AstroProjects Expanding Universe
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Expanding Universe
In the Expanding Universe project you will get a chance to see for yourself the expansion of the universe. Your measurements will add to those made by other participants, and help construct a graph similar to that first produced by Edwin Hubble in the 1920's, when he showed that the farther away a galaxy is the faster it is receding from us. Using data from the Sloan Digital Sky Survey (SDSS), you will measure the brightness of the brightest galaxies in several clusters of galaxies and use this as a relative measure of how far away they are. The same Sloan data will also tell you the redshift of each cluster and this will tell you how fast it is receding from us.
A Sloan Digital Sky Survey image of ACO1185, a cluster of galaxies 140 Mpc (450 million light years) away. This cluster has a redshift of z=0.033 and is receding from us at a speed of 10000kms-1.
OutlineStudents can choose the activities which most suit their interest, age and ability
Introduction 1
Instructions 5
1. Choose a galaxy cluster and look at it 5
2. Find out how far your cluster extends in the sky 6
3. Find the ten brightest galaxies in your cluster 8
4. Find the redshift of your cluster 9
5. Add your measurements to a simple on-line Hubble Diagrams 11
6. Understanding the Hubble Diagrams 12
Acknowledgements 13
Introduction
Astronomers now know that the whole universe is expanding, so, wherever you are within it, distant galaxies will always appear to be receding from you. Scientists assume that the universe is expanding at the same rate in all directions and at every point in space. If this is true, as we think it is, the velocity at which a given galaxy or cluster of galaxies recedes from us will be proportional to how far away it is. In other words, an object twice as far away will have twice the recession velocity.
This discovery is known as Hubble's Law, after the American astronomer Edwin Hubble, who first provided observational evidence for it. In words Hubble’s Law is:
recession velocity = constant x distance
In symbols:
where the recession velocity is usually measured in km s-1, and the distance is usually measured in Mpc. is a constant called The Hubble Constant which is believed to have the value 71kms1Mpc1.
Note on distance units Astronomers use parsecs rather than light years to measure large distances. 1pc=3.26lightyears, so 1Mpc=3.26 million light years. The nearest bright galaxy to us, the Andromeda Galaxy, is 2.5 million light years away, or a bit under 1Mpc. Distances to clusters of galaxies range upwards from about 20Mpc .
By 1929 the redshifts of 46 nearby galaxies had been measured. From these redshifts their recession velocities could be calculated, assuming that the redshifts were due to the Doppler effect. In symbols:
where is the recession velocity, is the redshift, and is the velocity of light in a vacuum.
Hubble estimated the distances to 24 of these galaxies by measuring the magnitudes of the very brightest stars which were just visible in the galaxy images from the Mount Wilson 100 inch Telescope in California. The absolute magnitudes of these very bright stars were estimated by comparing their magnitudes with those of very special stars in the very nearest galaxies whose absolute brightness was known. These stars are called Cepheid variables.
Cepheid variable stars vary in brightness in a regular way with periods of several days. What is so very useful about them is that their period depends quite precisely on their brightness. In other words, if you measure the period of a Cepheid variable, you know how bright it really is, (its absolute magnitude). If you then measure how bright it looks in a telescope image (its apparent magnitude) you can easily work out how far away it is.
Although Hubble only had measurements for 24 nearby galaxies, and his values for the galaxy distances are now known to be gross underestimates, his graph did show clearly for the first time that recession velocity increased approximately linearly with distance, and that the universe must therefore be expanding at a uniform rate.
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Edwin Hubble and the 100 inch telescope at Mount Wilson Observatory in California. (Caltech.)
Hubble’s 1929 graph of recession velocity in km s-1 against distance in parsecs for 24 galaxies (solid and open circles represent different ways of correcting for the motion of the Sun through space). (Private collection.)
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The idea of an expanding universe illustrated by an expanding balloon on which small pieces of cotton wool have been stuck to represent galaxies
The idea of an expanding universe was not a new one. In particular, it fitted in very nicely with the predictions of Einstein's General Theory of Relativity, which had been published a few years earlier in 1915. According to Einstein's theory, we should not think of the universe expanding into space, but of space itself expanding, rather like a three dimensional version of the two-dimensional surface of a balloon expanding as the balloon is blown up.
Seen from this point of view, the redshift in light from a distant object is caused by the expansion of space, and is known as cosmological redshift. As light waves travel they expand with the space they are travelling through, so the wavelength gets longer. Visible light waves therefore get shifted towards the red end of the visible spectrum. The same formula applies to cosmological redshift as to Doppler shifts.
You can read more about this in the background sheet Understanding Cosmological Redshift.
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Hubble, and his colleague Milton Humason, went on to investigate whether Hubble's law still held at much larger distances. Their idea was to use clusters of galaxies rather than individual galaxies. They made the bold assumption that the fifth brightest galaxy in every cluster would have approximately the same brightness, so that measuring how bright it appeared in the sky would give a good estimate of relative distance.
The investigation that you are going to carry out is very similar to theirs. You will look at Sloan Digital Sky Survey images of clusters of galaxies, and use Sloan measurements of apparent brightness and redshift to repeat Hubble and Humason's investigations using galaxy clusters. However, you will add an extra dimension to their experiment by looking not just at fifth brightest galaxies, but also the brightest, second brightest, third, fourth, sixth and tenth brightest galaxies, and comparing the graphs that you get. This will be easy to do, because the Sloan software has already automatically catalogued and measured all the objects it has imaged.
Instructions
1. Choose a galaxy cluster and look at it
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Cluster coords and relative distances
ACO 2199 at the default zoom
ACO 2199 at zoom -1
ACO 2199 at zoom -2
ACO 2199 at zoom -3
- Open the list of clusters
· Click the link List of clusters for Hubble diagram on the left hand side of the Expanding Universe webpage.
A spreadsheet opens giving the names and coordinates of several hundred clusters from the Abell Catalogue and an estimate of their relative distances based on the magnitude of the tenth brightest galaxy in each cluster (as measured by Abell and the colleagues who compiled the Abell Catalogue).
- Choose a cluster to examine
More distant clusters are harder to analyse than nearer ones, so it is suggested that you choose one with a relative distance of 5 or less to start with.
· Make a note of the cluster name (e.g. ACO 2199), and its coordinates (ra and dec).
- Open an image in the SDSS Finding Chart Tool
· Click the SDSS Finding Chart Tool link on the left hand side of the Expanding Universe webpage,
· Type or paste in the coordinates of you chosen cluster.
· Click the Get Image button.
- Explore the cluster
· Zoom out and in until you think your image just contains the whole cluster, as judged by eye.
You can see on the left that a zoom of -3 is needed to see the whole of cluster ACO 2199. Zooming out any more makes the cluster too small and hard to see as the image below shows.
ACO 2199 at zoom -4
· You may find it clearer if you click the Invert Image box on the left to give a white background as shown below.
Inverted image of ACO 2199 at zoom -3
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2. Find out how far your cluster extends in the sky
By eye it is hard to see exactly how far the cluster extends. Fortunately the Finding Chart has some very powerful tools to make this task easier.
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How to show galaxies brighter than magnitude 17
- Galaxies brighter than a given magnitude
· Select Invert Image.
· Type g r(0,17) into the space on the left hand side
· Click Get Image.
Galaxies brighter than magnitude 17 are marked with green triangles (mauve when the image is inverted).
- Find how far the cluster extends
It is difficult to determine the 'edge' of a cluster of galaxies without measuring all the redshifts of the component galaxies. This is because some galaxies that appear to be part of a cluster may actually be 'foreground' or 'background' galaxies that just happen to lie along the same line of sight from the SDSS telescope.
Furthermore, clusters tend not to have well defined edges anyway, frequently tailing off gradually, and sometimes connecting to other clusters.
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For these reasons, your judgement as to which galaxies are 'inside' a 'cluster' and which are outside will inevitably be somewhat subjective, and different people will reach different conclusions. Fortunately this is unlikely to affect your results.
· Try marking galaxies brighter than different maximum magnitudes, and at the same time try different zooms, until you think you are reasonably confident where the 'edge' of your galaxy is.
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Here are the results of trying various combinations of zoom and minimum magnitude for ACO 2199:
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Brighter than mag 19 at zoom -5
Brighter than mag 19 at zoom -4
Brighter than mag 20 at zoom -5
Brighter than mag 20 at zoom -4
Brighter than mag 21 at zoom -5
Brighter than mag 20 at zoom -4
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· Choose the magnitude limit and zoom which show clearest how far the cluster probably extends.
(In the case of ACO 2199 shown above, magnitude 20 at zoom -4 give as clear an indication as any.)
· Print this image out as large as possible.
· Mark where you think the 'edge' of the galaxy is in pencil, as shown below.
The approximate ‘edge’ of cluster ACO 2199 marked on a printout of the Finding Chart
at zoom -4 showing galaxies of magnitude 20 and brighter
· If possible, also mark the ‘edge’ of the cluster on a blank overhead projector sheet.
3. Find the ten brightest galaxies in your cluster
· Still in the Finding Chart tool, mark all the galaxies up to magnitude 14 by typing g r(0, 14) in the space provided and clicking Get Image.
· If this includes fewer than 10 galaxies within the cluster area, increase the 14 to 14.5, then to 15, and so on until you have at least 10 galaxies marked.
· Now make a printout with the brightest galaxies marked by small triangles.
ACO 2199 in the Finding Chart at zoom -4 with galaxies brighter than magnitude 15 marked
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· Make a note of the current zoom and then switch to the Navigate tool by clicking the small Navi link below the SDSS logo at top left.
· Set the same zoom as you were using in the Finding Chart tool.
The Navigate link in the top left hand corner of the Finding Chart window
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ACO 2199 in the Navigate tool with a bright galaxy selected. Notice the panel on the right giving the galaxy magnitude in the r waveband and the thumbnail below which enables you to be sure that you have selected the correct galaxy.
· Click in turn on each of the bright galaxies within the cluster area in your printout that are marked with small triangles.