Summary The student will analyze the distribution of matter in the Universe from the distances to galaxies in the Hubble Deep Field. Background and Theory




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Large Scale Structure in the Hubble Deep Field



Summary The student will analyze the distribution of matter in the Universe from the distances to galaxies in the Hubble Deep Field.

Background and Theory
As we look at galaxies at distances of 10 or 12 billion light years, we are viewing the Universe as it was 10 or 12 billion years ago. The concept of the finite speed of light and look-back time means we actually can see our Universe as it was a few billion years after its creation.

Take a look at the Hubble Deep Field, an image that takes us far out into space and far back in time. There are thousands of galaxies of many shapes and colors. By deep, astronomers mean dim and distant. This is an image of the faintest objects ever detected. It reaches 30th magnitude, or about 4 billion times fainter than the naked human eye can see. To create it, the Hubble Space Telescope exposed its electronic detectors for about 100 hours over the course of 10 days, pointed at the tiny region of space near the constellation Ursae Majoris.


This image covers an area about 1/100 that of the full Moon. After this image was obtained, the Earth-based, 10-meter Keck telescope was used to observe the faint blue galaxies in the image. Astronomers have concluded that the small blue shards are among the most distant objects ever seen. These objects may represent galaxies caught in the act of formation. In all, the number of galaxies in the image implies that there are tens of billions of galaxies in the observable universe.
Take a closer look at the reproduction of the Hubble Deep Field. Next to many of the galaxies is the redshift, z, for that galaxy (except for a few cases, the corresponding galaxy is usually the galaxy located to the upper left of the redshift number). For nearby galaxies, where z is much less than 1, the redshift is defined as:

Where ' is the measured wavelength, is the rest wavelength, and v is the recessional velocity. If you look closely at a few of the galaxies in the Deep Field, you will note that there are redshifts of 1.36, 2.80, 3.23, even 4.02. Does this mean v/c > 1 and these galaxies are traveling faster than the speed of light?

Well, no. Once the redshift of a galaxy approaches 1, we must take Einstein's special relativity into account. We use a modified formula of:

As the recessional velocity of the galaxy approaches the speed of light, the denominator becomes very small, so z approaches infinity.



T
he relation between recession velocity and distance was established by Edwin Hubble, and astronomers have continued to refine measurements of distance to obtain the rate of expansion of the Universe, know as the Hubble Constant, measured in km s-1 Mpc-1. Observations with the Hubble Space Telescope and of the Cosmic Microwave Background Radiation have established that the value of Ho is near 72 km s-1 Mpc-1. Using the Hubble constant and the definition of redshift, we can establish the relationship between distance and redshift, shown below. Objects with zero redshift are in our local universe, and increasingly distant objects have larger and larger redshifts. The most distant galaxies yet observed have redshifts near 7, corresponding to recession velocities of more than 95% of the speed of light.
Procedure
Since the redshifts of objects are related to their distances, knowing the redshifts allows us to determine the distance to each galaxy in the Hubble Deep Field and to examine the actual distribution of galaxies in this portion of the sky.
Examine the redshifts for the galaxies in the HDF. Do we find galaxies at all redshifts in this direction in space, or are the galaxies clustered at particular redshifts (or distances)?
An easy way to examine the distribution of galaxies with distance is to construct a histogram. Count the number of galaxies in each redshift bin from z=0.0 to z=4.0. Bins of size 0.1 in redshift are a good choice.
Using the annotated image of the HDF, plot a histogram of the number of galaxies in each redshift bin.



  1. Can you see possible large scale structure such as clustering? If so, at what redshifts? (Look for redshifts where many galaxies are found.)



  1. Are there voids in this field? If so, at what redshifts? (Voids are regions of space or redshifts where few galaxies are found.)



  1. At what distances or "look back" times do the voids and regions of clustering occur?



  1. This is an extremely small "pencil beam" of the Universe. Can you find a cluster of galaxies, identified as a region of the image where a number of galaxies are close together in this 2-D image, with each of those galaxies having similar cosmological redshifts. Can you find a group of galaxies that might be classified as a cluster?




This exercise is based on one developed at the University of Washington (© 1999 University of Washington) and has been revised for use in the "Exploring the Dark Universe" Workshop for teachers at Indiana University.


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