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HST Photometry of 47 Tuc and Analysis of the Stellar Luminosity Function in Milky-Way Clusters

We present V and I photometry for a field 5' from the center of 47 Tuc. The field was imaged with the HST WFPC2 as part of the Medium Deep Survey project. The luminosity function (LF) continually rises in the domain $5 < M_I < 9$ with a slope $Δlog Φ(M) / ΔM \sim 0.15$ and then drops off sharply. We compare our LF with that derived by De Marchi \& Paresce for a neighbouring HST field. The two independent LFs are very similar in the entire range of luminosities probed ($M_I < 10$). Comparisons are also made to other HST LFs derived by several authors for different clusters in the Galaxy. We use the KS test to assess the significance of the differences found. The LFs obtained with HST are consistent with being derived from the same population down to $M_I \sim 9.0$. Beyond that, statistically significant variations arise. Globular cluster LFs also differ according to the prominence of a plateau in the bright end ($5 < M_I < 6.5$). Mass functions are sensitive to the mass-luminosity relation. Different approaches to deriving the 47 Tuc mass function from its LF lead to markedly different results at the low mass end. For $M > 0.4 M_\odot$, the 47 Tuc mass function is significantly different from that of \wcen. The calibrated HST $M_V(V-I)$ colour-magnitude diagrams (CMDs) show a trend with metallicity in the sense of metal richer systems having redder CMDs for a fixed absolute magnitude. The main-sequence becomes shallower with increasing metallicity. For metal-rich systems, the CMDs derived from HST are in general agreement with previous ground-based studies. However, the CMDs of metal poor subdwarfs observed from the ground are shallower than those of globular clusters observed with HST.