The VMC Survey. XVIII. Radial dependence of the low-mass, 0.55--0.82 $M_{\odot }$ stellar mass function in the Galactic globular cluster 47 Tucanae

We use near-infrared observations obtained as part of the {\sl Visible and Infrared Survey Telescope for Astronomy} (VISTA) Survey of the Magellanic Clouds (VMC), as well as two complementary {\sl Hubble Space Telescope} ({\sl HST}) data sets, to study the luminosity and mass functions as a function of clustercentric radius of the main-sequence stars in the Galactic globular cluster 47 Tucanae. The {\sl HST} observations indicate a relative deficit in the numbers of faint stars in the central region of the cluster compared with its periphery, for $18.75\le m_{\mathrm{F}606\mathrm{W}}\le 20.9$ mag (corresponding to a stellar mass range of $0.55<m_{\ast }\mathrm{/}{M}_{\odot }<0.73$). The stellar number counts at ${6.7}^{\mathrm{\prime }}$ from the cluster core show a deficit for $17.62\leq m_{\rm F606W}\leq 19.7$mag(i\mathrm{.}e\mathrm{.},$0.65<m_\ast/{M_\odot}<0.82$), which is consistent with expectations from mass segregation. The VMC-based stellar mass functions exhibit power-law shapes for masses in the range $0.55<m_{\ast }\mathrm{/}{M}_{\odot }<0.82$. These power laws are characterized by an almost constant slope, $\alpha$. The radial distribution of the power-law slopes $\alpha$ thus shows evidence of the importance of both mass segregation and tidal stripping, for both the first- and second-generation stars in 47 Tuc.