We have used the NASA Infra-Red Telescope Facility ( IRTF ) to observe the nuclear stellar cluster in the nearby , face-on , giant Scd spiral IC 342 .
From high resolution ( \lambda / \Delta \lambda = 21500 ) spectra at the ^ { 12 } CO ( 2-0 ) bandhead at 2.3 \ > { \mu { m } } we derive a line-of-sight stellar velocity dispersion \sigma = ( 33 \pm 3 ) \ > { km } { s } ^ { -1 } .

To interpret this observation we construct dynamical models based on the Jeans equation for a spherical system .
The light distribution of the cluster is modeled using an isophotal analysis of an HST V-band image from the HST Data Archive , combined with new ground-based K-band imaging .
Under the assumption of an isotropic velocity distribution , the observed kinematics imply a K-band mass-to-light ratio M / L _ { K } = 0.05 , and a cluster mass M \approx 6 \times 10 ^ { 6 } \ > { M _ { \odot } } .
We model the mass-to-light ratio with the ‘ starburst99 ’ stellar population synthesis models of Leitherer and collaborators , and infer a best-fitting cluster age in the range 10 ^ { 6.8 - 7.8 } years .
Although this result depends somewhat on a number of uncertainties in the modeling ( e.g. , the assumed extinction along the line-of-sight towards the nucleus , the IMF of the stellar population model , and the velocity dispersion anisotropy of the cluster ) , none of these can be plausibly modified to yield a significantly larger age .
Also , the inferred age is consistent with that found in our previous study based on the near-infrared absorption line equivalent widths of the cluster ( Böker , Förster-Schreiber & Genzel 1997 ) .

Recent HST observations of large samples of spiral galaxies have shown that nuclear stellar clusters are very common in intermediate to late-type spirals .
The cluster in IC 342 is more luminous than the clusters found in most other nearby spiral galaxies .
If the nuclear stellar clusters in spiral galaxies all have a mass similar to that of the cluster in IC 342 , then stellar population synthesis models indicate a median age for these clusters of several Gyrs .
This may be consistent with a scenario in which each spiral galaxy has only one episode of nuclear star cluster formation .
On the other hand , the incidence of young nuclear star clusters may be high enough to indicate that the formation of these clusters is a recurring phenomenon .
Age and population studies for a larger sample of galaxies are necessary to distinguish between these scenarios , and to determine how these nuclear stellar clusters are related to the secular evolution of their environment .

As a byproduct of our analysis , we infer that IC 342 can not have any central black hole more massive than 5 \times 10 ^ { 5 } \ > { M _ { \odot } } .
This is \sim 6 times less massive than the black hole inferred to exist in our Galaxy , consistent with the accumulating evidence that galaxies with less massive bulges harbor less massive black holes .