Annu. Rev. Astron. Astrophys. 1999. 37: 603-648 Copyright © 1999 by Annual Reviews. All rights reserved

6.3. Relationship to Global Characteristics of Parent Population

Each UVX candidate represents a potential channel to be filled by its evolving post-main sequence parent population. At least five global population parameters are known to be important in determining the occupation of the various channels. The effects of these have been reviewed in GR and Chiosi (1996). Yi et al (1997b) nicely illustrate the effects of age, abundance, and mass-loss parameters on color-magnitude diagrams, integrated spectra, and broad-band UV colors. The single most important variable is mass loss on the giant branch, followed by helium abundance (Y).

Age : As a population ages, its turnoff mass decreases, with M_TO ~ 0.96 t₁₀^-0.2 M, where t₁₀ is the age in units of 10 Gyr. For a given amount of RGB mass loss, older stars will have smaller M_ENV and will fall at higher ZAHB temperatures. The UVX is therefore expected to increase with age, though probably in a strongly nonlinear fashion. At large enough ages, all stars evolving up the RGB will become hot EHB or PRGB objects.

Y : An increase in helium abundance has important effects on post-giant branch evolution (GR, Horch et al 1992, DOR). Because of the increase in mean molecular weight, turnoff masses at a given age are smaller, which yields smaller M_ENV for a given amount of RGB mass loss. A higher initial helium abundance also causes stars with a given M_ENV to burn more of their hydrogen envelope during the core He-burning phase, producing AGB-manqué behavior for a larger range of M_ENV's (Horch et al Table 1; DOR Figure 6). Increasing Y from 0.27 to 0.47 roughly quadruples the total E₁₅₀₀ for a uniform distribution of M_ENV's (DOR).

Z : The strong correlation between the UVX and line strengths discussed in Section 5.2 makes metal abundance effects on hot star evolution of particular interest. Based on the example of the globular clusters, one might suppose that metal abundance determines the prevalence of hot HB stars. To the contrary, theoretical models show that Z has little direct effect on either the EHB or post-EHB phases of evolution (e.g. Dorman et al 1993, DOR). Instead, these are governed mainly by M_ENV. Although increased metallicity does increase M_TO for a given age, thereby decreasing ZAHB temperatures for a given amount of RGB mass loss, hot HB stars can appear at any metal abundance as long as envelope masses are small enough. This is demonstrated in the grids of metal-rich HB models cited in Section 6.2 and was first illustrated in integrated light by Ciardullo & Demarque (1978). However, for higher metallicities, T_e for medium-envelope (0.05-0.15 M) stars is strongly decreased. This implies that a uniform distribution of M_ENV will lead to a bimodal distribution of ZAHB temperatures at higher metallicities (Dorman et al 1993, D'Cruz et al 1996).

There has been less exploration of advanced evolution with relative abundance variations among the metals. D'Cruz et al (1996) found no qualitative changes in behavior for models with [O/Fe] = +0.75. However, as discussed in Section 5.2, models incorporating variable abundance ratios among the metals would seem to be essential if the empirical line strength correlations are to be understood.

These theoretical expectations on the secondary status of metallicity effects on HB temperatures have good empirical support. The bluest UV colors in Figure 6 occur not for the most metal-poor globular clusters but for those of intermediate metallicity. Small numbers of EHB and related stars have recently been found in globular clusters with heavily populated red HBs (NGC 362, Dorman et al 1997; 47 Tucanæ, O'Connell et al 1997), and large numbers of hot HB stars are present in the relatively metal-rich clusters NGC 6388 and 6441 (with Z ~ 0.25 Z, Rich et al 1997). Other clusters with EHB stars may range up to Z ~ 3 Z (NGC 6791, Liebert et al 1994).

Y / Z : There is good evidence from the study of emission lines in low-metallicity galaxies that helium abundance is coupled to metal abundance (e.g. Wilson & Rood 1994, Izotov & Thuan 1998). Values of Y / Z ~ 3-4 have been derived for low metallicity environments. If these apply to E galaxies, then the smaller effects on EHB and post-HB evolution of metallicity enhancements for Z Z are strongly amplified by the effects of Y enhancement, as emphasized by GR. The dramatic increases in post-HB UV output found by Horch et al (1992) in metal-rich models were actually produced by the accompanying He effects (Y is increased to ~ 0.35-0.45 for Z 2 Z in their models). Jørgensen & Thejll (1993) estimated that Y / Z > 2.5 is needed to produce a strong positive correlation between metal abundance and UVX above Z, for normal ranges of age and RGB mass loss. DOR (Section 8.3) emphasize that there is very little known about Y / Z for solar abundances or above and that most available chemical evolution models suggest smaller He enhancements than for low abundances. DOR also point out that EHB stars exist in clusters and the Galactic field at moderate metallicites, and presumably moderate Ys, so that extreme Z or Y enhancements are not essential to their production.

Mass Loss : Mass loss is the most important determinant of post-RGB evolution in low-mass stars but is also the most difficult to evaluate because of a paucity of both empirical evidence and theoretical exploration. RGB mass loss is usually modeled using the Reimers (1977) prescription:  

where _R is a mass loss efficiency parameter, L is the luminosity, g is the surface gravity, and R is the radius, with L, g, and R in solar units. This formula is based on dimensional analysis rather than a well-grounded physical theory. It is consistent with the available observational data, which indicate only that mass loss increases with luminosity and decreasing surface temperature, reaching a maximum just prior to the He flash (reviewed in Dupree 1986). The Reimers prescription implicitly includes composition and age dependences through their influence on stellar structure, and hence L, g, and R. Although _R is the principal mass-loss parameter in this formulation, empirically there is always a significant spread in the effective _R (e.g. Rood 1973), which produces a range M_ENV on the ZAHB. There is no theory for the spread at the moment, so it appears in evolutionary synthesis models as an additional free parameter.

To produce a typical globular cluster blue horizontal branch requires _R ~ 0.2-0.5 (e.g. Renzini 1981b, Yi et al 1997b) if cluster ages are ~ 15 Gyr. Such values are therefore regarded as "normal" and are widely used in galaxy spectral modeling. However, the globular cluster values would increase if the lower ages of ~ 12 Gyr favored by the recent Hipparchos recalibration of distance indicators are adopted (Yi et al 1999). Furthermore, there is very little evidence on whether globular cluster _R values are appropriate in other kinds of stellar populations. It is physically plausible that _R would increase with metal abundance, owing to grain formation, for instance. GR explored the consequences of assuming that _R 1 + (Z / Z_crit), where Z_crit is a critical threshold. D'Cruz et al (1996), Yi et al (1997b) considered models for a range of _R up to 1.2, the former including self-consistently the effects of mass loss on evolution near the RGB tip and the "hot flasher" phenomenon. They find that production of EHB stars in populations with Z Z requires _R 0.7, with total mass loss of ~ 0.5 M per star for ages 10 Gyr. D'Cruz et al found that a smooth distribution of _R on the RGB leads to a strongly bimodal distribution of ZAHB temperatures if Z Z. The models imply that increases of _R of only a factor of 2-3 over canonical globular cluster values are sufficient to produce a large population of EHB and post-EHB stars for normal ranges of age, Z, and Y.

The hot flash phenomenon is one way of routing a significant fraction of the evolving population into HB objects with M_ENV < 0.05 M without the need for "fine tuning" of mass loss. D'Cruz et al (1996) showed that as long as mass loss near the RGB He flash luminosity is above a critical threshold (corresponding to _R ~ 0.7, but not necessarily tied to the Reimers prescription), EHB stars will always be produced via the hot-flash mechanism. Neither the _R values nor the range of values ( _R) producing EHB objects vary much with metallicity from globular cluster to supersolar values. The mechanism produces a natural concentration to a narrow range of T_e. There is also improving empirical evidence from the cluster and field samples (Section 6.2) that EHB populations do occur in nature at a wide range of metallicities. Thus, there are no obvious obstacles to the production of EHB stars through enhanced mass loss.

Although the Reimers law provides a useful schematic for exploring mass-loss effects on the UVX, a much improved physical theory is needed. Preliminary hydrodynamic models (e.g. Bowen & Willson 1991, Willson et al 1996) suggest a sudden onset of mass loss at a critical luminosity and a strong metallicity dependence, effects that may not be well modeled by a simple scaling law.

Other Parameters : There are certainly other processes that can influence the production of hot stars in old populations. Sweigart (1997) showed that deep mixing in the outer envelopes of RGB stars, which results in enhanced surface He abundances, encourages the production of hot HB stars and AGB-manqué behavior. Larger mixing is presumably related to higher stellar rotation rates. The dynamical environment of galaxies could therefore influence the UVX by way of stellar spin distributions. Ferraro et al (1998) find that gaps in the hot HBs of different globular clusters occur at similar temperatures, suggesting that RGB mass loss is a multimode process. Good candidate mechanisms have not yet been identified.