Sub-galactic scaling relations between X-ray luminosity, star formation rate, and stellar mass

X-ray luminosity (L_X) originating from high-mass X-ray binaries (HMXBs) is tightly correlated with the host galaxy's star formation rate (SFR). We explore this connection at sub-galactic scales spanning ∼7 dex in SFR and ∼8 dex in specific SFR (sSFR). There is good agreement with established relations down to SFR ≃ 10^-3 M $_{\odot }\, \rm {yr^{-1}}$ , below which an excess of X-ray luminosity emerges. This excess likely arises from low-mass X-ray binaries. The intrinsic scatter of the L_X-SFR relation is constant, not correlated with SFR. Different star formation indicators scale with L_X in different ways, and we attribute the differences to the effect of star formation history. The SFR derived from H α shows the tightest correlation with X-ray luminosity because H α emission probes stellar populations with ages similar to HMXB formation time-scales, but the H α-based SFR is reliable only for $\rm sSFR{\gt }10^{-12}$ M $_{\odot }\, \rm {yr^{-1}}$ /M_⊙.