Assignment 2
Hubble Law
Due: August 19, 2010


Introduction

The Hubble Law is one of the fundamental pieces of observational evidence upon which our modern theory (the Big Bang Theory) of the structure and evolution of the Universe is built. Here, we investigate the Hubble Law.

1. First determine the redshift of the objects.

The above is a sample stellar spectrum. Because the light from galaxies (in the visual part of the spectrum) is roughly the sum of the light from billions of stars, normal galactic spectra will resemble those of a set of stars. For stars like the Sun, the two lines produced by Calcium II (ionized calcium), known as the H and K lines, are very strong and are expected to appear prominently in galactic spectra. The wavelengths of these two lines are 0.3934 and 0.3968 microns (1 micron = 10-6 meters) for K and H lines, respectively.


Get the redshifts for the following galaxy clusters using the spectrum of the representative galaxy shown for each cluster,


The observed K and H lines are marked by the head of the arrow. The location of the rest wavelength of the lines is marked by the end of the arrow. The length of the arrow then gives the change in the wavelength of the K and H Ca II lines caused by the expansion of the Universe.

To calculate the redshift of each galaxy, first measure the lengths of the arrows in centimeters. Next, note that the positions marked by the letters a and e are at wavelengths 0.3889 and 0.4472 microns so that points a and e are separated by 0.4472 microns - 0.3889 microns = 0.0583 microns. Use this information to get the scale for the spectrum. Using the lengths of the arrows and the scale for the spectrum, find the change in wavelength of the K and H Ca II lines in microns. Fill in the Change in K and H wavelength, and Redshift columns in the following Table. Recall that the redshift z is given by

where the Greek letter lambda stands for wavelength. For the rest wavelength, use the average of the Calcium II K and H lines, 0.3951 microns.


Galaxy Cluster

Change in K and H wavelength

Redshift

Distance

Virgo

 

 

59,000,000 ly

Ursa Major

 

 

 

Corona Borealis

 

 

 

Bootes

 

 

 

Hydra

 

 

 

2. We supplied the Distance to Virgo galaxy cluster in the above Table. Under the assumption that all galaxies have the same diameter, estimate the distances to the other galaxies by comparing how large they are in comparson to the size of M87 (the galaxy shown for the Virgo cluster of galaxies). Enter your estimates in the above Table.

3. Make a plot of the redshift versus distance for the 5 galaxy clusters using redshift as the vertical axis and Distance for the horizontal axis. This plot forms Hubble's Law.