Department of Physics University of Durham   Level One

The Hertzsprung-Russell Diagram of a Globular Cluster

Aims of the Experiment

  1. To introduce the measurement of colours and magnitudes of stars.
  2. To discuss the properties of globular clusters.
  3. To illustrate some of the stages of stellar evolution.
  4. To measure the Hertzsprung-Russell (colour-magnitude) diagram for the globular cluster NGC 104.
  5. To estimate the apparent magnitude of the Horizontal Branch and hence the distance to the cluster.


In the following experiment you will be measuring the colours and magnitudes of stars in a globular cluster from a CCD image. By plotting this information on a colour-magnitude diagram you can study the evolution of stars within the globular cluster. Finally, using some of the features seen in the colour-magnitude diagram you can estimate the distance of the globular cluster from us.

Globular Clusters

Globular clusters are systems of between 0.1-1 million stars, gravitationally-bound into a single structure about 100 light-years across. This is a picture of a typical globular cluster (GC), NGC 104. Notice the strongly peaked distribution of stars and spherical symmetry - both indicating a stable gravitationally-bound system. The typical separation of stars in a globular cluster is around 1 light year (thus star-star collisions are rare, although the high stellar density will effect the dynamics of binary-star systems), so the brightest stars in the sky seen from a point within the GC would have similar brightnesses to those seen in the sky from Earth. The one significant difference about the view within the GC would be the brightness of the night sky itself, where the diffuse background of faint stars in the cluster would make the sky relatively bright compared to that seen from the Earth.

The astrophysical study of globular clusters forms an important and major part of modern astronomy, providing information on some of the most fundamental problems in astronomy. Globular clusters are important for a number of reasons:

  • The homogeneity of the stasr in these clusters (note the similar colours of all the stars in the image of NGC104 above) indicates that they have similar chemical compositions and similar ages. This makes them the simplest systems to use to test theoretical models of star formation and evolution.
  • Furthermore, globular clusters are some of the oldest stellar systems known and thus estimates of their ages can be used to constrain the age of the Universe as a whole.
  • Finally, the distribution of their ages, and correlations between cluster ages and metal abundances makes these systems an invaluable probe into the processes of galaxy formation.
  • To date about 160 globular clusters have been discovered in our Galaxy, and large numbers are seen around other galaxies in the local Universe. The figure below shows the distribution of 132 globular clusters, plotted in Galactocentric coordinates. The centre of the Galaxy is at the centre of the plot and the plane of the disk lies across the middle of the figure. You can see that the distribution of globular clusters does not follow that of the disk of the Galaxy, rather the globular clusters are distributed in a spherical halo around the Galactic centre. This is because these clusters of stars formed early on in the history of the Galaxy, before the majority of the proto-galactic material had settled into a disk. The apparent absence of globular clusters in the plane of the disk of our Galaxy arises from a combination of two effects. Firstly, the high obscuration from dust in the disk of the galaxy makes GC's hard to find in directions close to the disk. Secondly, any globular clusters on orbits close to the plane of the disk may be tidally stripped and destroyed through interactions with the disk of the galaxy.

    As mentioned above, the stars of any one globular cluster share a common history (age, chemical abundance, etc) and differ one from the other only in their original mass. They thus form ideal candidates for the study of stellar evolution. In the following section we will investigate how the observed colours and magnitudes of stars in GC's can be used to identify different stages in stellar evolution.

    Hertzsprung-Russell Diagrams

    In the early 20th Century two astronomers, Hertzsprung (a Danish amateur astronomer) and Russell (an American astronomer), had the same idea - to classify stars on the basis of their luminosity and the temperature of their photospheres. The luminosities of the stars can be simply calculated from their apparent magnitudes if their distances are known, to estimate the temperatures of the stars we can use the relationship between the colours of stars and their effective temperatures, red stars being cooler than blue stars. A star's colour is defined as the difference in its appararent magnitudes through two different filters, for example observations of stars through B and V filters can be used to determine their (B-V) colours. Hence by plotting luminosity versus temperature, or the equivalent observables: absolute magnitude and colour, we can construct a Hertzsprung-Russell (H-R) diagram, see below.

    Rather than a random distribution of points, the H-R diagram shows a number of regions which are preferentially populated by stars. This structure in the H-R diagram indicates a common set of physical processes apply to stars in particular regions of the diagram. Most stars (90%) in the local neighbourhood lie on a sequence from hot, luminous stars to cool, dim ones - the Main Sequence (MS). A star's position on the main sequence is determined by its mass, the lifetime of a star on the MS also depends on the star's mass. More massive stars burn their Hydrogen fuel faster and evolve off the MS quickly (as discussed below), in contrast low mass stars can remain stable on the MS for a considerable fraction of the age of the Universe. For a population of stars with the same age, as found in a globular cluster, as the population ages the brighter, more massive stars, will begin to leave the MS, this results in the turn off point on the MS moving to lower luminosities. Such an evolutionary trend can be used to estimate the age of a stellar population.

    Shown above is an example of an H-R diagram for the globular cluster M5. Various regions of the H-R diagram are identified: Main Sequence (MS); Turn off (TO); Red Giant Branch (RGB); Helium flash occurs here at tip of RGB (Tip); Horizontal Branch (HB); Schwarzschild gap in the HB (Gap); Asymptotic Giant Branch (AGB); the final stellar remnants, White Dwarfs (WD), will lie off the bottom of the diagram. These regions show the main phases of stellar evolution and are explained below.

    The description above is for intermediate and low mass stars, i.e. stars with masses of less than about 5-6 times that of our Sun.

    The important feature of the H-R diagram for the purpose of the remainder of this exercise is that certain phases of stellar evolution are associated with well-defined luminosities of stars during these phases. If such a feature can be identified on the H-R diagram for a group of stars then it can be used to estimate the distance to the stars from their apparent luminosities. In what follows, the CCD exposures we are working with are not long enough to reach down to the faintness needed to detect the turn-off point at the end of the MS - so the features we will be dealing with are the RGB/AGB/HB parts of diagram. In particular, you are to measure the apparent magnitude of the Horizontal Branch in NGC 104 and using the known absolute magnitude of this feature (measured from other GC's with known distances) then determine the distance of NGC 104 from the Earth.

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