Readers may get an impression by reading the previous sections that we have solid and successful theories. Quite contrarily, there are several critical issues to be understood before we can ever claim so.
Theorists (including myself) often interpret the UV vs Mg2
relation as a metallicity effect on the UV flux. However, it
should be noted that Mg2 strength may not be representative of the
overall metallicity. In fact, it has been known that elliptical
galaxies are enhanced in
-elements with respect
to iron. We then naturally wonder if it is not the overall metallicity but
-enhancement that
generates the UV upturn. To perform this test, we need
-enhanced stellar
models. The Y2 Isochrones group have released their
-enhanced
stellar models for the main sequence (MS) through red giant branch (RGB)
(Kim et al. 2002).
But, no -enhanced HB
models are publicly available yet.
-enhancement can have
severalimpacts on the galaxy spectral evolution. First, it changes the
stellar evolutionary time scale, as CNO abundance affects the
nuclear generation rates. Second, it changes opacities and thus
the surface temperatures of stars. These two effects will make a
change in the mass loss computed using a parameterised formula,
such as the
Reimers (1975)
formula. For a fixed mass loss efficiency, we
find the -enhanced
([/Fe] = 0.3-0.6) tracks
yield 
0.03
M
smaller mass loss at ages 5-8Gyr but
0.03
M
greater mass loss at ages
8 Gyr, compared
to the standard
([/Fe] = 0)
tracks. -enhancement
must have similar opacity effects on the HB evolution, while its effect
on the mass loss on the HB should be negligible.
Thus its effects are expected to be greater to the MS to RGB than
to the HB phase. Considering this, I have decided to inspect the
overall effects of
-enhancement by just
adopting new
-enhanced MS through RGB
tracks, ignoring the change in the HB models. My earlier review
(Yi & Yoon 2004)
shows the results for two metallicities and three values of
-enhancement.
It can be summarised as follows. In old metal-poor models
-enhancement causes a
positive effect to the
relative UV strength because (1) it causes a slight increase in
mass loss on the RGB and (2) it causes MS stars and red giants to
be redder and fainter in V band. The
[/Fe] = 0.3 model
roughly reproduces the SED of a typical UV-strong metal-poor
globular cluster, which is satisfying. The metal-rich models
on the other hand do not show any appreciable change in response to
-enhancement. Because
giant elliptical galaxies are largely
metal-rich (roughly solar) and the light contribution from
metal-poor stars is not substantial, it is unlikely for
-enhancement to play a
major role to the UV upturn.
4.2. EHB stars in star clusters
With the HST spatial resolution, a number of studies have found hot, extended horizontal branch (EHB) stars in globular clusters (e.g., Piotto et al. 1999). They are efficient UV sources and important candidates for the main UV sources in elliptical galaxies; but canonical population synthesis models have difficulty reproducing them as they are observed (number density, colours and brightness).
NGC 6791 is a particularly interesting case. This old (8-9 Gyr) metal-rich (twice solar) open cluster is unique resembling the stellar populations of the giant elliptical galaxies. Strikingly, 9 out of its 32 seemingly-HB stars have the properties of typical EHB stars (Kaluzny & Udalski 1992; Liebert et al. 1994), while canonical models do not predict any (Yong et al. 2000). It is critical to understand the origin of these old hot metal-rich stars. Landsman et al. (1998), based on UIT data, concluded that NGC 6791, if observed from afar without fore/background stellar contamination, would exhibit a UV upturn just like the ones seen in elliptical galaxies.
Through detailed synthetic HB modelling we found that it is
impossible to generate an HB with such a severely-bimodal colour
distribution as shown in this cluster, unless an extremely (and
unrealistically) large mass dispersion is adopted. In the hope of
finding a mechanism that produces such an HB
Yong et al. (2000)
explored the effect of mass loss on the HB. Yong et al. found
that with some mass loss taking place on the HB
( 10-9 -
10-10
M
yr-1) HB stars born cool quickly
become hot, suggesting that mass loss on the HB might be an
effective mechanism of producing such stars.
Vink & Cassisi (2002)
however pointed out that the level of the
mass loss assumed by Yong et al. is too high to justify in their
radiation pressure calculations in the context of single-star evolution.
Green et al. (2000)
reported that most of these hot stars in NGC 6791 are in binary
systems. If they are close binaries and experience mass transfer
it would be an effective mechanism for mass loss.
But at the moment it is difficult to conclude whether
binarity had causality on their EHB nature or not.
SdB/O stars, the central objects of this conference, may be the field counterparts of the EHB stars in clusters. They have the properties similar to those of the UV sources in the UV-upturn galaxies. Surprisingly, more than 70% of sdB stars are found to be in binary systems (Saffer et al. 2000; Maxted et al. 2001).
Han et al. (2003)
used a binary population synthesis technique to
study the effects of binary evolution and found that 75-90% of
sdB stars should be in binaries. SdBs are detected to be in a
small mass range centred at 0.5
M, but
Han et al.
found that the range should be in truth as wide as 0.3 through 0.8
M. They
predict a birthrate of 0.05 yr-1 for
Population I stars and 6 million sdB stars in the disc. Assuming
the Galactic Disc mass of 5 × 1010
M, this
means roughly 100 sdB stars per 106
M. In a
back-of-the-envelope calculation, there are roughly a few thousand
HB stars per million solar mass in globular cluster populations.
A comparison between the sdB rate (100 per 106
M) and
that of the HB (say, 5000 per 106
M)
suggests that an old
disc population may develop 1 sdB star for 50 HB stars (2%). This
sounds by and large reasonable from the EHB-to-HB number ratio
found in globular clusters. But it is hardly impressive from the
perspective of searching for copious UV sources in galaxies.
For comparison, NGC 6791 has roughly 30% (8 EHB-like stars
out of 32 HB-like stars) and the UV-brightest Galactic globular cluster
Cen
has 20%. These two examples show an order of magnitude
higher values of EHB-to-HB ratio than deduced from a simple estimation
based on the binary population synthesis models. Yet, even
Cen
does not exhibit a UV upturn as observed
in giant elliptical galaxies: FUV-V is comparable but
FUV-NUV is 1-2 magnitudes redder than found in ellipticals.
If this calculation is
realistic at least within an order, binary mass transfer may not be
sufficient to provide the origin of the majority of the UV sources in
UV-upturn galaxies. On the other hand, a larger sdB production rate
might be plausible in elliptical galaxy environment due to large age
and/or large metallicity.
A considerably more detailed investigation was presented by Han et al. (2007). They constructed the population synthesis models including binaries of varied properties (in mass ratio and separation). The conclusions from their prediction can be summarised as (1) most of the UV light of ellipticals comes from binary sdB stars (2) a UV upturn starts to appear as early as when the galaxy is 1.5 Gyr old (3) and the FUV-V colour stays virtually constant since then. This is an important prediction because this is the first study that realistically consider binary products in population models. One immediately notices that the item (3) contradicts the single-star population models of Yi et al. (1999) discussed in Section 3.3 and Figure 2.
There are other important issues as well. For example, the late-stage flash mixing scenarios and the like (D'Cruz et al. 1996; Brown et al. 2001) may also be effective ways of producing hot stars (such as sdB stars) in old populations. Their typical temperature range (Teff >> 20,000 K) and the predicted birthrate may not be entirely consistent with the UV upturn shown in elliptical galaxies, however.
Another important observational constraint comes from the HST UV images of M32. First, Brown et al. (2000) found that PAGB stars are two orders of magnitudes fewer than predicted by simple stellar evolution theory. This is significant as PAGB stars are thought to account for 10-30% of the UV flux in the UV-upturn galaxies (Ferguson & Davidsen 1993). More importantly, they find too many faint hot HB stars to reproduce with standard population models that are based on the mass loss rate calibrated to the globular cluster HB morphology. It is possible to reproduce the observed number of hot stars in M32-type populations if a greater mass loss rate is used, which would be consistent with the variable mass loss hypothesis (Willson et al. 1996; Yi et al. 1997b, 1998). But theoretical justification is a problem again.