The Large Magellanic Cloud Globular Cluster NGC 1866: New Data, New Models, New Analysis

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Abstract
We present a new deep (down to V ~ 24) photometry of a wide region (~6' × 6') around the Large Magellanic Cloud globular cluster NGC 1866. Our sample is much larger (by more than a factor of 3) than any previous photometry and with a main sequence (MS) that may be considered complete, down to at least 3 mag below the brightest MS star; such an occurrence allows a meaningful and robust comparison with various theoretical scenarios produced by means of models computed with the evolutionary code FRANEC. Both age and present-day mass function slope, α, are derived by a fit to the available MS and by the use of the parameter Δσ, which is simply the difference, in σ, between the observed and the predicted integrated MS luminosity functions. Our main conclusions are as follows: (1) The adoption of standard models (i.e., computed by adopting the Schwarzschild criterion to fix the border of the convective core) allows a fair fit to the MS for an age of the order of 100–140 Myr and a present-day mass function having a slope α between 2.3 and 1.9, the exact values depending on the adopted distance modulus. It is moreover possible to reproduce the average He clump luminosity while the total number of stars predicted in the He clump is twice the observed value; this means that we reobtain and confirm the first finding of Becker & Mathews, according to whom the simple adoption of a "classical" scenario leads to a neat discrepancy concerning the prediction of the number of stars in the He clump. (2) The adoption of models computed by increasing the size of the convective core by a certain amount—i.e., 0.25Hp—leads to a fair fit to the MS only for a visual distance modulus (m - M)V 18.6, an age t 200 Myr, and a mass function slope α 2.2. In this case, the total number of He clump stars is well reproduced, although the luminosity function of the He clump itself is predicted to be systematically less luminous than observed. The previous conclusions are based on the assumption that there is no appreciable population of binaries in NGC 1866. Though there are not yet sufficient data on the frequency of binary systems in these clusters, we analyze how the previous scenarios would change if a consistent (30%) population of binary systems were present in the cluster. This choice is based on the fact that a fraction of binaries of the order of 30% has already been found in NGC 1818, a cluster similar to NGC 1866. The inclusion of a 30% binary population leads to the following additional conclusions: (3) The adoption of the standard models now leads to a good fit to the entire luminosity function—i.e., MS, turnoff, and He clump stars—for a visual distance modulus (m - M)V = 18.8, an age t 100 Myr, and a mass function slope α 2.4, thus largely removing the "classical" discrepancy between observed and predicted number of stars in the He-burning clump. The quoted visual distance modulus constrains the unreddened distance modulus (m - M)0 within 18.50 and 18.62, depending on the reddening (whose most common values available in the literature range from 0.05 to 0.10). (4) At variance with the last point, the fit obtained by using models computed with an enlarged convective core gets worse when a binary component is taken into account. This is because of the fact that the presence of binary systems increases the existing discrepancy between the observed and predicted clump luminosity, since the He clump is predicted to be even less luminous than in absence of binaries. As a consequence of this analysis, we think that the next step toward a proper understanding of NGC 1866 and similar clusters, must include the accurate determination of the frequency of binary systems, which we hope will be performed with the incoming Cycle 8 Hubble Space Telescope observations of NGC 1866.
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