Main Sequence Turn-off Ages
For Star Clusters we can measure ages
from the Main-Sequence Turnoff. The nice thing about a cluster of stars is
that all the stars are at the same distance and it seems that clusters have
only a single burst of star formation, so all the stars in one cluster are the
same age. As a cluster ages, the mass of
the main-sequence turnoff stars decreases. By determining the mass of the main-sequence turnoff stars, we get the
age of the cluster.
The connection between stellar mass and age
depends on your stellar evolutionary model. A stellar model is constructed by solving the
four basic equations of stellar structure: (1) conservation of mass; (2)
conservation of energy; (3) hydrostatic equilibrium and (4) energy transport
via radiation, convection and/or conduction. The evolution of a star may be
followed by computing a static stellar structure model, updating the
composition profile to reflect the changes due to nuclear reactions and/or
mixing due to convection, and then re-computing the stellar structure model.
Uncertainty
from convection
There are a number of uncertainties associated
with stellar evolution models, and hence, age estimates based on the models.
Probably the least understood aspect of stellar modeling is the treatment of
convection. Numerical simulations hold promise for the future, but at present one
must view properties of stellar models which depend on the treatment of
convection to be uncertain, and subject to possibility large systematic errors.
Main sequence, and red giant branch globular cluster stars have surface
convection zones. Hence, the surface properties of the stellar models (such as
its effective temperature, or color) are rather uncertain. Horizontal branch
stars have convective cores, so the predicted luminosities and lifetimes of
these stars are subject to possible systematic errors.
Uncertainty
from diffusion
Given the known uncertainties in the models,
the luminosity (absolute magnitude) of the main-sequence turn-off has the
smallest theoretical errors, and is the preferred method for obtaining the
absolute ages of globular clusters (Chaboyer 1996). The theoretical calibration
of age as a function of the luminosity of the main-sequence turn-off has
changed somewhat over the last several years. It has long been realized that
diffusion (the settling of helium relative to hydrogen) could shorten the
predicted main sequence lifetimes of stars.
However, it was not clear if diffusion actually occurred in stars, so
this process had been ignored in most calculations.
Recent helioseismic studies of the Sun have shown that diffusion likely occurs in the Sun (Guenther 1996). The Sun is a typical main sequence star, whose structure (convective envelope, radiative interior) is quite similar to main sequence globular cluster stars. Thus, as diffusion occurs in the Sun, it appears likely that diffusion also occurs in main sequence globular cluster stars. Modern calculations find that the inclusion of diffusion, together with an improved equation of state, lead to a ~ 2 Gyr (14%) reduction in the estimated ages of the oldest globular clusters. The excellent agreement between theoretical solar models and the Sun suggest that future improvements in stellar models will likely only lead to small (less than ~ 5%) changes in the derived ages of globular cluster stars.
Uncertainty
from abundance calculations
A detailed
Uncertainty from distance measurement
The use of the luminosity of the main sequence
turn-off as an age indicator requires that the distance to the globular cluster
be known. Determining distances is one of the most difficult tasks in astronomy,
and is always fraught with uncertainty. The release of the Hipparcos data set
of parallaxes to nearby stars has suggested that a revision in the conventional
globular cluster distance scale is necessary. Hipparcos did not directly
determine the distance to any globular clusters, but did provide the distance
to a number of nearby metal-poor main sequence stars. Assuming that globular
cluster stars have identical properties to these nearby stars, the nearby stars
can serve as calibrators of the intrinsic luminosity of metal-poor main
sequence stars and the distance to a globular cluster determined. This
technique is referred to as main
sequence fitting.
There have been a number of papers which have
used the Hipparcos data set to determine the distance to globular clusters
using main sequence fitting. Three of these papers conclude that globular
clusters are further away than previously believed, leading to a reduction in
the derived ages. The remaining paper concluded that the Hipparcos data did not
lead to a revision in the globular cluster distance scale. However, this work
included binary stars in the main sequence fitting. When the known binaries are
removed from the fit, then all four papers are in agreement; the Hipparcos data
yields larger distances (and hence, younger ages) for globular clusters. (Chaboyer 1998) considered four distance
determination techniques in addition to using the Hipparcos data, including
Astrometrics, white dwarf sequence fitting, calibration of RR Lyr stars via the
LMC, and theoretical HB models. They concluded that the five independent
distance estimates to globular clusters all led to younger globular
cluster ages.
Table 1
Estimates
for the oldest age of the globular clusters
|
Age
(Gyr) |
Distance
Measurement |
Reference |
|
11.5 ± 1.3 |
five independent studies |
Chaboyer, B. 1998 |
|
12 ± 1 |
main sequence fitting (Hipparcos) |
Reid, |
|
11.8 ± 1.2 |
main sequence fitting (Hipparcos) |
Gratton et al. 1997 |
|
14.0 ± 1.2 |
main sequence fitting (Hipparcos) including
binaries |
Pont, F. et al. 1998 |
|
12 ± 1 |
theoretical HB & main sequence fitting |
D'Antona , F. et al. 1997 |
|
12.2 ± 1.8 |
theoretical HB |
Salaris, M. et al. 1997 |
Despite the fact that these investigators used
a variety of theoretical stellar models (with differing input physics) and
different methods to determine the distance to the globular clusters, the
derived ages are remarkably similar, around 12 Gyr. These ages are ~ 3
Gyr younger than previous determinations, due to improved input physics used in
the models, and a longer distance scale to globular clusters. (Chaboyer 1998)
considered a variety of distance indicators and included a very detailed