  NGC 3621 is a late-type (Sd) spiral galaxy with an active nucleus, previously
detected through mid-infrared [Ne V] line emission. Archival Hubble Space
Telescope (HST) images reveal that the galaxy contains a bright and compact
nuclear star cluster. We present a new high-resolution optical spectrum of this
nuclear cluster, obtained with the ESI Spectrograph at the Keck Observatory.
The nucleus has a Seyfert 2 emission-line spectrum at optical wavelengths,
supporting the hypothesis that a black hole is present. The line-of-sight
stellar velocity dispersion of the cluster is sigma=43+/-3 km/s, one of the
largest dispersions measured for any nuclear cluster in a late-type spiral
galaxy. Combining this measurement with structural parameters measured from
archival HST images, we carry out dynamical modeling based on the Jeans
equation for a spherical star cluster containing a central point mass. The
maximum black hole mass consistent with the measured stellar velocity
dispersion is 3*10^6 solar masses. If the black hole mass is small compared
with the cluster's stellar mass, then the dynamical models imply a total
stellar mass of ~1*10^7 solar masses, which is consistent with rough estimates
of the stellar mass based on photometric measurements from HST images. From
structural decomposition of 2MASS images, we find no clear evidence for a bulge
in NGC 3621; the galaxy contains at most a very faint and inconspicuous
pseudobulge component (M_K>-17.6 mag). NGC 3621 provides one of the best
demonstrations that very late-type spirals can host both active nuclei and
nuclear star clusters, and that low-mass black holes can occur in disk galaxies
even in the absence of a substantial bulge.
