7 The RGB tip and above

The tip of the RGB is of special interest for three main reasons: (i) any AGB star brighter than the RGB tip is a candidate intermediate age star, hence may signal the presence of an intermediate age population (e.g. Iben & Renzini 1983), (ii) the RGB tip itself is directly used as a distance indicator (Lee et al. 1993; Salaris & Cassisi 1997; Sakai et al. 1999), and (iii) in any galaxy the luminosity function near the tip of the RGB has a direct impact on the distance determination using the surface brightness fluctuation method (Tonry & Schneider 1988).

Figure 27: The bulge RGB tip in different bands. The solid line is the theoretical tip location according to Salaris & Cassisi (1998), while the dashed line is the location of the tip empirically found by Ferraro et al. (2000). Big dots are the (20) stars that lie above the theoretical RGB tip in all the bands, while open circles are stars that lie above the tip in K but not in I. Crosses are blends even in the optical images.

Theoretical models indicate that the bolometric luminosity of the RGB tip (corresponding to the helium flash in the core) increases with metallicity by $\sim$0.25 mag per dex (Rood 1972; Sweigart & Gross 1978). However, due to increasing blanketing, in the I band the RGB tip magnitude appears to be independent of metallicity for [Fe/H] $\la-0.7$, i.e., in the range covered by globular clusters in the Galactic halo (Lee et al. 1993). The present data on the Galactic bulge offer an opportunity to explore the behavior of the RGB tip luminosity at higher metallicities, up to solar and beyond.

Figure 27a displays the (K,V-K) diagram of the combined WFI+2MASS field, for the upper RGB+AGB (K<10). Overplotted, as a solid line, is the location of the theoretical RGB tip for metallicities in the range from [M/H] =-2.35 to [M/H] =-0.28(extrapolated here to higher metallicity). For each metallicity, the RGB tip bolometric luminosities from the theoretical models of Salaris & Cassisi (1998) have been converted to K magnitudes and V-Kcolors using the empirical bolometric corrections from Montegriffo et al. (1998) and the analytical template RGBs described in Sect. 4. The empirical location of the RGB tip in the template globular clusters is also shown as a dotted line (from Ferraro et al. 2000), with the small offset between the theoretical and empirical RGB tips being probably due to poor statistics near the RGB tip in the template globular clusters.

In Fig. 27, 25 stars lie above the nominal RGB tip in K, and therefore are candidate AGB stars. Three more stars with very red colors (J-K>2.5) lie outside the limits of these plots. Two of them are included in the IRAS catalogue (IRAS 18061-3140 and IRAS 18069-3153) as OH-IR stars. The third one, missing in our optical CMD due to incompleteness (V mag for the other two stars is 20.7 and 23.7, respectively) is likely to be of the same nature. Two stars in the same CMD region are also present in the disk CMD from 2MASS, therefore suggesting that they are not tracers of a younger bulge population. As well known, in metal poor globular clusters ([Fe/H] $\la-1$) no AGB stars brighter than RGB tip have been found. However, a few stars brighter than the RGB tip do exists in more metal rich globulars, with many of them being long period variables (LPV, Frogel & Elias 1988; Guarnieri et al. 1997). The frequency of LPVs in metal rich globulars has been evaluated by Frogel & Whitelock (1998). From their Table 1, one derives an LPV frequency of $\sim$ $4/(10^6~L_{\rm K}^\odot$). The luminosity sampled by the combined WFI-2MASS field is 13.43 times larger than that sampled by the SOFI-LARGE field, i.e. $\sim$ $5.7\times 10^6~L_{\rm K}^\odot$, hence one would expect 23 LPVs, while 28 stars are found above the RGB tip. However, an inspection of their optical counterparts in the WFI frames reveals that 6 of them, shown as crosses in Fig. 27, are blended with other dimmer stars, and their intrinsic K-band luminosity will be somewhat dimmer than estimated on 2MASS data. Another 5 stars are definitely below the RGB tip in the optical CMD (Fig. 27b), and are plotted as open circles in the four panels of Fig. 27. Their location may result either from the resolution of 2MASS being much worse ($\sim$4 arcsec) than that of WFI ($\la$1 arcsec) and therefore these stars may have unresolved companions in near-IR, that make them artificially brighter. Alternatively they might be LPVs having been caught near minimum light at the time of WFI observations. Finally, our simulations show that $\sim$5 RGB stars are expected to be found above the nominal RGB tip due to the depth effect plus differential reddening. On the other hand, other LPVs may have been caught below the RGB, near minimum light. All in all we conclude that the number of stars brighter than the RGB tip is within the expectations as derived from the frequency of LPVs in globular clusters spanning nearly the same metallicity range of the bulge. Of course, not all stars brighter than the RGB tip in Fig. 27 may be LPVs, hence the present findings do not contradict the result of Frogel & Whitelock (1998), who argue for a deficit of LPVs in the bulge field compared to metal rich globulars. In any event, the bright AGB stars seen in the WFI-2MASS field do not favor the presence of a stellar population in the galactic bulge appreciably younger than the old, metal rich globular clusters, thus reinforcing the conclusion we have drawn from from the turnoff region.

The absolute bolometric magnitudes for the stars on the upper RGB and AGB have also been derived using the empirical bolometric corrections from Montegriffo et al. (1998) and the distance and reddening adopted in Sect. 4. The result is displayed in Fig. 28, showing that the bulge AGB stars extend $\sim$1 bolometric magnitude above the RGB tip, reaching $M_{\rm bol}\simeq -5.0$. This is just marginally brighter (by $\sim$0.2 mag) than the brightest known LPV member of a metal rich globular cluster, i.e. V4 in NGC 6553 (Guarnieri et al. 1997).

Figure 28: The absolute bolometric luminosity of upper RGB and AGB stars. The theoretical RGB tip luminosity is also shown as a solid line (the same as in Fig. 27). The bulge AGB stars appear to extend $\sim$1 bolometric magnitude above the RGB tip.

Concerning the use of the RGB tip as a standard candle, Fig. 27b shows that the I band magnitude of the tip drops by almost two magnitudes, from the lowest to the highest metallicity spanned by bulge stars. Clearly the I band luminosity of the tip cannot be used as a standard candle above [Fe/H]  $\simeq -0.7$. Also in the J band the tip luminosity appears to decrease slightly (Fig. 27c), while it increases slightly in the K band (Fig. 27a). In the H band instead the tip luminosity appears to be fairly constant, suggesting the use of this band for deriving RGB tip distances of stellar populations in the metallicity range -1.0 $\la$ [Fe/H] $\la$ 0.0. For even higher metallicities the K band may become more appropriate, as indicated by the theoretical RGB tip luminosity shown in Fig. 27a.

Figure 27 suggests also quite obvious considerations concerning the surface brightness fluctuation method. Clearly, the fluctuation magnitude will depend both on the particular band used, and on the specific metallicity distribution in each galaxy.