Department of Physics

University of Durham

Level One

The Colour-Magnitude Relation for Ellipticals

 Measuring the Colours and Magnitudes of Galaxies - The HST/WFPC2 image of the core of Cl0016+16 shown below is 730×750 pixels in size, with each pixel being 0.1 arcsec. The field size corresponds to about 500 kpc in diameter for a Hubble constant of 50 km/sec/Mpc. This is a true colour representation of the cluster made by combining frames taken with V (visual, around 5500Å) and I (near-infrared, centred at 8100Å) filters. When you click the cursor the program will draw a circle on the image around the galaxy you've centred on and will and output the magnitude and colour of this galaxy. The total magnitude of the galaxy is calculated by integrating the light in the galaxy out to a radius where the brightness of the galaxy falls below the noise in the background sky. A small correction is then applied for the light which would lie outside of this radius. In contrast the colour of the galaxy is measured within a small aperture (after subtracting the background light from the sky) fixed on the image of the galaxy on the I frame and then in the same aperture on the V frame. The ratio of the fluxes in these two images gives the colour of the galaxy. These values are written both at the top of the image (for the current galaxy) and should also all be listed on the Java console of your browser. The point will also be plotted on the colour-magnitude on the associated window. You should also note down which galaxies appear to have early-type morphology (E or S0) and which have late-type morphologies (spiral and irregular galaxies). Note, some of the galaxies in the frame are too faint for the program to centroid on.

Before starting your measurements read through the list of aims given below, keep these in mind while you select and measure colours and magnitudes for galaxies on the CCD image. When you decide you have a sufficient number of measurements to answer the questions listed above you can capture the C-M plot using XV (or similar), to make a hardcopy for yourself. You can use this to confirm the reliability of the fitting to the C-M relation you perform.

 Overview - By selecting galaxies from this true colour image of a small region in the distant rich cluster of galaxies Cl0016+16, the name gives a crude identification of the position of the cluster on the sky. You can investigate the structure of the cluster's colour-magnitude (C-M) diagram as a function of galaxy morphology and hence the colour-magnitude relation of early-type galaxies. The aim is to populate the C-M diagram sufficiently to tackle the following questions:

1. As you select galaxies note down their morphologies - a crude estimate, i.e. late-type or early-type, will be sufficient. You will need this information to complete your analysis. You should also note down any stars you might find. How faint do you feel you can reliably classify the galaxies into early- or late-type?
    
   
2. Notice the way in which the structure builds up in the C-M diagram as you select more galaxies. Can you identify any structure in the plot, what do such structures say about the properties of the galaxies in this distant cluster? Try selecting galaxies with similar colours, or with similar brightness, or all the galaxies with early-type morphologies. Which of these techniques gives the `fairest' representation of the total cluster galaxy population? Which is the most efficient for defining the color-magnitude relation for the early-type members of the cluster?
    
   
3. Estimate what proportion of galaxies in Cl0016+16 are early-type galaxies. What is a good way of defining this number: in terms of galaxies brighter than a given magnitude, or the fraction of the total number of galaxies in the cluster, or as a fraction of the galaxies within some area of the cluster? How did you go about measuring this?
    
   
4. Transfer your measurements to the fitting program on the PC and fit a linear relation to the early-type C-M relation. How do you deal with the outliers and contamination by non-early-type galaxies? How faint should you fit given your estimate of your ability to morphologically classify the galaxies?
    
   
5. The analysis section of this lab contains a number of measurements for you to perform using the fit to the C-M relation in Cl0016+16.

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