Astronomy 110 PRINT Name   __________________________ Fall 2005   Section 006 Homework 9 : The Hubble Law (Due Thursday, Dec 1, 2005)

This homework is about the Hubble law that relates the observed redshifts of galaxies to their distances. You'll be working with a real galaxy spectrum, which is plotted in the figure below. This is the spectrum of a galaxy in the Hubble Deep Field and was taken with a spectrograph on one of the Keck 10 meter telescopes on Mauna Kea.

• First, write in words what we mean by a galaxy's "redshift".

• Describe briefly what we mean by the Hubble law.

• The spectrum of a galaxy allows you to measure its redshift. In the spectrum above there is continuum light, some absorption lines (e.g. near 7600 A) and some emission lines that are named. The absorption near 7600 A actually comes from light interacting with the Earth's atmosphere, but the emission lines come from glowing gas in the galaxy in the HDF. H alpha is the red Balmer line of neutral hydrogen, O III comes from doubly ionized oxygen, and O II from singly ionized oxygen. The rest wavelengths of these emission lines are given in the table below.

 LINE REST WAVELENGTH OBSERVED WAVELENGTH REDSHIFT 6562.8 Angstroms O III 5006.8 Angstroms O II 3727 Angstroms

For each of the emission lines, measure its observed wavelength from the spectrum as accurately as you can, and enter it in the table, in Angstroms.

Calculate the redshift of each emission line, which is given by

redshift = (Observed wavelength / rest wavelength) -1

Enter your calculated redshifts in the table above. Now calculate the average redshift (the sum of your three redshifts divided by 3). This is an estimate of the redshift of the galaxy. Enter it here : Galaxy Redshift = _____________

• Is the galaxy moving toward us or away from us? _____________

• Knowing it's redshift, you can calculate the galaxy's velocity. For small redshifts this is simply, velocity = redshift x speed of light. Knowing the speed of light to be 3 x 105 km/s, calculate the galaxy's velocity and enter the answer here : _____________

• Knowing the galaxy's velocity, you can now find it's distance from the Hubble law.

velocity (km/s) = H x distance (Mpc)

where H is the Hubble constant, which you can take to be 65 km/s/Mpc. Calculate the distance to the galaxy in Mpc and enter it here : _____________

• What other method could you use to find the distance to this galaxy?