Dynamics of the Young Binary LMC Cluster NGC 1850

In this paper we have examined the age and internal dynamics of the young binary LMC cluster NGC 1850 using BV CCD images and echelle spectra of 52 supergiants. Isochrone fits to a BV color-magnitude diagram revealed that the primary cluster has an age of τ = 90+/-30 Myr while the secondary member has τ = 6+/-5 Myr. The reddening was found to be E(B- V)=0.17 mag. By surface brightness profiles were constructed out to R > 40 pc, and single-component King-Michie (KM) models were applied. The total cluster luminosity varied from L_B_ = 2.60-2.65 X 10^6^ L_B_sun_ and L_V_= 1.25 X 10^6^ as the anisotropy radius varied from infinity to three times the scale radius with the isotropic models providing the best agreement with the data. Simple tests were made to check for tidal truncation in the profiles and we concluded that there was slight evidence favoring truncation. The bright background and binary nature of NGC 1850 render this conclusion somewhat uncertain. Of the 52 stars with echelle spectra, a subset of 36 was used to study the cluster dynamics. The KM radial velocity distributions were fitted to these velocities yielding total cluster masses of 5.4 - 5.9+/-2.4 X 10^4^ M_sun_ corresponding to M/L_B_ = 0.02+/-0.01 M_sun_/L_B_sun_ or M/L_V_ = 0.05+/-0.02 M_sun_/L_V_sun_. A rotational signal in the radial velocities has been detected at the 93% confidence level implying a rotation axis at a position angle of 100^deg^. A variety of rotating models were fit to the velocity data assuming cluster ellipticities of ɛ = 0.1-0.3 These models provided slightly better agreement with the radial velocity data than the KM models and had masses that were systematically lower by a few percent. Values for the slope of the mass function were determined using the derived M/L, theoretical mass- luminosity relationships, and several forms for the IMF. The preferred value for the slope of a power-law IMF is a relatively shallow, x = 0.29^+0.3^_-0.8_ assuming the B band M/L or x = 0.71^+0.02^_-0.4^ for the V band.