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Using Binaries to Split the Age Dichotomy of the Universe (1Mar96)
(from NOAO HIGHLIGHTS!, NOAO Newsletter No. 45, March 1996)

An outstanding problem in modern cosmology is the persistent
discrepancy between the absolute ages of globular clusters and the
expansion age of the Universe. Recent ground and space-based
measurements of the Hubble constant imply an expansion age of about 10
Gyr for the Universe, while the ages of globular clusters are typically
estimated to be 12-16 Gyr. Although, much of the blame for this
discrepancy has traditionally been attributed to systematic errors in
the cosmological parameters, it is just as important to realize that
the absolute cluster ages may also be in significant error. The
globular cluster distance scale is crucial in properly defining the
luminosities of turnoff stars in globulars and is therefore crucial in
defining the age scale. Uncertainties in cluster ages derived from
isochrone-fitting techniques scale approximately as Delta log(Age)/Delta
log(D) ~ 2, where D is the distance. It is also important to realize
that the apparent beautiful accord between stellar evolutionary theory
and globular-cluster observations may be illusory. The best modern
models are simultaneously complex, but yet in some ways significantly
incomplete. New approaches to understanding the ages of clusters are
thus more than welcome. Mario Mateo (Michigan) and Lin Yan (ESO) are
working on this problem by using observations of binary stars in
globular clusters in a unique approach to help tie down both the
distances and ages of the systems.

Over the past few years, numerous groups have identified short-period
binaries in globular clusters. In itself, this is a bit of a revolution
since it was only a few years ago that the total number of known
binaries in clusters was believed to be very small (see Hut et al.
1992, PASP, 104, 981 for a review of the field). In late 1994, Mateo
and Yan reported the discovery of five short-period eclipsing binary
stars located at or just below the main sequence turnoff in the nearby
globular cluster M71 (see Figures 1 and 2). It was immediately apparent
to the two investigators that these stars provide a unique opportunity
to measure the distance to M71 independently of stellar evolutionary
models. These stars can also be used to test the reliability of ages
derived from stellar models.

One way to carry out the latter test was described by George Preston in
the context of determining the age of the oldest population in the
Galactic Bulge (1993, IAU 153, p. 101). Assuming only conservation of
mass, he noted that the evolution of short-period binaries can be
described with the equation M sub 1 + M sub 2 = M sub 1,0 + M sub 2,0
+ M sub L. That is, the total mass of the present-day binary equals
the mass of the initial binary plus any mass loss. This equation can be
rewritten as M sub 1,0 = M sub 1 (1+q)/(1 + Q + L), where q is the
present-day mass ratio, and Q, and L are the original mass ratio and
mass loss in terms of the mass of the initial primary star, M sub 1,0.
The most conservative assumption is L = 0 (no mass loss) and Q = 1.0
(equal-mass components initially) from which one can derive a lower
limit of the zero-age mass of the present-day primary,
M sub 1,0 ~/= 0.5 M sub 1 (1+q). The test demands a good estimate
of the present-day mass of the primary (M sub 1) and the mass ratio (q).

Four of the M71 binaries are located within 0.2 mag of the cluster
turnoff. Spectroscopy of these stars could therefore directly provide a
lower limit to the cluster turnoff mass, which can be critically
compared with predictions from models. The test requires no knowledge
of the cluster distance and is only weakly dependent on the reddening.
Moreover, this test provides a new sort of comparison between models
and observation: there is still no direct mass determination of any
non-degenerate stars in globular clusters.

Last September, Mateo and Yan used the R-C spectrograph on the KPNO 4-m
telescope to carry out time-resolved spectroscopy of
the five M71 eclipsing binaries. This project proved to be practical
because of the availability of multislits for the R-C spectrograph.
Four of the five variables could be observed simultaneously, along with
eight other cluster main-sequence stars, subgiants, and blue
stragglers. They observed the fifth variable by positioning one of the
multislits on it a few times per night. The non-variable 'check stars'
in M71 provide invaluable information on the importance of slit errors
as they monitored the binaries. The principal challenge was the faintness
of the variables whose mean V-band magnitudes range from about 18-19
and have periods ranging from 0.35-0.56 days.

Using the KPC-24 grating in second order, Mateo and Yan were able to
attain 5-8 km/s precision on these check stars per exposure. This is
better than they had expected and more than adequate for their purposes
(the expected velocity amplitudes are about 200 km/s, but these stars
rotate rapidly, and they were interested in very small mass
differences). They attained S/N of about 15 per resolution element for
each of the M71 binaries on individual 20-minute exposures. Such short
exposures were necessary to avoid significant phase smearing. Their
success suggests that similar observations of main-sequence binaries in
about 20-30 clusters could be done, rather than in just the 5-6 closest
systems.

         		[Figure not included]

	Figure 1. V-band light curves for the newly-discovered
	exlipsing binary stars in M71 (Yan and Mateo 1994).

Mateo and Yan obtained more than 30 epochs for four of the binaries,
and 10 epochs for the fifth system. In every case, they obtained good
data at the quadrature phases where the velocity amplitude--which
defines the mass scale--is largest. All of the M71 binaries turned out
to be double lined systems. One example of the cross-correlation
profile for one of the binaries near quadrature is shown in Figure 3.
Since there are excellent constraints on the orbital parameters (in
particular, the inclination) from the light curves of these stars, it
is possible to obtain reliable mass estimates of the individual
components. A detailed analysis of these measurements is underway.

	        	[Figure not included]


	Figure 2. A color magnitude diagram of M71 showing the
	locations of the eclipsing binaries.

Mateo and Yan are now actively monitoring dozens of other globulars for
both short-period and longer-period binaries at or below the
main-sequence turnoff. Virtually every well-studied globular contains
eclipsing systems. Their positive experience with M71 suggests that
they should be able to do effective follow-up spectroscopy of many of
these systems. Their ultimate goal is to test critically the
reliability of the absolute ages implied by modern evolutionary models
and, at the same time, provide a new distance scale for globulars based
on the binaries themselves.

	        	[Figure not included]

	Figure 3. Cross-correlation profiles for the spectra of
	one of the M71 variables from a single night. The double-
	peaked profiles indicate that both stars are being measured;
	the variations in the peak positions as a function of time
	is evident. Along with the excellent inclination information
	from the light curves, Mateo and Yan will be able to derive
	unambiguous and precise masses for both stars in most of
	the M71 systems.

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