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 ${\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$α$ shows the tightest correlation with X-ray luminosity because H$α$ emission probes stellar populations with ages similar to HMXB formation timescales, but the H$α$-based SFR is reliable only for $\rm sSFR{>}10^{-12}\,M_\odot \, yr^{-1}/M_\odot$.

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