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We derive the deepest, most complete near-IR luminosity function for Galactic bulge stars yet obtained based on new $JHK$ photometry for stars in two fields of Baade's Window. When combined with previously published data, we are able to construct a luminosity function over the range $5.5 \leq K_0 \leq 16.5$. The slope of the luminosity function as well as the top of the first ascent giant branch are consistent with expectations based on the Revised Yale Isochrones. Unfortunately, this consistency only sets weak constraints on the range in age and [Fe/H] for the Baade's Window stars.
A blue sequence of foreground stars is clearly visible on the $J-K, K$ color-magnitude diagrams we have derived.
We use the relationship between [Fe/H] and the giant branch slope derived from near-IR observations of metal rich globular clusters by (Kuchinski, L.E., Frogel, J.A., Terndrup, D.M., \& Persson, S.E. 1995, AJ, 109, 1131) to calculate the metallicity for several bulge fields along the minor axis. For Baade's Window we calculate that [Fe/H] $= -0.28 \pm 0.16$, consistent with the recent estimate of (McWilliam, A., \& Rich, R.M. 1994, ApJS, 91, 749), but somewhat lower than previous estimates based on CO and TiO absorption bands and the $JHK$ colors of the M giants by (Frogel, J. A., Terndrup, D.M., Blanco, V.M., \& Whitford, A.E. 1990, ApJ, 353, 494). Between b $= -3$ and -12 we find a gradient in [Fe/H] of $-0.06 \pm 0.03$ dex/degree, consistent with other, independent derivations.
We derive a helium abundance for Baade's Window with the $R$ and $R^\prime$ methods and find that Y $= 0.27 \pm 0.03$.
Finally, we find that the bolometric corrections for bulge K giants ($V - K \geq 2$) are in excellent agreement with empirical derivations based on observations of globular cluster and local field stars. However, for the redder M giants we find, as did Frogel and Whitford 1987, that the bolometric corrections differ by several tenths of a magnitude from those derived for field giants and adopted in the Revised Yale Isochrones. This difference most likely arises from the excess molecular blanketing in the V and I bands of the bulge giants relative to that seen in field stars.
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