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".

A galaxy's redshift is a measure of how its spectrum of light has been altered due to its motion away from us. In a process called the Doppler Effect, light waves seem to be spread out when a source emitting light waves is moving away from the observer. The spectral lines observed in the galaxy are at longer (or redder) wavelengths than they would be if the galaxy wasn't moving.

• Describe briefly what we mean by the Hubble law.

Hubble's Law says that an object's velocity away from an observer is directly proportional to its distance from the observer. In other words, the farther away something is the faster it is moving away from us.

• 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 8100 Angstroms 0.234 O III 5006.8 Angstroms 6150 Angstroms 0.228 O II 3727 Angstroms 4550 Angstroms 0.221

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 = 0.228

• Is the galaxy moving toward us or away from us? 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 : 6.83 x 104km/s

• 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 : 1050 Mpc

Note: Mpc is short for Mega-parsec a parsec is a measure of distance that astronomers use that is equal to about 3.2 light-years, and mega means a million, so: 1 Mpc=3.2 x 106 light-years.

• What other method could you use to find the distance to this galaxy?
To measure the distance to objects that are very far away, like this galaxy, we look for Type 1 supernovae. A Type 1 supernova is an exploding star system that includes a white dwarf. Type 1 supernovae are thought to have a set luminosity. We can calculate how far away a the supernova is by measuring how much light we observe from it (its flux, or brightness), and plugging in a set value for its luminosity.