSFR = SFR/M*) and constructed XLFs. To model the XLF dependence on sSFR, we fit a global XLF model, containing contributions from high-mass XRBs (HMXBs), low-mass XRBs (LMXBs), and background sources from the cosmic X-ray background (CXB) that respectively scale with SFR, M*, and sky area. We find an HMXB XLF that is more complex in shape than previously reported and an LMXB XLF that likely varies with sSFR, potentially due to an age dependence. When applying our global model to XLF data for each individual galaxy, we discover a few galaxy XLFs that significantly deviate from our model beyond statistical scatter. Most notably, relatively low-metallicity galaxies have an excess of HMXBs above ~10^38 erg/s and elliptical galaxies that have relatively rich populations of globular clusters (GCs) show excesses of LMXBs compared to the global model. Additional modeling of how the XRB XLF depends on stellar age, metallicity, and GC specific frequency is required to sufficiently characterize the XLFs of galaxies.
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