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HR Diagrams for Clusters
To construct an HR diagram, one needs to know the distance to each star because the
vertical axis requires that the absolute (not apparent) magnitude be plotted.
However, if all stars to be plotted are at the same distance (as is true for a cluster),
we can still construct an HR diagram, even if the true distance is not known.
We may term this
a relative HR diagram. If all stars are at the same distance, the effect of
changing that distance is just to slide the entire HR diagram up or down, but the
relative positions of the stars on the diagram remain the same. For many
applications it is these relative positions that are most
important.
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Age and Evolution
Open clusters are especially interesting as laboratories for the study of stellar evolution
because all the stars in an open cluster presumably formed at almost the same time
from similar material. Thus when we
study a young open cluster such as the Pleiades we see a sample of stars that are all about 100
million years old, but in an older cluster like M67
we see a sample of stars that are all about 5 billion years old, and
so on.
Ages of Open Clusters
Formation of new star clusters has presumably
been taking place since early in the
history of our galaxy and continues until today.
Therefore, we would expect to find open clusters with a wide range of ages,
from quite young to ages that are a significant fraction of that for the galaxy.
This expectation is confirmed by studies
of neighboring open clusters, which range in age from only a few million years
for NGC 2264
to
at least 8 billion years for NGC 6791. We shall see in the
next module that globular clusters are even older than this.
Estimating the Age of a Star Cluster
In the preceding paragraph we quoted some ages for clusters. To understand how
those ages are
determined, we need to jump ahead of our story briefly.
In Chapters 20 and 21 we shall consider the life cycles of stars in some detail. There we will
find that stars spend a finite amount of time on the main sequence, and then evolve to the
giant or supergiant regions of the HR diagram after their core hydrogen fuel is exhausted.
Furthermore, we shall find that the rate at which stars evolve through all phases of their
lives is governed primarily by their mass. The more massive a star, the more luminous it is
when on the main sequence. Therefore, the more luminous main sequence stars are more massive
and evolve
faster than less luminous ones.
When a cluster of stars forms, we expect a broad
distribution of masses for the individual stars,
from a fraction of a solar mass up to many tens of solar masses. The
more massive stars in this population will evolve more rapidly in all phases of their lives.
This means that the brighter (more massive) main sequence stars in the population evolve from
the main sequence to the giant region more quickly than the stars of intermediate brightness
(and intermediate mass), and these stars in turn evolve more quickly off the main sequence to
the giant region than the least luminous (and least massive) main sequence stars. The net
effect is that as time goes on the main sequence "peels off" into the giant region, as
the following figure illustrates.
The Turnoff Point
The turnoff point is the point on the HR diagram
defined by the most luminous (and therefore highest
temperature) main sequence star in the cluster. It is the point where the stars appear to
peel off the main sequence in the above diagram. The position of the turnoff point is
clearly related to the age of the cluster, since it moves to steadily lower luminosities
with time.
This
animation illustrates the evolution of the HR diagram for a cluster.
The ages of clusters are determined by comparing the turnoff points and detailed
distribution of stars in the HR diagram with that calculated from computer models of
stars (see the right panel).
HR Diagrams for Open Clusters
The following figure shows the combined
HR diagram for two young clusters that are close together.
(Only the brighter main sequence stars are shown because the fainter ones are difficult to
observe with confidence at the distance of the clusters.)
We can tell that the clusters
are young because they still contain many very luminous main sequence
stars and only a few giants and supergiants.
Detailed comparisons with theoretical models of stellar evolution suggest an
age of 10 million years or less for the open clusters h and chi Persei.
