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Department of Physics |
University of Durham |
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Level One |
The Hertzsprung-Russell Diagram of a globular cluster
Summary of Results
At this point you should have noted the following information in
your notebook:
- A hard copy of your Hertzsprung-Russell diagram for the
globular cluster (GC) NGC 104 with the
various different stellar classes marked on it.
- A list of magnitudes for the stars in the Horizontal Branch (HB), to which you have fitted a linear relation between HB magnitude and colour and from this estimated the apparent magnitude of the HB and its uncertainty at
a fixed colour: (B-V)=0.5.
- The absolute magnitude of the HB in a stellar population such
as that seen in NGC 104 and at a colour of (B-V)=0.5, is M = 1.05±0.05 magnitudes in V (this
has been estimated from other globular clusters for which independent
estimates of the distance are available). Using the mean apparent
magnitude of the HB from your measurements, estimate the distance
modulus for NGC 104 and hence the distance of the cluster in
kiloparsecs, as well as an error on this distance. The difference
between the apparent magnitude (m) and the absolute magnitude (M),
termed the distance modulus (µ), is related to the distance of the
source (r, in parsecs) as:
- What is your estimate of the distance of NGC 104? What is
your best estimate of the error in this measurement?
- Having measured the Horizontal Branch magnitude in
NGC 104, what do you feel are the main drawbacks of this technique
as a method for estimating distances to globular clusters?
- Determine by eye the magnitude of the Main Sequence Turn-off
(MSTO) in NGC 104 and estimate the uncertainty in your measurement.
Also estimate the average colour of the stars at the MSTO. Now use this
along with your previous linear fit to the HB magnitude to determine
the HB magnitude at the same colour as the MSTO. From these two values
calculate the difference in apparent V-band magnitude between the MSTO and the
HB in this cluster, dV(MSTO-HB) and the combined error in this estimate.
- Now you can use your measurement of dV(MSTO-HB) and its uncertainty in the relation given below to estimate the age of the stellar
population in NGC 104. t is the age of the system in units of years. This relation has been empirically estimated from globular clusters for which accurate age estimates are available.
- Compare your estimate of the age of NGC 104, with the ages of
other globular clusters you can find on the WWW (see for example the
discussion of M92 at http://www.seds.org/messier).
Conclusions
- The Hertzsprung-Russell diagram provides a powerful tool
for investigating the evolution of stellar populations. Using
simple photometric information it is possible to assign stars
to different evolutionary phases and investigate the relation
between these different phases.
- Globular clusters are remarkably homogeneous stellar
systems which exhibit the properties expected from simple, single age,
single metallicity stellar populations. Their simplicity allows us to
estimate distances and ages for these systems from their H-R diagrams.
Specifically, we used the apparent magnitude of a feature, the Horizontal
Branch, in the H-R diagram for NGC 104 to measure its distance and the
difference between the apparent magnitudes of the Horizontal Branch and
Main Sequence turn off to estimate the age of this globular cluster.
Further Reading and Information
The following sections of course text books will provide background
information on the astronomy discussed in this exercise.
- Colours and Magnitudes, Zeilik & Gregory, Ch 11, p224.
- Magnitudes, Zeilik, Ch 14.1, p304.
- Evolution of Stars, Tipler, Ch 42.3, p1400.
- Stellar Classification, Zeilik & Gregory, Ch 13, p251.
- Stellar Classification, Zeilik, Ch 14.4, p310.
- H-R Diagram, Zeilik & Gregory, Ch 13, p251.
- H-R Diagram, Zeilik, Ch 14.5, p313, Ch 16.2. p350.
- Globular clusters, Zeilik, Ch 16.7, p362.
Acknowledgments
Thanks to Pat Morris at Leeds University, Davison Soper
at Oregon and Harmut
Frommert and SEDS for some of the
plots and text used in the background of this experiment. Also thanks
to the Royal Society and University of New South Wales who paid
enough for me to be able to sit and write this listening to the rain in
Sydney while drinking good scotch.
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