The mass function of the Arches cluster from Gemini adaptive optics data

We have analysed high resolution adaptive optics (AO) science demonstration data of the young, massive stellar cluster Arches near the Galactic Center, obtained with the Gemini North telescope in combination with the University of Hawai'i AO system Hokupa'a. The AO H and K' photometry is calibrated using HST/NICMOS observations in the equivalent filters F160W and F205W obtained by Figer et al. (1999). The calibration procedure allows a detailed comparison of the ground-based adaptive optics observations against diffraction limited space-based photometry. The spatial resolution as well as the overall signal-to-noise ratio of the Gemini/Hokupa'a data is comparable to the HST/NICMOS data. The low Strehl ratio of only a few percent is the dominant limiting factor in the Gemini AO science demonstration data as opposed to space-based observations. After a thorough technical comparison, the Gemini and HST data are used in combination to study the spatial distribution of stellar masses in the Arches cluster. Arches is one of the densest young clusters known in the Milky Way, with a central density of similar to3 x 10(5) M. pc(-3) and a total mass of about 10(4) M.. A strong colour gradient is observed over the cluster field. The visual extinction increases by DeltaA(v) similar to 10 mag over a distance of 15 from the cluster core. Extinction maps reveal a low-extinction cavity in the densest parts of Arches (R less than or equal to 500), indicating the depletion of dust due to stellar winds or photo-evaporation. We correct for the change in extinction over the field and show that the slope of the mass function is strongly influenced by the effects of differential extinction. We obtain present-day mass function slopes of Gamma similar to -0.8 +/- 0.2 in the mass range 6 < M < 65 M. from both data sets. The spatial analysis reveals a steepening of the mass function slope from close to zero in the cluster center to Gamma similar to -1.7 +/- 0.7 at R > 10, in accordance with a Salpeter slope (Gamma = -1.35). The bias in the mass function towards high-mass stars in the Arches center is a strong indication for mass segregation. The dynamical and relaxation timescales for Arches are estimated, and possible mass segregation effects are discussed with respect to cluster formation models.