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We present the first high spatial resolution Chandra X-ray study of NGC 2244, the 2 Myr old stellar cluster immersed in the Rosette Nebula. Over 900 X-ray sources are detected; 77% have optical or FLAMINGOS near-infrared (NIR) stellar counterparts an d are mostly previously uncatalogued young stellar cluster members. All known OB stars with spectral type earlier than B1 are detected and the X-ray selected stellar population is estimated to be nearly complete between 0.5 and 3 Msun. The X-ray luminosity function (XLF) ranges from 29.4<logLx<32 ergs/s in the hard (2-8keV) band. By comparing the NGC 2244 and Orion Nebula Cluster XLFs, we estimate a total population of 2000 stars in NGC 2244. A number of further results emerge from our analysis: The XLF and the associated K-band luminosity function indicate a normal Salpeter initial mass function (IMF) for NGC 2244. This is inconsistent with the top-heavy IMF reported from earlier optical studies that lacked a good census of <4Msun stars. The spatial distribution of X-ray stars is strongly concentrated around the central O5 star, HD 46150. The other early O star, HD 46223, has few companions. The clusters stellar radial density profile shows two distinctive structures. This double structure, combined with the absence of mass segregation, indicates that this cluster is not in dynamical equilibrium. The spatial distribution of X-ray selected K-excess disk stars and embedded stars is asymmetric with an apparent deficit towards the north. The fraction of X-ray-selected cluster members with K-band excesses caused by inner protoplanetary disks is 6%, slightly lower than the 10% disk fraction estimated from the FLAMINGOS study based on the NIR-selected sample. This is due to the high efficiency of X-ray surveys in locating disk-free T Tauri stars.[Abridged]
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