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We have used the NASA Infra-Red Telescope Facility (IRTF) to observe thenuclear stellar cluster in the nearby, face-on, giant Scd spiral IC 342. Fromhigh resolution (R = 21500) spectra at the 12CO (2-0) bandhead at 2.3 micron wederive a line-of-sight stellar velocity dispersion sigma = (33 +- 3) km/s.  To interpret this observation we construct dynamical models based on theJeans equation for a spherical system. The light distribution of the cluster ismodeled using an isophotal analysis of an HST V-band image from the HST DataArchive, combined with new ground-based K-band imaging. Under the assumption ofan isotropic velocity distribution, the observed kinematics imply a K-bandmass-to-light ratio M/L_K = 0.05, and a cluster mass M ~ 6 times 10^6 Msun. Wemodel the mass-to-light ratio with the `starburst99' stellar populationsynthesis models of Leitherer and collaborators, and infer a best-fittingcluster age in the range 63-630 Myears. Although this result depends somewhaton a number of uncertainties in the modeling (e.g., the assumed extinctionalong the line-of-sight towards the nucleus, the IMF of the stellar populationmodel, and the velocity dispersion anisotropy of the cluster), none of thesecan be plausibly modified to yield a significantly larger age. We discuss theimplications of this result on possible scenarios for the frequency of nuclearstarbursts and their impact on secular evolution of spiral galaxy nuclei.  As a byproduct of our analysis, we infer that IC 342 cannot have any centralblack hole more massive than 0.5 million solar masses. This is ~ 6 times lessmassive than the black hole inferred to exist in our Galaxy, consistent withthe accumulating evidence that galaxies with less massive bulges harbor lessmassive black holes.Comment: 27 pages, incl. 9 figures, submitted to The Astronomical Journa

CO Band Head Spectroscopy of IC 342: Mass and Age of the Nuclear Star Cluster