The Virgo cluster is so close to us that it doesn’t all fit even on a Schmidt plate – this picture only shows the centre. So in this exercise we will concentrate on a different cluster, Hydra I (also known as Abell 1060, being the 1060th cluster in Abell’s catalogue of clusters). We have a plate of this, called Abell 1060, or J7442 or 10:34-27:22. Get it out on the light table and have a look. The cluster of galaxies is obvious in the centre.
Hydra I is a cluster very similar to Virgo. It is about the same size, same mass, and has a similar number of galaxies. However, it is much further away, as is obvious from the plate. This means the whole cluster fits comfortably on one Schmidt plate.
In the first half of this exercise, we will estimate the distance to the Hydra I cluster. Getting distances is always a difficult exercise in astronomy; we can’t take a ruler to anything outside our Solar System (our rockets are much too slow), and triangulating only works to distances of about 20 parsecs, so we have to use other techniques. A common method for measuring distances is so-called ‘standard candles’. As an analogy, imagine you are looking through a telescope at a very far-away lightbulb. If you can measure the amount of light coming into your telescope from the lightbulb, and you know that it is a 60W tungsten filament bulb, you can calculate exactly how far away it is by comparing the measured brightness in your telescope to what you get from the same kind of lightbulb in your desk lamp one metre away. This technique works great for lightbulbs, but its a little trickier for stars and galaxies. The biggest problem of course is that no two stars or galaxies are exactly alike, so you don’t always have a nearby reference point that is totally reliable. Another issue, especially when using brightness scales, is that the space between source and telescope isn’t empty, and the stuff in between distorts the image you see, biasing your results.
The method we will use in this exercise is galaxy diameters. If we know how big a galaxy really is, and could measure how big it appears, by simple trigonometry we can work out how far away it is. We can measure the apparent size of the galaxies in Hydra I using the magnifying eyepiece with a measuring scale. Try measuring the size of a few. The plate scale of all the plates is \(1.12\) arcmin per mm. So if you measure a galaxy as being 2mm long, its apparent size will be the angle \(2.24\) arcmin.
We can measure the apparent size of galaxies in the cluster, but what is their real size? How big is a galaxy? Well, one galaxy we know the size of quite well is our own, the Milky Way. Here’s where we make our first whopping great assumption. Why don’t we assume that the Milky Way is perfectly typical? I.e., let us assume that all the galaxies in Hydra I are just like ours: they have radii of 15 kpc.
So pick a bunch of galaxies in Hydra I and measure their diameters. Some of them will be nearly edge-on, but that shouldn’t stop you measuring them. Multiply by the plate scale to get their angular size and work out how far away they are. You can get an answer for every galaxy you measure, and they won’t all be the same. Throw out any ludicrously discrepant values, and average the rest to get your best guess of the distance to Hydra I.
One big problem is measuring the galaxy sizes. After all, galaxies don’t have sharp edges, they just gradually fade out of visibilty so where do you define the edge? There isn’t really a good answer, the most you can do is be self-consistent.
What distance do you get? A good estimate is ∼55 Mpc, but don’t worry if your answer is far from this, it is a very difficult measurement. Each student in the group should do their own measurements and you should compare the results of each group member. How might you go about improving your estimate?
By far the worst feature of this calculation is the assumption that these galaxies out in a distant cluster are just like our own galaxy. There are all sorts of reasons why this may not be true. For one, this cluster is a lot bigger than our local group, so statistically speaking it likely includes a few rather large galaxies. Also, it is quite likely that galaxies form differently in big clusters. If galaxies in Hydra are nothing like the Milky Way, how can we get around this problem? One way is to be selective in our choice of galaxies to measure. We know that our galaxy, the Milky Way, is a spiral galaxy. So try measuring a distance using only spiral galaxies in Hydra I; see section 2.4 below for a description of different galaxy types. Has your answer changed? We also know that the Milky Way is one of the largest spiral galaxies in the local group, so perhaps it is similar to the largest spiral galaxies in Hydra I. Try getting a distance just from them.
Even this doesn’t necessarily help us very much: we’ve no good reason to believe that even large spiral galaxies in Hydra I should be like the Milky Way. A much better assumption would be that the galaxies in Hydra I are just like the galaxies in Virgo. After all, both clusters are about the same size, mass and density. It seems very plausible that the galaxies in Virgo should at least resemble those in Hydra 1.
Here is a better method (using Virgo) to try and measure the distance to Hydra I:
Pick the ten biggest spirals and ten biggest ellipticals in each cluster. Throw out any that look too bizarre – you want to compare the two clusters, so if in one you find, say, some seriously warped colliding galaxies which aren’t in the other cluster, you should throw them out. If you can’t find ten good ones, choose eight or five – if you can find more than ten, using them all will improve the accuracy of this method.
Measure the sizes of all these galaxies, using the eyepiece with a scale. It doesn’t actually matter how you do this, so long as you do it the same way on each cluster. Try and think of a consistent way of measuring the sizes.
Find the average apparent size (in arcmin) of the ten spirals and of the ten ellipticals in each cluster, \(r_{v}^{s}\) (mean size of Virgo spirals), \(r_{h}^{e}\) (mean size of Hydra ellipticals) etc.
For an object of a given size \(r\) at a distance \(d\), the angular size will be \(\theta=r/d\) where \(\theta\) is measured in radians (why?). This only applies if \(d\) is very much greater than \(r\) which is certainly true here. Therefore, if we assume the ten brightest of each type of galaxy are the same size in each cluster, the ratio of the distance to Hydra I (\(d_{h}\)) to the distance to Virgo (\(d_{v}\)) is given by
from the spirals, and
from the ellipticals. These two numbers should be the same, to within the errors. Are they? If you think one is more accurate, use it (justify this decision in your notes). Otherwise, average the two numbers. It is always worth measuring anything two ways to have a check.
A recent measurement (http://arxiv.org/abs/astro-ph/0702510) puts the distance to the Virgo cluster as \(16.5\pm 0.1\) Mpc. Use this, plus the ratios measured above, to find the distance to Hydra I.
How does this answer compare with the earlier one? If they are different, what is this telling us about the relative sizes of galaxies in Hydra I and our galaxy?