Annu. Rev. Astron. Astrophys. 1996. 34: 461-510 Copyright © 1996 by Annual Reviews. All rights reserved

2.3. Uncertainty in L^TO Due to Unconventional Physics

In the late 1970s and early 1980s the possibility that the Gravitational constant G varied with time received considerable attention, due largely to the fact that this feature was common to three prominent cosmologies - Brans-Dicke (1961), Hoyle-Narlikar (1972a, b), Dirac (1974). Some of the early tests of the implications of these theories for stellar evolution seemed to lead to satisfactory results (e.g. see Canuto & Lodenquai 1977, VandenBerg 1977, Maeder 1977). Even when potential difficulties, such as the apparent incompatibility of Dirac's theory with the observed characteristics of the microwave background, were pointed out (Steigman 1978), it was often possible to accommodate those objections by revising the theory (cf Canuto & Hsieh 1978). Using their flavor of gravitational theory, Canuto & Hsieh (1981) showed that it was possible for the estimated ages of GCs to decrease from 15 Gyr, under canonical assumptions, to < 10 Gyr, if G varied at a rate ( / G -6 × 10^-11 yr^-1) that was consistent with observed limits at that time (see Van Flandern 1981).

However, those limits are now very much tighter. Taylor & Weisberg (1989) have determined that / G = (1.2 ± 1.3) × 10^-11 yr^-1 from pulse time-of-arrival observations of the binary pulsar PSR1913+16 over the previous 14 years. Their data are completely consistent with Einstein's Theory of General Relativity. In addition, Müller et al (1991) obtain / G = (0.01 ± 1.04) × 10^-11 yr^-1 from 20 years worth of lunar laser ranging data. These results essentially eliminate the possibility of temporal variations in G being a factor in the determination of GC ages.

More promising, perhaps, is the following idea: If nonbaryonic Weakly Interacting Massive Particles (or WIMPs) constitute the dark matter in the Universe, then they might be accreted by stars and affect their evolution (Steigman et al 1978, Press & Spergel 1985). Being massive, they would tend to collect in the cores of stars, and by virtue of being weakly interacting, they would provide an efficient means of central energy transport. If such particles resided in the Sun, for instance, they could lower the central temperature enough to enable a solution to the solar neutrino problem (Faulkner & Gilliland 1985, Spergel & Press 1985). This would require WIMP masses between approximately 2 and 7 GeV and interaction cross sections with nuclei within an order of magnitude (or so) of 10^-35 cm² [see Dearborn, Griest & Raffelt (1991), who also discuss recent experimental limits on these properties]. Furthermore, according to Faulkner & Swenson (1988, 1993), the deduced turnoff ages of globular clusters would be ~ 20% less than canonical estimates, if their member stars acquired sufficient numbers of WIMPs to isothermalize the innermost 10% of their masses.

The main testable prediction, as far as GCs are concerned, is that stars containing WIMPs will leave the main sequence somewhat sooner than canonical stellar models would predict, due to the isothermal core effect, and spend more time on the subgiant branch, because they have extra hydrogen to burn in the shell-narrowing phase. That is, an observed luminosity function should show an excess of subgiants and giants relative to the number of turnoff stars, if WIMP models are more realistic than standard calculations. Surprisingly, this is actually seen in the luminosity-function data for a number of GCs (see Stetson 1991, VandenBerg & Stetson 1991, Faulkner & Swenson 1993, Bolte 1994). However - and this poses a problem - these "anomalies" appear to be present in the observations of only the extremely metal-deficient clusters; i.e. the same ones that show strong evidence for progressive mixing along the RGB. As shown in Section 2.5, new observations for M5 appear to conform remarkably well to standard evolutionary predictions, as do the available luminosity-function data for 47 Tuc (see Bergbusch & VandenBerg 1992). One is tempted to think that something to do with the deep-mixing phenomenon, rather than WIMPs, is the more likely cause of the unexpected luminosity function features.

However, models have not yet been constructed for GC stars that incorporate the very detailed theory for the accretion (and evaporation) of WIMPs that has been developed by Gould (1990), Gould & Raffelt (1990a, b). These models may predict something quite different from calculations that attempt to mimic the effects of WIMPs by imposing (albeit in a self-consistent way) an isothermal core structure on an otherwise normal stellar model. Thus further work is certainly warranted - even though there are other indications that the WIMP hypothesis faces an uphill battle. For instance, using the Gould/Gould-Raffelt theory, Turck-Chièze et al (1993) find that solar models containing WIMPs do not appear to satisfy helioseismic constraints as well as Standard Solar Models. Also, VandenBerg & Stetson (1991) have suggested that WIMPs would likely suppress the formation of convective cores in the 1.3 M turnoff stars in the old open cluster M67. If this happened, then the observed gap feature at M_V 3.5 (see the recent CMD by Montgomery, Marschall & Janes 1993) would not be produced. (It is possible, of course, that the density of WIMPs is much greater in the halo of the Galaxy than in the disk and that the evolution of the Sun and M67 stars would be little affected.) In addition, WIMPs may (Renzini 1987) or may not (Spergel & Faulkner 1988) cause difficulties for our understanding of the horizontal-branch phase of low-mass stars (also see Dearborn et al 1990).

It would be premature to conclude that WIMPs, or the very similar "halons" that Finzi (1991, 1992) has proposed, or other dark matter candidates like axions (Peccei & Quinn 1977;, Dearborn, Schramm & Steigman 1986;, Isern, Hernanz & Garcia-Berro 1992) do not affect stellar ages (if they exist). But neither can one give very serious consideration to the possibility that they do, at least at this time. There appears to be a number of difficulties for the WIMP hypothesis to overcome, and the other suggestions have simply not been adequately developed and tested to pose a serious challenge to standard stellar evolutionary theory.