What excites the optical emission in X-ray-selected galaxies?

We present a study of $1347$ galaxies at $z<0.35$ with detected nuclear X-ray emission and optical emission line diagnostics in the Baldwin-Phillips-Terlevich (BPT) diagram. This sample was obtained by cross-matching the X-ray Multi-Mirror Mission Observatory - Newton (XMM-Newton) DR10 catalogue with Sloan Digital Sky Survey (SDSS) DR17 galaxies with well-measured line ratios. The distribution of these sources in the BPT diagram covers all three excitation regimes: Ionized Hydrogen (HII) regions (23\%), `composites' (30\%), and Seyfert galaxies with the low ionization nuclear emission line regions (LINERs) (47\%). In contrast, the fraction of objects classified as active galactic nuclei (AGN) in the SDSS subsample selected for cross-match with XMM-Newton is only 13\%. This fact illustrates that X-ray emission from galaxies commonly points towards the presence of AGN. Our data show, for the first time, a clear dependence of the BPT position on the ratio of the X-ray to $H\alpha$ fluxes. Sources dominated by X-ray emission lie in the Seyfert and LINER regimes of the BPT diagram. Most sources with a low X-ray-to-$H\alpha$-luminosity ratio, $log_{10}(L_X/L_{H\alpha}) < 1.0$, lie in the HII regime. In our sample, there are even 45 galaxies that have $L^{Star}_{XR}/L^{Total}_{Xray}>0.5$. In contrast, the positions of the sample members in the BPT diagram exhibit {no} dependence on the X-ray hardness ratio. Our finding suggests that the X-ray-to-$H\alpha$ ratio can help us to differentiate galaxies whose X-ray flux is dominated by an AGN {from galaxies with} central X-ray binaries and other stellar X-ray sources.