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 galaxys star-formation rate (SFR). We explore this connection at sub-galactic scales spanning ${sim}$7 dex in SFR and ${sim}$8 dex in specific SFR (sSFR). There is good agreement with established relations down to ${rm SFR {simeq} 10^{-3},M_odot , yr^{-1}}$, 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$alpha$ shows the tightest correlation with X-ray luminosity because H$alpha$ emission probes stellar populations with ages similar to HMXB formation timescales, but the H$alpha$-based SFR is reliable only for $rm sSFR{>}10^{-12},M_odot , yr^{-1}/M_odot$.