Angular momentum and local gravitational instability in galaxy discs: does $Q$ correlate with $j$ or $M$?

We introduce a new diagnostic for exploring the link between angular momentum and local gravitational instability in galaxy discs. Our diagnostic incorporates the latest developments in disc instability research, is fully consistent with approximations that are widely used for measuring the stellar specific angular momentum, $j_{\star }=J_{\star }\mathrm{/}{M}_{\star }$, and is also very simple. We show that such a disc instability diagnostic hardly correlates with $j_{\star }$ or $M_{\star }$, and is remarkably constant across spiral galaxies of any given type (Sa$\text{\hspace{0.17em}⁣}-\text{\hspace{0.17em}⁣}$Sd), stellar mass ($M_{\star }={10}^{9.5}\text{\hspace{0.17em}⁣}-\text{\hspace{0.17em}⁣}{10}^{11.5}{\mathrm{M}}_{\odot }$) and velocity dispersion anisotropy (${\sigma }_{z\star }\mathrm{/}{\sigma }_{R\star }=0\text{\hspace{0.17em}⁣}-\text{\hspace{0.17em}⁣}1$). The fact that $M_{\star }$ is tightly correlated with star formation rate ($\mathrm{S}\mathrm{F}\mathrm{R}$), molecular gas mass ($M_{\mathrm{m}\mathrm{o}\mathrm{l}}$), metallicity ($12+\log \mathrm{O}\mathrm{/}\mathrm{H}$) and other fundamental galaxy properties thus implies that nearby star-forming spirals self-regulate to a quasi-universal disc stability level. This proves the existence of the self-regulation process postulated by several star formation models, but also raises important caveats.