The Galactic center is the most active site of star formation in the Milky Way Galaxy , where particularly high-mass stars have formed very recently and are still forming today .
However , since we are looking at the Galactic center through the Galactic disk , knowledge of extinction is crucial when studying this region .
The Arches cluster is a young , massive starburst cluster near the Galactic center .
We observed the Arches cluster out to its tidal radius using K _ { s } -band imaging obtained with NAOS/CONICA at the VLT combined with Subaro/Cisco J -band data to gain a full understanding of the cluster mass distribution .
We show that the determination of the mass of the most massive star in the Arches cluster , which had been used in previous studies to establish an upper mass limit for the star formation process in the Milky Way , strongly depends on the assumed slope of the extinction law .
Assuming the two regimes of widely used infrared extinction laws , we show that the difference can reach up to 30 % for individually derived stellar masses and \Delta A _ { Ks } \sim 1 magnitude in acquired K _ { s } -band extinction , while the present-day mass function slope changes by \sim 0.17 dex .
The present-day mass function slope derived assuming the more recent extinction law increases from a flat slope of \alpha _ { Nishi } = -1.50 \pm 0.35 in the core ( r < 0.2 pc ) to \alpha _ { Nishi } = -2.21 \pm 0.27 in the intermediate annulus ( 0.2 < r < 0.4 pc ) , where the Salpeter slope is -2.3 .
The mass function steepens to \alpha _ { Nishi } = -3.21 \pm 0.30 in the outer annulus ( 0.4 < r < 1.5 pc ) , indicating that the outer cluster region is depleted of high-mass stars .
This picture is consistent with mass segregation owing to the dynamical evolution of the cluster .