Annu. Rev. Astron. Astrophys. 1999. 37: 603-648
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6.2. Single Star Candidates

Since there were no ready-made local analogues for UVX populations, it was necessary to explore alternatives from a largely theoretical perspective. The seminal discussion of the various low-mass candidates for the UVX sources was presented by Greggio & Renzini (1990, hereafter GR; an updated overview is in Greggio & Renzini 1999). They discussed primarily single-star candidates, since the parameter space for binaries is much larger. Here, we also defer discussion of the possible involvement of binaries until a later section.

On the basis of the UV/optical colors, the UVX is estimated to contribute ~ 2-3% of the bolometric luminosity in the most metal rich galaxies such as NGC 1399 and 4649 (GR). While this is not large, the challenge is to identify a mechanism for producing sufficient numbers of high-temperature stars in old populations. If the relevant evolutionary phase is short-lived compared with the lifetime of the galaxy, then the number of stars in this phase is proportional to its evolutionary lifetime. In this circumstance, the "fuel consumption theorem" shows that its contribution to the bolometric luminosity of the galaxy is proportional to the total amount of nuclear fuel consumed during the phase, which can be estimated directly from interiors models (Tinsley 1980, Renzini 1981a, Renzini & Buzzoni 1986, GR). Interesting candidates for the UVX will therefore have temperatures over ~ 20000 K and will burn up to ~ 0.01 Modot of hydrogen or ~ 0.1 Modot of helium (GR). Dorman et al (1995, hereafter DOR) used a similar approach to estimate that the integrated monochromatic energy release at 1500 Å of suitable candidate evolutionary phases must be E1500 gtapprox 4 × 10-3 LV,odot Å-1, where LV,odot = 4.51 × 1032 ergs s-1.

The evolutionary phases of interest all occur after a low-mass star has begun moving up the red giant branch. HR diagram loci for the main types of UVX candidates that have been explored to date are illustrated in Figure 8. The general considerations are described in GR. The evolutionary trajectory of a low-mass star following He core ignition at the tip of the red giant branch is governed mainly by its envelope mass, MENV. Since the He core mass is ~ 0.5 Modot and is relatively insensitive to other parameters, MENV ~ MTO - DeltaM - 0.5 Modot, where MTO is the turnoff mass and DeltaM is the total mass loss during the red giant phase, which, in globular cluster stars, amounts to ~ 0.1-0.3 Modot, or 10-40% of the initial mass. The variance in mass loss leads to a scatter in MENV and hence in the initial temperature of the subsequent core He-burning stage on the "zero-age" horizontal branch (ZAHB). Envelope masses on the HB range up to ~ 0.4 Modot. The lower is MENV, the hotter is the ZAHB location (e.g. Iben & Rood 1970, Rood 1973, Sweigart 1987, Dorman 1992). Envelopes smaller than 0.05 Modot correspond to Te(ZAHB) gtapprox 14000 K. After ~ 100 Myr, helium becomes exhausted in the center of the star, which then contains both helium-burning and hydrogen-burning shells moving outward.

Figure 8

Figure 8. Schematic evolutionary tracks for the principal post-horizontal branch evolutionary phases described in Section 6. Envelope masses on the horizontal branch increase from left to right. For Z ~ Zodot, they are MENV ~ 0.03 Modot at the left hand (hot) edge and ~ 0.05 Modot at the heavy separator line, which marks the cool end of the "extreme horizontal branch" (shaded). The segment of the "P-AGB" track (solid line) which rises to the right of log Te ~ 3.6 corresponds to the AGB. Detailed evolutionary tracks for these phases are shown, for example, by Dorman et al (1993).

If MENV is large enough, post-HB stars develop a deep convective envelope, evolve to lower temperatures, and ascend the cool asymptotic giant branch (AGB), leaving it only at high luminosity near the AGB tip, when rapid mass loss and thermal shell pulsing remove the envelope. Subsequent evolution in this case involves a rapid (104-105 yr) contraction and heating (the post-AGB or PAGB phase), in some cases with the formation of a planetary nebula, followed by cooling and fading on the white dwarf remnant sequence. Much of the pre-white dwarf time is spent at high temperatures, Te > 50000 K. PAGB models for low-mass stars have been computed by Schönberner (1983), Blöcker & Schönberner (1990), Vassiliadis & Wood (1994). The great majority of stars now near or above the main sequence turnoff in globular clusters will pass through the PAGB channel.

More exotic evolution can occur in the case of very small envelopes. For MENV ltapprox 0.05 Modot the post-HB star may evolve to higher temperatures before it reaches the AGB tip or even before it approaches the cool AGB. These cases produce, respectively, post-early AGB (PEAGB) and AGB-manqué ("failed AGB") stars (see Figure 8). The first detailed models were described by Brocato et al (1990), Caloi (1989), respectively (though similar behavior had been noted in early models by Sweigart et al 1974, Gingold 1976). Their internal structure is similar to that of an AGB star (a double shell source) but with much thinner envelopes. They burn about the same amount of fuel as do the more familiar cool AGB stars, but they do so at much higher Te (~ 25000 K). Their post-HB paths in the HR diagram can be convoluted. AGB-manqué lifetimes are ~ 107 yr, considerably longer than for the PAGB phase, after which stars evolve directly to the remnant cooling sequence. Typical E1500's for these "slow blue" post-HB phases (Horch et al 1992) are comparable to those of the hot HB phase (DOR Figure 6). Grids of such models, for a wide range of metallicities, have been computed by Castellani & Tornambè (1991), Castellani et al (1992), Horch et al (1992), Dorman et al (1993), Bertelli et al (1994), Castellani et al (1994), Yi et al (1997a).

The least massive envelope (~ 0.05 Modot, if Y ~ Yodot; see Dorman et al 1993, Table 1) capable of producing a classical PAGB star yields a boundary on the ZAHB between what is now called the "extreme HB" (EHB) (to higher temperatures) and the normal HB. This is marked on Figure 8. AGB-manqué progenitors occupy the hot end of the EHB, while PEAGB progenitors occupy the end adjacent to the normal HB. Note that the normal main sequence for massive stars (not shown) crosses the HB locus at Te ~ 10000 K, and that HB objects hotter than this fall below the main sequence in the classical "hot subdwarf" regime.

Another variety of hot star can be produced directly from the first ascent red giant branch if mass loss is large enough to remove the convective envelope before core He ignition. In this case, the post-RGB (PRGB) object evolves rapidly to the white-dwarf cooling sequence without passing through the HB phase. Some such objects may experience a late He-flash while on the cooling sequence as their central temperatures rise owing to gravitational core contraction. These "hot flashers" will then move to a position slightly below the EHB and follow subsequent post-EHB tracks similar to normal EHB stars. The hot flash effect was demonstrated by Castellani & Castellani (1993), and more detailed models including the secular effects of mass loss during advanced RGB evolution have been computed by D'Cruz et al (1996).

Remnants on the white dwarf cooling sequence are the inevitable descendants of all the preceding types of stars. During their early evolution, white dwarfs are still hot enough to emit UV photons, and their potential contribution to galaxy light can be estimated by integrating down the cooling curve. Magris & Bruzual (1993), Landsman et al (1998) find that hot white dwarfs (residing on the cooling curve for ltapprox 200 Myr) can contribute up to ~ 10% of the far-UV light produced by their parent PAGB phases (less if their parents were EHB stars). This is too small to be of practical importance in normal circumstances. Unless one invokes an IMF truncated below ~ 1.5 Modot, the integrated spectrum of the cooling curve also does not contain the strong Ly-alpha satellite features claimed by Bica et al (1996) to be present in IUE spectra of galaxies.

Finally, the much-studied "blue stragglers" (Bailyn 1995), which are warm stars lying near the main sequence but above the turnoff luminosity in star clusters, are too cool to be viable UVX candidates. They generally have temperatures below 10000 K. However, they may influence the mid-UV spectrum of old populations (Spinrad et al 1997, Landsman et al 1998).

A common characteristic of the viable UVX candidates is their extreme sensitivity to small changes in properties. Differences of only a few 0.01 Modot in envelope mass for hot HB stars produce large changes in the type of post-HB track followed and the resulting E1500 (e.g. see DOR Figure 6). Likewise, models for PAGB stars show that their UV output is extraordinarily sensitive to core mass. Schönberner's (1983) 0.546 Modot model has a lifetime 20× longer than for his 0.565 Modot model and has E1500 a factor of 6.8 larger (DOR; GR Figure 3).

Likely individual examples of all these candidate types have been found in local star clusters and the Galactic field. Imaging with space telescopes has produced a fairly large sample of PAGB, EHB, AGB-manqué, and related post-HB stars in some globular clusters (e.g. in omega Cen, Whitney et al 1994, 1998; NGC 6752, Landsman et al 1996; NGC 2808, Sosin et al 1997; NGC 6338 and 6441, Rich et al 1997; M13 and M80, Ferraro et al 1998). A smaller sample of similar sources has been identified in the open clusters NGC 188 and 6791 (Liebert et al 1994, Landsman et al 1998), and Landsman et al estimate that NGC 188 and 6791 would have UV upturns in their integrated light as strong as any E galaxy. Over 1500 hot subdwarfs (sdO, sdB, and related types) are now known in the Galactic field. As first shown by Greenstein & Sargent (1974), many of these are EHB and post-EHB stars (Heber 1992, Saffer et al 1994). Kinematical studies show that some hot subdwarfs are members of the old, metal-rich disk population of the Galaxy (Thejll et al 1997). The field and open cluster examples are important cases since they demonstrate that EHB objects are not confined to low-metallicity environments. NGC 6791, in particular, has [Fe/H] ~ +0.5 (Kaluzny & Rucinski 1995).

DOR summarized integrated UV outputs for the several main candidate UVX star types. PAGB tracks have E1500 < 0.001 LV,odot Gyr Å-1. They therefore cannot be solely responsible for the brightest UV-upturn cases, as first pointed out by GR and Castellani & Tornambè (1991). However, the EHB, PEAGB, and AGB-manqué phases burn more H + He fuel at high Te's, by factors of ~ 3-30, than classical PAGB stars and therefore are excellent UVX candidates.

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