We have derived the Galactic bulge initial mass function of the SWEEPS field in the mass range 0.15 \lesssim M / M _ { \odot } \lesssim 1.0 , using deep photometry collected with the Advanced Camera for Surveys on the Hubble Space Telescope .
Observations at several epochs , spread over 9 years , allowed us to separate the disk and bulge stars down to very faint magnitudes , F 814 W \approx 26 mag , with a proper-motion accuracy better than 0.5 mas/yr ( 20 km/s ) .
This allowed us to determine the initial mass function of the pure bulge component uncontaminated by disk stars for this low-reddening field in the Sagittarius window .
In deriving the mass function , we took into account the presence of unresolved binaries , errors in photometry , distance modulus and reddening , as well as the metallicity dispersion and the uncertainties caused by adopting different theoretical color-temperature relations .
We found that the Galactic bulge initial mass function can be fitted with two power laws with a break at M \sim 0.56 M _ { \odot } , the slope being steeper ( \alpha = -2.41 \pm 0.50 ) for the higher masses , and shallower ( \alpha = -1.25 \pm 0.20 ) for the lower masses .
In the high-mass range , our derived mass function agrees well with the mass function derived for other regions of the bulge .
In the low-mass range however , our mass function is slightly shallower , which suggests that separating the disk and bulge components is particularly important in the low-mass range .
The slope of the bulge mass function is also similar to the slope of the mass function derived for the disk in the high-mass regime , but the bulge mass function is slightly steeper in the low-mass regime .
We used our new mass function to derive stellar mass–to–light values for the Galactic bulge and we obtained 2.1 \leq M / L _ { F 814 W } \leq 2.4 and 3.1 \leq M / L _ { F 606 W } \leq 3.6 according to different assumptions on the slope of the IMF for masses larger than 1 M _ { \odot } .