The Cepheid Distance to the Narrow-Line Seyfert 1 Galaxy NGC 4051

We derive a distance of $D = 16.6 \pm 0.3$~Mpc ($\mu=31.10\pm0.04$~mag) to the archetypal narrow-line Seyfert 1 galaxy NGC 4051 based on Cepheid Period--Luminosity relations and new Hubble Space Telescope multiband imaging. We identify 419 Cepheid candidates and estimate the distance at both optical and near-infrared wavelengths using subsamples of precisely-photometered variables (123 and 47 in the optical and near-infrared subsamples, respectively). We compare our independent photometric procedures and distance-estimation methods to those used by the SH0ES team and find agreement to 0.01~mag. The distance we obtain suggests an Eddington ratio $\dot{m} \approx 0.2$ for NGC 4051, typical of narrow-line Seyfert 1 galaxies, unlike the seemingly-odd value implied by previous distance estimates. We derive a peculiar velocity of $-490\pm34$~km~s$^{-1}$ for NGC 4051, consistent with the overall motion of the Ursa Major Cluster in which it resides. We also revisit the energetics of the NGC 4051 nucleus, including its outflow and mass accretion rates.