The Observational Study for Initial Mass Function of Compact Clusters in the Large Magellanic Cloud

The shape of the stellar initial mass function (IMF) is a very important unresolved issue in modern astrophysics because it plays a crucial role in many of the remaining big questions, e.g., the formation and evolution of the first stars and galaxies. The evolution of the stellar mass function (MF) is also important more generally, because the IMFs of many clusters and galaxies cannot be observed directly. However, we can derive their IMFs based on the present-day MF (PDMF) if—at least— we understand its evolution in detail. The Large Magellanic Cloud (LMC) is an ideal laboratory for studying the evolution of IMF because it contains a large population of rich star clusters with masses similar to Galactic globular clusters and covering ages from 0.001 to 10 Gyr (e.g., Beaulieu et al. 1999; Elson et al. 1999). This implies that we can study the MF at almost all evolutionary stages using the rich, compact clusters in the LMC. As part of Hubble Space Telescope (HST) program GO7307, we obtained high-quality imaging observations of six compact clusters in three pairs (pair I: NGC 1805 and NGC 1818; pair II: NGC 1831 and NGC 1868; and pair III: NGC 2209 and Hodge 14). Our six sample clusters have ages of 10–10 yr, with the additional constraint that the two clusters in each pair have similar ages, metallicities, total mass, and distance from the LMC center, yet different structural parameters (Beaulieu et al. 1999). We used the IRAF/APPHOT (Image Reduction and Analysis Facility/Aperture photometry) package to perform aperture photometry with 2 pixel aperture both onHST/ WFPC2 (Wide Field Planetary Camera 2) andHST/STIS (Space Telescope Imaging Spectrograph) observations and determined the aperture corrections for our photometry based on the model point-spread functions (PSFs) generated by Tiny Tim (Krist & Hook 2001). We used deep HST/STIS photometry of the carefully selected sample of rich, compact clusters in the LMC to derive their stellar MFs for masses below 1:0M⊙, which we combined with the MFs of de Grijs et al. (2002) above 1:0M⊙ to obtain complete MFs for all sample clusters. Firstly, we test our method based on NGC 1818 and found the NGC 1818 IMF is fully consistent with both the Kroupa (2001) solar neighborhood and Chabrier (2003) lognormal mass distribution within the uncertainties (Liu et al. 2009a). Then, we applied the method to all the samples and got their PDMF (Liu et al. 2009b). The observations were taken beyond the crowded cluster cores and only included stars at the half-mass radii. In addition, the relaxation timescales of low-mass stars are much longer than the equivalent periods for high-mass stars, so that dynamical evolution will not have affected the clusters’ stellar mass distributions below 1:0M⊙ noticeably. We have therefore provided unprecedented insights into the IMF in a low-density and low-metallicity extragalactic environment. To our knowledge, this is the first time that anyone has probed stellar (cluster) MFs to this depth in an extragalactic, low-metallicity environment (Liu et al. 2009a, 2009b). Based on our STIS observations, the MFs of our compact clusters are all identical to the standard Kroupa (2001) IMF below 1:0M⊙, within the uncertainties.