Department of Physics University of Durham   Level One

The Colour-Magnitude Relation for Elliptical Galaxies


Analysis

Having completed your catalogue of galaxies in Cl0016+16, we now wish to fit to the colour-magnitude relation of the early-type cluster members - the strong ridge-feature which is apparent in your colour-magnitude diagram. We list below the main steps you'll have to complete to derive the relationship between colour and magnitude for the early-type galaxies.

  1. Transfer your catalog of objects across from the Java browser to the Excel spreadsheet.
  2. Select a magnitude limit for your analysis. This should take into account both the observational errors on the colours measured from the CCD frame and your estimate of the limit of your ability to distinguish early- and late-type galaxies. Remove all those galaxies fainter than this limit from your catalog.
  3. Next, we wish to fit to the colour-magnitude relation of early-type galaxies in the cluster. You should therefore use your morphological classifications to remove all late-type galaxies from your catalogue.
  4. Fit the catalogue using the linear fitting functions within Excel. You should take account of the errors on the individual measurements when you undertake your fitting.

Now, we compare the predicted colour of a galaxy with an apparent magnitude of I=21 from your linear fit to the C-M relation with that observed for a galaxy with this luminosity in the local Universe. We take into account just the shifts in the filter passbands for observations of galaxies at high redshift. This predicts that an early-type galaxy with an apparent magnitude of I=21 in Cl0016+16 should have a colour of (V-I)=2.68±0.03. What is the difference between this colour and that derived from your fit? In what sense is the difference (are your observations bluer or redder than the prediction) and what might be the cause of this? Remember that you are observing the galaxies in Cl0016+16 at high redshift and hence seeing them as they appeared at substantially earlier epochs, due to the finite travel time for light, and that younger stellar populations tend to be bluer (as they have more young, massive blue stars in them).

The rate of change of (V-I) colour with age can be estimated from theoretical models of the evolution of simple stellar populations (based on observations of globular clusters and models of stellar structure). These indicate that the (V-I) colour of a galaxy (a significant time after the formation of the stars) should become redder at a rate of d(V-I)/dt = 0.05 magnitudes per Gyr. Taking the colour difference which you derived above and this rate of change of colour, estimate the how much younger the stars in Cl0016+16 appear to be compared to those in local Universe, this is the lookback time to Cl0016+16.

Finally, use your fit to the C-M relation to determine the magnitude of a galaxy which has an apparent colour of (V-I)=2.4. The equivalent rest-frame colour in a local cluster, corrected for the evolutionary effects discussed above, corresponds to an absolute magnitude of -21.3±0.1 in the I-band. Using the apparent (m) and absolute magnitudes (M) of the galaxy estimate the distance modulus (µ) for Cl0016+16 and hence the distance (r) to the cluster in parsecs (for Ho = 50 km/sec/Mpc).

 


Summary of Results

At this point you should have noted down the following information:

  • An estimate of the proportion of early-type galaxies in Cl0016+16.
  • A list of magnitudes, colours and morphologies for the galaxies in Cl0016+16, from which you have calculated a fit to the colour-magnitude relation for early-type galaxies in this cluster.
  • Using your fit, you have compared the expected colour of an I=21 early-type galaxy with that observed in the cluster. What is this difference in colours, and what causes this?
  • Using the theoretical predictions of the evolution of the colour of an early-type galaxy with age, turn your estimate of the colour difference into a value of the lookback-time to Cl0016+16. What is your best estimate of the error in this measurement?
  • Using the apparent magnitude of a galaxy with a given colour and absolute magnitude, you should calculate the distance modulus for Cl0016+16.
  • Suggest any shortcomings of using the Colour-Magnitude relationship as a distance indicator.

  • Conclusions

    1. Galaxy morphology provides an objective classification of galaxies which provides some insight into the physical processes acting during their formation and evolution.
    2. Clusters of galaxies are the most massive collapsed systems in the local Universe. Their luminous galaxy populations are dominated by early-type galaxies.
    3. Elliptical galaxies in clusters show a tight correlation between colour and luminosity or mass. These galaxies exhibit remarkably homogeneous stellar populations as expected from simple, single age, single metallicities models of stellar evolution.
    4. The Colour-Magnitude diagram provides a powerful tool for investigating the evolution of galaxy populations.


    Further Reading and Information

    The following sections of course text books will provide background information on the astronomy discussed in this exercise.

    1. Colours and Magnitudes, Zeilik & Gregory, Ch 11, p224.
    2. Magnitudes, Zeilik, Ch 14.1, p304.
    3. Morphological Classification of Galaxies, Tipler, Ch 42.6, p1409.
    4. Galaxy Morphology, Zeilik & Gregory, Ch 21, p414.
    5. Galaxy Morphology, Zeilik, Ch 19.2, p435.
    6. Clusters of Galaxies, Zeilik & Gregory, Ch 23, p447.
    7. Galaxy Clusters, Zeilik, Ch 19.6, p447.

    The Extragalactic and Cosmology group at Durham is one of the leading research groups in Europe investigating the growth and evolution of structure in the Universe, including rich clusters. The observational work undertaken in Durham on clusters focuses on the evolution of their galaxy populations, searches for clusters in the early Universe and the X-ray emission from clusters. Theoretical research into clusters includes work on their use in cosmological tests and predictions of the results from the observational investigations. More details of the research into clusters of galaxies undertaken in Durham can be found here. Finally, here is a Further exercise illustrating galaxy morphology.

    Acknowledgments

    Thanks to Richard Bower for the original concept for this web lab. 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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