HR Diagram

In this exercise, you will be presented with background information on the topic of interest, including lecture notes. After reviewing that material, you should download and print out the PDF of the problem. Finally with the problem in front of you, open up the image tool and use it to analyse the images in order to answer the questions on the PDF. Write on the printout of the problem and bring it to class.




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 Cluster

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:

Distribution of Globular Clusters

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 to the left 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-Russel Diagrams: Introduction

HR Diagram Plot

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 apparent 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 figure above.

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.

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.

Hertzsprung-Russel Diagrams: Regions

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 in the following pages.

The Main Sequence - this is where stars spend most of their lifetime consuming Hydrogen in their cores via nuclear fusion. Our Sun is still on the main sequence. The MS extends below the bottom of the figure, but owing to the faintness of the stars they weren't detected in the observations used to construct this figure.

Turn Off - As the hydrogen fuel in a star's core runs out the core begins to collapse due to gravity and the star moves away from the main sequence. At the turn off nearly all the central fuel is gone.

Red Giant Branch - When the central fuel is gone, hydrogen starts to burn in an envelope around a dense helium core. The star's outer regions expand due to this new energy input. As the emitting surface area of the star's photosphere increases so does its apparent brightness, also as it expands the photosphere cools (as it becomes cooler, the colour of the star becomes redder). The star thus moves up and to the right on the H-R diagram, climbing the Red Giant Branch (RGB).

Helium Flash - At the tip of the RGB the helium rich core ignites and helium fusion begins. This ignition of the core causes the star to move rapidly down the H-R diagram to the Horizontal Branch region.

Horizontal Branch - the HB is the region inhabited by stars which are burning Helium in their cores, converting it into Carbon. A strong feature of the HB in this particular globular cluster, M5, is a Gap in the HB.

Gap in HB - The HB in M5 is separated into two section - a Blue HB and a Red HB - separated by a gap. The gap indicates a region of instability in the physics of the stellar envelope which results in stars in this region quickly evolving either onto the red or blue flavors of HB. HB morphology differs between globular clusters, some GC's show both Blue and Red HB, some one and not the other.

Asymptotic Giant Branch - As the central helium fuel runs out, shell burning starts again around the core. This time however two shells are formed, the inner one burning Helium and the outer burning Hydrogen. The star now moves off the HB and up the Asymptotic Giant Branch (AGB) blowing off it's outer layers.


White Dwarf - Loss of the complete envelope of the star on the AGB leaves the central hot white dwarf in the middle of a planetary nebula (an example of which is shown above).

PDF of Assignment

Print out the following PDF file, print out and answer using the interactive tool below.

PDF of Assignment

Interactive Measurement Tool

Overview - By selecting stars with a range of colors and brightnesses off this true colour image of a small region in the globular cluster Hertzsprung-Russell (H-R) diagram resulting from stellar evolution. The image is a composite made up of three separate images taken in the ultraviolet (3800Å, U), blue (4500Å, B) and visual (5500Å, V).

47 Tuc

Measuring the Colors and Magnitudes of Stars - The CCD image shown to the left (and in the Globular Cluster Viewer) is 750 x 450 pixels in size, with each pixel being 0.5 arcsec. When you click the cursor on the position of a star the program will centroid on that star (and draw a circle around the star selected) and then integrate the flux within the same aperture on the B and V images of the field, estimate the background in the region around the star and subtract this off the aperture fluxes to give the total flux in the B and V passbands. Converted into magnitudes these two fluxes will give the color and apparent magnitude of the star, which are written to the output. These values are written both at the top of the image (for the current star) and should also all be listed on the Java console of your browser. The point will also be plotted on the figure in the attached window. Note, some of the stars in the frame are too faint for the program to centroid on.

Plotter Example

Example Plot - When a star lies in the Horizontal Branch region (marked by the box) of the H-R diagram note down the magnitude and color of the star. By averaging together the magnitudes of all the stars which you select in this region you should be able to estimate not only the apparent magnitude of the HB in NGC 104, but also the statistical error in your estimate.

Open Interactive Measurement Tool