Department of Physics University of Durham   Level One
School of Physics University of New South Wales   General Education

Measuring the Hubble Constant

Calculation and Discussion of Results

At this point you should have the following information:

  • List of angular sizes for the 15 galaxies in the sample, along with estimated errors on each measurement.
  • For each galaxy the measured wavelengths of spectral features you have identified.
  •  Determining the Redshifts -

    For each galaxy you can estimate the redshift, z from each of the spectral features you have measured, using the restframe wavelengths of the features given in the table. The redshift is simply given by:

    The values of z from the different lines should be in good agreement, if they're not you have probably misidentified a feature in the spectrum - go back and take a second look. Average the different redshift estimates for each galaxy and use the scatter between the values to determine the statistical accuracy of each redshift.

     Putting it all together - The figure below shows the apparent angular size of a galaxy as it relates its real physical size (D) and distance (R). We next need to convert the redshift measurements made above into recession velocities in km/sec and the angular diameters measured earlier for the galaxies in arcseconds into radians using the conversions given below. The last piece of information needed to estimate the Hubble Constant from your observations is the mean diameter of a galaxy, D. D is estimated to be typically 20 kpc using the sizes of nearby giant Spiral galaxies for which accurate distances have been measured from Cepheid variable stars. You can now estimate the Hubble Constant from each of your galaxies and then average these individual measurements together to estimate a mean value of the Hubble Constant from the sample as a whole. What is the statistical error in your measurement?

    Summary & Conclusions

  • Your estimate of the Hubble Constant, with an associated error.
  • A table showing the measurements on which your estimate is based. As well as your calculations, clearly set out.
  • A discussion of the various questions raised below and on the previous pages
  •  Additional Factors - Here are a number of issues about the measurement you made above which you should discuss.
    1. Plot up the values you measure for the Hubble Constant from each individual galaxy against the recession velocity of the galaxy, do you see any trend? What might be causing such an effect and how would you most easily remove it from the fit?
    2. Do you see any correlation between the morphological types and colours of the galaxies and their spectral properties - as indicated by the different spectral features you used to estimate the redshifts?
    3. If the Elliptical galaxies (these are generally yellow in colour and do not have spiral arms) have a typical size of only D = 16 kpc, rather than the D = 20 kpc estimated from the sample of local giant Spiral galaxies, how will this effect your fit and hence your estimate of the Hubble Constant?
    4. In the light of your answers to the questions above do you think that using the physical size of galaxies is a useful way to estimate the Hubble Constant?

    Further Reading and Information

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

    1. Hubble's Law, Tipler, Ch 42.6, p1412.
    2. Hubble's Law, Zeilik & Gregory, Ch 22, p433.
    3. Hubble's Law, Zeilik, Ch 7.4, p138, Ch 19.8, p440.
    4. Hubble's Law, Kaufmann & Comins, Ch 15.10.
    5. Morphological Classification of Galaxies, Tipler, Ch 42.6, p1409.
    6. Galaxy Morphology, Zeilik & Gregory, Ch 21, p414.
    7. Galaxy Morphology, Zeilik, Ch 19.2, p435.
    8. Galaxy Morphology, Kaufmann & Comins, Ch 15.1.

    The Extragalactic and Cosmology group in the Physics Department at Durham is one of the leading research groups in Europe tackling the properties of galaxies in the distant Universe and their formation and evolution. This research includes work on the Hubble Deep Field, gravitational lensing and theoretical work on galaxy formation and evolution. More details of the research undertaken in Durham can be found here.


    Thanks to Dennis Zartisky for the original concept behind this lab and also Luis Mendoza, Doug Scott for some of the plots and text used in the background of this experiment. Also thanks to the PPARC, the Royal Society and the University of New South Wales who paid enough for me to be able to sit and write this while enjoying the sunny vistas from my window in Sydney and drinking yet more good scotch.

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