Assignment 1
Hubble Law
Due: in class on 19 January 2012


Introduction

The Hubble Law is one of the fundamental pieces of observational evidence upon which modern cosmological theory (the Big Bang Theory) is based. Here, we see how the Hubble Law was first found.

1. The first step is to determine the redshift of a set of galaxies.

Spectrum

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. In the spectrum above, the H and K lines can be seen at the left end (the blue end) of the spectrum.


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


For the spectra shown above, note the following:


The redshift of a galaxy is defined as the relative change in the wavelength of a spectral line of a given element. That is, we compare the difference in the observed wavelength of a line and the rest wavelength of the line to rest wavelength of the line. The redshift z is then formally 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, use the relative sizes of the images given above to 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.