S104 The Virtual Telescope script

[All sky map]
What you see here is an image of the complete night sky, obtained at visible wavelengths. The bright band running across the middle is the Milky Way. I've labelled the positions of eight distant clusters of galaxies for you. Clusters are named after the constellations in which they lie, and in this case we have clusters called "Perseus", "Ursa Major", "Bootes", "Coma", "Hercules", "Leo", "Hydra" and "Gemini". These clusters are the objects that you'll be using in your investigation of the Hubble constant.
Although you can't see anything in the small squares showing the locations of the clusters on this image, you will be able to do so using the virtual telescope.
The aim of this activity is to measure speeds and distances of these clusters; to plot a graph of speed versus distance; and so calculate the Hubble constant from the gradient of that graph. You'll probably find it easier if you start with one of the clusters that's relatively nearby, such as Coma, Perseus or Hercules - so click on one of the buttons to select the cluster that you want to investigate first.

[Imager]
This is the view obtained using an instrument called the imager, which displays the image of the cluster as seen through the telescope. When using the imager there are two other important instruments that are available to you. These are the spectrometer and the photometer. The spectrometer measures the spectrum of any galaxy that you select from the image, and from the spectrum you can work out the speed at which the galaxy is moving.
The photometer measures the brightnesses of all the galaxies in the image, and you can use this information to find the distance to the cluster.

[Clicking on galaxy with no instrument selected]
At the moment you haven't got an instrument selected. You'll have to select either the spectrometer or the photometer in order to make measurements.

[Photometer selected]
The photometer is now ready for use. Click on the "start photometry" button to take the measurements.

[Spectrometer selected]
The spectrometer is now ready for use. Click on any galaxy in the image to obtain its spectrum. If you have difficulty seeing where the galaxies are then click on the "galaxy labels" button in the bottom left hand corner of the screen.

[Start photometry]
The photometer measures the brightnesses, in Watts per square metre, of the brightest galaxies in the cluster and it displays the results as a table of these brightnesses.

In order to find the distance to the cluster, we assume that the tenth brightest galaxy has a standard luminosity. So, you need to select the tenth brightest galaxy from this list. If you need help finding the tenth brightest, press the "sort list" button, and this will sort the galaxies in descending order of brightness. Click on the brightness value that you want to select.

[value selected in table]
Your selected value for the tenth brightest galaxy can now be used to calculate the distance to the cluster. To carry out the calculation, press the calculate button.

[After calculation]
You now have a value for the distance to this cluster. You can add it to your results for this cluster by clicking on the "add to results" button.

[wrong result during photometry]
This result looks a little odd to me. Are you sure that you selected the tenth brightest galaxy? If you want to repeat your measurement, press the "Start again" button.

[after clicking on galaxy in spectrometer mode]
The spectrometer measures the spectrum of the selected galaxy over the wavelength range 350 to 650 nanometres. The spectrum of your target galaxy is shown here by the purple trace. If the galaxy is moving, then lines in the spectrum will be Doppler shifted. So it would be useful if we could compare this with the spectrum of a galaxy which we know isn't moving relative to us. The spectrometer has already measured such a spectrum, and you can display it by clicking on the "reference spectrum" button. Display this reference spectrum now.

[after displaying reference spectrum]
The reference spectrum is displayed as a grey trace. Notice that there's a similar pattern of spectral lines in both the spectrum of the galaxy and the reference spectrum. Line the cursor up carefully on one of the features in the galaxy spectrum, and click on the mouse button. Then carefully click on the corresponding feature in the reference spectrum. If you make a mistake doing this, you can start again by clicking on the "start again" button.

[after clicking on reference spectrum]
You have now measured the wavelength of a feature in the galaxy spectrum and, hopefully, the wavelength of the same feature in the reference spectrum. The redshift and recession speed can be found by pressing the calculate button. Remember, the redshift is just the shift in wavelength divided by the rest wavelength, and the recession speed is equal to the redshift multiplied by the speed of light.

[if wrong feature identified in reference spectrum relative to galaxy spectrum]
This result looks a bit suspect to me. Are you sure that you identified the same feature in both spectra? If you want to repeat your measurements, press the "start again" button.

[wrong measurement from spectra, negative redshift obtained]
Now this result looks a little odd. You have obtained a negative value for the redshift, z. This would mean that the galaxy is moving towards us, and that would be quite a surprising result. Perhaps it would be a good idea to check whether you measured the feature in the galaxy spectrum first and then in the reference spectrum. If you want to repeat your measurements, press the "start again" button.

[after successfully calculating when using spectrometer]
OK, this looks like a reasonable result. You can add it to your results for this cluster by clicking on the "add to results" button.

[Calculate clicked with reference spectrum not visible]
You must display the reference spectrum before proceeding.

[after clicking on the galaxy spectrum]
You now need to measure the wavelength from the reference spectrum of the same feature that you have already measured in the galaxy spectrum.

[after measuring galaxy speeds]
The speed of the galaxy that you have just found has now been added to the table on the left hand side of the screen. It would be a good idea to measure the speeds of 2 or 3 galaxies in this cluster, to check that they give results within a few hundred kilometres per second of each other. If you repeat observations of galaxies in this cluster using the spectrometer, then the results will be tabulated here, and the mean speed will be calculated from all of your measured speeds.

[After adding result to table]
The distance to the galaxy that you have just found using data from the photometer has now been added to section on the right hand side of the screen. Unless you think that you have made a mistake in choosing the tenth brightest galaxy, there's no need to repeat your photometric measurement for this cluster. It's a good idea to do the spectroscopy on this cluster next. To do this you need to display the image of the cluster again, and this can be done by clicking on the "imager" button.

[do more measurements]
To do more spectroscopic or photometric measurements on this cluster, you need to display the image of the cluster again and this can be done by clicking on the "imager" button. If you want to do measurements of a different cluster, you should display the "all sky map" again.

[Once you've successfully calculated a speed and distance]
Now that you have a value for the speed and the distance to this cluster, you can add these results to the final results table using the button at the bottom right-hand side of the screen.

[After adding results to final results table]
This is where the results for individual clusters are brought together. Ideally, you should have a speed and a distance for each of the eight clusters of galaxies, but fewer clusters may still give you a reasonable result. When you think that you have enough results, click on the Plot graph button.

[graph plotted]
The graph shows the recession speeds and distances for all the clusters you've measured. A best-fit straight line has been drawn through your data and the gradient of this line is the Hubble constant in units of kilometres per second per megaparsec.

[right value of Hubble constant]
Your value for the Hubble constant looks fine to me. The currently accepted value for it is around 70 kilometres per second per megaparsec, but measurements by various astronomers have recently given values as low as 50 or as high as 80 kilometres per second per megaparsec.
Anyway, congratulations on completing your observations with the Virtual Telescope. Make a note of your value for the Hubble constant and then close down the telescope.

[Hubble constant too low]
Your value for the Hubble constant seems a bit low to me.

[Hubble constant too high]
Your value for the Hubble constant seems a bit high to me.

[wrong Hubble constant]
Perhaps you should try observing a few more clusters of galaxies. Alternatively, if any of the data points on your graph seem out of line with the others, then perhaps you've made a mistake with the observations of that cluster. In either case, take some more measurements, then replot the graph using your new results, and calculate the Hubble constant again.