Clusters Background Information: Observing | ![]() |
So we need to a measure the velocity of galaxies in a cluster, as well as a measure of the cluster's size. How do we do this? Measuring velocities: We can use the galaxies' Doppler shift to get their velocities. By taking a spectrum of the light from a galaxy, we can measure the observed wavelength shifts of certain absorption or emission lines in the galaxy to get the velocity:
A galaxy's velocity arises from two sources: the cosmological expansion, which carries the cluster away from us, and the galaxy's internal velocity within the cluster. It's this second part that we are interested in -- that's controlled by the size and mass of the cluster. The problem is that the Doppler shift only measures the line-of-sight velocity of the galaxy -- that is, the velocity towards or away from us. If the galaxy has much "sideways" motion, we wouldn't detect that. So from measuring one galaxy's velocity, we don't really know much about the typical speeds of galaxies in the cluster. Instead, we have to observe many galaxies, and infer the typical speed by looking at the spread in velocities, something called the velocity dispersion. If we measure velocities of many galaxies and make a histogram, it might look like this:
![]() The width of the histogram tells us the spread in velocities, or the velocity dispersion, while the average velocity tells us about how fast the cluster as a whole is moving away from us due to the cosmlogical expansion of the universe.
The velocity dispersion, called Measuring size: Okay, so how do we measure the size of a cluster? There is no sharp edge to a cluster, so how do we define size? There are several definitions, some easier to measure than others. One way is to fit the distribution of galaxies to a model, and use some "characteristic radius" of the fitted model (ie the radius where the density drops in half, for example). Another simple way is to use something called the "half light radius" or "effective radius" (Re). What we do here is measure the brightness of each galaxy in the cluster, and then define the radius in the cluster inside of which half the galaxy light is contained. This is the definition we will use in the JavaLab. But remember that we measure the angular size of the cluster -- in other words the apparent size on the sky. For a cluster of fixed physical size, the further away it is, the smaller it would appear to be. So we need to convert the observed size (in arc seconds) to a true physical size (in megaparsecs, for example) -- in other words, we need the distance. How do we get that? Well, by measuring the velocities, we also measured the cosmological velocity -- the so-called "redshift" -- of the cluster. If we know the Hubble constant (H0), we can derive the distance from
and then convert the angular size to physical size by
Now we are set to calculate masses... |