A 10,000-solar-mass black hole in the nucleus of a bulgeless dwarf galaxy

The motions of gas and stars in the nuclei of nearby large galaxies have demonstrated that massive black holes are common and that their masses strongly correlate with the stellar velocity dispersion $\sigma_{\star}$ of the bulge. This correlation suggests that massive black holes and galaxies influence each other's growth. Dynamical measurements are less reliable when the sphere of influence is unresolved, thus it remains unknown whether this correlation exists in galaxies much smaller than the Milky Way, as well as what fraction of these galaxies have central black holes. Light echoes from photoionized clouds around accreting black holes, in combination with the velocity of these clouds, yield a direct mass measurement that circumvents this difficulty. Here we report an exceptionally low reverberation delay of $83\pm14$ minutes between variability in the accretion disk and high velocity H$\alpha$ emission from the nucleus of the bulgeless dwarf galaxy NGC~4395. Combined with the H$\alpha$ line-of-sight velocity dispersion $\sigma_{\rm line}=426\pm1$~km~s$^{-1}$, this lag determines a mass of about 10,000~$M_{\odot}$ for the black hole. This mass is among the smallest central black hole masses reported, near the low end of expected masses for heavy "seeds", and the best direct mass measurement for a galaxy of this size. Despite the lack of a bulge, NGC~4395 is consistent with the $M_{\rm BH} - \sigma_{\star}$ relation when $\sigma_{\star}$ is measured from the central region. This indicates that the relation need not originate from hierarchical galaxy assembly nor from black hole feedback.