Rotational Variation Allows for Narrow Age Spread in the Extended Main Sequence Turnoff of Massive Cluster NGC 1846

The color-magnitude diagrams (CMDs) of intermediate-age star clusters (less than ~ 2 Gyr) are much more complex than those predicted by coeval, nonrotating stellar evolution models. Their observed extended main sequence turnoffs (eMSTOs) could result from variations in stellar age, stellar rotation, or both. The physical interpretation of eMSTOs is largely based on the complex mapping between stellar models -- themselves functions of mass, rotation, orientation, and binarity -- and the CMD. In this paper, we compute continuous probability densities in three-dimensional color, magnitude, and vsini space for individual stars in a cluster's eMSTO, based on a rotating stellar evolution model. These densities enable the rigorous inference of cluster properties from a stellar model, or, alternatively, constraints on the stellar model from the cluster's CMD. We use the MIST stellar evolution models to jointly infer the age dispersion, the rotational distribution, and the binary fraction of the Large Magellanic Cloud cluster NGC 1846. We derive an age dispersion of ~ 70-80 Myr, approximately half the earlier estimates due to nonrotating models. This finding agrees with the conjecture that rotational variation is largely responsible for eMSTOs. However, the MIST models do not provide a satisfactory fit to all stars in the cluster and achieve their best agreement at an unrealistically high binary fraction. The lack of agreement near the main-sequence turnoff suggests specific physical changes to the stellar evolution models, including a lower mass for the Kraft break and potentially enhanced main sequence lifespans for rapidly rotating stars.