1. Estimate the distances to the above galaxies by comparing the apparent sizes of the galaxy images in the above figure. Roughly speaking, the larger the galaxy image, the closer is the galaxy. The most nearby galaxy, Virgo, has an angular size on the sky of ~150" and is at a distance of 16 Million parsecs (16 Mpc). Note-- " is an angular unit on the sky known as an arc second. 1 arc second = 1 " = 1/3,600 of 1 degree. The unit Mpc is a distance; Mpc = Mega-parsec = 1 million parsecs, where 1 parsec = 3.3 light years = 3.1x1013 kilometers.
Galaxy |
Size | Distance | Measured Wavelength |
Change in Wavelength | Redshift, z | speed |
Virgo | 150" | 16 Mpc | ||||
Ursa Major | ||||||
Corona | ||||||
Bootes | ||||||
Hydra |
2. Determine the redshifts and speed of recession for each of the above galaxies. Use the CaII K line. The CaII H & K lines are the two prominent dark lines which flank the vertical area seen near the left end of the spectrum of Virgo; the CaII K line is left dark line. The rest wavelength of the CaII K line is 3,934 Angstroms. The letters a-g are at wavelengths: a=3,888.7 Angstroms, b=3,964.7 Angstroms, c=4,026.2 Angstroms, d=4,143.8 Angstroms, e=4,471.5 Angstroms, f=4,713.1 Angstroms, g=5,015.7 Angstroms. Given a-g, estimate the wavelengths for the CaII K line in each galaxy spectrum (the change in the wavelength of the CaII K line is roughly given by the length of the horizontal arrow in each figure).
The redshift z is defined by
For small z,
The velocity relation is not correct for large z; the proper interpretation for the redshift for large z is that the redshift is caused by the expansion of the Universe.
3. Plot the speed versus distance D for the above galaxies. Note that c, the speed of light, is 300,000 km/s. Your plot forms the Hubble relation.
