The relation between globular cluster systems and supermassive black holes in spiral galaxies. The case study of NGC 4258

We aim to explore the relationship between globular cluster total number, $N_{\rm GC}$, and central black hole mass, $M_\bullet$, in spiral galaxies, and compare it with that recently reported for ellipticals. We present results for the Sbc galaxy NGC 4258, from Canada France Hawaii Telescope data. Thanks to water masers with Keplerian rotation in a circumnuclear disk, NGC 4258 has the most precisely measured extragalactic distance and supermassive black hole mass to date. The globular cluster (GC) candidate selection is based on the ($u^*\ -\ i^\prime$) vs. ($i^\prime\ -\ K_s$) diagram, which is a superb tool to distinguish GCs from foreground stars, background galaxies, and young stellar clusters, and hence can provide the best number counts of GCs from photometry alone, virtually free of contamination, even if the galaxy is not completely edge-on. The mean optical and optical-near infrared colors of the clusters are consistent with those of the Milky Way and M 31, after extinction is taken into account. We directly identify 39 GC candidates; after completeness correction, GC luminosity function extrapolation and correction for spatial coverage, we calculate a total $N_{\rm GC} = 144\pm31^{+38}_{-36}$ (random and systematic uncertainties, respectively). We have thus increased to 6 the sample of spiral galaxies with measurements of both $M_\bullet$ and $N_{\rm GC}$. NGC 4258 has a specific frequency $S_{\rm N} = 0.4\pm0.1$ (random uncertainty), and is consistent within 2$\sigma$ with the $N_{\rm GC}$ vs. $M_\bullet$ correlation followed by elliptical galaxies. The Milky Way continues to be the only spiral that deviates significantly from the relation.